Spectral properties of the massless relativistic quartic oscillator

NASA Astrophysics Data System (ADS)

Durugo, Samuel O.; Lőrinczi, József

2018-03-01

An explicit solution of the spectral problem of the non-local Schrödinger operator obtained as the sum of the square root of the Laplacian and a quartic potential in one dimension is presented. The eigenvalues are obtained as zeroes of special functions related to the fourth order Airy function, and closed formulae for the Fourier transform of the eigenfunctions are derived. These representations allow to derive further spectral properties such as estimates of spectral gaps, heat trace and the asymptotic distribution of eigenvalues, as well as a detailed analysis of the eigenfunctions. A subtle spectral effect is observed which manifests in an exponentially tight approximation of the spectrum by the zeroes of the dominating term in the Fourier representation of the eigenfunctions and its derivative.

Sturm-Liouville eigenproblems with an interior pole

NASA Technical Reports Server (NTRS)

Boyd, J. P.

1981-01-01

The eigenvalues and eigenfunctions of self-adjoint Sturm-Liouville problems with a simple pole on the interior of an interval are investigated. Three general theorems are proved, and it is shown that as n approaches infinity, the eigenfunctions more and more closely resemble those of an ordinary Sturm-Liouville problem. The low-order modes differ significantly from those of a nonsingular eigenproblem in that both eigenvalues and eigenfunctions are complex, and the eigenvalues for all small n may cluster about a common value in contrast to the widely separated eigenvalues of the corresponding nonsingular problem. In addition, the WKB is shown to be accurate for all n, and all eigenvalues of a normal one-dimensional Sturm-Liouville equation with nonperiodic boundary conditions are well separated.

High-performance dynamic quantum clustering on graphics processors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wittek, Peter, E-mail: peterwittek@acm.org

2013-01-15

Clustering methods in machine learning may benefit from borrowing metaphors from physics. Dynamic quantum clustering associates a Gaussian wave packet with the multidimensional data points and regards them as eigenfunctions of the Schroedinger equation. The clustering structure emerges by letting the system evolve and the visual nature of the algorithm has been shown to be useful in a range of applications. Furthermore, the method only uses matrix operations, which readily lend themselves to parallelization. In this paper, we develop an implementation on graphics hardware and investigate how this approach can accelerate the computations. We achieve a speedup of up tomore » two magnitudes over a multicore CPU implementation, which proves that quantum-like methods and acceleration by graphics processing units have a great relevance to machine learning.« less

Virasoro symmetry of the constrained multicomponent Kadomtsev-Petviashvili hierarchy and its integrable discretization

NASA Astrophysics Data System (ADS)

Li, Chuanzhong; He, Jingsong

2016-06-01

We construct Virasoro-type additional symmetries of a kind of constrained multicomponent Kadomtsev-Petviashvili (KP) hierarchy and obtain the Virasoro flow equation for the eigenfunctions and adjoint eigenfunctions. We show that the algebraic structure of the Virasoro symmetry is retained under discretization from the constrained multicomponent KP hierarchy to the discrete constrained multicomponent KP hierarchy.

Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inverse Scattering

NASA Astrophysics Data System (ADS)

Pelinovsky, Dmitry E.; Sulem, Catherine

A complete set of eigenfunctions is introduced within the Riemann-Hilbert formalism for spectral problems associated to some solvable nonlinear evolution equations. In particular, we consider the time-independent and time-dependent Schrödinger problems which are related to the KdV and KPI equations possessing solitons and lumps, respectively. Non-standard scalar products, orthogonality and completeness relations are derived for these problems. The complete set of eigenfunctions is used for perturbation theory and bifurcation analysis of eigenvalues supported by the potentials under perturbations. We classify two different types of bifurcations of new eigenvalues and analyze their characteristic features. One type corresponds to thresholdless generation of solitons in the KdV equation, while the other predicts a threshold for generation of lumps in the KPI equation.

The Uniform Convergence of Eigenfunction Expansions of Schrödinger Operator in the Nikolskii Classes {H}_{p}^{\\alpha }(\\bar{\\Omega })

NASA Astrophysics Data System (ADS)

Jamaludin, N. A.; Ahmedov, A.

2017-09-01

Many boundary value problems in the theory of partial differential equations can be solved by separation methods of partial differential equations. When Schrödinger operator is considered then the influence of the singularity of potential on the solution of the partial differential equation is interest of researchers. In this paper the problems of the uniform convergence of the eigenfunction expansions of the functions from corresponding to the Schrödinger operator with the potential from classes of Sobolev are investigated. The spectral function corresponding to the Schrödinger operator is estimated in closed domain. The isomorphism of the Nikolskii classes is applied to prove uniform convergence of eigenfunction expansions of Schrödinger operator in closed domain.

Vision-Based Autonomous Sensor-Tasking in Uncertain Adversarial Environments

DTIC Science & Technology

2015-01-02

motion segmentation and change detection in crowd behavior. In particular we investigated Finite Time Lyapunov Exponents, Perron Frobenius Operator and...deformation tensor [11]. On the other hand, eigenfunctions of, the Perron Frobenius operator can be used to detect Almost Invariant Sets (AIS) which are... Perron Frobenius operator. Finally, Figure 1.12d shows the ergodic partitions (EP) obtained based on the eigenfunctions of the Koopman operator

FAST TRACK COMMUNICATION: Free form of the Foldy-Wouthuysen transformation in external electromagnetic fields

NASA Astrophysics Data System (ADS)

Murguía, Gabriela; Raya, Alfredo

2010-10-01

We derive the exact Foldy-Wouthuysen transformation for Dirac fermions in a time-independent external electromagnetic field in the basis of the Ritus eigenfunctions, namely the eigenfunctions of the operator (γ sdot Π)2, with Πμ = pμ - eAμ. On this basis, the transformation acquires a free form involving the dynamical quantum numbers induced by the field.

FIBER OPTICS: Method of calculation of the propagation constant for guided modes

NASA Astrophysics Data System (ADS)

Ardasheva, L. I.; Sadykov, Nail R.; Chernyakov, V. E.

1992-09-01

A new method of calculating the propagation constants and wave eigenfunctions of guided modes is proposed for axisymmetric translationally invariant fiber-optic waveguides with arbitrary refractive index profiles. The method is based on solving a parabolic scalar wave equation. A comparison is made between the numerical solution under steady-state conditions and the eigenfunctions of single-mode and multimode waveguides.

Bodywork as systemic and inter-enactive competence: participatory process management in Feldenkrais® Method and Zen Shiatsu

PubMed Central

Kimmel, Michael; Irran, Christine; Luger, Martin A.

2014-01-01

Feldenkrais and Shiatsu enable somatic learning through continuous tactile coupling, a real-time interpersonal dynamic unfolding in a safe dyadic sphere. The first part of our micro-ethnographic study draws on process vignettes and subjective theories to demonstrate how bodywork is infused with systemic sensitivities and awareness for non-linear process management. Expressed in dynamic systems parlance, both disciplines foster metastability, adaptivity, and self-organization in the client's somato-personal system by progressively reconfiguring systemic dispositions, i.e., an attractor landscape. Doing so requires a keen embodied apperception of hierarchies of somato-systemic order. Bodyworkers learn to explore these in their eigenfunction (joints, muscles, fascia), discriminate coordinative organization in small ensembles, and monitor large-scale dynamic interplay. The practitioner's “extended body” reaching forth into the client's through a resonance loop eventually becomes part of this. Within a bodywork session, practitioners modulate this hierarchical functional architecture. Their ability for sensorially staying apace of systemic emergence allows them to respond to minute changes and customize reactions in a zone of proximal development (dynamic immediacy). They stimulate the client's system with a mix of perturbing and stabilizing interventions that oscillate between eigenfunctions and their coordinative integration. Practical knowledge for “soft-assembling” non-linear synergies is crucial for this (cumulative local effects, high-level functions “slaving” the system, etc.). The paper's second part inventorizes the bodyworker's operative tool-box—micro-skills providing the wherewithal for context-intelligent intervention. Practitioners deploy “educated senses” and a repertoire of hands-on techniques (grips, stretches, etc.) against a backdrop of somatic habits (proper posture, muscle activation, gaze patterns, etc.). At this level, our study addresses a host of micro-skills through the lens of enactive cognitive science. PMID:25628576

Generation of coherent states of photon-added type via pathway of eigenfunctions

NASA Astrophysics Data System (ADS)

Górska, K.; Penson, K. A.; Duchamp, G. H. E.

2010-09-01

We obtain and investigate the regular eigenfunctions of simple differential operators xr dr + 1/dxr + 1, r = 1, 2, ..., with the eigenvalues equal to 1. With the help of these eigenfunctions, we construct a non-unitary analogue of a boson displacement operator which will be acting on the vacuum. In this way, we generate collective quantum states of the Fock space which are normalized and equipped with the resolution of unity with the positive weight functions that we obtain explicitly. These states are thus coherent states in the sense of Klauder. They span the truncated Fock space without first r lowest-lying basis states: |0rang, |1rang, ..., |r - 1rang. These states are squeezed, sub-Poissonian in nature and reminiscent of photon-added states in Agarwal and Tara (1991 Phys. Rev. A 43 492).

Accuracy of analytic energy level formulas applied to hadronic spectroscopy of heavy mesons

NASA Technical Reports Server (NTRS)

Badavi, Forooz F.; Norbury, John W.; Wilson, John W.; Townsend, Lawrence W.

1988-01-01

Linear and harmonic potential models are used in the nonrelativistic Schroedinger equation to obtain article mass spectra for mesons as bound states of quarks. The main emphasis is on the linear potential where exact solutions of the S-state eigenvalues and eigenfunctions and the asymptotic solution for the higher order partial wave are obtained. A study of the accuracy of two analytical energy level formulas as applied to heavy mesons is also included. Cornwall's formula is found to be particularly accurate and useful as a predictor of heavy quarkonium states. Exact solution for all partial waves of eigenvalues and eigenfunctions for a harmonic potential is also obtained and compared with the calculated discrete spectra of the linear potential. Detailed derivations of the eigenvalues and eigenfunctions of the linear and harmonic potentials are presented in appendixes.

On the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_1^\\alpha ({T^N})

NASA Astrophysics Data System (ADS)

Ahmedov, Anvarjon; Materneh, Ehab; Zainuddin, Hishamuddin

2017-09-01

The relevance of waves in quantum mechanics naturally implies that the decomposition of arbitrary wave packets in terms of monochromatic waves plays an important role in applications of the theory. When eigenfunction expansions does not converge, then the expansions of the functions with certain smoothness should be considered. Such functions gained prominence primarily through their application in quantum mechanics. In this work we study the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_p^α ({T^N}), related to the self-adjoint extension of the Laplace operator in torus TN . The sufficient conditions for summability is obtained using the modified Poisson formula. Isomorphism properties of the elliptic differential operators is applied in order to obtain estimation for the Fourier series of the functions from the classes of Liouville L_p^α .

Multicomponent integrable reductions in the Kadomtsev-Petviashvilli hierarchy

NASA Astrophysics Data System (ADS)

Sidorenko, Jurij; Strampp, Walter

1993-04-01

New types of reductions of the Kadomtsev-Petviashvili (KP) hierarchy are considered on the basis of Sato's approach. Within this approach the KP hierarchy is represented by infinite sets of equations for potentials u2,u3,..., of pseudodifferential operators and their eigenfunctions Ψ and adjoint eigenfunctions Ψ*. The KP hierarchy was studied under constraints of the following type (∑ni=1 ΨiΨ*i)x = Sκ,x where Sκ,x are symmetries for the KP equation and Ψi(λi), Ψ*i(λi) are eigenfunctions with eigenvalue λi. It is shown that for the first three cases κ=2,3,4 these constraints give rise to hierarchies of 1+1-dimensional commuting flows for the variables u2, Ψ1,...,Ψn, Ψ*1,...,Ψ*n. Bi-Hamiltonian structures for the new hierarchies are presented.

The Theory of Quantized Fields. III

DOE R&D Accomplishments Database

Schwinger, J.

1953-05-01

In this paper we discuss the electromagnetic field, as perturbed by a prescribed current. All quantities of physical interest in various situations, eigenvalues, eigenfunctions, and transformation probabilities, are derived from a general transformation function which is expressed in a non-Hermitian representation. The problems treated are: the determination of the energy-momentum eigenvalues and eigenfunctions for the isolated electromagnetic field, and the energy eigenvalues and eigenfunctions for the field perturbed by a time-independent current that departs from zero only within a finite time interval, and for a time-dependent current that assumes non-vanishing time-independent values initially and finally. The results are applied in a discussion of the intra-red catastrophe and of the adiabatic theorem. It is shown how the latter can be exploited to give a uniform formulation for all problems requiring the evaluation of transition probabilities or eigenvalue displacements.

Unified heat kernel regression for diffusion, kernel smoothing and wavelets on manifolds and its application to mandible growth modeling in CT images.

PubMed

Chung, Moo K; Qiu, Anqi; Seo, Seongho; Vorperian, Houri K

2015-05-01

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel method is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, the method is applied to characterize the localized growth pattern of mandible surfaces obtained in CT images between ages 0 and 20 by regressing the length of displacement vectors with respect to a surface template. Copyright © 2015 Elsevier B.V. All rights reserved.

Non-localization of eigenfunctions for Sturm-Liouville operators and applications

NASA Astrophysics Data System (ADS)

Liard, Thibault; Lissy, Pierre; Privat, Yannick

2018-02-01

In this article, we investigate a non-localization property of the eigenfunctions of Sturm-Liouville operators Aa = -∂xx + a (ṡ) Id with Dirichlet boundary conditions, where a (ṡ) runs over the bounded nonnegative potential functions on the interval (0 , L) with L > 0. More precisely, we address the extremal spectral problem of minimizing the L2-norm of a function e (ṡ) on a measurable subset ω of (0 , L), where e (ṡ) runs over all eigenfunctions of Aa, at the same time with respect to all subsets ω having a prescribed measure and all L∞ potential functions a (ṡ) having a prescribed essentially upper bound. We provide some existence and qualitative properties of the minimizers, as well as precise lower and upper estimates on the optimal value. Several consequences in control and stabilization theory are then highlighted.

Fission matrix-based Monte Carlo criticality analysis of fuel storage pools

DOE Office of Scientific and Technical Information (OSTI.GOV)

Farlotti, M.; Ecole Polytechnique, Palaiseau, F 91128; Larsen, E. W.

2013-07-01

Standard Monte Carlo transport procedures experience difficulties in solving criticality problems in fuel storage pools. Because of the strong neutron absorption between fuel assemblies, source convergence can be very slow, leading to incorrect estimates of the eigenvalue and the eigenfunction. This study examines an alternative fission matrix-based Monte Carlo transport method that takes advantage of the geometry of a storage pool to overcome this difficulty. The method uses Monte Carlo transport to build (essentially) a fission matrix, which is then used to calculate the criticality and the critical flux. This method was tested using a test code on a simplemore » problem containing 8 assemblies in a square pool. The standard Monte Carlo method gave the expected eigenfunction in 5 cases out of 10, while the fission matrix method gave the expected eigenfunction in all 10 cases. In addition, the fission matrix method provides an estimate of the error in the eigenvalue and the eigenfunction, and it allows the user to control this error by running an adequate number of cycles. Because of these advantages, the fission matrix method yields a higher confidence in the results than standard Monte Carlo. We also discuss potential improvements of the method, including the potential for variance reduction techniques. (authors)« less

The shifted harmonic approximation and asymptotic SU(2) and SU(1,1) Clebsch-Gordan coefficients

NASA Astrophysics Data System (ADS)

Rowe, D. J.; de Guise, Hubert

2010-12-01

Clebsch-Gordan coefficients of SU(2) and SU(1,1) are defined as eigenfunctions of a linear operator acting on the tensor product of the Hilbert spaces for two irreps of these groups. The shifted harmonic approximation is then used to solve these equations in asymptotic limits in which these eigenfunctions approach harmonic oscillator wavefunctions and thereby derive asymptotic expressions for these Clebsch-Gordan coefficients.

Eigenfunctions and heat kernels of super Maass Laplacians on the super Poincaré upper half-plane

NASA Astrophysics Data System (ADS)

Oshima, Kazuto

1992-03-01

Heat kernels of ``super Maass Laplacians'' are explicitly constructed on super Poincaré upper half-plane by a serious treatment of a complete set of eigenfunctions. By component decomposition an explicit treatment can be done for arbitrary weight and a knowledge of classical Maass Laplacians becomes helpful. The result coincides with that of Aoki [Commun. Math. Phys. 117, 405 (1988)] which was obtained by solving differential equations.

Spin eigen-states of Dirac equation for quasi-two-dimensional electrons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eremko, Alexander, E-mail: eremko@bitp.kiev.ua; Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua; Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua

Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shownmore » that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.« less

Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

PubMed Central

Chung, Moo K.; Qiu, Anqi; Seo, Seongho; Vorperian, Houri K.

2014-01-01

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface. PMID:25791435

Spatial modeling in ecology: the flexibility of eigenfunction spatial analyses.

PubMed

Griffith, Daniel A; Peres-Neto, Pedro R

2006-10-01

Recently, analytical approaches based on the eigenfunctions of spatial configuration matrices have been proposed in order to consider explicitly spatial predictors. The present study demonstrates the usefulness of eigenfunctions in spatial modeling applied to ecological problems and shows equivalencies of and differences between the two current implementations of this methodology. The two approaches in this category are the distance-based (DB) eigenvector maps proposed by P. Legendre and his colleagues, and spatial filtering based upon geographic connectivity matrices (i.e., topology-based; CB) developed by D. A. Griffith and his colleagues. In both cases, the goal is to create spatial predictors that can be easily incorporated into conventional regression models. One important advantage of these two approaches over any other spatial approach is that they provide a flexible tool that allows the full range of general and generalized linear modeling theory to be applied to ecological and geographical problems in the presence of nonzero spatial autocorrelation.

Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems.

PubMed

Luo, Biao; Huang, Tingwen; Wu, Huai-Ning; Yang, Xiong

2015-11-01

The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.

Counting nodal domains on surfaces of revolution

NASA Astrophysics Data System (ADS)

Karageorge, Panos D.; Smilansky, Uzy

2008-05-01

We consider eigenfunctions of the Laplace-Beltrami operator on special surfaces of revolution. For this separable system, the nodal domains of the (real) eigenfunctions form a checkerboard pattern, and their number νn is proportional to the product of the angular and the 'surface' quantum numbers. Arranging the wavefunctions by increasing values of the Laplace-Beltrami spectrum, we obtain the nodal sequence, whose statistical properties we study. In particular, we investigate the distribution of the normalized counts \\frac{\

On Nonlinear Functionals of Random Spherical Eigenfunctions

NASA Astrophysics Data System (ADS)

Marinucci, Domenico; Wigman, Igor

2014-05-01

We prove central limit theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combines asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and total variation bounds for Gaussian subordinated fields. We discuss applications to geometric functionals like the defect and invariant statistics, e.g., polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.

Two charges on a plane in a magnetic field: hidden algebra, (particular) integrability, polynomial eigenfunctions

NASA Astrophysics Data System (ADS)

Turbiner, A. V.; Escobar-Ruiz, M. A.

2013-07-01

The quantum mechanics of two Coulomb charges on a plane (e1, m1) and (e2, m2) subject to a constant magnetic field B perpendicular to the plane is considered. Four integrals of motion are explicitly indicated. It is shown that for two physically important particular cases, namely that of two particles of equal Larmor frequencies, {e_c} \\propto \\frac{e_1}{m_1}-\\frac{e_2}{m_2}=0 (e.g. two electrons) and one of a neutral system (e.g. the electron-positron pair, hydrogen atom) at rest (the center-of-mass momentum is zero) some outstanding properties occur. They are the most visible in double polar coordinates in CMS (R, ϕ) and relative (ρ, φ) coordinate systems: (i) eigenfunctions are factorizable, all factors except one with the explicit ρ-dependence are found analytically, they have definite relative angular momentum, (ii) dynamics in the ρ-direction is the same for both systems, it corresponds to a funnel-type potential and it has hidden sl(2) algebra, at some discrete values of dimensionless magnetic fields b ⩽ 1, (iii) particular integral(s) occur, (iv) the hidden sl(2) algebra emerges in finite-dimensional representation, thus, the system becomes quasi-exactly-solvable and (v) a finite number of polynomial eigenfunctions in ρ appear. Nine families of eigenfunctions are presented explicitly.

Possibility of modifying the growth trajectory in Raeini Cashmere goat.

PubMed

Ghiasi, Heydar; Mokhtari, M S

2018-03-27

The objective of this study was to investigate the possibility of modifying the growth trajectory in Raeini Cashmere goat breed. In total, 13,193 records on live body weight collected from 4788 Raeini Cashmere goats were used. According to Akanke's information criterion (AIC), the sing-trait random regression model included fourth-order Legendre polynomial for direct and maternal genetic effect; maternal and individual permanent environmental effect was the best model for estimating (co)variance components. The matrices of eigenvectors for (co)variances between random regression coefficients of direct additive genetic were used to calculate eigenfunctions, and different eigenvector indices were also constructed. The obtained results showed that the first eigenvalue explained 79.90% of total genetic variance. Therefore, changing the body weights applying the first eigenfunction will be obtained rapidly. Selection based on the first eigenvector will cause favorable positive genetic gains for all body weight considered from birth to 12 months of age. For modifying the growth trajectory in Raeini Cashmere goat, the selection should be based on the second eigenfunction. The second eigenvalue accounted for 14.41% of total genetic variance for body weights that is low in comparison with genetic variance explained by the first eigenvalue. The complex patterns of genetic change in growth trajectory observed under the third and fourth eigenfunction and low amount of genetic variance explained by the third and fourth eigenvalues.

Rotational Parameters from Vibronic Eigenfunctions of Jahn-Teller Active Molecules

NASA Astrophysics Data System (ADS)

Garner, Scott M.; Miller, Terry A.

2017-06-01

The structure in rotational spectra of many free radical molecules is complicated by Jahn-Teller distortions. Understanding the magnitudes of these distortions is vital to determining the equilibrium geometric structure and details of potential energy surfaces predicted from electronic structure calculations. For example, in the recently studied {\\widetilde{A}^2E^{''} } state of the NO_3 radical, the magnitudes of distortions are yet to be well understood as results from experimental spectroscopic studies of its vibrational and rotational structure disagree with results from electronic structure calculations of the potential energy surface. By fitting either vibrationally resolved spectra or vibronic levels determined by a calculated potential energy surface, we obtain vibronic eigenfunctions for the system as linear combinations of basis functions from products of harmonic oscillators and the degenerate components of the electronic state. Using these vibronic eigenfunctions we are able to predict parameters in the rotational Hamiltonian such as the Watson Jahn-Teller distortion term, h_1, and compare with the results from the analysis of rotational experiments.

A variable-order laminated plate theory based on the variational-asymptotical method

NASA Technical Reports Server (NTRS)

Lee, Bok W.; Sutyrin, Vladislav G.; Hodges, Dewey H.

1993-01-01

The variational-asymptotical method is a mathematical technique by which the three-dimensional analysis of laminated plate deformation can be split into a linear, one-dimensional, through-the-thickness analysis and a nonlinear, two-dimensional, plate analysis. The elastic constants used in the plate analysis are obtained from the through-the-thickness analysis, along with approximate, closed-form three-dimensional distributions of displacement, strain, and stress. In this paper, a theory based on this technique is developed which is capable of approximating three-dimensional elasticity to any accuracy desired. The asymptotical method allows for the approximation of the through-the-thickness behavior in terms of the eigenfunctions of a certain Sturm-Liouville problem associated with the thickness coordinate. These eigenfunctions contain all the necessary information about the nonhomogeneities along the thickness coordinate of the plate and thus possess the appropriate discontinuities in the derivatives of displacement. The theory is presented in this paper along with numerical results for the eigenfunctions of various laminated plates.

Ultrarelativistic bound states in the spherical well

DOE Office of Scientific and Technical Information (OSTI.GOV)

Żaba, Mariusz; Garbaczewski, Piotr

2016-07-15

We address an eigenvalue problem for the ultrarelativistic (Cauchy) operator (−Δ){sup 1/2}, whose action is restricted to functions that vanish beyond the interior of a unit sphere in three spatial dimensions. We provide high accuracy spectral data for lowest eigenvalues and eigenfunctions of this infinite spherical well problem. Our focus is on radial and orbital shapes of eigenfunctions. The spectrum consists of an ordered set of strictly positive eigenvalues which naturally splits into non-overlapping, orbitally labelled E{sub (k,l)} series. For each orbital label l = 0, 1, 2, …, the label k = 1, 2, … enumerates consecutive lth seriesmore » eigenvalues. Each of them is 2l + 1-degenerate. The l = 0 eigenvalues series E{sub (k,0)} are identical with the set of even labeled eigenvalues for the d = 1 Cauchy well: E{sub (k,0)}(d = 3) = E{sub 2k}(d = 1). Likewise, the eigenfunctions ψ{sub (k,0)}(d = 3) and ψ{sub 2k}(d = 1) show affinity. We have identified the generic functional form of eigenfunctions of the spherical well which appear to be composed of a product of a solid harmonic and of a suitable purely radial function. The method to evaluate (approximately) the latter has been found to follow the universal pattern which effectively allows to skip all, sometimes involved, intermediate calculations (those were in usage, while computing the eigenvalues for l ≤ 3).« less

Crossing symmetry in alpha space

NASA Astrophysics Data System (ADS)

Hogervorst, Matthijs; van Rees, Balt C.

2017-11-01

We initiate the study of the conformal bootstrap using Sturm-Liouville theory, specializing to four-point functions in one-dimensional CFTs. We do so by decomposing conformal correlators using a basis of eigenfunctions of the Casimir which are labeled by a complex number α. This leads to a systematic method for computing conformal block decompositions. Analyzing bootstrap equations in alpha space turns crossing symmetry into an eigenvalue problem for an integral operator K. The operator K is closely related to the Wilson transform, and some of its eigenfunctions can be found in closed form.

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators.

PubMed

Bardhan, Jaydeep P; Knepley, Matthew G; Brune, Peter

2015-01-01

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson-Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online.

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators

PubMed Central

Bardhan, Jaydeep P.; Knepley, Matthew G.; Brune, Peter

2015-01-01

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood’s classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson–Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online. PMID:26273581

Methods in the study of discrete upper hybrid waves

NASA Astrophysics Data System (ADS)

Yoon, P. H.; Ye, S.; Labelle, J.; Weatherwax, A. T.; Menietti, J. D.

2007-11-01

Naturally occurring plasma waves characterized by fine frequency structure or discrete spectrum, detected by satellite, rocket-borne instruments, or ground-based receivers, can be interpreted as eigenmodes excited and trapped in field-aligned density structures. This paper overviews various theoretical methods to study such phenomena for a one-dimensional (1-D) density structure. Among the various methods are parabolic approximation, eikonal matching, eigenfunction matching, and full numerical solution based upon shooting method. Various approaches are compared against the full numerical solution. Among the analytic methods it is found that the eigenfunction matching technique best approximates the actual numerical solution. The analysis is further extended to 2-D geometry. A detailed comparative analysis between the eigenfunction matching and fully numerical methods is carried out for the 2-D case. Although in general the two methods compare favorably, significant differences are also found such that for application to actual observations it is prudent to employ the fully numerical method. Application of the methods developed in the present paper to actual geophysical problems will be given in a companion paper.

A low dimensional dynamical system for the wall layer

NASA Technical Reports Server (NTRS)

Aubry, N.; Keefe, L. R.

1987-01-01

Low dimensional dynamical systems which model a fully developed turbulent wall layer were derived.The model is based on the optimally fast convergent proper orthogonal decomposition, or Karhunen-Loeve expansion. This decomposition provides a set of eigenfunctions which are derived from the autocorrelation tensor at zero time lag. Via Galerkin projection, low dimensional sets of ordinary differential equations in time, for the coefficients of the expansion, were derived from the Navier-Stokes equations. The energy loss to the unresolved modes was modeled by an eddy viscosity representation, analogous to Heisenberg's spectral model. A set of eigenfunctions and eigenvalues were obtained from direct numerical simulation of a plane channel at a Reynolds number of 6600, based on the mean centerline velocity and the channel width flow and compared with previous work done by Herzog. Using the new eigenvalues and eigenfunctions, a new ten dimensional set of ordinary differential equations were derived using five non-zero cross-stream Fourier modes with a periodic length of 377 wall units. The dynamical system was integrated for a range of the eddy viscosity prameter alpha. This work is encouraging.

Quasi-exact solvability and entropies of the one-dimensional regularised Calogero model

NASA Astrophysics Data System (ADS)

Pont, Federico M.; Osenda, Omar; Serra, Pablo

2018-05-01

The Calogero model can be regularised through the introduction of a cutoff parameter which removes the divergence in the interaction term. In this work we show that the one-dimensional two-particle regularised Calogero model is quasi-exactly solvable and that for certain values of the Hamiltonian parameters the eigenfunctions can be written in terms of Heun’s confluent polynomials. These eigenfunctions are such that the reduced density matrix of the two-particle density operator can be obtained exactly as well as its entanglement spectrum. We found that the number of non-zero eigenvalues of the reduced density matrix is finite in these cases. The limits for the cutoff distance going to zero (Calogero) and infinity are analysed and all the previously obtained results for the Calogero model are reproduced. Once the exact eigenfunctions are obtained, the exact von Neumann and Rényi entanglement entropies are studied to characterise the physical traits of the model. The quasi-exactly solvable character of the model is assessed studying the numerically calculated Rényi entropy and entanglement spectrum for the whole parameter space.

Spectral transform and orthogonality relations for the Kadomtsev-Petviashvili I equation

NASA Astrophysics Data System (ADS)

Boiti, M.; Leon, J. J.-P.; Pempinelli, F.

1989-10-01

We define a new spectral transform r(k, l) of the potential u in the time dependent Schrödinger equation (associated to the KPI equation). Orthogonality relations for the sectionally holomorphic eigenfunctions of the Schrödinger equation are used to express the spectral transform f( k, l) previously introduced by Manakov and Fokas and Ablowitz in terms of r( k, l). The main advantage of the new spectral transform r( k, l) is that its definition does not require to introduce an additional nonanalytic eigenfunction N. Characterization equations for r( k, l) are also obtained.

The exact eigenfunctions and eigenvalues of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

NASA Technical Reports Server (NTRS)

Reimers, J. R.; Heller, E. J.

1985-01-01

Exact eigenfunctions for a two-dimensional rigid rotor are obtained using Gaussian wave packet dynamics. The wave functions are obtained by propagating, without approximation, an infinite set of Gaussian wave packets that collectively have the correct periodicity, being coherent states appropriate to this rotational problem. This result leads to a numerical method for the semiclassical calculation of rovibrational, molecular eigenstates. Also, a simple, almost classical, approximation to full wave packet dynamics is shown to give exact results: this leads to an a posteriori justification of the De Leon-Heller spectral quantization method.

Properties of natural frequencies and harmonic bending vibrations of a rod at one end of which is concentrated inertial load

NASA Astrophysics Data System (ADS)

Aliyev, Ziyatkhan S.; Guliyeva, Sevinc B.

2017-11-01

In this paper we consider a spectral problem that describes the bending vibrations of a homogeneous rod, in cross-sections of which the longitudinal force acts, the left end of which is fixed and on the right end an inertial mass is concentrated. We give a general characteristic of the location of the eigenvalues on the real axis, we study the structure of root spaces and oscillation properties of eigenfunctions, we investigate the basic properties in the space Lp, 1 < p < ∞, of the system of eigenfunctions of this problem.

Two charges on plane in a magnetic field I. “Quasi-equal” charges and neutral quantum system at rest cases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Escobar-Ruiz, M.A., E-mail: mauricio.escobar@nucleares.unam.mx; Turbiner, A.V., E-mail: turbiner@nucleares.unam.mx

Low-lying bound states for the problem of two Coulomb charges of finite masses on a plane subject to a constant magnetic field B perpendicular to the plane are considered. Major emphasis is given to two systems: two charges with the equal charge-to-mass ratio (quasi-equal charges) and neutral systems with concrete results for the hydrogen atom and two electrons (quantum dot). It is shown that for these two cases, when a neutral system is at rest (the center-of-mass momentum is zero), some outstanding properties occur: in double polar coordinates in CMS (R,ϕ) and relative (ρ,φ) coordinate systems (i) the eigenfunctions aremore » factorizable, all factors except for ρ-dependent are found analytically, they have definite relative angular momentum, (ii) dynamics in ρ-direction is the same for both systems being described by a funnel-type potential; (iii) at some discrete values of dimensionless magnetic fields b≤1 the system becomes quasi-exactly-solvable and a finite number of eigenfunctions in ρ are polynomials. The variational method is employed. Trial functions are based on combining for the phase of a wavefunction (a) the WKB expansion at large distances, (b) the perturbation theory at small distances (c) with a form of the known analytically (quasi-exactly-solvable) eigenfunctions. Such a form of trial function appears as a compact uniform approximation for lowest eigenfunctions. For the lowest states with relative magnetic quantum numbers s=0,1,2 this approximation gives not less than 7 s.d., 8 s.d., 9 s.d., respectively, for the total energy E(B) for magnetic fields 0.049a.u.« less

On the Aharonov-Bohm Operators with Varying Poles: The Boundary Behavior of Eigenvalues

NASA Astrophysics Data System (ADS)

Noris, Benedetta; Nys, Manon; Terracini, Susanna

2015-11-01

We consider a magnetic Schrödinger operator with magnetic field concentrated at one point (the pole) of a domain and half integer circulation, and we focus on the behavior of Dirichlet eigenvalues as functions of the pole. Although the magnetic field vanishes almost everywhere, it is well known that it affects the operator at the spectral level (the Aharonov-Bohm effect, Phys Rev (2) 115:485-491, 1959). Moreover, the numerical computations performed in (Bonnaillie-Noël et al., Anal PDE 7(6):1365-1395, 2014; Noris and Terracini, Indiana Univ Math J 59(4):1361-1403, 2010) show a rather complex behavior of the eigenvalues as the pole varies in a planar domain. In this paper, in continuation of the analysis started in (Bonnaillie-Noël et al., Anal PDE 7(6):1365-1395, 2014; Noris and Terracini, Indiana Univ Math J 59(4):1361-1403, 2010), we analyze the relation between the variation of the eigenvalue and the nodal structure of the associated eigenfunctions. We deal with planar domains with Dirichlet boundary conditions and we focus on the case when the singular pole approaches the boundary of the domain: then, the operator loses its singular character and the k-th magnetic eigenvalue converges to that of the standard Laplacian. We can predict both the rate of convergence and whether the convergence happens from above or from below, in relation with the number of nodal lines of the k-th eigenfunction of the Laplacian. The proof relies on the variational characterization of eigenvalues, together with a detailed asymptotic analysis of the eigenfunctions, based on an Almgren-type frequency formula for magnetic eigenfunctions and on the blow-up technique.

Numerical Aspects of Eigenvalue and Eigenfunction Computations for Chaotic Quantum Systems

NASA Astrophysics Data System (ADS)

Bäcker, A.

Summary: We give an introduction to some of the numerical aspects in quantum chaos. The classical dynamics of two-dimensional area-preserving maps on the torus is illustrated using the standard map and a perturbed cat map. The quantization of area-preserving maps given by their generating function is discussed and for the computation of the eigenvalues a computer program in Python is presented. We illustrate the eigenvalue distribution for two types of perturbed cat maps, one leading to COE and the other to CUE statistics. For the eigenfunctions of quantum maps we study the distribution of the eigenvectors and compare them with the corresponding random matrix distributions. The Husimi representation allows for a direct comparison of the localization of the eigenstates in phase space with the corresponding classical structures. Examples for a perturbed cat map and the standard map with different parameters are shown. Billiard systems and the corresponding quantum billiards are another important class of systems (which are also relevant to applications, for example in mesoscopic physics). We provide a detailed exposition of the boundary integral method, which is one important method to determine the eigenvalues and eigenfunctions of the Helmholtz equation. We discuss several methods to determine the eigenvalues from the Fredholm equation and illustrate them for the stadium billiard. The occurrence of spurious solutions is discussed in detail and illustrated for the circular billiard, the stadium billiard, and the annular sector billiard. We emphasize the role of the normal derivative function to compute the normalization of eigenfunctions, momentum representations or autocorrelation functions in a very efficient and direct way. Some examples for these quantities are given and discussed.

On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator

NASA Astrophysics Data System (ADS)

Korda, Milan; Mezić, Igor

2018-04-01

Extended dynamic mode decomposition (EDMD) (Williams et al. in J Nonlinear Sci 25(6):1307-1346, 2015) is an algorithm that approximates the action of the Koopman operator on an N-dimensional subspace of the space of observables by sampling at M points in the state space. Assuming that the samples are drawn either independently or ergodically from some measure μ , it was shown in Klus et al. (J Comput Dyn 3(1):51-79, 2016) that, in the limit as M→ ∞, the EDMD operator K_{N,M} converges to K_N, where K_N is the L_2(μ )-orthogonal projection of the action of the Koopman operator on the finite-dimensional subspace of observables. We show that, as N → ∞, the operator K_N converges in the strong operator topology to the Koopman operator. This in particular implies convergence of the predictions of future values of a given observable over any finite time horizon, a fact important for practical applications such as forecasting, estimation and control. In addition, we show that accumulation points of the spectra of K_N correspond to the eigenvalues of the Koopman operator with the associated eigenfunctions converging weakly to an eigenfunction of the Koopman operator, provided that the weak limit of the eigenfunctions is nonzero. As a by-product, we propose an analytic version of the EDMD algorithm which, under some assumptions, allows one to construct K_N directly, without the use of sampling. Finally, under additional assumptions, we analyze convergence of K_{N,N} (i.e., M=N), proving convergence, along a subsequence, to weak eigenfunctions (or eigendistributions) related to the eigenmeasures of the Perron-Frobenius operator. No assumptions on the observables belonging to a finite-dimensional invariant subspace of the Koopman operator are required throughout.

Persistence versus extinction for a class of discrete-time structured population models.

PubMed

Jin, Wen; Smith, Hal L; Thieme, Horst R

2016-03-01

We provide sharp conditions distinguishing persistence and extinction for a class of discrete-time dynamical systems on the positive cone of an ordered Banach space generated by a map which is the sum of a positive linear contraction A and a nonlinear perturbation G that is compact and differentiable at zero in the direction of the cone. Such maps arise as year-to-year projections of population age, stage, or size-structure distributions in population biology where typically A has to do with survival and individual development and G captures the effects of reproduction. The threshold distinguishing persistence and extinction is the principal eigenvalue of (II−A)(−1)G'(0) provided by the Krein-Rutman Theorem, and persistence is described in terms of associated eigenfunctionals. Our results significantly extend earlier persistence results of the last two authors which required more restrictive conditions on G. They are illustrated by application of the results to a plant model with a seed bank.

Propagation-invariant beams with quantum pendulum spectra: from Bessel beams to Gaussian beam-beams.

PubMed

Dennis, Mark R; Ring, James D

2013-09-01

We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly periodic Mathieu functions in azimuth, depend on a field strength parameter. When the parameter is zero, pendulum beams are Bessel beams, and as the parameter approaches infinity, they resemble transversely propagating one-dimensional Gaussian wave packets (Gaussian beam-beams). Pendulum beams are the eigenfunctions of an operator that interpolates between the squared angular momentum operator and the linear momentum operator. The analysis reveals connections with Mathieu beams, and insight into the paraxial approximation.

On the basis property of the system of eigenfunctions and associated functions of a one-dimensional Dirac operator

NASA Astrophysics Data System (ADS)

Savchuk, A. M.

2018-04-01

We study a one-dimensional Dirac system on a finite interval. The potential (a 2× 2 matrix) is assumed to be complex- valued and integrable. The boundary conditions are assumed to be regular in the sense of Birkhoff. It is known that such an operator has a discrete spectrum and the system \\{\\mathbf{y}_n\\}_1^∞ of its eigenfunctions and associated functions is a Riesz basis (possibly with brackets) in L_2\\oplus L_2. Our results concern the basis property of this system in the spaces L_μ\\oplus L_μ for μ\

A new approach to the Schrödinger equation with rational potentials

NASA Astrophysics Data System (ADS)

Dong, Ming-de; Chu, Jue-Hui

1984-04-01

A new analytic theory is established for the Schrödinger equation with a rational potential, including a complete classification of the regular eigenfunctions into three different types, an exact method of obtaining wavefunctions, an explicit formulation of the spectral equation (3 x 3 determinant) etc. All representations are exhibited in a unifying way via function-theoretic methods and therefore given in explicit form, in contrast to the prevailing discussion appealing to perturbation or variation methods or continued-fraction techniques. The irregular eigenfunctions at infinity can be obtained analogously and will be discussed separately as another solvable case for singular potentials.

Comment on "Calculations for the one-dimensional soft Coulomb problem and the hard Coulomb limit".

PubMed

Carrillo-Bernal, M A; Núñez-Yépez, H N; Salas-Brito, A L; Solis, Didier A

2015-02-01

In the referred paper, the authors use a numerical method for solving ordinary differential equations and a softened Coulomb potential -1/√[x(2)+β(2)] to study the one-dimensional Coulomb problem by approaching the parameter β to zero. We note that even though their numerical findings in the soft potential scenario are correct, their conclusions do not extend to the one-dimensional Coulomb problem (β=0). Their claims regarding the possible existence of an even ground state with energy -∞ with a Dirac-δ eigenfunction and of well-defined parity eigenfunctions in the one-dimensional hydrogen atom are questioned.

Quadratic Forms and Semiclassical Eigenfunction Hypothesis for Flat Tori

NASA Astrophysics Data System (ADS)

T. Sardari, Naser

2018-03-01

Let Q( X) be any integral primitive positive definite quadratic form in k variables, where {k≥4}, and discriminant D. For any integer n, we give an upper bound on the number of integral solutions of Q( X) = n in terms of n, k, and D. As a corollary, we prove a conjecture of Lester and Rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given eigenspace of the Laplacian on the flat torus {T^d} for {d≥ 5}. This conjecture is motivated by the work of Berry [2,3] on the semiclassical eigenfunction hypothesis.

Expressive body movement responses to music are coherent, consistent, and low dimensional.

PubMed

Amelynck, Denis; Maes, Pieter-Jan; Martens, Jean Pierre; Leman, Marc

2014-12-01

Embodied music cognition stresses the role of the human body as mediator for the encoding and decoding of musical expression. In this paper, we set up a low dimensional functional model that accounts for 70% of the variability in the expressive body movement responses to music. With the functional principal component analysis, we modeled individual body movements as a linear combination of a group average and a number of eigenfunctions. The group average and the eigenfunctions are common to all subjects and make up what we call the commonalities. An individual performance is then characterized by a set of scores (the individualities), one score per eigenfunction. The model is based on experimental data which finds high levels of coherence/consistency between participants when grouped according to musical education. This shows an ontogenetic effect. Participants without formal musical education focus on the torso for the expression of basic musical structure (tempo). Musically trained participants decode additional structural elements in the music and focus on body parts having more degrees of freedom (such as the hands). Our results confirm earlier studies that different body parts move differently along with the music.

An eigenfunction method for reconstruction of large-scale and high-contrast objects.

PubMed

Waag, Robert C; Lin, Feng; Varslot, Trond K; Astheimer, Jeffrey P

2007-07-01

A multiple-frequency inverse scattering method that uses eigenfunctions of a scattering operator is extended to image large-scale and high-contrast objects. The extension uses an estimate of the scattering object to form the difference between the scattering by the object and the scattering by the estimate of the object. The scattering potential defined by this difference is expanded in a basis of products of acoustic fields. These fields are defined by eigenfunctions of the scattering operator associated with the estimate. In the case of scattering objects for which the estimate is radial, symmetries in the expressions used to reconstruct the scattering potential greatly reduce the amount of computation. The range of parameters over which the reconstruction method works well is illustrated using calculated scattering by different objects. The method is applied to experimental data from a 48-mm diameter scattering object with tissue-like properties. The image reconstructed from measurements has, relative to a conventional B-scan formed using a low f-number at the same center frequency, significantly higher resolution and less speckle, implying that small, high-contrast structures can be demonstrated clearly using the extended method.

Darboux theorems and Wronskian formulas for integrable systems I. Constrained KP flows

NASA Astrophysics Data System (ADS)

Oevel, W.

1993-05-01

Generalizations of the classical Darboux theorem are established for pseudo-differential scattering operators of the form L = limit∑i=0N u i∂ i + limitΣi=1m Φ i∂ -1limitΨi†i. Iteration of the Darboux transformations leads to a gauge transformed operator with coefficients given by Wronskian formulas involving a set of eigenfunctions of L. Nonlinear integrable partial differential equations are associated with the scattering operator L which arise as a symmetry reduction of the multicomponent KP hierarchy. With a suitable linear time evolution for the eigenfunctions the Darboux transformation is used to obtain solutions of the integrable equations in terms of Wronskian determinants.

On a difficulty in eigenfunction expansion solutions for the start-up of fluid flow

NASA Astrophysics Data System (ADS)

Christov, Ivan C.

2015-11-01

Most mathematics and engineering textbooks describe the process of ``subtracting off'' the steady state of a linear parabolic partial differential equation as a technique for obtaining a boundary-value problem with homogeneous boundary conditions that can be solved by separation of variables (i.e., eigenfunction expansions). While this method produces the correct solution for the start-up of the flow of, e.g., a Newtonian fluid between parallel plates, it can lead to erroneous solutions to the corresponding problem for a class of non-Newtonian fluids. We show that the reason for this is the non-rigorous enforcement of the start-up condition in the textbook approach, which leads to a violation of the principle of causality. Nevertheless, these boundary-value problems can be solved correctly using eigenfunction expansions, and we present the formulation that makes this possible (in essence, an application of Duhamel's principle). The solutions obtained by this new approach are shown to agree identically with those obtained by using the Laplace transform in time only, a technique that enforces the proper start-up condition implicitly (hence, the same error cannot be committed). Supported, in part, by NSF Grant DMS-1104047 and the U.S. DOE (Contract No. DE-AC52-06NA25396) through the LANL/LDRD Program.

Waves propagating over a two-layer porous barrier on a seabed

NASA Astrophysics Data System (ADS)

Lin, Qiang; Meng, Qing-rui; Lu, Dong-qiang

2018-05-01

A research of wave propagation over a two-layer porous barrier, each layer of which is with different values of porosity and friction, is conducted with a theoretical model in the frame of linear potential flow theory. The model is more appropriate when the seabed consists of two different properties, such as rocks and breakwaters. It is assumed that the fluid is inviscid and incompressible and the motion is irrotational. The wave numbers in the porous region are complex ones, which are related to the decaying and propagating behaviors of wave modes. With the aid of the eigenfunction expansions, a new inner product of the eigenfunctions in the two-layer porous region is proposed to simplify the calculation. The eigenfunctions, under this new definition, possess the orthogonality from which the expansion coefficients can be easily deduced. Selecting the optimum truncation of the series, we derive a closed system of simultaneous linear equations for the same number of the unknown reflection and transmission coefficients. The effects of several physical parameters, including the porosity, friction, width, and depth of the porous barrier, on the dispersion relation, reflection and transmission coefficients are discussed in detail through the graphical representations of the solutions. It is concluded that these parameters have certain impacts on the reflection and transmission energy.

Algorithm for Stabilizing a POD-Based Dynamical System

NASA Technical Reports Server (NTRS)

Kalb, Virginia L.

2010-01-01

This algorithm provides a new way to improve the accuracy and asymptotic behavior of a low-dimensional system based on the proper orthogonal decomposition (POD). Given a data set representing the evolution of a system of partial differential equations (PDEs), such as the Navier-Stokes equations for incompressible flow, one may obtain a low-dimensional model in the form of ordinary differential equations (ODEs) that should model the dynamics of the flow. Temporal sampling of the direct numerical simulation of the PDEs produces a spatial time series. The POD extracts the temporal and spatial eigenfunctions of this data set. Truncated to retain only the most energetic modes followed by Galerkin projection of these modes onto the PDEs obtains a dynamical system of ordinary differential equations for the time-dependent behavior of the flow. In practice, the steps leading to this system of ODEs entail numerically computing first-order derivatives of the mean data field and the eigenfunctions, and the computation of many inner products. This is far from a perfect process, and often results in the lack of long-term stability of the system and incorrect asymptotic behavior of the model. This algorithm describes a new stabilization method that utilizes the temporal eigenfunctions to derive correction terms for the coefficients of the dynamical system to significantly reduce these errors.

Commensurability effects in one-dimensional Anderson localization: Anomalies in eigenfunction statistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kravtsov, V.E., E-mail: kravtsov@ictp.it; Landau Institute for Theoretical Physics, 2 Kosygina st., 117940 Moscow; Yudson, V.I., E-mail: yudson@isan.troitsk.ru

Highlights: > Statistics of normalized eigenfunctions in one-dimensional Anderson localization at E = 0 is studied. > Moments of inverse participation ratio are calculated. > Equation for generating function is derived at E = 0. > An exact solution for generating function at E = 0 is obtained. > Relation of the generating function to the phase distribution function is established. - Abstract: The one-dimensional (1d) Anderson model (AM), i.e. a tight-binding chain with random uncorrelated on-site energies, has statistical anomalies at any rational point f=(2a)/({lambda}{sub E}) , where a is the lattice constant and {lambda}{sub E} is the demore » Broglie wavelength. We develop a regular approach to anomalous statistics of normalized eigenfunctions {psi}(r) at such commensurability points. The approach is based on an exact integral transfer-matrix equation for a generating function {Phi}{sub r}(u, {phi}) (u and {phi} have a meaning of the squared amplitude and phase of eigenfunctions, r is the position of the observation point). This generating function can be used to compute local statistics of eigenfunctions of 1d AM at any disorder and to address the problem of higher-order anomalies at f=p/q with q > 2. The descender of the generating function P{sub r}({phi}){identical_to}{Phi}{sub r}(u=0,{phi}) is shown to be the distribution function of phase which determines the Lyapunov exponent and the local density of states. In the leading order in the small disorder we derived a second-order partial differential equation for the r-independent ('zero-mode') component {Phi}(u, {phi}) at the E = 0 (f=1/2 ) anomaly. This equation is nonseparable in variables u and {phi}. Yet, we show that due to a hidden symmetry, it is integrable and we construct an exact solution for {Phi}(u, {phi}) explicitly in quadratures. Using this solution we computed moments I{sub m} = N< vertical bar {psi} vertical bar {sup 2m}> (m {>=} 1) for a chain of the length N {yields} {infinity} and found an essential difference between their m-behavior in the center-of-band anomaly and for energies outside this anomaly. Outside the anomaly the 'extrinsic' localization length defined from the Lyapunov exponent coincides with that defined from the inverse participation ratio ('intrinsic' localization length). This is not the case at the E = 0 anomaly where the extrinsic localization length is smaller than the intrinsic one. At E = 0 one also observes an anomalous enhancement of large moments compatible with existence of yet another, much smaller characteristic length scale.« less

FAST TRACK COMMUNICATION: SUSY transformations with complex factorization constants: application to spectral singularities

NASA Astrophysics Data System (ADS)

Samsonov, Boris F.

2010-10-01

Supersymmetric (SUSY) transformation operators with complex factorization constants are analyzed as operators acting in the Hilbert space of functions square integrable on the positive semiaxis. The obtained results are applied to Hamiltonians possessing spectral singularities which are non-Hermitian SUSY partners of self-adjoint operators. A new regularization procedure for the resolution of the identity operator in terms of a continuous biorthonormal set of the non-Hermitian Hamiltonian eigenfunctions is proposed. It is also argued that if the binorm of continuous spectrum eigenfunctions is interpreted in the same way as the norm of similar functions in the usual Hermitian case, then one can state that the function corresponding to a spectral singularity has zero binorm.

Nodal domains of a non-separable problem—the right-angled isosceles triangle

NASA Astrophysics Data System (ADS)

Aronovitch, Amit; Band, Ram; Fajman, David; Gnutzmann, Sven

2012-03-01

We study the nodal set of eigenfunctions of the Laplace operator on the right-angled isosceles triangle. A local analysis of the nodal pattern provides an algorithm for computing the number νn of nodal domains for any eigenfunction. In addition, an exact recursive formula for the number of nodal domains is found to reproduce all existing data. Eventually, we use the recursion formula to analyse a large sequence of nodal counts statistically. Our analysis shows that the distribution of nodal counts for this triangular shape has a much richer structure than the known cases of regular separable shapes or completely irregular shapes. Furthermore, we demonstrate that the nodal count sequence contains information about the periodic orbits of the corresponding classical ray dynamics.

Inverse scattering transform for the KPI equation on the background of a one-line soliton*Inverse scattering transform for the KPI equation on the background of a one-line soliton

NASA Astrophysics Data System (ADS)

Fokas, A. S.; Pogrebkov, A. K.

2003-03-01

We study the initial value problem of the Kadomtsev-Petviashvili I (KPI) equation with initial data u(x1,x2,0) = u1(x1)+u2(x1,x2), where u1(x1) is the one-soliton solution of the Korteweg-de Vries equation evaluated at zero time and u2(x1,x2) decays sufficiently rapidly on the (x1,x2)-plane. This involves the analysis of the nonstationary Schrödinger equation (with time replaced by x2) with potential u(x1,x2,0). We introduce an appropriate sectionally analytic eigenfunction in the complex k-plane where k is the spectral parameter. This eigenfunction has the novelty that in addition to the usual jump across the real k-axis, it also has a jump across a segment of the imaginary k-axis. We show that this eigenfunction can be reconstructed through a linear integral equation uniquely defined in terms of appropriate scattering data. In turn, these scattering data are uniquely constructed in terms of u1(x1) and u2(x1,x2). This result implies that the solution of the KPI equation can be obtained through the above linear integral equation where the scattering data have a simple t-dependence.

Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions

NASA Astrophysics Data System (ADS)

Prinari, Barbara; Demontis, Francesco; Li, Sitai; Horikis, Theodoros P.

2018-04-01

The inverse scattering transform (IST) with non-zero boundary conditions at infinity is developed for an m × m matrix nonlinear Schrödinger-type equation which, in the case m = 2, has been proposed as a model to describe hyperfine spin F = 1 spinor Bose-Einstein condensates with either repulsive interatomic interactions and anti-ferromagnetic spin-exchange interactions (self-defocusing case), or attractive interatomic interactions and ferromagnetic spin-exchange interactions (self-focusing case). The IST for this system was first presented by Ieda et al. (2007) , using a different approach. In our formulation, both the direct and the inverse problems are posed in terms of a suitable uniformization variable which allows to develop the IST on the standard complex plane, instead of a two-sheeted Riemann surface or the cut plane with discontinuities along the cuts. Analyticity of the scattering eigenfunctions and scattering data, symmetries, properties of the discrete spectrum, and asymptotics are derived. The inverse problem is posed as a Riemann-Hilbert problem for the eigenfunctions, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is provided. In addition, the general behavior of the soliton solutions is analyzed in detail in the 2 × 2 self-focusing case, including some special solutions not previously discussed in the literature.

A technique for designing active control systems for astronomical telescope mirrors

NASA Technical Reports Server (NTRS)

Howell, W. E.; Creedon, J. F.

1973-01-01

The problem of designing a control system to achieve and maintain the required surface accuracy of the primary mirror of a large space telescope was considered. Control over the mirror surface is obtained through the application of a corrective force distribution by actuators located on the rear surface of the mirror. The design procedure is an extension of a modal control technique developed for distributed parameter plants with known eigenfunctions to include plants whose eigenfunctions must be approximated by numerical techniques. Instructions are given for constructing the mathematical model of the system, and a design procedure is developed for use with typical numerical data in selecting the number and location of the actuators. Examples of actuator patterns and their effect on various errors are given.

Singularities at the contact point of two kissing Neumann balls

NASA Astrophysics Data System (ADS)

Nazarov, Sergey A.; Taskinen, Jari

2018-02-01

We investigate eigenfunctions of the Neumann Laplacian in a bounded domain Ω ⊂Rd, where a cuspidal singularity is caused by a cavity consisting of two touching balls, or discs in the planar case. We prove that the eigenfunctions with all of their derivatives are bounded in Ω ‾, if the dimension d equals 2, but in dimension d ≥ 3 their gradients have a strong singularity O (| x - O|-α), α ∈ (0 , 2 -√{ 2 } ] at the point of tangency O. Our study is based on dimension reduction and other asymptotic procedures, as well as the Kondratiev theory applied to the limit differential equation in the punctured hyperplane R d - 1 ∖ O. We also discuss other shapes producing thinning gaps between touching cavities.

The tunneling effect for a class of difference operators

NASA Astrophysics Data System (ADS)

Klein, Markus; Rosenberger, Elke

We analyze a general class of self-adjoint difference operators H𝜀 = T𝜀 + V𝜀 on ℓ2((𝜀ℤ)d), where V𝜀 is a multi-well potential and 𝜀 is a small parameter. We give a coherent review of our results on tunneling up to new sharp results on the level of complete asymptotic expansions (see [30-35]).Our emphasis is on general ideas and strategy, possibly of interest for a broader range of readers, and less on detailed mathematical proofs. The wells are decoupled by introducing certain Dirichlet operators on regions containing only one potential well. Then the eigenvalue problem for the Hamiltonian H𝜀 is treated as a small perturbation of these comparison problems. After constructing a Finslerian distance d induced by H𝜀, we show that Dirichlet eigenfunctions decay exponentially with a rate controlled by this distance to the well. It follows with microlocal techniques that the first n eigenvalues of H𝜀 converge to the first n eigenvalues of the direct sum of harmonic oscillators on ℝd located at several wells. In a neighborhood of one well, we construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low-lying eigenvalues of H𝜀. These are obtained from eigenfunctions or quasimodes for the operator H𝜀, acting on L2(ℝd), via restriction to the lattice (𝜀ℤ)d. Tunneling is then described by a certain interaction matrix, similar to the analysis for the Schrödinger operator (see [22]), the remainder is exponentially small and roughly quadratic compared with the interaction matrix. We give weighted ℓ2-estimates for the difference of eigenfunctions of Dirichlet-operators in neighborhoods of the different wells and the associated WKB-expansions at the wells. In the last step, we derive full asymptotic expansions for interactions between two “wells” (minima) of the potential energy, in particular for the discrete tunneling effect. Here we essentially use analysis on phase space, complexified in the momentum variable. These results are as sharp as the classical results for the Schrödinger operator in [22].

Analytical solutions of the planar cyclic voltammetry process for two soluble species with equal diffusivities and fast electron transfer using the method of eigenfunction expansions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Samin, Adib; Lahti, Erik; Zhang, Jinsuo, E-mail: zhang.3558@osu.edu

Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extendedmore » to cases that are more general and may be useful for benchmarking purposes.« less

Exact vibration analysis of a double-nanobeam-systems embedded in an elastic medium by a Hamiltonian-based method

NASA Astrophysics Data System (ADS)

Zhou, Zhenhuan; Li, Yuejie; Fan, Junhai; Rong, Dalun; Sui, Guohao; Xu, Chenghui

2018-05-01

A new Hamiltonian-based approach is presented for finding exact solutions for transverse vibrations of double-nanobeam-systems embedded in an elastic medium. The continuum model is established within the frameworks of the symplectic methodology and the nonlocal Euler-Bernoulli and Timoshenko beam beams. The symplectic eigenfunctions are obtained after expressing the governing equations in a Hamiltonian form. Exact frequency equations, vibration modes and displacement amplitudes are obtained by using symplectic eigenfunctions and end conditions. Comparisons with previously published work are presented to illustrate the accuracy and reliability of the proposed method. The comprehensive results for arbitrary boundary conditions could serve as benchmark results for verifying numerically obtained solutions. In addition, a study on the difference between the nonlocal beam and the nonlocal plate is also included.

Parallel momentum input by tangential neutral beam injections in stellarator and heliotron plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nishimura, S., E-mail: nishimura.shin@lhd.nifs.ac.jp; Nakamura, Y.; Nishioka, K.

The configuration dependence of parallel momentum inputs to target plasma particle species by tangentially injected neutral beams is investigated in non-axisymmetric stellarator/heliotron model magnetic fields by assuming the existence of magnetic flux-surfaces. In parallel friction integrals of the full Rosenbluth-MacDonald-Judd collision operator in thermal particles' kinetic equations, numerically obtained eigenfunctions are used for excluding trapped fast ions that cannot contribute to the friction integrals. It is found that the momentum inputs to thermal ions strongly depend on magnetic field strength modulations on the flux-surfaces, while the input to electrons is insensitive to the modulation. In future plasma flow studies requiringmore » flow calculations of all particle species in more general non-symmetric toroidal configurations, the eigenfunction method investigated here will be useful.« less

Wigner functions for fermions in strong magnetic fields

NASA Astrophysics Data System (ADS)

Sheng, Xin-li; Rischke, Dirk H.; Vasak, David; Wang, Qun

2018-02-01

We compute the covariant Wigner function for spin-(1/2) fermions in an arbitrarily strong magnetic field by exactly solving the Dirac equation at non-zero fermion-number and chiral-charge densities. The Landau energy levels as well as a set of orthonormal eigenfunctions are found as solutions of the Dirac equation. With these orthonormal eigenfunctions we construct the fermion field operators and the corresponding Wigner-function operator. The Wigner function is obtained by taking the ensemble average of the Wigner-function operator in global thermodynamical equilibrium, i.e., at constant temperature T and non-zero fermion-number and chiral-charge chemical potentials μ and μ_5, respectively. Extracting the vector and axial-vector components of the Wigner function, we reproduce the currents of the chiral magnetic and separation effect in an arbitrarily strong magnetic field.

Using Nested Contractions and a Hierarchical Tensor Format To Compute Vibrational Spectra of Molecules with Seven Atoms.

PubMed

Thomas, Phillip S; Carrington, Tucker

2015-12-31

We propose a method for solving the vibrational Schrödinger equation with which one can compute hundreds of energy levels of seven-atom molecules using at most a few gigabytes of memory. It uses nested contractions in conjunction with the reduced-rank block power method (RRBPM) described in J. Chem. Phys. 2014, 140, 174111. Successive basis contractions are organized into a tree, the nodes of which are associated with eigenfunctions of reduced-dimension Hamiltonians. The RRBPM is used recursively to compute eigenfunctions of nodes in bases of products of reduced-dimension eigenfunctions of nodes with fewer coordinates. The corresponding vectors are tensors in what is called CP-format. The final wave functions are therefore represented in a hierarchical CP-format. Computational efficiency and accuracy are significantly improved by representing the Hamiltonian in the same hierarchical format as the wave function. We demonstrate that with this hierarchical RRBPM it is possible to compute energy levels of a 64-D coupled-oscillator model Hamiltonian and also of acetonitrile (CH3CN) and ethylene oxide (C2H4O), for which we use quartic potentials. The most accurate acetonitrile calculation uses 139 MB of memory and takes 3.2 h on a single processor. The most accurate ethylene oxide calculation uses 6.1 GB of memory and takes 14 d on 63 processors. The hierarchical RRBPM shatters the memory barrier that impedes the calculation of vibrational spectra.

A simple method for finding explicit analytic transition densities of diffusion processes with general diploid selection.

PubMed

Song, Yun S; Steinrücken, Matthias

2012-03-01

The transition density function of the Wright-Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright-Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation-selection balance.

A Simple Method for Finding Explicit Analytic Transition Densities of Diffusion Processes with General Diploid Selection

PubMed Central

Song, Yun S.; Steinrücken, Matthias

2012-01-01

The transition density function of the Wright–Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright–Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation–selection balance. PMID:22209899

Reduced dynamical model of the vibrations of a metal plate

NASA Astrophysics Data System (ADS)

Moreno, D.; Barrientos, Bernardino; Perez-Lopez, Carlos; Mendoza-Santoyo, Fernando; Guerrero, J. A.; Funes, M.

2005-02-01

The Proper Orthogonal Decomposition (POD) method is applied to the vibrations analysis of a metal plate. The data obtained from the metal plate under vibrations were measured with a laser vibrometer. The metal plate was subject to vibrations with an electrodynamical shaker in a range of frequencies from 100 to 5000 Hz. The deformation measurements were taken on a quarter of the plate in a rectangular grid of 7 x 8 points. The plate deformation measurements were used to calculate the eigenfunctions and the eigenvalues. It was found that a large fraction of the total energy of the deformation is contained within the first six POD modes. The essential features of the deformation are thus described by only the six first eigenfunctions. A reduced order model for the dynamical behavior is then constructed using Galerkin projection of the equation of motion for the vertical displacement of a plate.

Using Peano Curves to Construct Laplacians on Fractals

NASA Astrophysics Data System (ADS)

Molitor, Denali; Ott, Nadia; Strichartz, Robert

2015-12-01

We describe a new method to construct Laplacians on fractals using a Peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain Julia sets. The Peano curve allows us to visualize eigenfunctions of the Laplacian by graphing the pullback to the circle. We study in detail three fractals: the pentagasket, the octagasket and the magic carpet. We also use the method for two nonfractal self-similar sets, the torus and the equilateral triangle, obtaining appealing new visualizations of eigenfunctions on the triangle. In contrast to the many familiar pictures of approximations to standard Peano curves, that do no show self-intersections, our descriptions of approximations to the Peano curves have self-intersections that play a vital role in constructing graph approximations to the fractal with explicit graph Laplacians that give the fractal Laplacian in the limit.

Quantum field theory in spaces with closed timelike curves

NASA Astrophysics Data System (ADS)

Boulware, David G.

1992-11-01

Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.

Boundary Concentration for Eigenvalue Problems Related to the Onset of Superconductivity

NASA Astrophysics Data System (ADS)

del Pino, Manuel; Felmer, Patricio L.; Sternberg, Peter

We examine the asymptotic behavior of the eigenvalue μ(h) and corresponding eigenfunction associated with the variational problem in the regime h>>1. Here A is any vector field with curl equal to 1. The problem arises within the Ginzburg-Landau model for superconductivity with the function μ(h) yielding the relationship between the critical temperature vs. applied magnetic field strength in the transition from normal to superconducting state in a thin mesoscopic sample with cross-section Ω 2. We first carry out a rigorous analysis of the associated problem on a half-plane and then rigorously justify some of the formal arguments of [BS], obtaining an expansion for μ while also proving that the first eigenfunction decays to zero somewhere along the sample boundary when Ω is not a disc. For interior decay, we demonstrate that the rate is exponential.

Disconjugacy, regularity of multi-indexed rationally extended potentials, and Laguerre exceptional polynomials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grandati, Y.; Quesne, C.

2013-07-15

The power of the disconjugacy properties of second-order differential equations of Schrödinger type to check the regularity of rationally extended quantum potentials connected with exceptional orthogonal polynomials is illustrated by re-examining the extensions of the isotonic oscillator (or radial oscillator) potential derived in kth-order supersymmetric quantum mechanics or multistep Darboux-Bäcklund transformation method. The function arising in the potential denominator is proved to be a polynomial with a nonvanishing constant term, whose value is calculated by induction over k. The sign of this term being the same as that of the already known highest degree term, the potential denominator has themore » same sign at both extremities of the definition interval, a property that is shared by the seed eigenfunction used in the potential construction. By virtue of disconjugacy, such a property implies the nodeless character of both the eigenfunction and the resulting potential.« less

Diskoseismology: Probing accretion disks. II - G-modes, gravitational radiation reaction, and viscosity

NASA Technical Reports Server (NTRS)

Nowak, Michael A.; Wagoner, Robert V.

1992-01-01

A scalar potential is used to derive a single partial differential equation governing the oscillation of a disk. The eigenfunctions and eigenfrequencies of a variety of disk models are found to fall into two main classes which are analogous to the p-modes and g-modes in the sun. Specifically, the eigenfunctions and eigenfrequencies of isothermal disks are computed, and the way in which these results can be generalized to other disk models is indicated. The (assumed) relatively small rates of growth or damping of the modes due to various mechanisms, in particular gravitational radiation reaction and parameterized models of viscosity are also computed. It is found that for certain parameters the p-modes are unstable to gravitational radiation reaction (CFS instability), while both the p-modes and g-modes are unstable to viscosity unless highly anisotropic viscosity models are considered.

Vibrational treatment of the formic acid double minimum case in valence coordinates

NASA Astrophysics Data System (ADS)

Richter, Falk; Carbonnière, P.

2018-02-01

One single full dimensional valence coordinate HCOOH ground state potential energy surface accurate for both cis and trans conformers for all levels up to 6000 cm-1 relative to trans zero point energy has been generated at CCSD(T)-F12a/aug-cc-pVTZ level. The fundamentals and a set of eigenfunctions complete up to about 3120 and 2660 cm-1 for trans- and cis-HCOOH, respectively, have been calculated and assigned using the improved relaxation method of the Heidelberg multi-configuration time-dependent Hartree package and an exact expression for the kinetic energy in valence coordinates generated by the TANA program. The calculated trans fundamental transition frequencies agree with experiment to within 5 cm-1. A few reassignments are suggested. Our results discard any cis trans delocalization effects for vibrational eigenfunctions up to 3640 cm-1 relative to trans zero point energy.

Generalized Ince Gaussian beams

NASA Astrophysics Data System (ADS)

Bandres, Miguel A.; Gutiérrez-Vega, Julio C.

2006-08-01

In this work we present a detailed analysis of the tree families of generalized Gaussian beams, which are the generalized Hermite, Laguerre, and Ince Gaussian beams. The generalized Gaussian beams are not the solution of a Hermitian operator at an arbitrary z plane. We derived the adjoint operator and the adjoint eigenfunctions. Each family of generalized Gaussian beams forms a complete biorthonormal set with their adjoint eigenfunctions, therefore, any paraxial field can be described as a superposition of a generalized family with the appropriate weighting and phase factors. Each family of generalized Gaussian beams includes the standard and elegant corresponding families as particular cases when the parameters of the generalized families are chosen properly. The generalized Hermite Gaussian and Laguerre Gaussian beams correspond to limiting cases of the generalized Ince Gaussian beams when the ellipticity parameter of the latter tends to infinity or to zero, respectively. The expansion formulas among the three generalized families and their Fourier transforms are also presented.

Analytical bound-state solutions of the Schrödinger equation for the Manning-Rosen plus Hulthén potential within SUSY quantum mechanics

NASA Astrophysics Data System (ADS)

Ahmadov, A. I.; Naeem, Maria; Qocayeva, M. V.; Tarverdiyeva, V. A.

2018-01-01

In this paper, the bound-state solution of the modified radial Schrödinger equation is obtained for the Manning-Rosen plus Hulthén potential by using new developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial wave functions are defined for any l≠0 angular momentum case via the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. Thanks to both methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is presented. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary l states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.

Vortex knots in tangled quantum eigenfunctions

PubMed Central

Taylor, Alexander J.; Dennis, Mark R.

2016-01-01

Tangles of string typically become knotted, from macroscopic twine down to long-chain macromolecules such as DNA. Here, we demonstrate that knotting also occurs in quantum wavefunctions, where the tangled filaments are vortices (nodal lines/phase singularities). The probability that a vortex loop is knotted is found to increase with its length, and a wide gamut of knots from standard tabulations occur. The results follow from computer simulations of random superpositions of degenerate eigenstates of three simple quantum systems: a cube with periodic boundaries, the isotropic three-dimensional harmonic oscillator and the 3-sphere. In the latter two cases, vortex knots occur frequently, even in random eigenfunctions at relatively low energy, and are constrained by the spatial symmetries of the modes. The results suggest that knotted vortex structures are generic in complex three-dimensional wave systems, establishing a topological commonality between wave chaos, polymers and turbulent Bose–Einstein condensates. PMID:27468801

Vibrational modes of thin oblate clouds of charge

NASA Astrophysics Data System (ADS)

Jenkins, Thomas G.; Spencer, Ross L.

2002-07-01

A numerical method is presented for finding the eigenfunctions (normal modes) and mode frequencies of azimuthally symmetric non-neutral plasmas confined in a Penning trap whose axial thickness is much smaller than their radial size. The plasma may be approximated as a charged disk in this limit; the normal modes and frequencies can be found if the surface charge density profile σ(r) of the disk and the trap bounce frequency profile ωz(r) are known. The dependence of the eigenfunctions and equilibrium plasma shapes on nonideal components of the confining Penning trap fields is discussed. The results of the calculation are compared with the experimental data of Weimer et al. [Phys. Rev. A 49, 3842 (1994)] and it is shown that the plasma in this experiment was probably hollow and had mode displacement functions that were concentrated near the center of the plasma.

Adaptive eigenspace method for inverse scattering problems in the frequency domain

NASA Astrophysics Data System (ADS)

Grote, Marcus J.; Kray, Marie; Nahum, Uri

2017-02-01

A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion method.

DeepNAT: Deep convolutional neural network for segmenting neuroanatomy.

PubMed

Wachinger, Christian; Reuter, Martin; Klein, Tassilo

2018-04-15

We introduce DeepNAT, a 3D Deep convolutional neural network for the automatic segmentation of NeuroAnaTomy in T1-weighted magnetic resonance images. DeepNAT is an end-to-end learning-based approach to brain segmentation that jointly learns an abstract feature representation and a multi-class classification. We propose a 3D patch-based approach, where we do not only predict the center voxel of the patch but also neighbors, which is formulated as multi-task learning. To address a class imbalance problem, we arrange two networks hierarchically, where the first one separates foreground from background, and the second one identifies 25 brain structures on the foreground. Since patches lack spatial context, we augment them with coordinates. To this end, we introduce a novel intrinsic parameterization of the brain volume, formed by eigenfunctions of the Laplace-Beltrami operator. As network architecture, we use three convolutional layers with pooling, batch normalization, and non-linearities, followed by fully connected layers with dropout. The final segmentation is inferred from the probabilistic output of the network with a 3D fully connected conditional random field, which ensures label agreement between close voxels. The roughly 2.7million parameters in the network are learned with stochastic gradient descent. Our results show that DeepNAT compares favorably to state-of-the-art methods. Finally, the purely learning-based method may have a high potential for the adaptation to young, old, or diseased brains by fine-tuning the pre-trained network with a small training sample on the target application, where the availability of larger datasets with manual annotations may boost the overall segmentation accuracy in the future. Copyright © 2017 Elsevier Inc. All rights reserved.

Quantized discrete space oscillators

NASA Technical Reports Server (NTRS)

Uzes, C. A.; Kapuscik, Edward

1993-01-01

A quasi-canonical sequence of finite dimensional quantizations was found which has canonical quantization as its limit. In order to demonstrate its practical utility and its numerical convergence, this formalism is applied to the eigenvalue and 'eigenfunction' problem of several harmonic and anharmonic oscillators.

A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks

PubMed Central

Schaffer, Evan S.; Ostojic, Srdjan; Abbott, L. F.

2013-01-01

Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are governed by a single time constant. These models fail to replicate certain dynamic features of populations of spiking neurons, especially those involving synchronization. We present a complex-valued firing-rate model derived from an eigenfunction expansion of the Fokker-Planck equation and apply it to the linear, quadratic and exponential integrate-and-fire models. Despite being almost as simple as a traditional firing-rate description, this model can reproduce firing-rate dynamics due to partial synchronization of the action potentials in a spiking model, and it successfully predicts the transition to spike synchronization in networks of coupled excitatory and inhibitory neurons. PMID:24204236

Global point signature for shape analysis of carpal bones

NASA Astrophysics Data System (ADS)

Chaudhari, Abhijit J.; Leahy, Richard M.; Wise, Barton L.; Lane, Nancy E.; Badawi, Ramsey D.; Joshi, Anand A.

2014-02-01

We present a method based on spectral theory for the shape analysis of carpal bones of the human wrist. We represent the cortical surface of the carpal bone in a coordinate system based on the eigensystem of the two-dimensional Helmholtz equation. We employ a metric—global point signature (GPS)—that exploits the scale and isometric invariance of eigenfunctions to quantify overall bone shape. We use a fast finite-element-method to compute the GPS metric. We capitalize upon the properties of GPS representation—such as stability, a standard Euclidean (ℓ2) metric definition, and invariance to scaling, translation and rotation—to perform shape analysis of the carpal bones of ten women and ten men from a publicly-available database. We demonstrate the utility of the proposed GPS representation to provide a means for comparing shapes of the carpal bones across populations.

Dunkl-Darboux differential-difference operators

NASA Astrophysics Data System (ADS)

Khekalo, S. P.

2017-02-01

Using a natural generalization, we construct and study analogues of Dunkl differential-difference operators on the line. These analogues turn out to be closely connected with the so-called Burchnall- Chaundy-Adler-Moser polynomials and, therefore, with Darboux transforms. We find the eigenfunctions of these operators.

Induced Angular Momentum

ERIC Educational Resources Information Center

Parker, G. W.

1978-01-01

Discusses, classically and quantum mechanically, the angular momentum induced in the bound motion of an electron by an external magnetic field. Calculates the current density and its magnetic moment, and then uses two methods to solve the first-order perturbation theory equation for the required eigenfunction. (Author/GA)

Morphological evolution of Jinshan Trough in Hangzhou Bay (China) from 1960 to 2011

NASA Astrophysics Data System (ADS)

Liu, Yifei; Xia, Xiaoming; Chen, Shenliang; Jia, Jianjun; Cai, Tinglu

2017-11-01

An extensive system of tidal channels, starting with Jinshan Trough in the east, is located along the north shore of Hangzhou Bay, China. This contribution investigates the morphological evolution of Jinshan Trough by using 17 bathymetric charts from a series covering a period of 51 years from 1960 to 2011. Three stages of evolution during this period are distinguishable based on the morphology and annual mean volume data. The first stage (1960-1987) is characterized by extension of the trough; the second stage (1987-1996) is a relatively stable period with some adjustments in the trough morphology; the third stage (1996-2011) is marked by the processes of erosion and deposition in the beginning of the period and a subsequent slow erosion process. Spatio-temporal variability of the trough was evaluated by using empirical orthogonal function (EOF) analysis. The first eigenfunction indicates that erosion is the main evolution process and there exists three stages similar to those distinguished from volume variations. The second eigenfunction mainly reflects erosion and deposition in the northwest part of the trough located in the flood tidal current shadow area of the artificial headland in Jinshan. The third eigenfunction mainly reflects annual fluctuations of erosion and deposition in the side slope at the artificial headland in Jinshan. A particularly intense erosion process occurred between 1996 and 1998. The major effects on morphological evolution in Jinshan Trough from 1960 to 2011 were investigated and tentative conclusions were presented. Continuous coastal reclamations in Jinshan had the most pronounced effect on the morphological evolution during the first and the second stages. The storm surge had a pronounced effect on the evolution at the beginning of the third stage.

Wave chaos in a randomly inhomogeneous waveguide: spectral analysis of the finite-range evolution operator.

PubMed

Makarov, D V; Kon'kov, L E; Uleysky, M Yu; Petrov, P S

2013-01-01

The problem of sound propagation in a randomly inhomogeneous oceanic waveguide is considered. An underwater sound channel in the Sea of Japan is taken as an example. Our attention is concentrated on the domains of finite-range ray stability in phase space and their influence on wave dynamics. These domains can be found by means of the one-step Poincare map. To study manifestations of finite-range ray stability, we introduce the finite-range evolution operator (FREO) describing transformation of a wave field in the course of propagation along a finite segment of a waveguide. Carrying out statistical analysis of the FREO spectrum, we estimate the contribution of regular domains and explore their evanescence with increasing length of the segment. We utilize several methods of spectral analysis: analysis of eigenfunctions by expanding them over modes of the unperturbed waveguide, approximation of level-spacing statistics by means of the Berry-Robnik distribution, and the procedure used by A. Relano and coworkers [Relano et al., Phys. Rev. Lett. 89, 244102 (2002); Relano, Phys. Rev. Lett. 100, 224101 (2008)]. Comparing the results obtained with different methods, we find that the method based on the statistical analysis of FREO eigenfunctions is the most favorable for estimating the contribution of regular domains. It allows one to find directly the waveguide modes whose refraction is regular despite the random inhomogeneity. For example, it is found that near-axial sound propagation in the Sea of Japan preserves stability even over distances of hundreds of kilometers due to the presence of a shearless torus in the classical phase space. Increasing the acoustic wavelength degrades scattering, resulting in recovery of eigenfunction localization near periodic orbits of the one-step Poincaré map.

Elasticity solutions for a class of composite laminate problems with stress singularities

NASA Technical Reports Server (NTRS)

Wang, S. S.

1983-01-01

A study on the fundamental mechanics of fiber-reinforced composite laminates with stress singularities is presented. Based on the theory of anisotropic elasticity and Lekhnitskii's complex-variable stress potentials, a system of coupled governing partial differential equations are established. An eigenfunction expansion method is introduced to determine the orders of stress singularities in composite laminates with various geometric configurations and material systems. Complete elasticity solutions are obtained for this class of singular composite laminate mechanics problems. Homogeneous solutions in eigenfunction series and particular solutions in polynomials are presented for several cases of interest. Three examples are given to illustrate the method of approach and the basic nature of the singular laminate elasticity solutions. The first problem is the well-known laminate free-edge stress problem, which has a rather weak stress singularity. The second problem is the important composite delamination problem, which has a strong crack-tip stress singularity. The third problem is the commonly encountered bonded composite joints, which has a complex solution structure with moderate orders of stress singularities.

Quantum field theory in spaces with closed time-like curves

NASA Astrophysics Data System (ADS)

Boulware, D. G.

Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27(pi). A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.

Quadratic Zeeman effect in hydrogen Rydberg states: Rigorous error estimates for energy eigenvalues, energy eigenfunctions, and oscillator strengths

DOE Office of Scientific and Technical Information (OSTI.GOV)

Falsaperla, P.; Fonte, G.

1994-10-01

A variational method, based on some results due to T. Kato [Proc. Phys. Soc. Jpn. 4, 334 (1949)], and previously discussed is here applied to the hydrogen atom in uniform magnetic fields of tesla in order to calculate, with a rigorous error estimate, energy eigenvalues, energy eigenfunctions, and oscillator strengths relative to Rydberg states up to just below the field-free ionization threshold. Making use of a basis (parabolic Sturmian basis) with a size varying from 990 up to 5050, we obtain, over the energy range of [minus]190 to [minus]24 cm[sup [minus]1], all of the eigenvalues and a good part ofmore » the oscillator strengths with a remarkable accuracy. This, however, decreases with increasing excitation energy and, thus, above [similar to][minus]24 cm[sup [minus]1], we obtain results of good accuracy only for eigenvalues ranging up to [similar to][minus]12 cm[sup [minus]1].« less

Matrix eigenvalue method for free-oscillations modelling of spherical elastic bodies

NASA Astrophysics Data System (ADS)

Zábranová, E.; Hanyk, L.; Matyska, C.

2017-11-01

Deformations and changes of the gravitational potential of pre-stressed self-gravitating elastic bodies caused by free oscillations are described by means of the momentum and Poisson equations and the constitutive relation. For spherically symmetric bodies, the equations and boundary conditions are transformed into ordinary differential equations of the second order by the spherical harmonic decomposition and further discretized by highly accurate pseudospectral difference schemes on Chebyshev grids; we pay special attention to the conditions at the centre of the models. We thus obtain a series of matrix eigenvalue problems for eigenfrequencies and eigenfunctions of the free oscillations. Accuracy of the presented numerical approach is tested by means of the Rayleigh quotients calculated for the eigenfrequencies up to 500 mHz. Both the modal frequencies and eigenfunctions are benchmarked against the output from the Mineos software package based on shooting methods. The presented technique is a promising alternative to widely used methods because it is stable and with a good capability up to high frequencies.

Sum rules and other properties involving resonance projection operators. [for optical potential description of electron scattering from atoms and ions

NASA Technical Reports Server (NTRS)

Berk, A.; Temkin, A.

1985-01-01

A sum rule is derived for the auxiliary eigenvalues of an equation whose eigenspectrum pertains to projection operators which describe electron scattering from multielectron atoms and ions. The sum rule's right-hand side depends on an integral involving the target system eigenfunctions. The sum rule is checked for several approximations of the two-electron target. It is shown that target functions which have a unit eigenvalue in their auxiliary eigenspectrum do not give rise to well-defined projection operators except through a limiting process. For Hylleraas target approximations, the auxiliary equations are shown to contain an infinite spectrum. However, using a Rayleigh-Ritz variational principle, it is shown that a comparatively simple aproximation can exhaust the sum rule to better than five significant figures. The auxiliary Hylleraas equation is greatly simplified by conversion to a square root equation containing the same eigenfunction spectrum and from which the required eigenvalues are trivially recovered by squaring.

Analytical Solutions of the Schrödinger Equation for the Manning-Rosen plus Hulthén Potential Within SUSY Quantum Mechanics

NASA Astrophysics Data System (ADS)

Ahmadov, A. I.; Naeem, Maria; Qocayeva, M. V.; Tarverdiyeva, V. A.

2018-02-01

In this paper, the bound state solution of the modified radial Schrödinger equation is obtained for the Manning-Rosen plus Hulthén potential by implementing the novel improved scheme to surmount the centrifugal term. The energy eigenvalues and corresponding radial wave functions are defined for any l ≠ 0 angular momentum case via the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSYQM) methods. By using these two different methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary l states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.

Bi-orthogonality relations for fluid-filled elastic cylindrical shells: Theory, generalisations and application to construct tailored Green's matrices

NASA Astrophysics Data System (ADS)

Ledet, Lasse S.; Sorokin, Sergey V.

2018-03-01

The paper addresses the classical problem of time-harmonic forced vibrations of a fluid-filled cylindrical shell considered as a multi-modal waveguide carrying infinitely many waves. The forced vibration problem is solved using tailored Green's matrices formulated in terms of eigenfunction expansions. The formulation of Green's matrix is based on special (bi-)orthogonality relations between the eigenfunctions, which are derived here for the fluid-filled shell. Further, the relations are generalised to any multi-modal symmetric waveguide. Using the orthogonality relations the transcendental equation system is converted into algebraic modal equations that can be solved analytically. Upon formulation of Green's matrices the solution space is studied in terms of completeness and convergence (uniformity and rate). Special features and findings exposed only through this modal decomposition method are elaborated and the physical interpretation of the bi-orthogonality relation is discussed in relation to the total energy flow which leads to derivation of simplified equations for the energy flow components.

Multiple eigenmodes of the Rayleigh-Taylor instability observed for a fluid interface with smoothly varying density

NASA Astrophysics Data System (ADS)

Yu, C. X.; Xue, C.; Liu, J.; Hu, X. Y.; Liu, Y. Y.; Ye, W. H.; Wang, L. F.; Wu, J. F.; Fan, Z. F.

2018-01-01

In this article, multiple eigen-systems including linear growth rates and eigen-functions have been discovered for the Rayleigh-Taylor instability (RTI) by numerically solving the Sturm-Liouville eigen-value problem in the case of two-dimensional plane geometry. The system called the first mode has the maximal linear growth rate and is just extensively studied in literature. Higher modes have smaller eigen-values, but possess multi-peak eigen-functions which bring on multiple pairs of vortices in the vorticity field. A general fitting expression for the first four eigen-modes is presented. Direct numerical simulations show that high modes lead to appearances of multi-layered spike-bubble pairs, and lots of secondary spikes and bubbles are also generated due to the interactions between internal spikes and bubbles. The present work has potential applications in many research and engineering areas, e.g., in reducing the RTI growth during capsule implosions in inertial confinement fusion.

Numerical investigation of non-perturbative kinetic effects of energetic particles on toroidicity-induced Alfvén eigenmodes in tokamaks and stellarators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slaby, Christoph; Könies, Axel; Kleiber, Ralf

2016-09-15

The resonant interaction of shear Alfvén waves with energetic particles is investigated numerically in tokamak and stellarator geometry using a non-perturbative MHD-kinetic hybrid approach. The focus lies on toroidicity-induced Alfvén eigenmodes (TAEs), which are most easily destabilized by a fast-particle population in fusion plasmas. While the background plasma is treated within the framework of an ideal-MHD theory, the drive of the fast particles, as well as Landau damping of the background plasma, is modelled using the drift-kinetic Vlasov equation without collisions. Building on analytical theory, a fast numerical tool, STAE-K, has been developed to solve the resulting eigenvalue problem usingmore » a Riccati shooting method. The code, which can be used for parameter scans, is applied to tokamaks and the stellarator Wendelstein 7-X. High energetic-ion pressure leads to large growth rates of the TAEs and to their conversion into kinetically modified TAEs and kinetic Alfvén waves via continuum interaction. To better understand the physics of this conversion mechanism, the connections between TAEs and the shear Alfvén wave continuum are examined. It is shown that, when energetic particles are present, the continuum deforms substantially and the TAE frequency can leave the continuum gap. The interaction of the TAE with the continuum leads to singularities in the eigenfunctions. To further advance the physical model and also to eliminate the MHD continuum together with the singularities in the eigenfunctions, a fourth-order term connected to radiative damping has been included. The radiative damping term is connected to non-ideal effects of the bulk plasma and introduces higher-order derivatives to the model. Thus, it has the potential to substantially change the nature of the solution. For the first time, the fast-particle drive, Landau damping, continuum damping, and radiative damping have been modelled together in tokamak- as well as in stellarator geometry.« less

Pauli energy spectrum for twist-deformed spacetime

NASA Astrophysics Data System (ADS)

Daszkiewicz, Marcin

2018-04-01

In this paper, we define the Pauli Hamiltonian function for the twist-deformed N-enlarged Newton-Hooke spacetime provided by M. Daszkiewicz [Mod. Phys. Lett. A 27, 1250083 (2012)]. Further, we derive its energy spectrum, i.e. we find the corresponding eigenvalues as well as the proper eigenfunctions.

On the Time-Dependent Analysis of Gamow Decay

ERIC Educational Resources Information Center

Durr, Detlef; Grummt, Robert; Kolb, Martin

2011-01-01

Gamow's explanation of the exponential decay law uses complex "eigenvalues" and exponentially growing "eigenfunctions". This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based on real eigenvalues and square integrable wavefunctions. Observing that the time evolution of any…

Pseudospectra in non-Hermitian quantum mechanics

NASA Astrophysics Data System (ADS)

Krejčiřík, D.; Siegl, P.; Tater, M.; Viola, J.

2015-10-01

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

Mesoscopic Rings with Spin-Orbit Interactions

ERIC Educational Resources Information Center

Berche, Bertrand; Chatelain, Christophe; Medina, Ernesto

2010-01-01

A didactic description of charge and spin equilibrium currents on mesoscopic rings in the presence of spin-orbit interaction is presented. Emphasis is made on the non-trivial construction of the correct Hamiltonian in polar coordinates, the calculation of eigenvalues and eigenfunctions and the symmetries of the ground-state properties. Spin…

Completeness of the Coulomb Wave Functions in Quantum Mechanics

ERIC Educational Resources Information Center

Mukunda, N.

1978-01-01

Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)

Population of collective modes in light scattering by many atoms

NASA Astrophysics Data System (ADS)

Guerin, William; Kaiser, Robin

2017-05-01

The interaction of light with an atomic sample containing a large number of particles gives rise to many collective (or cooperative) effects, such as multiple scattering, superradiance, and subradiance, even if the atomic density is low and the incident optical intensity weak (linear optics regime). Tracing over the degrees of freedom of the light field, the system can be well described by an effective atomic Hamiltonian, which contains the light-mediated dipole-dipole interaction between atoms. This long-range interaction is at the origin of the various collective effects, or of collective excitation modes of the system. Even though an analysis of the eigenvalues and eigenfunctions of these collective modes does allow distinguishing superradiant modes, for instance, from other collective modes, this is not sufficient to understand the dynamics of a driven system, as not all collective modes are significantly populated. Here, we study how the excitation parameters, i.e., the driving field, determines the population of the collective modes. We investigate in particular the role of the laser detuning from the atomic transition, and demonstrate a simple relation between the detuning and the steady-state population of the modes. This relation allows understanding several properties of cooperative scattering, such as why superradiance and subradiance become independent of the detuning at large enough detuning without vanishing, and why superradiance, but not subradiance, is suppressed near resonance. We also show that the spatial properties of the collective modes allow distinguishing diffusive modes, responsible for radiation trapping, from subradiant modes.

The Effect of Global-Scale, Steady-State Convection and Elastic-Gravitational Asphericities on Helioseismic Oscillations

NASA Astrophysics Data System (ADS)

Lavely, Eugene M.; Ritzwoller, Michael H.

1992-06-01

In this paper we derive a theory, based on quasi-degenerate perturbation theory, that governs the effect of global-scale, steady-state convection and associated static asphericities in the elastic-gravitational variables (adiabatic bulk modulus kappa , density ρ , and gravitational potential φ ) on helioseismic eigenfrequencies and eigenfunctions and present a formalism with which this theory can be applied computationally. The theory rests on three formal assumptions: (1) that convection is temporally steady in a frame corotating with the Sun, (2) that accurate eigenfrequencies and eigenfunctions can be determined by retaining terms in the seismically perturbed equations of motion only to first order in p-mode displacement, and (3) that we are justified in retaining terms only to first order in convective velocity (this is tantamount to assuming that the convective flow is anelastic). The most physically unrealistic assumption is (1), and we view the results of this paper as the first step toward a more general theory governing the seismic effects of time-varying fields. Although the theory does not govern the seismic effects of non-stationary flows, it can be used to approximate the effects of unsteady flows on the acoustic wavefield if the flow is varying smoothly in time. The theory does not attempt to model seismic modal amplitudes since these are governed, in part, by the exchange of energy between convection and acoustic motions which is not a part of this theory. However, we show how theoretical wavefields can be computed given a description of the stress field produced by a source process such as turbulent convection. The basic reference model that will be perturbed by rotation, convection, structural asphericities, and acoustic oscillations is a spherically symmetric, non-rotating, non-magnetic, isotropic, static solar model that, when subject to acoustic oscillations, oscillates adiabatically. We call this the SNRNMAIS model. An acoustic mode of the SNRNMAIS model is denoted by k = (n,l,m), where n is the radial order, l is the harmonic degree, and m is the azimuthal order of the mode. The main result of the paper is the general matrix element Hn'n,l'lm'm for steady-state convection satisfying the anelastic condition with static structural asphericities. It is written in terms of the radial, scalar eigenfunctions of the SNRNMAIS model, resulting in equations (90)-(110). We prove Rayleigh's principle in our derivation of quasi-degenerate perturbation theory which, as a by-product, yields the general matrix element. Within this perturbative method, modes need not be exactly degenerate in the SNRNMAIS solar model to couple, only nearly so. General matrix elements compose the hermitian supermatrix Z. The eigenvalues of the supermatrix are the eigenfrequency perturbations of the convecting, aspherical model and the eigenvector components of Z are the expansion coefficients in the linear combination forming the eigenfunctions in which the eigenfunctions of the SNRNMAIS solar model act as basis functions. The properties of the Wigner 3j symbols and the reduced matrix elements composing Hn'n,l'lm' produce selection rules governing the coupling of SNRNMAIS modes that hold even for time-varying flows. We state selection rules for both quasi-degenerate and degenerate perturbation theories. For example, within degenerate perturbation theory, only odd-degree s toroidal flows and even degree structural asphericities, both with s <= 2l, will couple and/or split acoustic modes with harmonic degree l. In addition, the frequency perturbations caused by a toroidal flow display odd symmetry with respect to the degenerate frequency when ordered from the minimum to the maximum frequency perturbation. We consider the special case of differential rotation, the odd-degree, axisymmetric, toroidal component of general convection, and present the general matrix element and selection rules under quasi-degenerate perturbation theory. We argue that due to the spacing of modes that satisfy the selection rules, quasi-degenerate coupling can, for all practical purposes, be neglected in modelling the effect of low-degree differential rotation on helioseismic data. In effect, modes that can couple through low-degree differential rotation are too far separated in frequency to couple strongly. This is not the case for non-axisymmetric flows and asphericities where near degeneracies will regularly occur, and couplings can be relatively strong especially among SNRNMAIS modes within the same multiplet. All derivations are performed and all solutions are presented in a frame corotating with the mean solar angular rotation rate. Equation (18) shows how to transform the eigenfrequencies and eigenfunctions in the corotating frame into an inertial frame. The transformation has the effect that each eigenfunction in the inertial frame is itself time varying. That is, a mode of oscillation, which is defined to have a single frequency in the corotating frame, becomes multiply periodic in the inertial frame.

Evaluation of linearly solvable Markov decision process with dynamic model learning in a mobile robot navigation task.

PubMed

Kinjo, Ken; Uchibe, Eiji; Doya, Kenji

2013-01-01

Linearly solvable Markov Decision Process (LMDP) is a class of optimal control problem in which the Bellman's equation can be converted into a linear equation by an exponential transformation of the state value function (Todorov, 2009b). In an LMDP, the optimal value function and the corresponding control policy are obtained by solving an eigenvalue problem in a discrete state space or an eigenfunction problem in a continuous state using the knowledge of the system dynamics and the action, state, and terminal cost functions. In this study, we evaluate the effectiveness of the LMDP framework in real robot control, in which the dynamics of the body and the environment have to be learned from experience. We first perform a simulation study of a pole swing-up task to evaluate the effect of the accuracy of the learned dynamics model on the derived the action policy. The result shows that a crude linear approximation of the non-linear dynamics can still allow solution of the task, despite with a higher total cost. We then perform real robot experiments of a battery-catching task using our Spring Dog mobile robot platform. The state is given by the position and the size of a battery in its camera view and two neck joint angles. The action is the velocities of two wheels, while the neck joints were controlled by a visual servo controller. We test linear and bilinear dynamic models in tasks with quadratic and Guassian state cost functions. In the quadratic cost task, the LMDP controller derived from a learned linear dynamics model performed equivalently with the optimal linear quadratic regulator (LQR). In the non-quadratic task, the LMDP controller with a linear dynamics model showed the best performance. The results demonstrate the usefulness of the LMDP framework in real robot control even when simple linear models are used for dynamics learning.

An Introduction to Multilinear Formula Score Theory. Measurement Series 84-4.

ERIC Educational Resources Information Center

Levine, Michael V.

Formula score theory (FST) associates each multiple choice test with a linear operator and expresses all of the real functions of item response theory as linear combinations of the operator's eigenfunctions. Hard measurement problems can then often be reformulated as easier, standard mathematical problems. For example, the problem of estimating…

An Isoperimetric Inequality for Fundamental Tones of Free Plates

ERIC Educational Resources Information Center

Chasman, Laura

2009-01-01

We establish an isoperimetric inequality for the fundamental tone (first nonzero eigenvalue) of the free plate of a given area, proving the ball is maximal. Given tau greater than 0, the free plate eigenvalues omega and eigenfunctions upsilon are determined by the equation Delta Delta upsilon - tau Delta upsilon = omega upsilon together with…

Alternative Form of the Hydrogenic Wave Functions for an Extended, Uniformly Charged Nucleus.

ERIC Educational Resources Information Center

Ley-Koo, E.; And Others

1980-01-01

Presented are forms of harmonic oscillator attraction and Coulomb wave functions which can be explicitly constructed and which lead to numerical results for the energy eigenvalues and eigenfunctions of the atomic system. The Schrodinger equation and its solution and specific cases of muonic atoms illustrating numerical calculations are included.…

Teaching Qualitative Energy-Eigenfunction Shape with Physlets

ERIC Educational Resources Information Center

Belloni, Mario; Christian, Wolfgang; Cox, Anne J.

2007-01-01

More than 35 years ago, French and Taylor outlined an approach to teach students and teachers alike how to understand "qualitative plots of bound-state wave functions." They described five fundamental statements based on the quantum-mechanical concepts of probability and energy (total and potential), which could be used to deduce the shape of…

A High Frequency Model of Cascade Noise

NASA Technical Reports Server (NTRS)

Envia, Edmane

1998-01-01

Closed form asymptotic expressions for computing high frequency noise generated by an annular cascade in an infinite duct containing a uniform flow are presented. There are two new elements in this work. First, the annular duct mode representation does not rely on the often-used Bessel function expansion resulting in simpler expressions for both the radial eigenvalues and eigenfunctions of the duct. In particular, the new representation provides an explicit approximate formula for the radial eigenvalues obviating the need for solutions of the transcendental annular duct eigenvalue equation. Also, the radial eigenfunctions are represented in terms of exponentials eliminating the numerical problems associated with generating the Bessel functions on a computer. The second new element is the construction of an unsteady response model for an annular cascade. The new construction satisfies the boundary conditions on both the cascade and duct walls simultaneously adding a new level of realism to the noise calculations. Preliminary results which demonstrate the effectiveness of the new elements are presented. A discussion of the utility of the asymptotic formulas for calculating cascade discrete tone as well as broadband noise is also included.

Markov modeling of peptide folding in the presence of protein crowders

NASA Astrophysics Data System (ADS)

Nilsson, Daniel; Mohanty, Sandipan; Irbäck, Anders

2018-02-01

We use Markov state models (MSMs) to analyze the dynamics of a β-hairpin-forming peptide in Monte Carlo (MC) simulations with interacting protein crowders, for two different types of crowder proteins [bovine pancreatic trypsin inhibitor (BPTI) and GB1]. In these systems, at the temperature used, the peptide can be folded or unfolded and bound or unbound to crowder molecules. Four or five major free-energy minima can be identified. To estimate the dominant MC relaxation times of the peptide, we build MSMs using a range of different time resolutions or lag times. We show that stable relaxation-time estimates can be obtained from the MSM eigenfunctions through fits to autocorrelation data. The eigenfunctions remain sufficiently accurate to permit stable relaxation-time estimation down to small lag times, at which point simple estimates based on the corresponding eigenvalues have large systematic uncertainties. The presence of the crowders has a stabilizing effect on the peptide, especially with BPTI crowders, which can be attributed to a reduced unfolding rate ku, while the folding rate kf is left largely unchanged.

Quantum integrable systems from conformal blocks

NASA Astrophysics Data System (ADS)

Chen, Heng-Yu; Qualls, Joshua D.

2017-05-01

In this note, we extend the striking connections between quantum integrable systems and conformal blocks recently found in [M. Isachenkov and V. Schomerus, Phys. Rev. Lett. 117, 071602 (2016), 10.1103/PhysRevLett.117.071602] in several directions. First, we explicitly demonstrate that the action of the quartic conformal Casimir operator on general d-dimensional scalar conformal blocks can be expressed in terms of certain combinations of commuting integrals of motions of the two particle hyperbolic BC2 Calogero-Sutherland system. The permutation and reflection properties of the underlying Dunkl operators play crucial roles in establishing such a connection. Next, we show that the scalar superconformal blocks in superconformal field theories (SCFTs) with four and eight supercharges and suitable chirality constraints can also be identified with the eigenfunctions of the same Calogero-Sutherland system; this demonstrates the universality of such a connection. Finally, we observe that the so-called "seed" conformal blocks for constructing four point functions for operators with arbitrary space-time spins in four-dimensional CFTs can also be linearly expanded in terms of Calogero-Sutherland eigenfunctions.

Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

NASA Astrophysics Data System (ADS)

Guarnieri, F.; Moon, W.; Wettlaufer, J. S.

2017-09-01

Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with a negative constant drift, described by a Fokker-Planck equation with a potential V (x ) =-[b ln(x ) +a x ] , for b >0 and a <0 . The problem belongs to a family of Fokker-Planck equations with logarithmic potentials closely related to the Bessel process that has been extensively studied for its applications in physics, biology, and finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schrödinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a constant negative drift. We conclude with a comparison to other analytical methods and with numerical solutions.

A photometric mode identification method, including an improved non-adiabatic treatment of the atmosphere

NASA Astrophysics Data System (ADS)

Dupret, M.-A.; De Ridder, J.; De Cat, P.; Aerts, C.; Scuflaire, R.; Noels, A.; Thoul, A.

2003-02-01

We present an improved version of the method of photometric mode identification of Heynderickx et al. (\\cite{hey}). Our new version is based on the inclusion of precise non-adiabatic eigenfunctions determined in the outer stellar atmosphere according to the formalism recently proposed by Dupret et al. (\\cite{dup}). Our improved photometric mode identification technique is therefore no longer dependent on ad hoc parameters for the non-adiabatic effects. It contains the complete physical conditions of the outer atmosphere of the star, provided that rotation does not play a key role. We apply our method to the two slowly pulsating B stars HD 74560 and HD 138764 and to the beta Cephei star EN (16) Lac. Besides identifying the degree l of the pulsating stars, our method is also a tool for improving the knowledge of stellar interiors and atmospheres, by imposing constraints on parameters such as the metallicity and the mixing-length parameter alpha (a procedure we label non-adiabatic asteroseismology). The non-adiabatic eigenfunctions needed for the mode identification are available upon request from the authors.

Extraction and prediction of indices for monsoon intraseasonal oscillations: an approach based on nonlinear Laplacian spectral analysis

NASA Astrophysics Data System (ADS)

Sabeerali, C. T.; Ajayamohan, R. S.; Giannakis, Dimitrios; Majda, Andrew J.

2017-11-01

An improved index for real-time monitoring and forecast verification of monsoon intraseasonal oscillations (MISOs) is introduced using the recently developed nonlinear Laplacian spectral analysis (NLSA) technique. Using NLSA, a hierarchy of Laplace-Beltrami (LB) eigenfunctions are extracted from unfiltered daily rainfall data from the Global Precipitation Climatology Project over the south Asian monsoon region. Two modes representing the full life cycle of the northeastward-propagating boreal summer MISO are identified from the hierarchy of LB eigenfunctions. These modes have a number of advantages over MISO modes extracted via extended empirical orthogonal function analysis including higher memory and predictability, stronger amplitude and higher fractional explained variance over the western Pacific, Western Ghats, and adjoining Arabian Sea regions, and more realistic representation of the regional heat sources over the Indian and Pacific Oceans. Real-time prediction of NLSA-derived MISO indices is demonstrated via extended-range hindcasts based on NCEP Coupled Forecast System version 2 operational output. It is shown that in these hindcasts the NLSA MISO indices remain predictable out to ˜3 weeks.

Instability of rectangular jets

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Thies, Andrew T.

1993-01-01

The instability of rectangular jets is investigated using a vortex-sheet model. It is shown that such jets support four linearly independent families of instability waves. Within each family there are infinitely many modes. A way to classify these modes according to the characteristics of their mode shapes or eigenfunctions is proposed. It is demonstrated that the boundary element method can be used to calculate the dispersion relations and eigenfunctions of these instability wave modes. The method is robust and efficient. A parametric study of the instability wave characteristics has been carried out. A sample of the numerical results is reported here. It is found that the first and third modes of each instability wave family are corner modes. The pressure fluctuations associated with these instability waves are localized near the corners of the jet. The second mode, however, is a center mode with maximum fluctuations concentrated in the central portion of the jet flow. The center mode has the largest spatial growth rate. It is anticipated that as the instability waves propagate downstream the center mode would emerge as the dominant instability of the jet.

Quantum finance Hamiltonian for coupon bond European and barrier options.

PubMed

Baaquie, Belal E

2008-03-01

Coupon bond European and barrier options are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward interest rates are modeled as a two-dimensional quantum field theory and its Hamiltonian and state space is defined. European and barrier options are realized as transition amplitudes of the time integrated Hamiltonian operator. The double barrier option for a financial instrument is "knocked out" (terminated with zero value) if the price of the underlying instrument exceeds or falls below preset limits; the barrier option is realized by imposing boundary conditions on the eigenfunctions of the forward interest rates' Hamiltonian. The price of the European coupon bond option and the zero coupon bond barrier option are calculated. It is shown that, is general, the constraint function for a coupon bond barrier option can -- to a good approximation -- be linearized. A calculation using an overcomplete set of eigenfunctions yields an approximate price for the coupon bond barrier option, which is given in the form of an integral of a factor that results from the barrier condition times another factor that arises from the payoff function.

Numerical operator calculus in higher dimensions.

PubMed

Beylkin, Gregory; Mohlenkamp, Martin J

2002-08-06

When an algorithm in dimension one is extended to dimension d, in nearly every case its computational cost is taken to the power d. This fundamental difficulty is the single greatest impediment to solving many important problems and has been dubbed the curse of dimensionality. For numerical analysis in dimension d, we propose to use a representation for vectors and matrices that generalizes separation of variables while allowing controlled accuracy. Basic linear algebra operations can be performed in this representation using one-dimensional operations, thus bypassing the exponential scaling with respect to the dimension. Although not all operators and algorithms may be compatible with this representation, we believe that many of the most important ones are. We prove that the multiparticle Schrödinger operator, as well as the inverse Laplacian, can be represented very efficiently in this form. We give numerical evidence to support the conjecture that eigenfunctions inherit this property by computing the ground-state eigenfunction for a simplified Schrödinger operator with 30 particles. We conjecture and provide numerical evidence that functions of operators inherit this property, in which case numerical operator calculus in higher dimensions becomes feasible.

Supersymmetric quantum mechanics of the flux tube

NASA Astrophysics Data System (ADS)

Belitsky, A. V.

2016-12-01

The Operator Product Expansion approach to scattering amplitudes in maximally supersymmetric gauge theory operates in terms of pentagon transitions for excitations propagating on a color flux tube. These obey a set of axioms which allow one to determine them to all orders in 't Hooft coupling and confront against explicit calculations. One of the simplifying features of the formalism is the factorizability of multiparticle transitions in terms of single-particle ones. In this paper we extend an earlier consideration of a sector populated by one kind of excitations to the case of a system with fermionic as well as bosonic degrees of freedom to address the origin of the factorization. While the purely bosonic case was analyzed within an integrable noncompact open-spin chain model, the current case is solved in the framework of a supersymmetric sl (2 | 1) magnet. We find the eigenfunctions for the multiparticle system making use of the R-matrix approach. Constructing resulting pentagon transitions, we prove their factorized form. The discussion corresponds to leading order of perturbation theory.

Extracting spatial information from networks with low-order eigenvectors

NASA Astrophysics Data System (ADS)

Cucuringu, Mihai; Blondel, Vincent D.; Van Dooren, Paul

2013-03-01

We consider the problem of inferring meaningful spatial information in networks from incomplete information on the connection intensity between the nodes of the network. We consider two spatially distributed networks: a population migration flow network within the US, and a network of mobile phone calls between cities in Belgium. For both networks we use the eigenvectors of the Laplacian matrix constructed from the link intensities to obtain informative visualizations and capture natural geographical subdivisions. We observe that some low-order eigenvectors localize very well and seem to reveal small geographically cohesive regions that match remarkably well with political and administrative boundaries. We discuss possible explanations for this observation by describing diffusion maps and localized eigenfunctions. In addition, we discuss a possible connection with the weighted graph cut problem, and provide numerical evidence supporting the idea that lower-order eigenvectors point out local cuts in the network. However, we do not provide a formal and rigorous justification for our observations.

[Some comments on ecological field].

PubMed

Wang, D

2000-06-01

Based on the data of plant ecological field studies, this paper reviewed the conception of ecological field, field eigenfunctions, graphs of ecological field and its application of ecological field theory in explaining plant interactions. It is suggested that the basic character of ecological field is material, and based on the current research level, it is not sure whether ecological field is a kind of specific field different from general physical field. The author gave some comments on the formula and estimation of parameters of basic field function-ecological potential model on ecological field. Both models have their own characteristics and advantages in specific conditions. The author emphasized that ecological field had even more meaning of ecological methodology, and applying ecological field theory in describing the types and processes of plant interactions had three characteristics: quantitative, synthetic and intuitionistic. Field graphing might provide a new way to ecological studies, especially applying the ecological field theory might give an appropriate quantitative explanation for the dynamic process of plant populations (coexistence and interference competition).

The exact solution of the monoenergetic transport equation for critical cylinders

NASA Technical Reports Server (NTRS)

Westfall, R. M.; Metcalf, D. R.

1972-01-01

An analytic solution for the critical, monoenergetic, bare, infinite cylinder is presented. The solution is obtained by modifying a previous development based on a neutron density transform and Case's singular eigenfunction method. Numerical results for critical radii and the neutron density as a function of position are included and compared with the results of other methods.

On Superstability of Semigroups

NASA Technical Reports Server (NTRS)

Balakrishnan. A. V.

1997-01-01

This paper presents a brief report on superstable semigroups - abstract theory and some applications thereof. The notion of super stability is a strengthening of exponential stability and occurs in Timoshenko models of structures with self-straining material using pure (idealized) rate feed- back. It is also relevant to the problem of Riesz bases of eigenfunctions of infinitesimal generators under perturbation.

A Complete Set for the Maass Laplacians on the Pseudosphere

NASA Astrophysics Data System (ADS)

Oshima, K.

1989-02-01

We obtain a completeness relation from eigenfunctions of the Maass laplacians in terms of the pseudospherical polar coordinates. We derive addition theorems of ``generalized'' associated Legendre functions. With the help of the addition theorems, we get a simple path integral picture for a charged particle on the Poincaré upper half plane with a constant magnetic field.

Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Brody, Dorje C.

2018-04-01

The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads to a challenging open problem concerning the formulation of the eigenvalue problem in the momentum space. The WKB analysis gives the exact asymptotic behavior of the eigenfunction.

Simple One-Dimensional Quantum-Mechanical Model for a Particle Attached to a Surface

ERIC Educational Resources Information Center

Fernandez, Francisco M.

2010-01-01

We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schrodinger equation for a harmonic oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships…

On Closed Shells in Nuclei. II

DOE R&D Accomplishments Database

Mayer, M. G.

1949-04-01

Discussion on the use of spins and magnetic moments of the even-odd nuclei by Feenberg and Nordheim to determine the angular momentum of the eigenfunction of the odd particle; discussion of prevalence of isomerism in certain regions of the isotope chart; tabulated data on levels of square well potential, spectroscopic levels, spin term, number of states, shells and known spins and orbital assignments.

The Application of a Boundary Integral Equation Method to the Prediction of Ducted Fan Engine Noise

NASA Technical Reports Server (NTRS)

Dunn, M. H.; Tweed, J.; Farassat, F.

1999-01-01

The prediction of ducted fan engine noise using a boundary integral equation method (BIEM) is considered. Governing equations for the BIEM are based on linearized acoustics and describe the scattering of incident sound by a thin, finite-length cylindrical duct in the presence of a uniform axial inflow. A classical boundary value problem (BVP) is derived that includes an axisymmetric, locally reacting liner on the duct interior. Using potential theory, the BVP is recast as a system of hypersingular boundary integral equations with subsidiary conditions. We describe the integral equation derivation and solution procedure in detail. The development of the computationally efficient ducted fan noise prediction program TBIEM3D, which implements the BIEM, and its utility in conducting parametric noise reduction studies are discussed. Unlike prediction methods based on spinning mode eigenfunction expansions, the BIEM does not require the decomposition of the interior acoustic field into its radial and axial components which, for the liner case, avoids the solution of a difficult complex eigenvalue problem. Numerical spectral studies are presented to illustrate the nexus between the eigenfunction expansion representation and BIEM results. We demonstrate BIEM liner capability by examining radiation patterns for several cases of practical interest.

THEORETICAL p-MODE OSCILLATION FREQUENCIES FOR THE RAPIDLY ROTATING {delta} SCUTI STAR {alpha} OPHIUCHI

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deupree, Robert G., E-mail: bdeupree@ap.smu.ca

2011-11-20

A rotating, two-dimensional stellar model is evolved to match the approximate conditions of {alpha} Oph. Both axisymmetric and nonaxisymmetric oscillation frequencies are computed for two-dimensional rotating models which approximate the properties of {alpha} Oph. These computed frequencies are compared to the observed frequencies. Oscillation calculations are made assuming the eigenfunction can be fitted with six Legendre polynomials, but comparison calculations with eight Legendre polynomials show the frequencies agree to within about 0.26% on average. The surface horizontal shape of the eigenfunctions for the two sets of assumed number of Legendre polynomials agrees less well, but all calculations show significant departuresmore » from that of a single Legendre polynomial. It is still possible to determine the large separation, although the small separation is more complicated to estimate. With the addition of the nonaxisymmetric modes with |m| {<=} 4, the frequency space becomes sufficiently dense that it is difficult to comment on the adequacy of the fit of the computed to the observed frequencies. While the nonaxisymmetric frequency mode splitting is no longer uniform, the frequency difference between the frequencies for positive and negative values of the same m remains 2m times the rotation rate.« less

Quantum solvability of a general ordered position dependent mass system: Mathews-Lakshmanan oscillator

NASA Astrophysics Data System (ADS)

Karthiga, S.; Chithiika Ruby, V.; Senthilvelan, M.; Lakshmanan, M.

2017-10-01

In position dependent mass (PDM) problems, the quantum dynamics of the associated systems have been understood well in the literature for particular orderings. However, no efforts seem to have been made to solve such PDM problems for general orderings to obtain a global picture. In this connection, we here consider the general ordered quantum Hamiltonian of an interesting position dependent mass problem, namely, the Mathews-Lakshmanan oscillator, and try to solve the quantum problem for all possible orderings including Hermitian and non-Hermitian ones. The other interesting point in our study is that for all possible orderings, although the Schrödinger equation of this Mathews-Lakshmanan oscillator is uniquely reduced to the associated Legendre differential equation, their eigenfunctions cannot be represented in terms of the associated Legendre polynomials with integral degree and order. Rather the eigenfunctions are represented in terms of associated Legendre polynomials with non-integral degree and order. We here explore such polynomials and represent the discrete and continuum states of the system. We also exploit the connection between associated Legendre polynomials with non-integral degree with other orthogonal polynomials such as Jacobi and Gegenbauer polynomials.

The Three-Component Defocusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions

NASA Astrophysics Data System (ADS)

Biondini, Gino; Kraus, Daniel K.; Prinari, Barbara

2016-12-01

We present a rigorous theory of the inverse scattering transform (IST) for the three-component defocusing nonlinear Schrödinger (NLS) equation with initial conditions approaching constant values with the same amplitude as {xto±∞}. The theory combines and extends to a problem with non-zero boundary conditions three fundamental ideas: (i) the tensor approach used by Beals, Deift and Tomei for the n-th order scattering problem, (ii) the triangular decompositions of the scattering matrix used by Novikov, Manakov, Pitaevski and Zakharov for the N-wave interaction equations, and (iii) a generalization of the cross product via the Hodge star duality, which, to the best of our knowledge, is used in the context of the IST for the first time in this work. The combination of the first two ideas allows us to rigorously obtain a fundamental set of analytic eigenfunctions. The third idea allows us to establish the symmetries of the eigenfunctions and scattering data. The results are used to characterize the discrete spectrum and to obtain exact soliton solutions, which describe generalizations of the so-called dark-bright solitons of the two-component NLS equation.

Estimating amplitude ratios in boundary layer stability theory: a comparison between two approaches

NASA Astrophysics Data System (ADS)

Govindarajan, Rama; Narasimha, R.

2001-07-01

We first demonstrate that, if the contributions of higher-order mean flow are ignored, the parabolized stability equations (Bertolotti et al. 1992) and the ‘full’ non-parallel equation of Govindarajan & Narasimha (1995, hereafter GN95) are both equivalent to order R[minus sign]1 in the local Reynolds number R to Gaster's (1974) equation for the stability of spatially developing boundary layers. It is therefore of some concern that a detailed comparison between Gaster (1974) and GN95 reveals a small difference in the computed amplitude ratios. Although this difference is not significant in practical terms in Blasius flow, it is traced here to the approximation, in Gaster's method, of neglecting the change in eigenfunction shape due to flow non-parallelism. This approximation is not justified in the critical and the wall layers, where the neglected term is respectively O(R[minus sign]2/3) and O(R[minus sign]1) compared to the largest term. The excellent agreement of GN95 with exact numerical simulations, on the other hand, suggests that the effect of change in eigenfunction is accurately taken into account in that paper.

Mathematical modeling of two phase stratified flow in a microchannel with curved interface

NASA Astrophysics Data System (ADS)

Dandekar, Rajat; Picardo, Jason R.; Pushpavanam, S.

2017-11-01

Stratified or layered two-phase flows are encountered in several applications of microchannels, such as solvent extraction. Assuming steady, unidirectional creeping flow, it is possible to solve the Stokes equations by the method of eigenfunctions, provided the interface is flat and meets the wall with a 90 degree contact angle. However, in reality the contact angle depends on the pair of liquids and the material of the channel, and differs significantly from 90 degrees in many practical cases. For unidirectional flow, this implies that the interface is a circular arc (of constant curvature). We solve this problem within the framework of eigenfunctions, using the procedure developed by Shankar. We consider two distinct cases: (a) the interface meets the wall with the equilibrium contact angle; (b) the interface is pinned by surface treatment of the walls, so that the flow rates determine the apparent contact angle. We show that the contact angle appreciably affects the velocity profile and the volume fractions of the liquids, while limiting the range of flow rates that can be sustained without the interface touching the top/bottom walls. Non-intuitively, we find that the pressure drop is reduced when the more viscous liquid wets the wall.

Electromagnetic and scalar diffraction by a right-angled wedge with a uniform surface impedance

NASA Technical Reports Server (NTRS)

Hwang, Y. M.

1974-01-01

The diffraction of an electromagnetic wave by a perfectly-conducting right-angled wedge with one surface covered by a dielectric slab or absorber is considered. The effect of the coated surface is approximated by a uniform surface impedance. The solution of the normally incident electromagnetic problem is facilitated by introducing two scalar fields which satisfy a mixed boundary condition on one surface of the wedge and a Neumann of Dirichlet boundary condition on the other. A functional transformation is employed to simplify the boundary conditions so that eigenfunction expansions can be obtained for the resulting Green's functions. The eigenfunction expansions are transformed into the integral representations which then are evaluated asymptotically by the modified Pauli-Clemmow method of steepest descent. A far zone approximation is made to obtain the scattered field from which the diffraction coefficient is found for scalar plane, cylindrical or sperical wave incident on the edge. With the introduction of a ray-fixed coordinate system, the dyadic diffraction coefficient for plane or cylindrical EM waves normally indicent on the edge is reduced to the sum of two dyads which can be written alternatively as a 2 X 2 diagonal matrix.

Numerical operator calculus in higher dimensions

PubMed Central

Beylkin, Gregory; Mohlenkamp, Martin J.

2002-01-01

When an algorithm in dimension one is extended to dimension d, in nearly every case its computational cost is taken to the power d. This fundamental difficulty is the single greatest impediment to solving many important problems and has been dubbed the curse of dimensionality. For numerical analysis in dimension d, we propose to use a representation for vectors and matrices that generalizes separation of variables while allowing controlled accuracy. Basic linear algebra operations can be performed in this representation using one-dimensional operations, thus bypassing the exponential scaling with respect to the dimension. Although not all operators and algorithms may be compatible with this representation, we believe that many of the most important ones are. We prove that the multiparticle Schrödinger operator, as well as the inverse Laplacian, can be represented very efficiently in this form. We give numerical evidence to support the conjecture that eigenfunctions inherit this property by computing the ground-state eigenfunction for a simplified Schrödinger operator with 30 particles. We conjecture and provide numerical evidence that functions of operators inherit this property, in which case numerical operator calculus in higher dimensions becomes feasible. PMID:12140360

An analysis of the vertical structure equation for arbitrary thermal profiles

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.; Dee, Dick P.

1989-01-01

The vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations.

An analysis of the vertical structure equation for arbitrary thermal profiles

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.; Dee, Dick P.

1987-01-01

The vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations.

Modal element method for potential flow in non-uniform ducts: Combining closed form analysis with CFD

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Baumeister, Joseph F.

1994-01-01

An analytical procedure is presented, called the modal element method, that combines numerical grid based algorithms with eigenfunction expansions developed by separation of variables. A modal element method is presented for solving potential flow in a channel with two-dimensional cylindrical like obstacles. The infinite computational region is divided into three subdomains; the bounded finite element domain, which is characterized by the cylindrical obstacle and the surrounding unbounded uniform channel entrance and exit domains. The velocity potential is represented approximately in the grid based domain by a finite element solution and is represented analytically by an eigenfunction expansion in the uniform semi-infinite entrance and exit domains. The calculated flow fields are in excellent agreement with exact analytical solutions. By eliminating the grid surrounding the obstacle, the modal element method reduces the numerical grid size, employs a more precise far field boundary condition, as well as giving theoretical insight to the interaction of the obstacle with the mean flow. Although the analysis focuses on a specific geometry, the formulation is general and can be applied to a variety of problems as seen by a comparison to companion theories in aeroacoustics and electromagnetics.

The construction of partner potential from the general potential Rosen-Morse and Manning Rosen in 4 dimensional Schrodinger system

NASA Astrophysics Data System (ADS)

Nathalia Wea, Kristiana; Suparmi, A.; Cari, C.; Wahyulianti

2017-11-01

The solution of the Schrodinger equation with physical potential is the important part in quantum physics. Many methods have been developed to resolve the Schrodinger equation. The Nikiforov-Uvarov method and supersymmetric method are the most methods that interesting to be explored. The supersymmetric method not only used to solve the Schrodinger equation but also used to construct the partner potential from a general potential. In this study, the Nikiforov-Uvarov method was used to solve the Schrodinger equation while the supersymmetric method was used to construction partner potential. The study about the construction of the partner potential from general potential Rosen-Morse and Manning Rosen in D-dimensional Schrodinger system has been done. The partner potential was obtained are solvable. By using the Nikiforov-Uvarov method the eigenfunction of the Schrodinger equation in D-dimensional system with general potential Rosen-Morse and Manning Rosen and the Schrodinger equation in D-dimensional system with partner potential Rosen-Morse and Manning Rosen are determined. The eigenfunctions are different between the Schrodinger equation with general potential and the Schrodinger potential with the partner potential.

Student Solution Manual for Essential Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-02-01

1. Matrices and vector spaces; 2. Vector calculus; 3. Line, surface and volume integrals; 4. Fourier series; 5. Integral transforms; 6. Higher-order ODEs; 7. Series solutions of ODEs; 8. Eigenfunction methods; 9. Special functions; 10. Partial differential equations; 11. Solution methods for PDEs; 12. Calculus of variations; 13. Integral equations; 14. Complex variables; 15. Applications of complex variables; 16. Probability; 17. Statistics.

Essential Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-02-01

1. Matrices and vector spaces; 2. Vector calculus; 3. Line, surface and volume integrals; 4. Fourier series; 5. Integral transforms; 6. Higher-order ODEs; 7. Series solutions of ODEs; 8. Eigenfunction methods; 9. Special functions; 10. Partial differential equations; 11. Solution methods for PDEs; 12. Calculus of variations; 13. Integral equations; 14. Complex variables; 15. Applications of complex variables; 16. Probability; 17. Statistics; Appendices; Index.

A semi-inverse variational method for generating the bound state energy eigenvalues in a quantum system: the Dirac Coulomb type-equation

NASA Astrophysics Data System (ADS)

Libarir, K.; Zerarka, A.

2018-05-01

Exact eigenspectra and eigenfunctions of the Dirac quantum equation are established using the semi-inverse variational method. This method improves of a considerable manner the efficiency and accuracy of results compared with the other usual methods much argued in the literature. Some applications for different state configurations are proposed to concretize the method.

Control of Spatially Inhomogeneous Shear Flows

DTIC Science & Technology

2009-11-27

vectors fi with unit norm represent the eigenfunctions of H∗H, i.e. H∗ Hfi = σ 2i fi , (3.11) then the output energy will be given by the square of the so...modes, it is convenient to show that φoci are the eigenmodes of PQ; multiplying (3.11) with Lc yields LcH∗ Hfi = PQφoci = σ 2i φoci . (3.18) The

The Convergence Problems of Eigenfunction Expansions of Elliptic Differential Operators

NASA Astrophysics Data System (ADS)

Ahmedov, Anvarjon

2018-03-01

In the present research we investigate the problems concerning the almost everywhere convergence of multiple Fourier series summed over the elliptic levels in the classes of Liouville. The sufficient conditions for the almost everywhere convergence problems, which are most difficult problems in Harmonic analysis, are obtained. The methods of approximation by multiple Fourier series summed over elliptic curves are applied to obtain suitable estimations for the maximal operator of the spectral decompositions. Obtaining of such estimations involves very complicated calculations which depends on the functional structure of the classes of functions. The main idea on the proving the almost everywhere convergence of the eigenfunction expansions in the interpolation spaces is estimation of the maximal operator of the partial sums in the boundary classes and application of the interpolation Theorem of the family of linear operators. In the present work the maximal operator of the elliptic partial sums are estimated in the interpolation classes of Liouville and the almost everywhere convergence of the multiple Fourier series by elliptic summation methods are established. The considering multiple Fourier series as an eigenfunction expansions of the differential operators helps to translate the functional properties (for example smoothness) of the Liouville classes into Fourier coefficients of the functions which being expanded into such expansions. The sufficient conditions for convergence of the multiple Fourier series of functions from Liouville classes are obtained in terms of the smoothness and dimensions. Such results are highly effective in solving the boundary problems with periodic boundary conditions occurring in the spectral theory of differential operators. The investigations of multiple Fourier series in modern methods of harmonic analysis incorporates the wide use of methods from functional analysis, mathematical physics, modern operator theory and spectral decomposition. New method for the best approximation of the square-integrable function by multiple Fourier series summed over the elliptic levels are established. Using the best approximation, the Lebesgue constant corresponding to the elliptic partial sums is estimated. The latter is applied to obtain an estimation for the maximal operator in the classes of Liouville.

An approximation theory for nonlinear partial differential equations with applications to identification and control

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kunisch, K.

1982-01-01

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

Condition for a Bounded System of Klein-Gordon Particles in Electric and Magnetic Fields

NASA Astrophysics Data System (ADS)

Kisoglu, Hasan Fatih; Sogut, Kenan

2018-07-01

We investigate the motion of relativistic spinless particles in an external electromagnetic field that is considered to has a constant magnetic field and a time-dependent electric field. For such a system, we obtain analytical eigenfunctions through Asymptotic Iteration Method. We also obtain a condition of choosing the external magnetic field for which the system is bounded with usage of the method in perturbation theory.

The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system

NASA Technical Reports Server (NTRS)

Yeon, Kyu Hwang; Um, Chung IN; George, T. F.

1994-01-01

The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.

Efficient, massively parallel eigenvalue computation

NASA Technical Reports Server (NTRS)

Huo, Yan; Schreiber, Robert

1993-01-01

In numerical simulations of disordered electronic systems, one of the most common approaches is to diagonalize random Hamiltonian matrices and to study the eigenvalues and eigenfunctions of a single electron in the presence of a random potential. An effort to implement a matrix diagonalization routine for real symmetric dense matrices on massively parallel SIMD computers, the Maspar MP-1 and MP-2 systems, is described. Results of numerical tests and timings are also presented.

Finite-mode analysis by means of intensity information in fractional optical systems.

PubMed

Alieva, Tatiana; Bastiaans, Martin J

2002-03-01

It is shown how a coherent optical signal that contains only a finite number of Hermite-Gauss modes can be reconstructed from the knowledge of its Radon-Wigner transform-associated with the intensity distribution in a fractional-Fourier-transform optical system-at only two transversal points. The proposed method can be generalized to any fractional system whose generator transform has a complete orthogonal set of eigenfunctions.

Particle in a Uniform Magnetic Field Under the Symmetric Gauge: The Eigenfunctions and the Time Evolution of Wave Packets

ERIC Educational Resources Information Center

de Brito, P. E.; Nazareno, H. N.

2007-01-01

In the present work we treat the problem of a particle in a uniform magnetic field along the symmetric gauge, so chosen since the wavefunctions present the required cylindrical symmetry. It is our understanding that by means of this work we can make a contribution to the teaching of the present subject, as well as encourage students to use…

The Direct Effect of Toroidal Magnetic Fields on Stellar Oscillations: An Analytical Expression for the General Matrix Element

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kiefer, René; Schad, Ariane; Roth, Markus

2017-09-10

Where is the solar dynamo located and what is its modus operandi? These are still open questions in solar physics. Helio- and asteroseismology can help answer them by enabling us to study solar and stellar internal structures through global oscillations. The properties of solar and stellar acoustic modes are changing with the level of magnetic activity. However, until now, the inference on subsurface magnetic fields with seismic measures has been very limited. The aim of this paper is to develop a formalism to calculate the effect of large-scale toroidal magnetic fields on solar and stellar global oscillation eigenfunctions and eigenfrequencies.more » If the Lorentz force is added to the equilibrium equation of motion, stellar eigenmodes can couple. In quasi-degenerate perturbation theory, this coupling, also known as the direct effect, can be quantified by the general matrix element. We present the analytical expression of the matrix element for a superposition of subsurface zonal toroidal magnetic field configurations. The matrix element is important for forward calculations of perturbed solar and stellar eigenfunctions and frequency perturbations. The results presented here will help to ascertain solar and stellar large-scale subsurface magnetic fields, and their geometric configuration, strength, and change over the course of activity cycles.« less

Quadratic Zeeman effect for hydrogen: A method for rigorous bound-state error estimates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fonte, G.; Falsaperla, P.; Schiffrer, G.

1990-06-01

We present a variational method, based on direct minimization of energy, for the calculation of eigenvalues and eigenfunctions of a hydrogen atom in a strong uniform magnetic field in the framework of the nonrelativistic theory (quadratic Zeeman effect). Using semiparabolic coordinates and a harmonic-oscillator basis, we show that it is possible to give rigorous error estimates for both eigenvalues and eigenfunctions by applying some results of Kato (Proc. Phys. Soc. Jpn. 4, 334 (1949)). The method can be applied in this simple form only to the lowest level of given angular momentum and parity, but it is also possible tomore » apply it to any excited state by using the standard Rayleigh-Ritz diagonalization method. However, due to the particular basis, the method is expected to be more effective, the weaker the field and the smaller the excitation energy, while the results of Kato we have employed lead to good estimates only when the level spacing is not too small. We present a numerical application to the {ital m}{sup {ital p}}=0{sup +} ground state and the lowest {ital m}{sup {ital p}}=1{sup {minus}} excited state, giving results that are among the most accurate in the literature for magnetic fields up to about 10{sup 10} G.« less

A semi-analytical method for near-trapped mode and fictitious frequencies of multiple scattering by an array of elliptical cylinders in water waves

NASA Astrophysics Data System (ADS)

Chen, Jeng-Tzong; Lee, Jia-Wei

2013-09-01

In this paper, we focus on the water wave scattering by an array of four elliptical cylinders. The null-field boundary integral equation method (BIEM) is used in conjunction with degenerate kernels and eigenfunctions expansion. The closed-form fundamental solution is expressed in terms of the degenerate kernel containing the Mathieu and the modified Mathieu functions in the elliptical coordinates. Boundary densities are represented by using the eigenfunction expansion. To avoid using the addition theorem to translate the Mathieu functions, the present approach can solve the water wave problem containing multiple elliptical cylinders in a semi-analytical manner by introducing the adaptive observer system. Regarding water wave problems, the phenomena of numerical instability of fictitious frequencies may appear when the BIEM/boundary element method (BEM) is used. Besides, the near-trapped mode for an array of four identical elliptical cylinders is observed in a special layout. Both physical (near-trapped mode) and mathematical (fictitious frequency) resonances simultaneously appear in the present paper for a water wave problem by an array of four identical elliptical cylinders. Two regularization techniques, the combined Helmholtz interior integral equation formulation (CHIEF) method and the Burton and Miller approach, are adopted to alleviate the numerical resonance due to fictitious frequency.

Reexamination of relaxation of spins due to a magnetic field gradient: Identity of the Redfield and Torrey theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Golub, R.; Rohm, Ryan M.; Swank, C. M.

2011-02-15

There is an extensive literature on magnetic-gradient-induced spin relaxation. Cates, Schaefer, and Happer, in a seminal publication, have solved the problem in the regime where diffusion theory (the Torrey equation) is applicable using an expansion of the density matrix in diffusion equation eigenfunctions and angular momentum tensors. McGregor has solved the problem in the same regime using a slightly more general formulation using the Redfield theory formulated in terms of the autocorrelation function of the fluctuating field seen by the spins and calculating the correlation functions using the diffusion-theory Green's function. The results of both calculations were shown to agreemore » for a special case. In the present work, we show that the eigenfunction expansion of the Torrey equation yields the expansion of the Green's function for the diffusion equation, thus showing the identity of this approach with that of the Redfield theory. The general solution can also be obtained directly from the Torrey equation for the density matrix. Thus, the physical content of the Redfield and Torrey approaches are identical. We then introduce a more general expression for the position autocorrelation function of particles moving in a closed cell, extending the range of applicability of the theory.« less

The Direct Effect of Toroidal Magnetic Fields on Stellar Oscillations: An Analytical Expression for the General Matrix Element

NASA Astrophysics Data System (ADS)

Kiefer, René; Schad, Ariane; Roth, Markus

2017-09-01

Where is the solar dynamo located and what is its modus operandi? These are still open questions in solar physics. Helio- and asteroseismology can help answer them by enabling us to study solar and stellar internal structures through global oscillations. The properties of solar and stellar acoustic modes are changing with the level of magnetic activity. However, until now, the inference on subsurface magnetic fields with seismic measures has been very limited. The aim of this paper is to develop a formalism to calculate the effect of large-scale toroidal magnetic fields on solar and stellar global oscillation eigenfunctions and eigenfrequencies. If the Lorentz force is added to the equilibrium equation of motion, stellar eigenmodes can couple. In quasi-degenerate perturbation theory, this coupling, also known as the direct effect, can be quantified by the general matrix element. We present the analytical expression of the matrix element for a superposition of subsurface zonal toroidal magnetic field configurations. The matrix element is important for forward calculations of perturbed solar and stellar eigenfunctions and frequency perturbations. The results presented here will help to ascertain solar and stellar large-scale subsurface magnetic fields, and their geometric configuration, strength, and change over the course of activity cycles.

Fourth-order convergence of a compact scheme for the one-dimensional biharmonic equation

NASA Astrophysics Data System (ADS)

Fishelov, D.; Ben-Artzi, M.; Croisille, J.-P.

2012-09-01

The convergence of a fourth-order compact scheme to the one-dimensional biharmonic problem is established in the case of general Dirichlet boundary conditions. The compact scheme invokes value of the unknown function as well as Pade approximations of its first-order derivative. Using the Pade approximation allows us to approximate the first-order derivative within fourth-order accuracy. However, although the truncation error of the discrete biharmonic scheme is of fourth-order at interior point, the truncation error drops to first-order at near-boundary points. Nonetheless, we prove that the scheme retains its fourth-order (optimal) accuracy. This is done by a careful inspection of the matrix elements of the discrete biharmonic operator. A number of numerical examples corroborate this effect. We also present a study of the eigenvalue problem uxxxx = νu. We compute and display the eigenvalues and the eigenfunctions related to the continuous and the discrete problems. By the positivity of the eigenvalues, one can deduce the stability of of the related time-dependent problem ut = -uxxxx. In addition, we study the eigenvalue problem uxxxx = νuxx. This is related to the stability of the linear time-dependent equation uxxt = νuxxxx. Its continuous and discrete eigenvalues and eigenfunction (or eigenvectors) are computed and displayed graphically.

A singular-value method for reconstruction of nonradial and lossy objects.

PubMed

Jiang, Wei; Astheimer, Jeffrey; Waag, Robert

2012-03-01

Efficient inverse scattering algorithms for nonradial lossy objects are presented using singular-value decomposition to form reduced-rank representations of the scattering operator. These algorithms extend eigenfunction methods that are not applicable to nonradial lossy scattering objects because the scattering operators for these objects do not have orthonormal eigenfunction decompositions. A method of local reconstruction by segregation of scattering contributions from different local regions is also presented. Scattering from each region is isolated by forming a reduced-rank representation of the scattering operator that has domain and range spaces comprised of far-field patterns with retransmitted fields that focus on the local region. Methods for the estimation of the boundary, average sound speed, and average attenuation slope of the scattering object are also given. These methods yielded approximations of scattering objects that were sufficiently accurate to allow residual variations to be reconstructed in a single iteration. Calculated scattering from a lossy elliptical object with a random background, internal features, and white noise is used to evaluate the proposed methods. Local reconstruction yielded images with spatial resolution that is finer than a half wavelength of the center frequency and reproduces sound speed and attenuation slope with relative root-mean-square errors of 1.09% and 11.45%, respectively.

Collisionless tearing instability of a bi-Maxwellian neutral sheet - An integrodifferential treatment with exact particle orbits

NASA Technical Reports Server (NTRS)

Burkhart, G. R.; Chen, J.

1989-01-01

The integrodifferential equation describing the linear tearing instability in the bi-Maxwellian neutral sheet is solved without approximating the particle orbits or the eigenfunction psi. Results of this calculation are presented. Comparison between the exact solution and the three-region approximation motivates the piecewise-straight-line approximation, a simplification that allows faster solution of the integrodifferential equation, yet retains the important features of the exact solution.

A generalized Jaynes-Cummings model: The relativistic parametric amplifier and a single trapped ion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ojeda-Guillén, D., E-mail: dojedag@ipn.mx; Mota, R. D.; Granados, V. D.

2016-06-15

We introduce a generalization of the Jaynes-Cummings model and study some of its properties. We obtain the energy spectrum and eigenfunctions of this model by using the tilting transformation and the squeezed number states of the one-dimensional harmonic oscillator. As physical applications, we connect this new model to two important and novelty problems: the relativistic parametric amplifier and the quantum simulation of a single trapped ion.

Closed form solution for a double quantum well using Gröbner basis

NASA Astrophysics Data System (ADS)

Acus, A.; Dargys, A.

2011-07-01

Analytical expressions for the spectrum, eigenfunctions and dipole matrix elements of a square double quantum well (DQW) are presented for a general case when the potential in different regions of the DQW has different heights and the effective masses are different. This was achieved by using a Gröbner basis algorithm that allowed us to disentangle the resulting coupled polynomials without explicitly solving the transcendental eigenvalue equation.

A garden of orchids: a generalized Harper equation at quadratic irrational frequencies

NASA Astrophysics Data System (ADS)

Mestel, B. D.; Osbaldestin, A. H.

2004-10-01

We consider a generalized Harper equation at quadratic irrational flux, showing, in the strong coupling limit, the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set. This work generalizes previous analyses which have considered only the golden mean case. Projections of the renormalization strange sets are illustrated analogous to the 'orchid' present in the golden mean case.

Piston flow in a two-dimensional channel

NASA Astrophysics Data System (ADS)

Katopodes, Fotini V.; Davis, A. M. J.; Stone, H. A.

2000-05-01

A solution using biorthogonal eigenfunctions is presented for viscous flow caused by a piston in a two-dimensional channel. The resulting infinite set of linear equations is solved using Spence's optimal weighting function method [IMA J. Appl. Math. 30, 107 (1983)]. The solution is compared to that with a shear-free piston surface; in the latter configuration the fluid more rapidly approaches the Poiseuille flow profile established away from the face of the piston.

Finite element method for calculating spectral and optical characteristics of axially symmetric quantum dots

NASA Astrophysics Data System (ADS)

Gusev, A. A.; Chuluunbaatar, O.; Vinitsky, S. I.; Derbov, V. L.; Hai, L. L.; Kazaryan, E. M.; Sarkisyan, H. A.

2018-04-01

We present new calculation schemes using high-order finite element method implemented on unstructured grids with triangle elements for solving boundary-value problems that describe axially symmetric quantum dots. The efficiency of the algorithms and software is demonstrated by benchmark calculations of the energy spectrum, the envelope eigenfunctions of electron, hole and exciton states, and the direct interband light absorption in conical and spheroidal impenetrable quantum dots.

Topological phase transition measured in a dissipative metamaterial

NASA Astrophysics Data System (ADS)

Rosenthal, Eric I.; Ehrlich, Nicole K.; Rudner, Mark S.; Higginbotham, Andrew P.; Lehnert, K. W.

2018-06-01

We construct a metamaterial from radio-frequency harmonic oscillators, and find two topologically distinct phases resulting from dissipation engineered into the system. These phases are distinguished by a quantized value of bulk energy transport. The impulse response of our circuit is measured and used to reconstruct the band structure and winding number of circuit eigenfunctions around a dark mode. Our results demonstrate that dissipative topological transport can occur in a wider class of physical systems than considered before.

Numerical Methods of Parameter Identification for Problems Arising in Elasticity.

DTIC Science & Technology

1982-06-01

Theorem 2.21 remains essentially unchanged by the inclusion of this new term . We now turn to a concrete realization of the approximate identification...cost if it had been accomplished under contract or if it had been done in-house in terms of manpower and/or dollars? ( ) a. MAN-YEARS ( ) b. $ 4...eigenfunction) state approximations were applied to a class of hyperbolic and parabolic equations, and also used in [7 ], where spline-based state

Fluid Motion in a Spinning, Coning Cylinder via Spatial Eigenfunction Expansion.

DTIC Science & Technology

1987-08-01

PRESSURE AND MOMENT COEFFICIENTS The velocity, pressure and moment exerted by the liquid on the container are quantities of physical interest calculated...with collocation; these are denoted by LS and COL, respectively. Of the physical parameters, the calculation is more sensitive to Re and f than A...Applied Ntate’atics and Physics (ZAMP), Vol. 33, pp. 189-201, March 1982. 4I REFERENCES (continued) 13. Gerber, N., and Sedney, R., "Moment on a

Asymptotic theory of a slender rotating beam with end masses.

NASA Technical Reports Server (NTRS)

Whitman, A. M.; Abel, J. M.

1972-01-01

The method of matched asymptotic expansions is employed to solve the singular perturbation problem of the vibrations of a rotating beam of small flexural rigidity with concentrated end masses. The problem is complicated by the appearance of the eigenvalue in the boundary conditions. Eigenfunctions and eigenvalues are developed as power series in the perturbation parameter beta to the 1/2 power, and results are given for mode shapes and eigenvalues through terms of the order of beta.

Modeling and Control of Large Flexible Structures.

DTIC Science & Technology

1984-07-31

59 4.5 Spectral factorization using the Hilbert transform 62 4.6 Gain computations 64 4.7 Software development and control system performance 66 Part...in the Hilbert space - L2(S) with the natural inner product, ,>. In many cases A O has a discrete spectrum with associated 2 eigenfunctions which...Davis and Barry 1977) ( Greenberg , MacCamy Nisel and 1968). The natural boundary~.; ’? , : conditions for (17) are in terms of s(zt) at s-O and 1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorbachev, D V; Ivanov, V I

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.

Application of satellite data to tropic/subtropic moisture coupling

NASA Technical Reports Server (NTRS)

Mcguirk, J. P.; Thompson, A. H.

1985-01-01

The objective is to develop analysis tools for use of satellite data to interpret synoptic-scale systems in data-void regions. Interim goals are to: (1) quantify the synoptic information content of satellite data; and (2) utilize these data in the diagnosis of moisture bursts in the eastern tropical Pacific Ocean. Researchers developed and implemented a statistical procedure for using TIROS N microwave data to infer infrared channel data for overcast conditions; they used the same procedure for deducing full TIROS N channel radiance profiles from NOAA 5 VTPR channel data over regions where the TIROS N data are missing. An empirical orthogonal function analysis of twice-daily channel radiance fields over the tropical eastern Pacific was completed. The vertically oriented eigenfunctions were interpreted in terms of typical meteorological events. The horizontal distribution of the eigenfunction amplitudes relates these meteorological signals to moisture bursts. A pair of moisture burst climatologies is complete: one of four years using infrared imagery (including the highly anomalous 1982 to 83 cold season); the other implementing 850 to 200 mb wind analyses in conjunction with GOES imagery. A number of different evaluations of the synoptic evolution of moisture fields (enhanced infrared imagery, moisture channel data, FGGE humidity analysis, and in situ station and sounding observations) are compared. All have limitations; all can be utilized together; all together are still less than adequate in the tropical Pacific.

The Renner effect in triatomic molecules with application to CH+, MgNC and NH2.

PubMed

Jensen, Per; Odaka, Tina Erica; Kraemer, W P; Hirano, Tsuneo; Bunker, P R

2002-03-01

We have developed a computational procedure, based on the variational method, for the calculation of the rovibronic energies of a triatomic molecule in an electronic state that become degenerate at the linear nuclear configuration. In such an electronic state the coupling caused by the electronic orbital angular momentum is very significant and it is called the Renner effect. We include it, and the effect of spin-orbit coupling, in our program. We have developed the procedure to the point where spectral line intensities can be calculated so that absorption and emission spectra can be simulated. In order to gain insight into the nature of the eigenfunctions, we have introduced and calculated the overall bending probability density function f(p) of the states. By projecting the eigenfunctions onto the Born-Oppenheimer basis, we have determined the probability density functions f+(rho) and f-(rho) associated with the individual Born-Oppenheimer states phi(-)elec and phi(+)elec. At a given temperature the Boltzmann averaged value of the f(p) over all the eigenstates gives the bending probability distribution function F(rho), and this can be related to the result of a Coulomb Explosion Imaging (CEI) experiment. We review our work and apply it to the molecules CH2+, MgNC and NH2, all of which are of astrophysical interest.

Wave excited motion of a body floating on water confined between two semi-infinite ice sheets

NASA Astrophysics Data System (ADS)

Ren, K.; Wu, G. X.; Thomas, G. A.

2016-12-01

The wave excited motion of a body floating on water confined between two semi-infinite ice sheets is investigated. The ice sheet is treated as an elastic thin plate and water is treated as an ideal and incompressible fluid. The linearized velocity potential theory is adopted in the frequency domain and problems are solved by the method of matched eigenfunctions expansion. The fluid domain is divided into sub-regions and in each sub-region the velocity potential is expanded into a series of eigenfunctions satisfying the governing equation and the boundary conditions on horizontal planes including the free surface and ice sheets. Matching is conducted at the interfaces of two neighbouring regions to ensure the continuity of the pressure and velocity, and the unknown coefficients in the expressions are obtained as a result. The behaviour of the added mass and damping coefficients of the floating body with the effect of the ice sheets and the excitation force are analysed. They are found to vary oscillatorily with the wave number, which is different from that for a floating body in the open sea. The motion of the body confined between ice sheets is investigated, in particular its resonant behaviour with extremely large motion found to be possible under certain conditions. Standing waves within the polynya are also observed.

Passive control of coherent structures in a modified backwards-facing step flow

NASA Astrophysics Data System (ADS)

Ormonde, Pedro C.; Cavalieri, André V. G.; Silva, Roberto G. A. da; Avelar, Ana C.

2018-05-01

We study a modified backwards-facing step flow, with the addition of two different plates; one is a baseline, impermeable plate and the second a perforated one. An experimental investigation is carried out for a turbulent reattaching shear layer downstream of the two plates. The proposed setup is a model configuration to study how the plate characteristics affect the separated shear layer and how turbulent kinetic energies and large-scale coherent structures are modified. Measurements show that the perforated plate changes the mean flow field, mostly by reducing the intensity of reverse flow close to the bottom wall. Disturbance amplitudes are significantly reduced up to five step heights downstream of the trailing edge of the plate, more specifically in the recirculation region. A loudspeaker is then used to introduce phase-locked, low-amplitude perturbations upstream of the plates, and phase-averaged measurements allow a quantitative study of large-scale structures in the shear-layer. The evolution of such coherent structures is evaluated in light of linear stability theory, comparing the eigenfunction of the Kelvin-Helmholtz mode to the experimental results. We observe a close match of linear-stability eigenfunctions with phase-averaged amplitudes for the two tested Strouhal numbers. The perforated plate is found to reduce the amplitude of the Kelvin-Helmholtz coherent structures in comparison to the baseline, impermeable plate, a behavior consistent with the predicted amplification trends from linear stability.

Electromagnetic Coupling of Negative Parity Nucleon Resonances N (1535) Based on Nonrelativistic Constituent Quark Model

NASA Astrophysics Data System (ADS)

Parsaei, Sara; Rajabi, Ali Akbar

2018-01-01

The electromagnetic transition between the nucleon and excited baryons has long been recognized as an important source of information for understanding strong interactions in the domain of quark confinement. We study the electromagnetic properties of the excitation of the negative parity the N*(1535) resonances in the nonrelativistic constituent quark model at large momentum transfers and have performed a calculation the longitudinal and transverse helicity amplitudes. Since the helicity amplitudes depend strongly on the quark wave function in this paper, we consider the baryon as a simple, non-relativistically three-body quark model and also consider a hypercentral potential scheme for the internal baryon structure, which makes three-body forces among three quarks. Since the hyper central potential depends only on the hyper radius, therefore, the Cornell potential which is a combination of the Coulombic-like term plus a linear confining term is considered as the potential for interaction between quarks. In our work, in solving the Schrodinger equation with the Cornell potential, the Nikiforov-Uvarov method employed, and the analytic eigen-energies and eigen-functions obtained. By using the obtained eigen-functions, the transition amplitudes calculated. We show that our results in the range {{{Q}}}2> 2 {{GeV}}2 lead to an overall better agreement with the experimental data in comparison with the other three non-relativistic quark models.

Fast, purely growing collisionless reconnection as an eigenfunction problem related to but not involving linear whistler waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bellan, Paul M.

If either finite electron inertia or finite resistivity is included in 2D magnetic reconnection, the two-fluid equations become a pair of second-order differential equations coupling the out-of-plane magnetic field and vector potential to each other to form a fourth-order system. The coupling at an X-point is such that out-of-plane even-parity electric and odd-parity magnetic fields feed off each other to produce instability if the scale length on which the equilibrium magnetic field changes is less than the ion skin depth. The instability growth rate is given by an eigenvalue of the fourth-order system determined by boundary and symmetry conditions. Themore » instability is a purely growing mode, not a wave, and has growth rate of the order of the whistler frequency. The spatial profile of both the out-of-plane electric and magnetic eigenfunctions consists of an inner concave region having extent of the order of the electron skin depth, an intermediate convex region having extent of the order of the equilibrium magnetic field scale length, and a concave outer exponentially decaying region. If finite electron inertia and resistivity are not included, the inner concave region does not exist and the coupled pair of equations reduces to a second-order differential equation having non-physical solutions at an X-point.« less

Learned helplessness in the multiple sclerosis population.

PubMed

McGuinness, S

1996-06-01

The purpose of this cross-sectional, descriptive study was to describe the relationships between learned helplessness and disease status, functional and social disability, and disease activity in the multiple sclerosis population. Additionally, the relationships between learned helplessness and age, disease duration, education and marital and employment status were evaluated. Self-report instruments with established validity and reliability in the multiple sclerosis population were used to collect the data. Learned helplessness was significantly positively correlated with social and functional disability. Although not significant at the .05 level, disease status and disease activity were also positively correlated with learned helplessness. Additionally, unemployed individuals were more likely to be helpless than employed individuals. Overall, the results suggest that learned helplessness is related to negative health indicators in the multiple sclerosis population. Nursing interventions to decrease or prevent learned helplessness may be appropriate in this population.

FAST TRACK COMMUNICATION: Two interacting atoms in a cavity: exact solutions, entanglement and decoherence

NASA Astrophysics Data System (ADS)

Torres, J. M.; Sadurní, E.; Seligman, T. H.

2010-05-01

We address the problem of two interacting atoms of different species inside a cavity and find the explicit solutions of the corresponding eigenvalues and eigenfunctions using a new variant. This model encompasses various commonly used models. By way of example we obtain closed expressions for concurrence and purity as a function of time for the case where the cavity is prepared in a number state. We discuss the behaviour of these quantities and their relative behaviour in the concurrence-purity plane.

Numerical methods for studying anharmonic oscillator approximations to the phi super 4 sub 2 quantum field theory

NASA Technical Reports Server (NTRS)

Isaacson, D.; Marchesin, D.; Paes-Leme, P. J.

1980-01-01

This paper is an expanded version of a talk given at the 1979 T.I.C.O.M. conference. It is a self-contained introduction, for applied mathematicians and numerical analysts, to quantum mechanics and quantum field theory. It also contains a brief description of the authors' numerical approach to the problems of quantum field theory, which may best be summarized by the question; Can we compute the eigenvalues and eigenfunctions of Schrodinger operators in infinitely many variables.

S-matrix method for the numerical determination of bound states.

NASA Technical Reports Server (NTRS)

Bhatia, A. K.; Madan, R. N.

1973-01-01

A rapid numerical technique for the determination of bound states of a partial-wave-projected Schroedinger equation is presented. First, one needs to integrate the equation only outwards as in the scattering case, and second, the number of trials necessary to determine the eigenenergy and the corresponding eigenfunction is considerably less than in the usual method. As a nontrivial example of the technique, bound states are calculated in the exchange approximation for the e-/He+ system and l equals 1 partial wave.

Chiral behaviour of the wave functions for three wave guides in the vicinity of an exceptional point of third order

NASA Astrophysics Data System (ADS)

Heiss, Walter Dieter; Wunner, Günter

2017-12-01

A matrix model that has been used to describe essential features of a parity-time symmetric set-up of three coupled wave guides is investigated. The emphasis of the study lies on the occurrence of an exceptional point of third order. It is demonstrated that the eigenfunctions in close vicinity of the exceptional point have a distinctive chiral behaviour. Using data describing realistic situations it is argued that such chiral behaviour can be tested experimentally.

FIBER AND INTEGRATED OPTICS: Propagation of circularly polarized light along a curved trajectory

NASA Astrophysics Data System (ADS)

Sadykov, Nail R.

1992-10-01

How the eigenfunction of an optical fiber is affected by a slight curvature at bends of the fiber without twisting is analyzed. The effect of a twisting of the ray trajectory in the case with curvature is examined theoretically by the geometric-optics approach. The results are used to analyze the problem of the turning of a meridional ray due to a circular polarization in a multimode optical fiber with a parabolic profile of the refractive index.

Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams

PubMed Central

Abedi, Maryam

2014-01-01

This work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. The Legendre orthogonal polynomials are used as the beam eigenfunctions. Natural frequencies and mode shapes of various Timoshenko beams are presented to demonstrate the efficiency of the methodology. PMID:24574879

Theoretical Limits of Damping Attainable by Smart Beams with Rate Feedback

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1997-01-01

Using a generally accepted model we present a comprehensive analysis (within the page limitation) of an Euler- Bernoulli beam with PZT sensor-actuator and pure rate feedback. The emphasis is on the root locus - the dependence of the attainable damping on the feedback gain. There is a critical value of the gain beyond which the damping decreases to zero. We construct the time-domain response using semigroup theory, and show that the eigenfunctions form a Riesz basis, leading to a 'modal' expansion.

Invariant criteria for bound states, degree of ionization, and plasma phase transition

NASA Technical Reports Server (NTRS)

Girardeau, M. D.

1990-01-01

Basis invariant characterizations of bound states and bound fraction of a partially ionized hydrogen plasma are given in terms of properties of the spectrum of eigenvalues and eigenfunctions of the equilibrium quantum statistical one-proton-one-electron reduced density matrix. It is suggested that these can be used to place theories of a proposed plasma-ionization phase transition on a firm foundation. This general approach may be relevant to cosmological questions such as the quark deconfinement-confinement transition.

Exact solution to the Schrödinger’s equation with pseudo-Gaussian potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iacob, Felix, E-mail: felix@physics.uvt.ro; Lute, Marina, E-mail: marina.lute@upt.ro

2015-12-15

We consider the radial Schrödinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of energy levels for the bound states are calculated along with their corresponding normalized wave-functions. The case of positive energy levels, known as meta-stable states, is also discussed and the magnitude of transmission coefficient through the potential barrier is evaluated.

κ-deformed Dirac oscillator in an external magnetic field

NASA Astrophysics Data System (ADS)

Chargui, Y.; Dhahbi, A.; Cherif, B.

2018-04-01

We study the solutions of the (2 + 1)-dimensional κ-deformed Dirac oscillator in the presence of a constant transverse magnetic field. We demonstrate how the deformation parameter affects the energy eigenvalues of the system and the corresponding eigenfunctions. Our findings suggest that this system could be used to detect experimentally the effect of the deformation. We also show that the hidden supersymmetry of the non-deformed system reduces to a hidden pseudo-supersymmetry having the same algebraic structure as a result of the κ-deformation.

ODPEVP: A program for computing eigenvalues and eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm-Liouville problem

NASA Astrophysics Data System (ADS)

Chuluunbaatar, O.; Gusev, A. A.; Vinitsky, S. I.; Abrashkevich, A. G.

2009-08-01

A FORTRAN 77 program is presented for calculating with the given accuracy eigenvalues, eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm-Liouville problem with the parametric third type boundary conditions on the finite interval. The program calculates also potential matrix elements - integrals of the eigenfunctions multiplied by their first derivatives with respect to the parameter. Eigenvalues and matrix elements computed by the ODPEVP program can be used for solving the bound state and multi-channel scattering problems for a system of the coupled second-order ordinary differential equations with the help of the KANTBP programs [O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Commun. 177 (2007) 649-675; O. Chuluunbaatar, A.A. Gusev, S.I. Vinitsky, A.G. Abrashkevich, Comput. Phys. Commun. 179 (2008) 685-693]. As a test desk, the program is applied to the calculation of the potential matrix elements for an integrable 2D-model of three identical particles on a line with pair zero-range potentials, a 3D-model of a hydrogen atom in a homogeneous magnetic field and a hydrogen atom on a three-dimensional sphere. Program summaryProgram title: ODPEVP Catalogue identifier: AEDV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDV_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3001 No. of bytes in distributed program, including test data, etc.: 24 195 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IV Operating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XP RAM: depends on the number and order of finite elements; the number of points; and the number of eigenfunctions required. Test run requires 4 MB Classification: 2.1, 2.4 External routines: GAULEG [3] Nature of problem: The three-dimensional boundary problem for the elliptic partial differential equation with an axial symmetry similar to the Schrödinger equation with the Coulomb and transverse oscillator potentials is reduced to the two-dimensional one. The latter finds wide applications in modeling of photoionization and recombination of oppositively charged particles (positrons, antiprotons) in the magnet-optical trap [4], optical absorption in quantum wells [5], and channeling of likely charged particles in thin doped films [6,7] or neutral atoms and molecules in artificial waveguides or surfaces [8,9]. In the adiabatic approach [10] known in mathematics as Kantorovich method [11] the solution of the two-dimensional elliptic partial differential equation is expanded over basis functions with respect to the fast variable (for example, angular variable) and depended on the slow variable (for example, radial coordinate ) as a parameter. An averaging of the problem by such a basis leads to a system of the second-order ordinary differential equations which contain potential matrix elements and the first-derivative coupling terms (see, e.g., [12,13,14]). The purpose of this paper is to present the finite element method procedure based on the use of high-order accuracy approximations for calculating eigenvalues, eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm-Liouville problem with the parametric third type boundary conditions on the finite interval. The program developed calculates potential matrix elements - integrals of the eigenfunctions multiplied by their derivatives with respect to the parameter. These matrix elements can be used for solving the bound state and multi-channel scattering problems for a system of the coupled second-order ordinary differential equations with the help of the KANTBP programs [1,2]. Solution method: The parametric self-adjoined Sturm-Liouville problem with the parametric third type boundary conditions is solved by the finite element method using high-order accuracy approximations [15]. The generalized algebraic eigenvalue problem AF=EBF with respect to a pair of unknown ( E,F) arising after the replacement of the differential problem by the finite-element approximation is solved by the subspace iteration method using the SSPACE program [16]. First derivatives of the eigenfunctions with respect to the parameter which contained in potential matrix elements of the coupled system equations are obtained by solving the inhomogeneous algebraic equations. As a test desk, the program is applied to the calculation of the potential matrix elements for an integrable 2D-model of three identical particles on a line with pair zero-range potentials described in [1,17,18], a 3D-model of a hydrogen atom in a homogeneous magnetic field described in [14,19] and a hydrogen atom on a three-dimensional sphere [20]. Restrictions: The computer memory requirements depend on: the number and order of finite elements; the number of points; and the number of eigenfunctions required. Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see sections below and listing for details). The user must also supply DOUBLE PRECISION functions POTCCL and POTCC1 for evaluating potential function U(ρ,z) of Eq. (1) and its first derivative with respect to parameter ρ. The user should supply DOUBLE PRECISION functions F1FUNC and F2FUNC that evaluate functions f(z) and f(z) of Eq. (1). The user must also supply subroutine BOUNCF for evaluating the parametric third type boundary conditions. Running time: The running time depends critically upon: the number and order of finite elements; the number of points on interval [z,z]; and the number of eigenfunctions required. The test run which accompanies this paper took 2 s with calculation of matrix potentials on the Intel Pentium IV 2.4 GHz. References:O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Comm. 177 (2007) 649-675 O. Chuluunbaatar, A.A. Gusev, S.I. Vinitsky, A.G. Abrashkevich, Comput. Phys. Comm. 179 (2008) 685-693. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986. O. Chuluunbaatar, A.A. Gusev, S.I. Vinitsky, V.L. Derbov, L.A. Melnikov, V.V. Serov, Phys. Rev. A 77 (2008) 034702-1-4. E.M. Kazaryan, A.A. Kostanyan, H.A. Sarkisyan, Physica E 28 (2005) 423-430. Yu.N. Demkov, J.D. Meyer, Eur. Phys. J. B 42 (2004) 361-365. P.M. Krassovitskiy, N.Zh. Takibaev, Bull. Russian Acad. Sci. Phys. 70 (2006) 815-818. V.S. Melezhik, J.I. Kim, P. Schmelcher, Phys. Rev. A 76 (2007) 053611-1-15. F.M. Pen'kov, Phys. Rev. A 62 (2000) 044701-1-4. M. Born, X. Huang, Dynamical Theory of Crystal Lattices, The Clarendon Press, Oxford, England, 1954. L.V. Kantorovich, V.I. Krylov, Approximate Methods of Higher Analysis, Wiley, New York, 1964. U. Fano, Colloq. Int. C.N.R.S. 273 (1977) 127;A.F. Starace, G.L. Webster, Phys. Rev. A 19 (1979) 1629-1640. C.V. Clark, K.T. Lu, A.F. Starace, in: H.G. Beyer, H. Kleinpoppen (eds.), Progress in Atomic Spectroscopy, Part C, Plenum, New York, 1984, pp. 247-320. O. Chuluunbaatar, A.A. Gusev, V.L. Derbov, M.S. Kaschiev, L.A. Melnikov, V.V. Serov, S.I. Vinitsky, J. Phys. A 40 (2007) 11485-11524. A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Comm. 85 (1995) 40-64. K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982. O. Chuluunbaatar, A.A. Gusev, M.S. Kaschiev, V.A. Kaschieva, A. Amaya-Tapia, S.Y. Larsen, S.I. Vinitsky, J. Phys. B 39 (2006) 243-269. Yu.A. Kuperin, P.B. Kurasov, Yu.B. Melnikov, S.P. Merkuriev, Ann. Phys. 205 (1991) 330-361. O. Chuluunbaatar, A.A. Gusev, V.P. Gerdt, V.A. Rostovtsev, S.I. Vinitsky, A.G. Abrashkevich, M.S. Kaschiev, V.V. Serov, Comput. Phys. Comm. 178 (2008) 301-330. A.G. Abrashkevich, M.S. Kaschiev, S.I. Vinitsky, J. Comp. Phys. 163 (2000) 328-348.

Rapid learning in visual cortical networks.

PubMed

Wang, Ye; Dragoi, Valentin

2015-08-26

Although changes in brain activity during learning have been extensively examined at the single neuron level, the coding strategies employed by cell populations remain mysterious. We examined cell populations in macaque area V4 during a rapid form of perceptual learning that emerges within tens of minutes. Multiple single units and LFP responses were recorded as monkeys improved their performance in an image discrimination task. We show that the increase in behavioral performance during learning is predicted by a tight coordination of spike timing with local population activity. More spike-LFP theta synchronization is correlated with higher learning performance, while high-frequency synchronization is unrelated with changes in performance, but these changes were absent once learning had stabilized and stimuli became familiar, or in the absence of learning. These findings reveal a novel mechanism of plasticity in visual cortex by which elevated low-frequency synchronization between individual neurons and local population activity accompanies the improvement in performance during learning.

Integrated methods for teaching population health.

PubMed

Sistrom, Maria Gilson; Zeigen, Laura; Jones, Melissa; Durham, Korana Fiol; Boudrot, Thomas

2011-01-01

The Institute of Medicine recommends reforms to public health education to better prepare the public health workforce. This study addresses the application of two of the recommended reforms in the population health nursing curriculum at one university: use of an ecological model and distance learning methods. Using interdisciplinary faculty, integrated teaching and learning methods, and a multimedia curriculum, this study examined the following question: can distance learning be designed to support learning goals and outcomes specific to an ecological approach and population health concepts in general? Course content was evaluated using students' perception of practice utility and understanding of population health concepts. Integrated teaching methods were evaluated using a scale as well as comparison to other student distance learning experiences within the university. Findings demonstrated that both the ecological model and distance learning methods were successfully used to teach population health to a large nursing student cohort. 2011, SLACK Incorporated.

Singular solution of the Feller diffusion equation via a spectral decomposition.

PubMed

Gan, Xinjun; Waxman, David

2015-01-01

Feller studied a branching process and found that the distribution for this process approximately obeys a diffusion equation [W. Feller, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley and Los Angeles, 1951), pp. 227-246]. This diffusion equation and its generalizations play an important role in many scientific problems, including, physics, biology, finance, and probability theory. We work under the assumption that the fundamental solution represents a probability density and should account for all of the probability in the problem. Thus, under the circumstances where the random process can be irreversibly absorbed at the boundary, this should lead to the presence of a Dirac delta function in the fundamental solution at the boundary. However, such a feature is not present in the standard approach (Laplace transformation). Here we require that the total integrated probability is conserved. This yields a fundamental solution which, when appropriate, contains a term proportional to a Dirac delta function at the boundary. We determine the fundamental solution directly from the diffusion equation via spectral decomposition. We obtain exact expressions for the eigenfunctions, and when the fundamental solution contains a Dirac delta function at the boundary, every eigenfunction of the forward diffusion operator contains a delta function. We show how these combine to produce a weight of the delta function at the boundary which ensures the total integrated probability is conserved. The solution we present covers cases where parameters are time dependent, thereby greatly extending its applicability.

The three-body problem with short-range interactions

NASA Astrophysics Data System (ADS)

Nielsen, E.; Fedorov, D. V.; Jensen, A. S.; Garrido, E.

2001-06-01

The quantum mechanical three-body problem is studied for general short-range interactions. We work in coordinate space to facilitate accurate computations of weakly bound and spatially extended systems. Hyperspherical coordinates are used in both the interpretation and as an integral part of the numerical method. Universal properties and model independence are discussed throughout the report. We present an overview of the hyperspherical adiabatic Faddeev equations. The wave function is expanded on hyperspherical angular eigenfunctions which in turn are found numerically using the Faddeev equations. We generalize the formalism to any dimension of space d greater or equal to two. We present two numerical techniques for solving the Faddeev equations on the hypersphere. These techniques are effective for short and intermediate/large distances including use for hard core repulsive potentials. We study the asymptotic limit of large hyperradius and derive the analytic behaviour of the angular eigenvalues and eigenfunctions. We discuss four applications of the general method. We first analyze the Efimov and Thomas effects for arbitrary angular momenta and for arbitrary dimensions d. Second we apply the method to extract the general behaviour of weakly bound three-body systems in two dimensions. Third we illustrate the method in three dimensions by structure computations of Borromean halo nuclei, the hypertriton and helium molecules. Fourth we investigate in three dimensions three-body continuum properties of Borromean halo nuclei and recombination reactions of helium atoms as an example of direct relevance for the stability of Bose-Einstein condensates.

From Jack to Double Jack Polynomials via the Supersymmetric Bridge

NASA Astrophysics Data System (ADS)

Lapointe, Luc; Mathieu, Pierre

2015-07-01

The Calogero-Sutherland model occurs in a large number of physical contexts, either directly or via its eigenfunctions, the Jack polynomials. The supersymmetric counterpart of this model, although much less ubiquitous, has an equally rich structure. In particular, its eigenfunctions, the Jack superpolynomials, appear to share the very same remarkable combinatorial and structural properties as their non-supersymmetric version. These super-functions are parametrized by superpartitions with fixed bosonic and fermionic degrees. Now, a truly amazing feature pops out when the fermionic degree is sufficiently large: the Jack superpolynomials stabilize and factorize. Their stability is with respect to their expansion in terms of an elementary basis where, in the stable sector, the expansion coefficients become independent of the fermionic degree. Their factorization is seen when the fermionic variables are stripped off in a suitable way which results in a product of two ordinary Jack polynomials (somewhat modified by plethystic transformations), dubbed the double Jack polynomials. Here, in addition to spelling out these results, which were first obtained in the context of Macdonal superpolynomials, we provide a heuristic derivation of the Jack superpolynomial case by performing simple manipulations on the supersymmetric eigen-operators, rendering them independent of the number of particles and of the fermionic degree. In addition, we work out the expression of the Hamiltonian which characterizes the double Jacks. This Hamiltonian, which defines a new integrable system, involves not only the expected Calogero-Sutherland pieces but also combinations of the generators of an underlying affine {widehat{sl}_2} algebra.

Singular solution of the Feller diffusion equation via a spectral decomposition

NASA Astrophysics Data System (ADS)

Gan, Xinjun; Waxman, David

2015-01-01

Feller studied a branching process and found that the distribution for this process approximately obeys a diffusion equation [W. Feller, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley and Los Angeles, 1951), pp. 227-246]. This diffusion equation and its generalizations play an important role in many scientific problems, including, physics, biology, finance, and probability theory. We work under the assumption that the fundamental solution represents a probability density and should account for all of the probability in the problem. Thus, under the circumstances where the random process can be irreversibly absorbed at the boundary, this should lead to the presence of a Dirac delta function in the fundamental solution at the boundary. However, such a feature is not present in the standard approach (Laplace transformation). Here we require that the total integrated probability is conserved. This yields a fundamental solution which, when appropriate, contains a term proportional to a Dirac delta function at the boundary. We determine the fundamental solution directly from the diffusion equation via spectral decomposition. We obtain exact expressions for the eigenfunctions, and when the fundamental solution contains a Dirac delta function at the boundary, every eigenfunction of the forward diffusion operator contains a delta function. We show how these combine to produce a weight of the delta function at the boundary which ensures the total integrated probability is conserved. The solution we present covers cases where parameters are time dependent, thereby greatly extending its applicability.

Maldives. Package on population education for special interest groups developed.

PubMed

1995-01-01

The Population Education Program of the Non-Formal Education Center has developed a package of Population Education for Special Interest Groups comprising a learning package and fieldworker's guide. The learning package is especially developed for teaching population education for out-of-school populations. Special interest groups in Maldives include newly married couples, adolescents, and working youth. Produced under the guidance of UNESCO, Bangkok, the package contains 36 different materials such as posters, charts, leaflets, booklets, stories, and illustrated booklets which may be taught in 36 to 45 periods. The materials deal with eight themes, namely, family size and family welfare, population and resources, delayed marriage and parenthood, responsible parenthood, population-related values and beliefs, women in development, AIDS/STD, and respect for old people. Accompanying the learning package is the fieldworker's guide used to teach the package. It contains individual guides for each of the 36 learning materials. The guide gives the titles of the materials, format, objectives of the materials, messages, target groups, and an overview of the content of each learning materials. The methodologies used for teaching the learning materials include role playing, group discussion, questioning, brainstorming, survey, creative writing, problem-solving and evaluation. The package will be used by fieldworkers to conduct island-based population education courses. full text

Analysis of Eigenvalue and Eigenfunction of Klein Gordon Equation Using Asymptotic Iteration Method for Separable Non-central Cylindrical Potential

NASA Astrophysics Data System (ADS)

Suparmi, A.; Cari, C.; Lilis Elviyanti, Isnaini

2018-04-01

Analysis of relativistic energy and wave function for zero spin particles using Klein Gordon equation was influenced by separable noncentral cylindrical potential was solved by asymptotic iteration method (AIM). By using cylindrical coordinates, the Klein Gordon equation for the case of symmetry spin was reduced to three one-dimensional Schrodinger like equations that were solvable using variable separation method. The relativistic energy was calculated numerically with Matlab software, and the general unnormalized wave function was expressed in hypergeometric terms.

Modal Ring Method for the Scattering of Electromagnetic Waves

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1993-01-01

The modal ring method for electromagnetic scattering from perfectly electric conducting (PEC) symmetrical bodies is presented. The scattering body is represented by a line of finite elements (triangular) on its outer surface. The infinite computational region surrounding the body is represented analytically by an eigenfunction expansion. The modal ring method effectively reduces the two dimensional scattering problem to a one-dimensional problem similar to the method of moments. The modal element method is capable of handling very high frequency scattering because it has a highly banded solution matrix.

Coherent States for the Two-Dimensional Dirac-Moshinsky Oscillator Coupled to an External Magnetic Field

NASA Astrophysics Data System (ADS)

Ojeda-Guillén, D.; Mota, R. D.; Granados, V. D.

2015-03-01

We show that the (2+1)-dimensional Dirac-Moshinsky oscillator coupled to an external magnetic field can be treated algebraically with the SU(1,1) group theory and its group basis. We use the su(1,1) irreducible representation theory to find the energy spectrum and the eigenfunctions. Also, with the su(1,1) group basis we construct the relativistic coherent states in a closed form for this problem. Supported by SNI-México, COFAA-IPN, EDI-IPN, EDD-IPN, SIP-IPN project number 20140598

Saturation of Alfvén modes in tokamaks

DOE PAGES

White, Roscoe; Gorelenkov, Nikolai; Gorelenkova, Marina; ...

2016-09-20

Here, the growth of Alfvén modes driven unstable by a distribution of high energy particles up to saturation is investigated with a guiding center code, using numerical eigenfunctions produced by linear theory and a numerical high energy particle distribution, in order to make detailed comparison with experiment and with models for saturation amplitudes and the modification of beam profiles. Two innovations are introduced. First, a very noise free means of obtaining the mode-particle energy and momentum transfer is introduced, and secondly, a spline representation of the actual beam particle distribution is used.

Variability of quasi-stationary planetary waves

NASA Technical Reports Server (NTRS)

Krivolutsky, A. A.; Petushkov, N. D.; Tarasenko, D. A.

1989-01-01

The results of the analysis of nonzonal perturbations (m = 1, 2, 3) of the geopotential field at a 30 mb level are presented. A long period modulation of the harmonics' amplitude is discovered. Calculations of eigenfunctions and eigennumbers of the Laplace tidal equation are carried out for a real latitudinal wind profile. The observed first zonal harmonic in different years is caused by the same mode. Thus, the difference in the wave amplitudes could not be accounted for by the difference in stratospheric zonal circulation in different years and should be related to tropospheric processes.

On the Discrete Spectrum of the Nonstationary Schrödinger Equation and Multipole Lumps of the Kadomtsev-Petviashvili I Equation

NASA Astrophysics Data System (ADS)

Villarroel, Javier; Ablowitz, Mark J.

The discrete spectrum of the nonstationary Schrödinger equation and localized solutions of the Kadomtsev-Petviashvili-I (KPI) equation are studied via the inverse scattering transform. It is shown that there exist infinitely many real and rationally decaying potentials which correspond to a discrete spectrum whose related eigenfunctions have multiple poles in the spectral parameter. An index or winding number is asssociated with each of these solutions. The resulting localized solutions of KPI behave as collection of individual humps with nonuniform dynamics.

Shannon entropy and avoided crossings in closed and open quantum billiards

NASA Astrophysics Data System (ADS)

Park, Kyu-Won; Moon, Songky; Shin, Younghoon; Kim, Jinuk; Jeong, Kabgyun; An, Kyungwon

2018-06-01

The relation between Shannon entropy and avoided crossings is investigated in dielectric microcavities. The Shannon entropy of the probability density for eigenfunctions in an open elliptic billiard as well as a closed quadrupole billiard increases as the center of the avoided crossing is approached. These results are opposite to those of atomic physics for electrons. It is found that the collective Lamb shift of the open quantum system and the symmetry breaking in the closed chaotic quantum system have equivalent effects on the Shannon entropy.

Long Time Quantum Evolution of Observables on Cusp Manifolds

NASA Astrophysics Data System (ADS)

Bonthonneau, Yannick

2016-04-01

The Eisenstein functions {E(s)} are some generalized eigenfunctions of the Laplacian on manifolds with cusps. We give a version of Quantum Unique Ergodicity for them, for {|{I}s| to ∞} and {R}s to d/2} with {{R}s - d/2 ≥ log log |{I}s| / log |{I}s|}. For the purpose of the proof, we build a semi-classical quantization procedure for finite volume manifolds with hyperbolic cusps, adapted to a geometrical class of symbols. We also prove an Egorov Lemma until Ehrenfest times on such manifolds.

Saturation of Alfvén modes in tokamaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

White, Roscoe; Gorelenkov, Nikolai; Gorelenkova, Marina

Here, the growth of Alfvén modes driven unstable by a distribution of high energy particles up to saturation is investigated with a guiding center code, using numerical eigenfunctions produced by linear theory and a numerical high energy particle distribution, in order to make detailed comparison with experiment and with models for saturation amplitudes and the modification of beam profiles. Two innovations are introduced. First, a very noise free means of obtaining the mode-particle energy and momentum transfer is introduced, and secondly, a spline representation of the actual beam particle distribution is used.

Coherent forward scattering as a signature of Anderson metal-insulator transitions

NASA Astrophysics Data System (ADS)

Ghosh, Sanjib; Miniatura, Christian; Cherroret, Nicolas; Delande, Dominique

2017-04-01

We show that the coherent forward scattering (CFS) interference peak amplitude sharply jumps from zero to a finite value upon crossing a metal-insulator transition. Extensive numerical simulations reveal that the CFS peak contrast obeys the one-parameter scaling hypothesis and gives access to the critical exponents of the transition. We also discover that the critical CFS peak directly controls the spectral compressibility at the transition where eigenfunctions are multifractal, and we demonstrate the universality of this property with respect to various types of disorder.

Eigenvalues of the Wentzell-Laplace operator and of the fourth order Steklov problems

NASA Astrophysics Data System (ADS)

Xia, Changyu; Wang, Qiaoling

2018-05-01

We prove a sharp upper bound and a lower bound for the first nonzero eigenvalue of the Wentzell-Laplace operator on compact manifolds with boundary and an isoperimetric inequality for the same eigenvalue in the case where the manifold is a bounded domain in a Euclidean space. We study some fourth order Steklov problems and obtain isoperimetric upper bound for the first eigenvalue of them. We also find all the eigenvalues and eigenfunctions for two kind of fourth order Steklov problems on a Euclidean ball.

Use of asymptotic methods in vibration analysis

NASA Technical Reports Server (NTRS)

Ashley, H.

1978-01-01

The derivation of dynamic differential equations, suitable for studying the vibrations of rotating, curved, slender structures was examined, and the Hamiltonian procedure was advocated for this purpose. Various reductions of the full system are displayed, which govern the vibrating troposkien when various order of magnitude restrictions are placed on important parameters. Possible advantages of the WKB asymptotic method for solving these classes of problems are discussed. A special case of this method is used illustratively to calculate eigenvalues and eigenfunctions for a flat turbine blade with small flexural stiffness.

The Stability and Interfacial Motion of Multi-layer Radial Porous Media and Hele-Shaw Flows

NASA Astrophysics Data System (ADS)

Gin, Craig; Daripa, Prabir

2017-11-01

In this talk, we will discuss viscous fingering instabilities of multi-layer immiscible porous media flows within the Hele-Shaw model in a radial flow geometry. We study the motion of the interfaces for flows with both constant and variable viscosity fluids. We consider the effects of using a variable injection rate on multi-layer flows. We also present a numerical approach to simulating the interface motion within linear theory using the method of eigenfunction expansion. We compare these results with fully non-linear simulations.

On the complexity of turbulence near a wall

NASA Technical Reports Server (NTRS)

Moin, Parviz

1992-01-01

Some measures of the intrinsic complexity of the near wall turbulence are reviewed. The number of modes required in an 'optimal' eigenfunction expansion is compared with the dimension obtained from the calculation of Liapunov exponents. These measures are of the same order, but they are very large. It is argued that the basic building block element of the near wall turbulence can be isolated in a small region of space (minimal flow unit). When the size of the domain is taken into account, the dimension becomes more manageable.

Spin eigenmodes of magnetic skyrmions and the problem of the effective skyrmion mass

NASA Astrophysics Data System (ADS)

Kravchuk, Volodymyr P.; Sheka, Denis D.; Rößler, Ulrich K.; van den Brink, Jeroen; Gaididei, Yuri

2018-02-01

The properties of magnon modes localized on a ferromagnetic skyrmion are studied. Mode eigenfrequencies display three types of asymptotic behavior for large skyrmion radius Rs, namely, ω0∝Rs-2 for the breathing mode and ω-|μ |∝Rs-1 and ω|μ |∝Rs-3 for modes with negative and positive azimuthal quantum numbers, respectively. A number of properties of the magnon eigenfunctions are determined. This enables us to demonstrate that the skyrmion dynamics for a traveling-wave ansatz obeys the massless Thiele equation.

An outflow boundary condition for aeroacoustic computations

NASA Technical Reports Server (NTRS)

Hayder, M. Ehtesham; Hagstrom, Thomas

1995-01-01

A formulation of boundary condition for flows with small disturbances is presented. The authors test their methodology in an axisymmetric jet flow calculation, using both the Navier-Stokes and Euler equations. Solutions in the far field are assumed to be oscillatory. If the oscillatory disturbances are small, the growth of the solution variables can be predicted by linear theory. Eigenfunctions of the linear theory are used explicitly in the formulation of the boundary conditions. This guarantees correct solutions at the boundary in the limit where the predictions of linear theory are valid.

Acoustics-turbulence interaction

NASA Technical Reports Server (NTRS)

Hussain, A. K. M. F.; Zaman, K. B. M. O.

1977-01-01

An investigation of the instability frequency was undertaken. Measurements revealed that the hot wire probe induces and sustains stable upstream oscillation of the free shear layer. The characteristics of the free shear layer tone are found to be different from the slit jet wedge edgetone phenomenon. The shear tone induced by a plane wedge in a plane free shear layer was then examined in order to further document the phenomenon. The eigenvalues and eigenfunctions of the tone fundamental show agreement with the spatial stability theory. A comprehensive summary of the results is also included.

Data-Driven Model Reduction and Transfer Operator Approximation

NASA Astrophysics Data System (ADS)

Klus, Stefan; Nüske, Feliks; Koltai, Péter; Wu, Hao; Kevrekidis, Ioannis; Schütte, Christof; Noé, Frank

2018-06-01

In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to approximate transfer operators and their eigenvalues, eigenfunctions, and eigenmodes. The goal is to point out similarities and differences between methods developed independently by the dynamical systems, fluid dynamics, and molecular dynamics communities such as time-lagged independent component analysis, dynamic mode decomposition, and their respective generalizations. As a result, extensions and best practices developed for one particular method can be carried over to other related methods.

Study of electron-related intersubband optical properties in three coupled quantum wells wires with triangular transversal section

NASA Astrophysics Data System (ADS)

Tiutiunnyk, A.; Tulupenko, V.; Akimov, V.; Demediuk, R.; Morales, A. L.; Mora-Ramos, M. E.; Radu, A.; Duque, C. A.

2015-11-01

This work concerns theoretical study of confined electrons in a low-dimensional structure consisting of three coupled triangular GaAs/AlxGa1-xAs quantum wires. Calculations have been made in the effective mass and parabolic band approximations. In the calculations a diagonalization method to find the eigenfunctions and eigenvalues of the Hamiltonian was used. A comparative analysis of linear and nonlinear optical absorption coefficients and the relative change in the refractive index was made, which is tied to the intersubband electron transitions.

Scattering of Dirac waves off Kerr black holes

NASA Astrophysics Data System (ADS)

Chakrabarti, Sandip K.; Mukhopadhyay, Banibrata

2000-10-01

Chandrasekhar separated the Dirac equation for spinning and massive particles in Kerr geometry into radial and angular parts. Here we solve the complete wave equation and find out how the Dirac wave scatters off Kerr black holes. The eigenfunctions, eigenvalues and reflection and transmission co-efficients are computed. We compare the solutions with several parameters to show how a spinning black hole recognizes the mass and energy of incoming waves. Very close to the horizon the solutions become independent of the particle parameters, indicating the universality of the behaviour.

Group level effects of social versus individual learning.

PubMed

Jost, Jürgen; Li, Wei

2013-06-01

We study the effects of learning by imitating others within the framework of an iterated game in which the members of two complementary populations interact via random pairing at each round. This allows us to compare both the fitness of different strategies within a population and the performance of populations in which members have access to different types of strategies. Previous studies reveal some emergent dynamics at the population level, when players learn individually. We here investigate a different mechanism in which players can choose between two different learning strategies, individual or social. Imitating behavior can spread within a mixed population, with the frequency of imitators varying over generation time. When compared to a pure population with solely individual learners, a mixed population with both individual and social learners can do better, independently of the precise learning scheme employed. We can then search for the best imitating strategy. Imitating the neighbor with the highest payoff turns out to be consistently superior. This is in agreement with findings in experimental and model studies that have been carried out in different settings.

Social learning and human mate preferences: a potential mechanism for generating and maintaining between-population diversity in attraction

PubMed Central

Little, Anthony C.; Jones, Benedict C.; DeBruine, Lisa M.; Caldwell, Christine A.

2011-01-01

Inspired by studies demonstrating mate-choice copying effects in non-human species, recent studies of attractiveness judgements suggest that social learning also influences human preferences. In the first part of our article, we review evidence for social learning effects on preferences in humans and other animals. In the second part, we present new empirical evidence that social learning not only influences the attractiveness of specific individuals, but can also generalize to judgements of previously unseen individuals possessing similar physical traits. The different conditions represent different populations and, once a preference arises in a population, social learning can lead to the spread of preferences within that population. In the final part of our article, we discuss the theoretical basis for, and possible impact of, biases in social learning whereby individuals may preferentially copy the choices of those with high status or better access to critical information about potential mates. Such biases could mean that the choices of a select few individuals carry the greatest weight, rapidly generating agreement in preferences within a population. Collectively, these issues suggest that social learning mechanisms encourage the spread of preferences for certain traits once they arise within a population and so may explain certain cross-cultural differences. PMID:21199841

Incremental Learning With Selective Memory (ILSM): Towards Fast Prostate Localization for Image Guided Radiotherapy

PubMed Central

Gao, Yaozong; Zhan, Yiqiang

2015-01-01

Image-guided radiotherapy (IGRT) requires fast and accurate localization of the prostate in 3-D treatment-guided radiotherapy, which is challenging due to low tissue contrast and large anatomical variation across patients. On the other hand, the IGRT workflow involves collecting a series of computed tomography (CT) images from the same patient under treatment. These images contain valuable patient-specific information yet are often neglected by previous works. In this paper, we propose a novel learning framework, namely incremental learning with selective memory (ILSM), to effectively learn the patient-specific appearance characteristics from these patient-specific images. Specifically, starting with a population-based discriminative appearance model, ILSM aims to “personalize” the model to fit patient-specific appearance characteristics. The model is personalized with two steps: backward pruning that discards obsolete population-based knowledge and forward learning that incorporates patient-specific characteristics. By effectively combining the patient-specific characteristics with the general population statistics, the incrementally learned appearance model can localize the prostate of a specific patient much more accurately. This work has three contributions: 1) the proposed incremental learning framework can capture patient-specific characteristics more effectively, compared to traditional learning schemes, such as pure patient-specific learning, population-based learning, and mixture learning with patient-specific and population data; 2) this learning framework does not have any parametric model assumption, hence, allowing the adoption of any discriminative classifier; and 3) using ILSM, we can localize the prostate in treatment CTs accurately (DSC ∼0.89) and fast (∼4 s), which satisfies the real-world clinical requirements of IGRT. PMID:24495983

Evolution of social versus individual learning in a subdivided population revisited: comparative analysis of three coexistence mechanisms using the inclusive-fitness method.

PubMed

Kobayashi, Yutaka; Ohtsuki, Hisashi

2014-03-01

Learning abilities are categorized into social (learning from others) and individual learning (learning on one's own). Despite the typically higher cost of individual learning, there are mechanisms that allow stable coexistence of both learning modes in a single population. In this paper, we investigate by means of mathematical modeling how the effect of spatial structure on evolutionary outcomes of pure social and individual learning strategies depends on the mechanisms for coexistence. We model a spatially structured population based on the infinite-island framework and consider three scenarios that differ in coexistence mechanisms. Using the inclusive-fitness method, we derive the equilibrium frequency of social learners and the genetic load of social learning (defined as average fecundity reduction caused by the presence of social learning) in terms of some summary statistics, such as relatedness, for each of the three scenarios and compare the results. This comparative analysis not only reconciles previous models that made contradictory predictions as to the effect of spatial structure on the equilibrium frequency of social learners but also derives a simple mathematical rule that determines the sign of the genetic load (i.e. whether or not social learning contributes to the mean fecundity of the population). Copyright © 2013 Elsevier Inc. All rights reserved.

With Educational Benefits for All: Campus Inclusion through Learning Communities Designed for Underserved Student Populations

ERIC Educational Resources Information Center

Fink, John E.; Hummel, Mary L.

2015-01-01

This chapter explores the practices of learning communities designed for specific, underserved student populations, highlighting on-campus examples and culminating with a synthesized list of core practices from these "inclusive" learning communities.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev, , Dr.

2017-10-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ω_i while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev, , Dr.

2017-09-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ωi while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev

2017-11-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ωi while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

Streak instability and generation of hairpin-vortices by a slotted jet in channel crossflow: Experiments and linear stability analysis

NASA Astrophysics Data System (ADS)

Philip, Jimmy; Karp, Michael; Cohen, Jacob

2016-01-01

Streaks and hairpin-vortices are experimentally generated in a laminar plane Poiseuille crossflow by injecting a continuous jet through a streamwise slot normal to the crossflow, with air as the working media. Small disturbances form stable streaks, however, higher disturbances cause the formation of streaks which undergo instability leading to the generation of hairpin vortices. Particular emphasis is placed on the flow conditions close to the generation of hairpin-vortices. Measurements are carried out in the cases of natural and phase-locked disturbance employing smoke visualisation, particle image velocimetry, and hot-wire anemometry, which include, the dominant frequency, wavelength, and the disturbance shape (or eigenfunctions) associated with the coherent part of the velocity field. A linear stability analysis for both one- and two-dimensional base-flows is carried out to understand the mechanism of instability and good agreement of wavelength and eigenfunctions are obtained when compared to the experimental data, and a slight under-prediction of the growth-rates by the linear stability analysis consistent with the final nonlinear stages in transitional flows. Furthermore, an energy analysis for both the temporal and spatial stability analysis revels the dominance of the symmetric varicose mode, again, in agreement with the experiments, which is found to be governed by the balance of the wallnormal shear and dissipative effects rather than the spanwise shear. In all cases the anti-symmetric sinuous modes governed by the spanwise shear are found to be damped both in analysis and in our experiments.

EIGENMODES OF THREE-DIMENSIONAL MAGNETIC ARCADES IN THE SUN’S CORONA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hindman, Bradley W.; Jain, Rekha, E-mail: hindman@solarz.colorado.edu

We develop a model of coronal-loop oscillations that treats the observed bright loops as an integral part of a larger three-dimensional (3D) magnetic structure comprised of the entire magnetic arcade. We demonstrate that magnetic arcades within the solar corona can trap MHD fast waves in a 3D waveguide. This is accomplished through the construction of a cylindrically symmetric model of a magnetic arcade with a potential magnetic field. For a magnetically dominated plasma, we derive a governing equation for MHD fast waves and from this equation we show that the magnetic arcade forms a 3D waveguide if the Alfvén speedmore » increases monotonically beyond a fiducial radius. Both magnetic pressure and tension act as restoring forces, instead of just tension as is generally assumed in 1D models. Since magnetic pressure plays an important role, the eigenmodes involve propagation both parallel and transverse to the magnetic field. Using an analytic solution, we derive the specific eigenfrequencies and eigenfunctions for an arcade possessing a discontinuous density profile. The discontinuity separates a diffuse cylindrical cavity and an overlying shell of denser plasma that corresponds to the bright loops. We emphasize that all of the eigenfunctions have a discontinuous axial velocity at the density interface; hence, the interface can give rise to the Kelvin–Helmholtz instability. Further, we find that all modes have elliptical polarization with the degree of polarization changing with height. However, depending on the line of sight, only one polarization may be clearly visible.« less

INTRODUCING CAFein, A NEW COMPUTATIONAL TOOL FOR STELLAR PULSATIONS AND DYNAMIC TIDES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Valsecchi, F.; Farr, W. M.; Willems, B.

2013-08-10

Here we present CAFein, a new computational tool for investigating radiative dissipation of dynamic tides in close binaries and of non-adiabatic, non-radial stellar oscillations in isolated stars in the linear regime. For the latter, CAFein computes the non-adiabatic eigenfrequencies and eigenfunctions of detailed stellar models. The code is based on the so-called Riccati method, a numerical algorithm that has been successfully applied to a variety of stellar pulsators, and which does not suffer from the major drawbacks of commonly used shooting and relaxation schemes. Here we present an extension of the Riccati method to investigate dynamic tides in close binaries.more » We demonstrate CAFein's capabilities as a stellar pulsation code both in the adiabatic and non-adiabatic regimes, by reproducing previously published eigenfrequencies of a polytrope, and by successfully identifying the unstable modes of a stellar model in the {beta} Cephei/SPB region of the Hertzsprung-Russell diagram. Finally, we verify CAFein's behavior in the dynamic tides regime by investigating the effects of dynamic tides on the eigenfunctions and orbital and spin evolution of massive main sequence stars in eccentric binaries, and of hot Jupiter host stars. The plethora of asteroseismic data provided by NASA's Kepler satellite, some of which include the direct detection of tidally excited stellar oscillations, make CAFein quite timely. Furthermore, the increasing number of observed short-period detached double white dwarfs (WDs) and the observed orbital decay in the tightest of such binaries open up a new possibility of investigating WD interiors through the effects of tides on their orbital evolution.« less

Identifying Social Learning in Animal Populations: A New ‘Option-Bias’ Method

PubMed Central

Kendal, Rachel L.; Kendal, Jeremy R.; Hoppitt, Will; Laland, Kevin N.

2009-01-01

Background Studies of natural animal populations reveal widespread evidence for the diffusion of novel behaviour patterns, and for intra- and inter-population variation in behaviour. However, claims that these are manifestations of animal ‘culture’ remain controversial because alternative explanations to social learning remain difficult to refute. This inability to identify social learning in social settings has also contributed to the failure to test evolutionary hypotheses concerning the social learning strategies that animals deploy. Methodology/Principal Findings We present a solution to this problem, in the form of a new means of identifying social learning in animal populations. The method is based on the well-established premise of social learning research, that - when ecological and genetic differences are accounted for - social learning will generate greater homogeneity in behaviour between animals than expected in its absence. Our procedure compares the observed level of homogeneity to a sampling distribution generated utilizing randomization and other procedures, allowing claims of social learning to be evaluated according to consensual standards. We illustrate the method on data from groups of monkeys provided with novel two-option extractive foraging tasks, demonstrating that social learning can indeed be distinguished from unlearned processes and asocial learning, and revealing that the monkeys only employed social learning for the more difficult tasks. The method is further validated against published datasets and through simulation, and exhibits higher statistical power than conventional inferential statistics. Conclusions/Significance The method is potentially a significant technological development, which could prove of considerable value in assessing the validity of claims for culturally transmitted behaviour in animal groups. It will also be of value in enabling investigation of the social learning strategies deployed in captive and natural animal populations. PMID:19657389

Learning Experiences in Population Education. Population Education Programme Service, Volume 3. For the Non-Formal Education System.

ERIC Educational Resources Information Center

United Nations Educational, Scientific, and Cultural Organization, Bangkok (Thailand). Regional Office for Education in Asia and the Pacific.

One of the main products of the Regional Workshop for the Development of Packages of Adequate Learning Requirements in Population is this prototype package of curriculum materials in population education. The workshop notes that one of the shortcomings of country programs in population education is that the content integrated in school subjects is…

The infinite well and Dirac delta function potentials as pedagogical, mathematical and physical models in quantum mechanics

NASA Astrophysics Data System (ADS)

Belloni, M.; Robinett, R. W.

2014-07-01

The infinite square well and the attractive Dirac delta function potentials are arguably two of the most widely used models of one-dimensional bound-state systems in quantum mechanics. These models frequently appear in the research literature and are staples in the teaching of quantum theory on all levels. We review the history, mathematical properties, and visualization of these models, their many variations, and their applications to physical systems. For the ISW and the attractive DDF potentials, Eq. (4) implies, as expected, that energy eigenfunctions will have a kink-a discontinuous first derivative at the location of the infinite jump(s) in the potentials. However, the large |p| behavior of the momentum-space energy eigenfunction given by Eq. (5) will be |ϕ(p)|∝1/p2. Therefore for the ISW and the attractive DDF potentials, expectation value of p will be finite, but even powers of p higher than 2 will not lead to convergent integrals. This analysis proves that despite the kinks in the ISW and attractive DDF eigenfunctions, is finite, and therefore yield appropriate solutions to the Schrödinger equation.The existence of power-law ‘tails’ of a momentum distribution as indicated in Eq. (5) in the case of ‘less than perfect’ potentials [41], including a 1/p2 power-law dependence for a singular potential (such as the DDF form) may seem a mathematical artifact, but we note two explicit realizations of exactly this type of behavior in well-studied quantum systems.As noted below (in Section 6.2) the momentum-space energy eigenfunction of the ground state of one of the most familiar (and singular) potentials, namely that of the Coulomb problem, is given by ϕ1,0,0(p)=√{8p0/π}p0/2 where p0=ħ/a0 with a0 the Bohr radius. This prediction for the p-dependence of the hydrogen ground state momentum-space distribution was verified by Weigold [42] and collaborators with measurements taken out to p-values beyond 1.4p0; well out onto the power-law ‘tail’.More recently, Tan [43] and others [44,45] have noted that for condensed matter or atomic systems with a large scattering length, so that the short-range interactions can actually be modeled as singular δ-functions, the momentum distribution also exhibits a large momentum ‘tail’ which falls off as C/k4. The constant of proportionality, C (or contact as it has come to be known), encodes important information on the microscopic physics, in much the way that the constants in Eq. (5) are related to the details of the 1D potential. In fact, in one review [46] of these developments, this connection has been described as “How the tail wags the dog in ultracold atomic gases”. Just as with the H-atom momentum distribution, experiments have verified this power-law behavior for both fermion [47,48] and more recently Bose systems [49].It is these connections, namely of exemplary results derived in simpler one-dimensional systems such as the ISW and DDF potentials which find parallels in more fundamental physical realizations, that motivate us to review many of the basic mathematical and physical results of these two ‘benchmark’ model potentials. We hope that both students and instructors alike involved in advanced undergraduate and graduate courses in quantum mechanics will find this survey useful. We trust that it will aid readers in exploring a wide array of physical effects, using rigorous mathematical methods, in the context of familiar one-dimensional systems, making use of otherwise hard-to-find results.

Learning Disabilities Research: Defining Populations.

ERIC Educational Resources Information Center

Lovitt, Thomas C.; Jenkins, Joseph R.

1979-01-01

The article emphasizes the need for a uniform format for defining the populations selected for research, particularly with learning disabled individuals. The population descriptions from three studies dealing with some aspect of reading are presented and scrutinized in terms of the four categories. (Author/DLS)

Comment on: Diffusion through a slab

NASA Astrophysics Data System (ADS)

Gieseler, U. D. J.; Kirk, J. G.

1997-05-01

Mahan [J. Math. Phys. 36, 6758 (1995)] has calculated the transmission coefficient and angular distribution of particles which enter a thick slab at normal incidence and which diffuse in the slab with linear anisotropic, non-absorbing, scattering. Using orthogonality relations derived by McCormick and Kuščer [J. Math. Phys. 6, 1939 (1965); 7, 2036 (1966)] for the eigenfunctions of the problem, this calculation is generalized to a boundary condition with particle input at arbitrary angles. It is also shown how to use the orthogonality relations to relax in a simple way the restriction to a thick slab.

Prediction of nonlinear evolution character of energetic-particle-driven instabilities

DOE PAGES

Duarte, Vinicius N.; Berk, H. L.; Gorelenkov, N. N.; ...

2017-03-17

A general criterion is proposed and found to successfully predict the emergence of chirping oscillations of unstable Alfvénic eigenmodes in tokamak plasma experiments. The model includes realistic eigenfunction structure, detailed phase-space dependences of the instability drive, stochastic scattering and the Coulomb drag. The stochastic scattering combines the effects of collisional pitch angle scattering and micro-turbulence spatial diffusion. Furthermore, the latter mechanism is essential to accurately identify the transition between the fixed-frequency mode behavior and rapid chirping in tokamaks and to resolve the disparity with respect to chirping observation in spherical and conventional tokamaks.

Observations on the Proper Orthogonal Decomposition

NASA Technical Reports Server (NTRS)

Berkooz, Gal

1992-01-01

The Proper Orthogonal Decomposition (P.O.D.), also known as the Karhunen-Loeve expansion, is a procedure for decomposing a stochastic field in an L(2) optimal sense. It is used in diverse disciplines from image processing to turbulence. Recently the P.O.D. is receiving much attention as a tool for studying dynamics of systems in infinite dimensional space. This paper reviews the mathematical fundamentals of this theory. Also included are results on the span of the eigenfunction basis, a geometric corollary due to Chebyshev's inequality and a relation between the P.O.D. symmetry and ergodicity.

Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fillion-Gourdeau, F., E-mail: filliong@CRM.UMontreal.ca; Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4; Lorin, E., E-mail: elorin@math.carleton.ca

2016-02-15

A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron–molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic balanced basis, which allows for an efficient and accurate determination of the Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain high accuracy. This numerical method is used to compute the energy spectrum of the two-center problem and then the evolution of eigenstate wavefunctions in an external electromagnetic field.

Asymptotic Behaviour of the Ground State of Singularly Perturbed Elliptic Equations

NASA Astrophysics Data System (ADS)

Piatnitski, Andrey L.

The ground state of a singularly perturbed nonselfadjoint elliptic operator defined on a smooth compact Riemannian manifold with metric aij(x)=(aij(x))-1, is studied. We investigate the limiting behaviour of the first eigenvalue of this operator as μ goes to zero, and find the logarithmic asymptotics of the first eigenfunction everywhere on the manifold. The results are formulated in terms of auxiliary variational problems on the manifold. This approach also allows to study the general singularly perturbed second order elliptic operator on a bounded domain in Rn.

Equivalences of the multi-indexed orthogonal polynomials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Odake, Satoru

2014-01-15

Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion. Multi-indexed orthogonal polynomials are labeled by a set of degrees of polynomial parts of virtual state wavefunctions. For multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson, and Askey-Wilson types, two different index sets may give equivalent multi-indexed orthogonal polynomials. We clarify these equivalences. Multi-indexed orthogonal polynomials with both type I and II indices are proportional to those of type I indices only (or type II indices only) with shifted parameters.

Prediction of nonlinear evolution character of energetic-particle-driven instabilities

NASA Astrophysics Data System (ADS)

Duarte, V. N.; Berk, H. L.; Gorelenkov, N. N.; Heidbrink, W. W.; Kramer, G. J.; Nazikian, R.; Pace, D. C.; Podestà, M.; Tobias, B. J.; Van Zeeland, M. A.

2017-05-01

A general criterion is proposed and found to successfully predict the emergence of chirping oscillations of unstable Alfvénic eigenmodes in tokamak plasma experiments. The model includes realistic eigenfunction structure, detailed phase-space dependences of the instability drive, stochastic scattering and the Coulomb drag. The stochastic scattering combines the effects of collisional pitch angle scattering and micro-turbulence spatial diffusion. The latter mechanism is essential to accurately identify the transition between the fixed-frequency mode behavior and rapid chirping in tokamaks and to resolve the disparity with respect to chirping observation in spherical and conventional tokamaks.

Free-stream disturbance, continuous Eigenfunctions, boundary-layer instability and transition

NASA Technical Reports Server (NTRS)

Grosch, C. E.

1980-01-01

A rational foundation is presented for the application of the linear shear flows to transition prediction, and an explicit method is given for carrying out the necessary calculations. The expansions used are shown to be complete. Sample calculations show that a typical boundary layer is very sensitive to vorticity disturbances in the inner boundary layer, near the critical layer. Vorticity disturbances three or four boundary layer thicknesses above the boundary are nearly uncoupled from the boundary layer in that the amplitudes of the discrete Tollmien-Schlicting waves are an extremely small fraction of the amplitude of the disturbance.

Swings and roundabouts: optical Poincaré spheres for polarization and Gaussian beams

NASA Astrophysics Data System (ADS)

Dennis, M. R.; Alonso, M. A.

2017-02-01

The connection between Poincaré spheres for polarization and Gaussian beams is explored, focusing on the interpretation of elliptic polarization in terms of the isotropic two-dimensional harmonic oscillator in Hamiltonian mechanics, its canonical quantization and semiclassical interpretation. This leads to the interpretation of structured Gaussian modes, the Hermite-Gaussian, Laguerre-Gaussian and generalized Hermite-Laguerre-Gaussian modes as eigenfunctions of operators corresponding to the classical constants of motion of the two-dimensional oscillator, which acquire an extra significance as families of classical ellipses upon semiclassical quantization. This article is part of the themed issue 'Optical orbital angular momentum'.

Dirac oscillator interacting with a topological defect

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carvalho, J.; Furtado, C.; Moraes, F.

In this work we study the interaction problem of a Dirac oscillator with gravitational fields produced by topological defects. The energy levels of the relativistic oscillator in the cosmic string and in the cosmic dislocation space-times are sensible to curvature and torsion associated to these defects and are important evidence of the influence of the topology on this system. In the presence of a localized magnetic field the energy levels acquire a term associated with the Aharonov-Bohm effect. We obtain the eigenfunctions and eigenvalues and see that in the nonrelativistic limit some results known in standard quantum mechanics are reached.

Analysis of the experimental level scheme of {sup 61}Cu using computational technique

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gupta, Anuradha, E-mail: annu1gupta1@gmail.com; Verma, Preeti, E-mail: preetiverma130587@gmail.com; Bharti, Arun, E-mail: arunbharti-2003@yahoo.co.in

2015-08-28

The high-spin structure in {sup 61}Cu nucleus is studied in terms of effective two body interaction. In order to take into account the deformed BCS basis, the basis states are expanded in terms of the core eigenfunctions. Yrast band with some other bands havew been obtained and back-bending in moment of inertia has also been calculated and compared with the available experimental data for {sup 61}Cu nucleus. On comparing the available experimental as well as other theoretical data, it is found that the treatment with PSM provides a satisfactory explanation of the available data.

Wentzel-Kramers-Brillouin method in the Bargmann representation. [of quantum mechanics

NASA Technical Reports Server (NTRS)

Voros, A.

1989-01-01

It is demonstrated that the Bargmann representation of quantum mechanics is ideally suited for semiclassical analysis, using as an example the WKB method applied to the bound-state problem in a single well of one degree of freedom. For the harmonic oscillator, this WKB method trivially gives the exact eigenfunctions in addition to the exact eigenvalues. For an anharmonic well, a self-consistent variational choice of the representation greatly improves the accuracy of the semiclassical ground state. Also, a simple change of scale illuminates the relationship of semiclassical versus linear perturbative expansions, allowing a variety of multidimensional extensions.

Nonadiabatic Eigenfunctions Can Have Amplitude, Signed Conical Nodes, or Signed Higher Order Nodes at a Conical Intersection with Circular Symmetry (Open Access Publisher’s Version)

DTIC Science & Technology

2017-09-26

for asymmetric vibrations, I ̂ = |x⟩⟨x| + |y⟩ ⟨y| is the electronic identity operator, and d is the vibrational displacement . The first line is an...positive displacement d in eq 4 gives the Jahn−Teller effect on a particle in a square 2D box46−48 expected from the Hellmann−Feynman theorem.49 The...and 3/2, all of which involve larger displacements than in Table 1. ■ RESULTS Figure 2 provides a complete characterization of the 12 lowest

MHD thermal instabilities in cool inhomogeneous atmospheres

NASA Technical Reports Server (NTRS)

Bodo, G.; Ferrari, A.; Massaglia, S.; Rosner, R.

1983-01-01

The formation of a coronal state in a stellar atmosphere is investigated. A numerical code is used to study the effects of atmospheric gradients and finite loop dimension on the scale of unstable perturbations, solving for oscillatory perturbations as eigenfunctions of a boundary value problem. The atmosphere is considered as initially isothermal, with density and pressure having scale heights fixed by the hydrostatic equations. Joule mode instability is found to be an efficient mechanism for current filamentation and subsequent heating in initially cool atmospheres. This instability is mainly effective at the top of magnetic loops and is not suppressed by thermal conduction.

On the Analytical and Numerical Properties of the Truncated Laplace Transform II

DTIC Science & Technology

2015-05-29

La,b)∗ ◦ La,b) (un)) (t) = ∫ b a 1 t+ s un(s)ds = α 2 nun (t). (32) Similarly, the left singular functions vn of La,b are eigenfunctions of the...odd in the sense that Un(s) = (−1) nUn (−s). (83) 3.5 Decay of the coefficients Since the left singular function vn (defined in (27)) is a smooth...is associated with the right singular function un via (41) and (42) and it is studied in [12]. Lemma 3.13. Suppose that un be the n+ 1-th right

Plane waves and structures in turbulent channel flow

NASA Technical Reports Server (NTRS)

Sirovich, L.; Ball, K. S.; Keefe, L. R.

1990-01-01

A direct simulation of turbulent flow in a channel is analyzed by the method of empirical eigenfunctions (Karhunen-Loeve procedure, proper orthogonal decomposition). This analysis reveals the presence of propagating plane waves in the turbulent flow. The velocity of propagation is determined by the flow velocity at the location of maximal Reynolds stress. The analysis further suggests that the interaction of these waves appears to be essential to the local production of turbulence via bursting or sweeping events in the turbulent boundary layer, with the additional suggestion that the fast acting plane waves act as triggers.

Eigenfunction fractality and pseudogap state near the superconductor-insulator transition.

PubMed

Feigel'man, M V; Ioffe, L B; Kravtsov, V E; Yuzbashyan, E A

2007-01-12

We develop a theory of a pseudogap state appearing near the superconductor-insulator (SI) transition in strongly disordered metals with an attractive interaction. We show that such an interaction combined with the fractal nature of the single-particle wave functions near the mobility edge leads to an anomalously large single-particle gap in the superconducting state near SI transition that persists and even increases in the insulating state long after the superconductivity is destroyed. We give analytic expressions for the value of the pseudogap in terms of the inverse participation ratio of the corresponding localization problem.

Nonlocal theory of beam-driven electron Bernstein waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jain, V.K.; Tripathi, V.K.

A nonlocal theory of electron Bernstein waves driven unstable by an axial beam (V = V/sub b/z-italic-circumflex) of finite width has been developed. Assuming a parabolic density profile for the background plasma, an equation describing the mode structure of the wave is obtained in the slab geometry. The eigenfunctions are found to be Hermite polynomials. Expressions for the growth rates of the instabilities caused by Cerenkov and slow cyclotron interactions are derived. The results of the theory are applied to explain some of the experimental observations of Jain and Christiansen (Phys. Lett. A 82, 127 (1981)).

The evolution of social learning rules: payoff-biased and frequency-dependent biased transmission.

PubMed

Kendal, Jeremy; Giraldeau, Luc-Alain; Laland, Kevin

2009-09-21

Humans and other animals do not use social learning indiscriminately, rather, natural selection has favoured the evolution of social learning rules that make selective use of social learning to acquire relevant information in a changing environment. We present a gene-culture coevolutionary analysis of a small selection of such rules (unbiased social learning, payoff-biased social learning and frequency-dependent biased social learning, including conformism and anti-conformism) in a population of asocial learners where the environment is subject to a constant probability of change to a novel state. We define conditions under which each rule evolves to a genetically polymorphic equilibrium. We find that payoff-biased social learning may evolve under high levels of environmental variation if the fitness benefit associated with the acquired behaviour is either high or low but not of intermediate value. In contrast, both conformist and anti-conformist biases can become fixed when environment variation is low, whereupon the mean fitness in the population is higher than for a population of asocial learners. Our examination of the population dynamics reveals stable limit cycles under conformist and anti-conformist biases and some highly complex dynamics including chaos. Anti-conformists can out-compete conformists when conditions favour a low equilibrium frequency of the learned behaviour. We conclude that evolution, punctuated by the repeated successful invasion of different social learning rules, should continuously favour a reduction in the equilibrium frequency of asocial learning, and propose that, among competing social learning rules, the dominant rule will be the one that can persist with the lowest frequency of asocial learning.

Animal social networks as substrate for cultural behavioural diversity.

PubMed

Whitehead, Hal; Lusseau, David

2012-02-07

We used individual-based stochastic models to examine how social structure influences the diversity of socially learned behaviour within a non-human population. For continuous behavioural variables we modelled three forms of dyadic social learning, averaging the behavioural value of the two individuals, random transfer of information from one individual to the other, and directional transfer from the individual with highest behavioural value to the other. Learning had potential error. We also examined the transfer of categorical behaviour between individuals with random directionality and two forms of error, the adoption of a randomly chosen existing behavioural category or the innovation of a new type of behaviour. In populations without social structuring the diversity of culturally transmitted behaviour increased with learning error and population size. When the populations were structured socially either by making individuals members of permanent social units or by giving them overlapping ranges, behavioural diversity increased with network modularity under all scenarios, although the proportional increase varied considerably between continuous and categorical behaviour, with transmission mechanism, and population size. Although functions of the form e(c)¹(m)⁻(c)² + (c)³(Log(N)) predicted the mean increase in diversity with modularity (m) and population size (N), behavioural diversity could be highly unpredictable both between simulations with the same set of parameters, and within runs. Errors in social learning and social structuring generally promote behavioural diversity. Consequently, social learning may be considered to produce culture in populations whose social structure is sufficiently modular. Copyright © 2011 Elsevier Ltd. All rights reserved.

Stochastic evolution in populations of ideas

PubMed Central

Nicole, Robin; Sollich, Peter; Galla, Tobias

2017-01-01

It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in learning has been seen to act similarly to mutation in evolution. We here propose a representation of reinforcement learning as a stochastic process in finite ‘populations of ideas’. The resulting birth-death dynamics has absorbing states and allows for the extinction or fixation of ideas, marking a key difference to mutation-selection processes in finite populations. We characterize the outcome of evolution in populations of ideas for several classes of symmetric and asymmetric games. PMID:28098244

Stochastic evolution in populations of ideas

NASA Astrophysics Data System (ADS)

Nicole, Robin; Sollich, Peter; Galla, Tobias

2017-01-01

It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in learning has been seen to act similarly to mutation in evolution. We here propose a representation of reinforcement learning as a stochastic process in finite ‘populations of ideas’. The resulting birth-death dynamics has absorbing states and allows for the extinction or fixation of ideas, marking a key difference to mutation-selection processes in finite populations. We characterize the outcome of evolution in populations of ideas for several classes of symmetric and asymmetric games.

A Story of African American Students as Mathematics Learners

ERIC Educational Resources Information Center

Morton, Crystal Hill

2014-01-01

Educational systems throughout the world serve students from diverse populations. Often students from minority populations (i.e. racial, ethnic, linguistic, cultural, economic) face unique challenges when learning in contexts based on the cultural traditions and learning theories of the majority population. These challenges often leave minority…

Learning-by-doing, population pressure, and the theory of demographic transition.

PubMed

Strulik, H

1997-01-01

The long-term effects of two interdependent relations between economic growth and population growth are discussed. The empirical work of Boserup (1981) was utilized, which focused on rural, sparsely populated economies with low income per capita. According to the formulation of the population-push hypothesis, learning-by-doing effects in production lead to increasing returns to scale and, therefore, to a positive correlation between economic and population growth. In accordance with the theory of demographic transition, the population growth rate initially increases with rising income levels and then declines. The approach originating from Cigno (1984) modified the economic model, which allowed the establishment of two different stable equilibria. Regarding this relationship, the existence and stability of low-income and high-income equilibrium was shown in a neoclassical growth model. Under plausible conditions a demo-economic transition from the first to the second steady-state took place. The instability of the Malthusian steady-state is also possible when a country develops along a path of economic growth which is compatible with the demographic transition. In this context, learning means the application of new techniques of agrarian production. In developed economies with a stable population the learning-or-doing decision lead to accumulation of human capital and the invention of new technologies and goods. The interdependence of income-determined population growth and learning-by-doing may serve as an explanation for the weak and partly controversial empirical support for an overall correlation between income and population growth. The result yielded a meaningful interpretation of the population-push hypothesis, which is consistent with the empirical findings on the correlation between economic and population growth.

Service Learning for At-Risk Student Populations: The Contextual Dynamism of Implementation

ERIC Educational Resources Information Center

Akin, Jacob T.; Vesely, Randall S.

2016-01-01

The central purpose of this article is to explore research, issues, and perspectives on the implementation of service learning programs to improve student achievement in at-risk student populations. The implementation of service learning programs takes place within multiple contexts and across several terrains. The complexities of implementing…

Increasing participation of people with learning disabilities in bowel screening.

PubMed

Gray, Jonathan

2018-03-08

Learning disability nurses have a key role in addressing the health inequalities experienced by people with learning disabilities. People with learning disabilities are less likely to participate in bowel screening than other sectors of the population, despite there being evidence of this population being at an increased risk of developing bowel cancer. There are a range of barriers at individual and systemic levels that impact on participation in bowel screening by people with learning disabilities. Actions to address these barriers have been identified in the literature and learning disability nurses are a key agent of change in enabling people with learning disabilities to participate in the national screening programmes.

Development of a Three-Dimensional PSE Code for Compressible Flows: Stability of Three-Dimensional Compressible Boundary Layers

NASA Technical Reports Server (NTRS)

Balakumar, P.; Jeyasingham, Samarasingham

1999-01-01

A program is developed to investigate the linear stability of three-dimensional compressible boundary layer flows over bodies of revolutions. The problem is formulated as a two dimensional (2D) eigenvalue problem incorporating the meanflow variations in the normal and azimuthal directions. Normal mode solutions are sought in the whole plane rather than in a line normal to the wall as is done in the classical one dimensional (1D) stability theory. The stability characteristics of a supersonic boundary layer over a sharp cone with 50 half-angle at 2 degrees angle of attack is investigated. The 1D eigenvalue computations showed that the most amplified disturbances occur around x(sub 2) = 90 degrees and the azimuthal mode number for the most amplified disturbances range between m = -30 to -40. The frequencies of the most amplified waves are smaller in the middle region where the crossflow dominates the instability than the most amplified frequencies near the windward and leeward planes. The 2D eigenvalue computations showed that due to the variations in the azimuthal direction, the eigenmodes are clustered into isolated confined regions. For some eigenvalues, the eigenfunctions are clustered in two regions. Due to the nonparallel effect in the azimuthal direction, the eigenmodes are clustered into isolated confined regions. For some eigenvalues, the eigenfunctions are clustered in two regions. Due to the nonparallel effect in the azimuthal direction, the most amplified disturbances are shifted to 120 degrees compared to 90 degrees for the parallel theory. It is also observed that the nonparallel amplification rates are smaller than that is obtained from the parallel theory.

Inverse-scattering-theory approach to the exact n→∞ solutions of O(n) ϕ⁴ models on films and semi-infinite systems bounded by free surfaces.

PubMed

Rutkevich, Sergei B; Diehl, H W

2015-06-01

The O(n) ϕ(4) model on a strip bounded by a pair of planar free surfaces at separation L can be solved exactly in the large-n limit in terms of the eigenvalues and eigenfunctions of a self-consistent one-dimensional Schrödinger equation. The scaling limit of a continuum version of this model is considered. It is shown that the self-consistent potential can be eliminated in favor of scattering data by means of appropriately extended methods of inverse scattering theory. The scattering data (Jost function) associated with the self-consistent potential are determined for the L=∞ semi-infinite case in the scaling regime for all values of the temperature scaling field t=(T-T(c))/T(c) above and below the bulk critical temperature T(c). These results are used in conjunction with semiclassical and boundary-operator expansions and a trace formula to derive exact analytical results for a number of quantities such as two-point functions, universal amplitudes of two excess surface quantities, the universal amplitude difference associated with the thermal singularity of the surface free energy, and potential coefficients. The asymptotic behaviors of the scaled eigenenergies and eigenfunctions of the self-consistent Schrödinger equation as function of x=t(L/ξ(+))(1/ν) are determined for x→-∞. In addition, the asymptotic x→-∞ forms of the universal finite-size scaling functions Θ(x) and ϑ(x) of the residual free energy and the Casimir force are computed exactly to order 1/x, including their x(-1)ln|x| anomalies.

A two-pronged approach to detecting ICB Stoneley modes

NASA Astrophysics Data System (ADS)

Jasperson, H. A.; Ye, J.; Shi, J.; De Hoop, M. V.

2017-12-01

Stoneley modes are special kinds of normal modes that are confined to the boundary between a fluid layer and a solid layer inside the Earth. Thus, these modes theoretically occur at the core-mantle boundary (CMB) and inner core boundary (ICB). CMB Stoneley modes were identified in observational data by Koelemeijer, et al. in 2013, but ICB Stoneley modes have remained relatively unexplored. Here we use a joint numerical and data-driven approach to identify ICB Stoneley modes from the deep 2013 Mw 8.3 Sea of Okhotsk earthquake. For the data-driven portion, we use 50 stacked traces from the USArray to identify potential occurrences of ICB Stoneley modes. Next, we verify each occurrence by comparing the spectrum to its equivalent from the shallow 2011 Mw 9.1 Tohoku earthquake. We also develop a novel computational approach to compute normal modes in a spherically symmetric non-rotating Earth building on the work of Wiggins (1976) and Buland and Gilbert (1984). We successfully resolve the clustering eigenvalue problem with non-orthogonal eigenfunctions from which Mineos suffers. By choosing the displacement/pressure formulation in the fluid outer core and handling boundary conditions properly, we remarkably project out the essential spectrum and provide the correct point spectrum. The utilization of weak variational form to perform the Rayleigh-Ritz procedure contributes to preserving the high accuracy across the solid-fluid boundary, which makes it possible to capture Stoneley modes' exponentially decaying behavior across the solid-fluid boundary, leading to more accurate and reliable eigenvalues and eigenfunctions. This allows us to compare the observation data and numerical computations. With this approach, we eliminate false signals from consideration, leaving only true ICB Stoneley mode peaks. In the future, information from these modes can be used to study the properties of the ICB and inner core.

Spectral analysis of localized rotating waves in parabolic systems.

PubMed

Beyn, Wolf-Jürgen; Otten, Denny

2018-04-13

In this paper, we study the spectra and Fredholm properties of Ornstein-Uhlenbeck operators [Formula: see text]where [Formula: see text] is the profile of a rotating wave satisfying [Formula: see text] as [Formula: see text], the map [Formula: see text] is smooth and the matrix [Formula: see text] has eigenvalues with positive real parts and commutes with the limit matrix [Formula: see text] The matrix [Formula: see text] is assumed to be skew-symmetric with eigenvalues (λ 1 ,…,λ d )=(±i σ 1 ,…,±i σ k ,0,…,0). The spectra of these linearized operators are crucial for the nonlinear stability of rotating waves in reaction-diffusion systems. We prove under appropriate conditions that every [Formula: see text] satisfying the dispersion relation [Formula: see text]belongs to the essential spectrum [Formula: see text] in L p For values Re λ to the right of the spectral bound for [Formula: see text], we show that the operator [Formula: see text] is Fredholm of index 0, solve the identification problem for the adjoint operator [Formula: see text] and formulate the Fredholm alternative. Moreover, we show that the set [Formula: see text]belongs to the point spectrum [Formula: see text] in L p We determine the associated eigenfunctions and show that they decay exponentially in space. As an application, we analyse spinning soliton solutions which occur in the Ginzburg-Landau equation and compute their numerical spectra as well as associated eigenfunctions. Our results form the basis for investigating the nonlinear stability of rotating waves in higher space dimensions and truncations to bounded domains. This article is part of the themed issue 'Stability of nonlinear waves and patterns and related topics'. © 2018 The Author(s).

The nodal count {0,1,2,3,…} implies the graph is a tree

PubMed Central

Band, Ram

2014-01-01

Sturm's oscillation theorem states that the nth eigenfunction of a Sturm–Liouville operator on the interval has n−1 zeros (nodes) (Sturm 1836 J. Math. Pures Appl. 1, 106–186; 373–444). This result was generalized for all metric tree graphs (Pokornyĭ et al. 1996 Mat. Zametki 60, 468–470 (doi:10.1007/BF02320380); Schapotschnikow 2006 Waves Random Complex Media 16, 167–178 (doi:10.1080/1745530600702535)) and an analogous theorem was proved for discrete tree graphs (Berkolaiko 2007 Commun. Math. Phys. 278, 803–819 (doi:10.1007/S00220-007-0391-3); Dhar & Ramaswamy 1985 Phys. Rev. Lett. 54, 1346–1349 (doi:10.1103/PhysRevLett.54.1346); Fiedler 1975 Czechoslovak Math. J. 25, 607–618). We prove the converse theorems for both discrete and metric graphs. Namely if for all n, the nth eigenfunction of the graph has n−1 zeros, then the graph is a tree. Our proofs use a recently obtained connection between the graph's nodal count and the magnetic stability of its eigenvalues (Berkolaiko 2013 Anal. PDE 6, 1213–1233 (doi:10.2140/apde.2013.6.1213); Berkolaiko & Weyand 2014 Phil. Trans. R. Soc. A 372, 20120522 (doi:10.1098/rsta.2012.0522); Colin de Verdière 2013 Anal. PDE 6, 1235–1242 (doi:10.2140/apde.2013.6.1235)). In the course of the proof, we show that it is not possible for all (or even almost all, in the metric case) the eigenvalues to exhibit a diamagnetic behaviour. In addition, we develop a notion of ‘discretized’ versions of a metric graph and prove that their nodal counts are related to those of the metric graph. PMID:24344337

Teaching population health and community-based care across diverse clinical experiences: integration of conceptual pillars and constructivist learning.

PubMed

Valentine-Maher, Sarah K; Van Dyk, Elizabeth J; Aktan, Nadine M; Bliss, Julie Beshore

2014-03-01

Nursing programs are challenged to prepare future nurses to provide care and affect determinants of health for individuals and populations. This article advances a pedagogical model for clinical education that builds concepts related to both population-level care and direct care in the community through a contextual learning approach. Because the conceptual pillars and hybrid constructivist approach allow for conceptual learning consistency across experiences, the model expands programmatic capacity to use diverse community clinical sites that accept only small numbers of students. The concept-based and hybrid constructivist learning approach is expected to contribute to the development of broad intellectual skills and lifelong learning. The pillar concepts include determinants of health and nursing care of population aggregates; direct care, based on evidence and best practices; appreciation of lived experience of health and illness; public health nursing roles and relationship to ethical and professional formation; and multidisciplinary collaboration. Copyright 2014, SLACK Incorporated.

'I could never have learned this in a lecture': transformative learning in rural health education.

PubMed

Prout, Sarah; Lin, Ivan; Nattabi, Barbara; Green, Charmaine

2014-05-01

Health indicators for rural populations in Australia continue to lag behind those of urban populations and particularly for Indigenous populations who make up a large proportion of people living in rural and remote Australia. Preparation of health practitioners who are adequately prepared to face the 'messy swamps' of rural health practice is a growing challenge. This paper examines the process of learning among health science students from several health disciplines from five Western Australian universities during 'Country Week': a one-week intensive experiential interprofessional education program in rural Western Australia. The paper weaves together strands of transformative theory of learning with findings from staff and student reflections from Country Week to explore how facilitated learning in situ can work to produce practitioners better prepared for rural health practice.

Learning to Estimate Dynamical State with Probabilistic Population Codes.

PubMed

Makin, Joseph G; Dichter, Benjamin K; Sabes, Philip N

2015-11-01

Tracking moving objects, including one's own body, is a fundamental ability of higher organisms, playing a central role in many perceptual and motor tasks. While it is unknown how the brain learns to follow and predict the dynamics of objects, it is known that this process of state estimation can be learned purely from the statistics of noisy observations. When the dynamics are simply linear with additive Gaussian noise, the optimal solution is the well known Kalman filter (KF), the parameters of which can be learned via latent-variable density estimation (the EM algorithm). The brain does not, however, directly manipulate matrices and vectors, but instead appears to represent probability distributions with the firing rates of population of neurons, "probabilistic population codes." We show that a recurrent neural network-a modified form of an exponential family harmonium (EFH)-that takes a linear probabilistic population code as input can learn, without supervision, to estimate the state of a linear dynamical system. After observing a series of population responses (spike counts) to the position of a moving object, the network learns to represent the velocity of the object and forms nearly optimal predictions about the position at the next time-step. This result builds on our previous work showing that a similar network can learn to perform multisensory integration and coordinate transformations for static stimuli. The receptive fields of the trained network also make qualitative predictions about the developing and learning brain: tuning gradually emerges for higher-order dynamical states not explicitly present in the inputs, appearing as delayed tuning for the lower-order states.

Learning to Estimate Dynamical State with Probabilistic Population Codes

PubMed Central

Sabes, Philip N.

2015-01-01

Tracking moving objects, including one’s own body, is a fundamental ability of higher organisms, playing a central role in many perceptual and motor tasks. While it is unknown how the brain learns to follow and predict the dynamics of objects, it is known that this process of state estimation can be learned purely from the statistics of noisy observations. When the dynamics are simply linear with additive Gaussian noise, the optimal solution is the well known Kalman filter (KF), the parameters of which can be learned via latent-variable density estimation (the EM algorithm). The brain does not, however, directly manipulate matrices and vectors, but instead appears to represent probability distributions with the firing rates of population of neurons, “probabilistic population codes.” We show that a recurrent neural network—a modified form of an exponential family harmonium (EFH)—that takes a linear probabilistic population code as input can learn, without supervision, to estimate the state of a linear dynamical system. After observing a series of population responses (spike counts) to the position of a moving object, the network learns to represent the velocity of the object and forms nearly optimal predictions about the position at the next time-step. This result builds on our previous work showing that a similar network can learn to perform multisensory integration and coordinate transformations for static stimuli. The receptive fields of the trained network also make qualitative predictions about the developing and learning brain: tuning gradually emerges for higher-order dynamical states not explicitly present in the inputs, appearing as delayed tuning for the lower-order states. PMID:26540152

Context Fear Learning Specifically Activates Distinct Populations of Neurons in Amygdala and Hypothalamus

ERIC Educational Resources Information Center

Trogrlic, Lidia; Wilson, Yvette M.; Newman, Andrew G.; Murphy, Mark

2011-01-01

The identity and distribution of neurons that are involved in any learning or memory event is not known. In previous studies, we identified a discrete population of neurons in the lateral amygdala that show learning-specific activation of a c-"fos"-regulated transgene following context fear conditioning. Here, we have extended these studies to…

Later Life Learning Experiences: Listening to the Voices of Chinese Elders in Hong Kong

ERIC Educational Resources Information Center

Tam, Maureen

2016-01-01

Governments' anxieties about ageing populations are mostly concerned with the costs of welfare, care and health provision which all have to be paid for by an ever dwindling working population. However, research in later life learning indicates the significant role that lifelong learning can play in promoting mental well-being and resilience, and…

Learned Helplessness and Depression in a Clinical Population: A Test of Two Behavioral Hypotheses

ERIC Educational Resources Information Center

And Others; Price, Kenneth P.

1978-01-01

This study was undertaken to extend the learned helplessness phenomenon to a clinical population and to test the competing hypotheses of Seligman and Lewinsohn. 96 male hospitalized psychiatric and medical patients were randomly assigned to one of four experimental conditions. Results replicate the learned helplessness phenomenon in a group of…

Assisting At-Risk Populations. Secondary Learning Guide 11. Project Connect. Linking Self-Family-Work.

ERIC Educational Resources Information Center

Emily Hall Tremaine Foundation, Inc., Hartford, CT.

This competency-based secondary learning guide on assisting at-risk populations (dropouts and homeless people) is part of a series that are adaptations of guides developed for adult consumer and homemaking education programs. The guides provide students with experiences that help them learn to do the following: make decisions; use creative…

Deep Learning for Population Genetic Inference.

PubMed

Sheehan, Sara; Song, Yun S

2016-03-01

Given genomic variation data from multiple individuals, computing the likelihood of complex population genetic models is often infeasible. To circumvent this problem, we introduce a novel likelihood-free inference framework by applying deep learning, a powerful modern technique in machine learning. Deep learning makes use of multilayer neural networks to learn a feature-based function from the input (e.g., hundreds of correlated summary statistics of data) to the output (e.g., population genetic parameters of interest). We demonstrate that deep learning can be effectively employed for population genetic inference and learning informative features of data. As a concrete application, we focus on the challenging problem of jointly inferring natural selection and demography (in the form of a population size change history). Our method is able to separate the global nature of demography from the local nature of selection, without sequential steps for these two factors. Studying demography and selection jointly is motivated by Drosophila, where pervasive selection confounds demographic analysis. We apply our method to 197 African Drosophila melanogaster genomes from Zambia to infer both their overall demography, and regions of their genome under selection. We find many regions of the genome that have experienced hard sweeps, and fewer under selection on standing variation (soft sweep) or balancing selection. Interestingly, we find that soft sweeps and balancing selection occur more frequently closer to the centromere of each chromosome. In addition, our demographic inference suggests that previously estimated bottlenecks for African Drosophila melanogaster are too extreme.

Deep Learning for Population Genetic Inference

PubMed Central

Sheehan, Sara; Song, Yun S.

2016-01-01

Given genomic variation data from multiple individuals, computing the likelihood of complex population genetic models is often infeasible. To circumvent this problem, we introduce a novel likelihood-free inference framework by applying deep learning, a powerful modern technique in machine learning. Deep learning makes use of multilayer neural networks to learn a feature-based function from the input (e.g., hundreds of correlated summary statistics of data) to the output (e.g., population genetic parameters of interest). We demonstrate that deep learning can be effectively employed for population genetic inference and learning informative features of data. As a concrete application, we focus on the challenging problem of jointly inferring natural selection and demography (in the form of a population size change history). Our method is able to separate the global nature of demography from the local nature of selection, without sequential steps for these two factors. Studying demography and selection jointly is motivated by Drosophila, where pervasive selection confounds demographic analysis. We apply our method to 197 African Drosophila melanogaster genomes from Zambia to infer both their overall demography, and regions of their genome under selection. We find many regions of the genome that have experienced hard sweeps, and fewer under selection on standing variation (soft sweep) or balancing selection. Interestingly, we find that soft sweeps and balancing selection occur more frequently closer to the centromere of each chromosome. In addition, our demographic inference suggests that previously estimated bottlenecks for African Drosophila melanogaster are too extreme. PMID:27018908

The effect of cultural interaction on cumulative cultural evolution.

PubMed

Nakahashi, Wataru

2014-07-07

Cultural transmission and cultural evolution are important for animals, especially for humans. I developed a new analytical model of cultural evolution, in which each newborn learns cultural traits from multiple individuals (exemplars) in parental generation, individually explores around learned cultural traits, judges the utility of known cultural traits, and adopts a mature cultural trait. Cultural evolutionary speed increases when individuals explore a wider range of cultural traits, accurately judge the skill level of cultural traits (strong direct bias), do not strongly conform to the population mean, increase the exploration range according to the variety of socially learned cultural traits (condition dependent exploration), and make smaller errors in social learning. Number of exemplars, population size, similarity of cultural traits between exemplars, and one-to-many transmission have little effect on cultural evolutionary speed. I also investigated how cultural interaction between two populations with different mean skill levels affects their cultural evolution. A population sometimes increases in skill level more if it encounters a less skilled population than if it does not encounter anyone. A less skilled population sometimes exceeds a more skilled population in skill level by cultural interaction between both populations. The appropriateness of this analytical method is confirmed by individual-based simulations. Copyright © 2014 Elsevier Ltd. All rights reserved.

Nurses on a mission: a professional service learning experience with the inner-city homeless.

PubMed

Lashley, Mary

2007-01-01

Nursing students can play a vital role in addressing the health care needs of the homeless. Through professional service learning experiences in community-based settings, students learn how to partner with key community leaders and agencies to meet the needs of underserved populations and provide culturally competent care to diverse populations. This article describes the development of a professional service learning experience with the homeless in which a community-academic partnership was created to meet community needs. In an era of declining health care resources, such innovative partnerships serve to reduce health disparities and improve access to care while preparing students for community-based practice with at-risk and vulnerable populations.

A finite element algorithm for high-lying eigenvalues with Neumann and Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Báez, G.; Méndez-Sánchez, R. A.; Leyvraz, F.; Seligman, T. H.

2014-01-01

We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions, or combinations of either for different parts of the boundary. We use an inverse power plus Gauss-Seidel algorithm to solve the generalized eigenvalue problem. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We checked the algorithm by comparing the cumulative level density of the spectrum obtained numerically with the theoretical prediction given by the Weyl formula. We found a systematic deviation due to the discretization, not to the algorithm itself.

Spectral singularities of complex scattering potentials and infinite reflection and transmission coefficients at real energies.

PubMed

Mostafazadeh, Ali

2009-06-05

Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which the reflection and transmission coefficients tend to infinity, i.e., they correspond to resonances having a zero width. We show that a waveguide modeled using such a potential operates like a resonator at the frequencies of spectral singularities. As a concrete example, we explore the spectral singularities of an imaginary PT-symmetric barrier potential and demonstrate the above resonance phenomenon for a certain electromagnetic waveguide.

Boundary-layer effects in composite laminates: Free-edge stress singularities, part 6

NASA Technical Reports Server (NTRS)

Wanag, S. S.; Choi, I.

1981-01-01

A rigorous mathematical model was obtained for the boundary-layer free-edge stress singularity in angleplied and crossplied fiber composite laminates. The solution was obtained using a method consisting of complex-variable stress function potentials and eigenfunction expansions. The required order of the boundary-layer stress singularity is determined by solving the transcendental characteristic equation obtained from the homogeneous solution of the partial differential equations. Numerical results obtained show that the boundary-layer stress singularity depends only upon material elastic constants and fiber orientation of the adjacent plies. For angleplied and crossplied laminates the order of the singularity is weak in general.

Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at Real Energies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mostafazadeh, Ali

2009-06-05

Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which the reflection and transmission coefficients tend to infinity, i.e., they correspond to resonances having a zero width. We show that a waveguide modeled using such a potential operates like a resonator at the frequencies of spectral singularities. As a concrete example, we explore the spectral singularities of an imaginary PT-symmetric barrier potential and demonstrate the above resonance phenomenon for a certain electromagnetic waveguide.

Electromagnetic propagation in PEC and absorbing curved S-ducts

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.

1988-01-01

A finite-element Galerkin formulation has been developed to study transverse magnetic (TM) wave propagation in 2-D S-curved ducts with both perfectly conducting and absorbing walls. The reflection and transmission at the entrances and the exits of the curved ducts are determined by coupling the finite-element solutions in the curved ducts to the eigenfunctions of an infinite, uniform, perfectly conducting duct. Example solutions are presented for a double mitred and S-ducts of various lengths. The length of the S-duct is found to significantly effect the reflective characteristics of the duct. Also, the effect of curvature on an absorbing duct is illustrated.

Analysis of the E2 transitions for /sup 3/H-/alpha/ cluster states of /sup 7/Li by the resonating group method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu Pu; Zhao Xuan; Zeng Fanan

1989-07-01

It is suggested that the ground state and the 1st, 2nd, and 3rd excited states of /sup 7/Li are /sup 3/H-/alpha/ cluster-structure states. Using the resonating group method (RGM), the eigenvalues and eigenfunctions of these states as well as the reduced E2 transition probabilities between these states are calculated and are consistent with the experimental values. The results show that the RGM is much better than the harmonic oscillator model used by Bernheim /ital et/ /ital al/. in predicting the E2 transition rates.

Effects of Shannon entropy and electric field on polaron in RbCl triangular quantum dot

NASA Astrophysics Data System (ADS)

M, Tiotsop; A, J. Fotue; S, C. Kenfack; N, Issofa; H, Fotsin; L, C. Fai

2016-04-01

In this paper, the time evolution of the quantum mechanical state of a polaron is examined using the Pekar type variational method on the condition of the electric-LO-phonon strong-coupling and polar angle in RbCl triangular quantum dot. We obtain the eigenenergies, and the eigenfunctions of the ground state, and the first excited state respectively. This system in a quantum dot can be treated as a two-level quantum system qubit and the numerical calculations are performed. The effects of Shannon entropy and electric field on the polaron in the RbCl triangular quantum dot are also studied.

Electron transport near the Mott transition in n-GaAs and n-GaN

NASA Astrophysics Data System (ADS)

Romanets, P. N.; Sachenko, A. V.

2016-01-01

In this paper, we study the temperature dependence of the conductivity and the Hall coefficient near the metal-insulator phase transition. A theoretical investigation is performed within the effective mass approximation. The variational method is used to calculate the eigenvalues and eigenfunctions of the impurity states. Unlike previous studies, we have included nonlinear corrections to the screened impurity potential, because the Thomas-Fermi approximation is incorrect for the insulator phase. It is also shown that near the phase transition the exchange interaction is essential. The obtained temperature dependencies explain several experimental measurements in gallium arsenide (GaAs) and gallium nitride (GaN).

Compressed modes for variational problems in mathematics and physics

PubMed Central

Ozoliņš, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley

2013-01-01

This article describes a general formalism for obtaining spatially localized (“sparse”) solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger’s equation in quantum mechanics. Sparsity is achieved by adding an regularization term to the variational principle, which is shown to yield solutions with compact support (“compressed modes”). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size. PMID:24170861

Acoustic response of a rectangular levitator with orifices

NASA Technical Reports Server (NTRS)

El-Raheb, Michael; Wagner, Paul

1990-01-01

The acoustic response of a rectangular cavity to speaker-generated excitation through waveguides terminating at orifices in the cavity walls is analyzed. To find the effects of orifices, acoustic pressure is expressed by eigenfunctions satisfying Neumann boundary conditions as well as by those satisfying Dirichlet ones. Some of the excess unknowns can be eliminated by point constraints set over the boundary, by appeal to Lagrange undetermined multipliers. The resulting transfer matrix must be further reduced by partial condensation to the order of a matrix describing unmixed boundary conditions. If the cavity is subjected to an axial temperature dependence, the transfer matrix is determined numerically.

Compressed modes for variational problems in mathematics and physics.

PubMed

Ozolins, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley

2013-11-12

This article describes a general formalism for obtaining spatially localized ("sparse") solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger's equation in quantum mechanics. Sparsity is achieved by adding an regularization term to the variational principle, which is shown to yield solutions with compact support ("compressed modes"). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size.

Systematic study of baryons in a three-body quark model

NASA Astrophysics Data System (ADS)

Aslanzadeh, M.; Rajabi, A. A.

2016-09-01

We investigated the structure of baryons within a three-body quark model based on hypercentral approach. We considered an SU(6)-invariant potential consisting of the well-known "Coulomb-plus-linear" potential plus some multipole interactions as V ( x) ∝ x - n with n > 2. Then, through an analytical solution, we obtained the energy eigenvalues and eigenfunctions of the three-body problem and evaluated some observables such as the mass spectrum of light baryons and both the electromagnetic elastic form factors, and the charge radii of nucleons. We compared our results with the experimental data and showed that the present model provides a good description of the observed resonances.

Laser location and manipulation of a single quantum tunneling channel in an InAs quantum dot.

PubMed

Makarovsky, O; Vdovin, E E; Patané, A; Eaves, L; Makhonin, M N; Tartakovskii, A I; Hopkinson, M

2012-03-16

We use a femtowatt focused laser beam to locate and manipulate a single quantum tunneling channel associated with an individual InAs quantum dot within an ensemble of dots. The intensity of the directed laser beam tunes the tunneling current through the targeted dot with an effective optical gain of 10(7) and modifies the curvature of the dot's confining potential and the spatial extent of its ground state electron eigenfunction. These observations are explained by the effect of photocreated hole charges which become bound close to the targeted dot, thus acting as an optically induced gate electrode.

The g Factors of Ground State of Ruby and Their Pressure-Induced Shifts

NASA Astrophysics Data System (ADS)

Ma, Dongping; Zhang, Hongmei; Chen, Jurong; Liu, Yanyun

1998-12-01

By using the theory of pressure-induced shifts and the eigenfunctions at normal and various pressures obtained from the diagonalization of the complete d3 energy matrix adopting C3v symmetry, g factors of the ground state of ruby and their pressure-induced shifts have been calculated. The results are in very good agreement with the experimental data. For the precise calculation of properties of the ground skate, it is necessary to take into account the effects of all the excited states by the diagonalization of the complete energy matrix. The project (Grant No. 19744001) supported by National Natural Science Foundation of China

Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory

NASA Astrophysics Data System (ADS)

Sciarappa, Antonio

2017-10-01

We provide a proposal, motivated by Separation of Variables and gauge theory arguments, for constructing exact solutions to the quantum Baxter equation associated to the N-particle relativistic Toda chain and test our proposal against numerical results. Quantum Mechanical non-perturbative corrections, essential in order to obtain a sensible solution, are taken into account in our gauge theory approach by considering codimension two defects on curved backgrounds (squashed S 5 and degenerate limits) rather than flat space; this setting also naturally incorporates exact quantization conditions and energy spectrum of the relativistic Toda chain as well as its modular dual structure.

Exactly and quasi-exactly solvable 'discrete' quantum mechanics.

PubMed

Sasaki, Ryu

2011-03-28

A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.

Content Development for 72,000 Learners: An Online Learning Environment for General Practitioners: A Case Study

ERIC Educational Resources Information Center

Pilat, Dirk

2016-01-01

Increasing workload due to reduced numbers of general practitioners, a population boom and an aging population has increased the need for accessible distance learning for the UK's primary care doctors. The Royal College of General Practitioners is now in its eighth year of delivering high quality e-learning to 72,000 registered users via its…

Levels of Engagement and Barriers to Physical Activity in a Population of Adults with Learning Disabilities

ERIC Educational Resources Information Center

Hawkins, Andrew; Look, Roger

2006-01-01

This study examined levels of, and barriers to, physical activity in a population of 19 adults with learning disabilities living in community supported accommodation, using diary records and semi-structured interviews with staff. The levels of physical activity were higher in the sample population than previous figures for adults with learning…

"I Could Never Have Learned This in a Lecture": Transformative Learning in Rural Health Education

ERIC Educational Resources Information Center

Prout, Sarah; Lin, Ivan; Nattabi, Barbara; Green, Charmaine

2014-01-01

Health indicators for rural populations in Australia continue to lag behind those of urban populations and particularly for Indigenous populations who make up a large proportion of people living in rural and remote Australia. Preparation of health practitioners who are adequately prepared to face the "messy swamps" of rural health…

Experimental evolution of slowed cognitive aging in Drosophila melanogaster.

PubMed

Zwoinska, Martyna K; Maklakov, Alexei A; Kawecki, Tadeusz J; Hollis, Brian

2017-03-01

Reproductive output and cognitive performance decline in parallel during aging, but it is unknown whether this reflects a shared genetic architecture or merely the declining force of natural selection acting independently on both traits. We used experimental evolution in Drosophila melanogaster to test for the presence of genetic variation for slowed cognitive aging, and assess its independence from that responsible for other traits' decline with age. Replicate experimental populations experienced either joint selection on learning and reproduction at old age (Old + Learning), selection on late-life reproduction alone (Old), or a standard two-week culture regime (Young). Within 20 generations, the Old + Learning populations evolved a slower decline in learning with age than both the Old and Young populations, revealing genetic variation for cognitive aging. We found little evidence for a genetic correlation between cognitive and demographic aging: although the Old + Learning populations tended to show higher late-life fecundity than Old populations, they did not live longer. Likewise, selection for late reproduction alone did not result in improved late-life learning. Our results demonstrate that Drosophila harbor genetic variation for cognitive aging that is largely independent from genetic variation for demographic aging and suggest that these two aspects of aging may not necessarily follow the same trajectories. © 2016 The Author(s). Evolution published by Wiley Periodicals, Inc. on behalf of The Society for the Study of Evolution.

Assortative social learning and its implications for human (and animal?) societies.

PubMed

Katsnelson, Edith; Lotem, Arnon; Feldman, Marcus W

2014-07-01

Choosing from whom to learn is an important element of social learning. It affects learner success and the profile of behaviors in the population. Because individuals often differ in their traits and capabilities, their benefits from different behaviors may also vary. Homophily, or assortment, the tendency of individuals to interact with other individuals with similar traits, is known to affect the spread of behaviors in humans. We introduce models to study the evolution of assortative social learning (ASL), where assorting on a trait acts as an individual-specific mechanism for filtering relevant models from which to learn when that trait varies. We show that when the trait is polymorphic, ASL may maintain a stable behavioral polymorphism within a population (independently of coexistence with individual learning in a population). We explore the evolution of ASL when assortment is based on a nonheritable or partially heritable trait, and when ASL competes with different non-ASL strategies: oblique (learning from the parental generation) and vertical (learning from the parent). We suggest that the tendency to assort may be advantageous in the context of social learning, and that ASL might be an important concept for the evolutionary theory of social learning. © 2014 The Author(s). Evolution © 2014 The Society for the Study of Evolution.

Machine Learning Based Classification of Microsatellite Variation: An Effective Approach for Phylogeographic Characterization of Olive Populations.

PubMed

Torkzaban, Bahareh; Kayvanjoo, Amir Hossein; Ardalan, Arman; Mousavi, Soraya; Mariotti, Roberto; Baldoni, Luciana; Ebrahimie, Esmaeil; Ebrahimi, Mansour; Hosseini-Mazinani, Mehdi

2015-01-01

Finding efficient analytical techniques is overwhelmingly turning into a bottleneck for the effectiveness of large biological data. Machine learning offers a novel and powerful tool to advance classification and modeling solutions in molecular biology. However, these methods have been less frequently used with empirical population genetics data. In this study, we developed a new combined approach of data analysis using microsatellite marker data from our previous studies of olive populations using machine learning algorithms. Herein, 267 olive accessions of various origins including 21 reference cultivars, 132 local ecotypes, and 37 wild olive specimens from the Iranian plateau, together with 77 of the most represented Mediterranean varieties were investigated using a finely selected panel of 11 microsatellite markers. We organized data in two '4-targeted' and '16-targeted' experiments. A strategy of assaying different machine based analyses (i.e. data cleaning, feature selection, and machine learning classification) was devised to identify the most informative loci and the most diagnostic alleles to represent the population and the geography of each olive accession. These analyses revealed microsatellite markers with the highest differentiating capacity and proved efficiency for our method of clustering olive accessions to reflect upon their regions of origin. A distinguished highlight of this study was the discovery of the best combination of markers for better differentiating of populations via machine learning models, which can be exploited to distinguish among other biological populations.

Learning experiences in population education: proposed guidelines and core messages.

PubMed

1984-01-01

As a result of the 1984 Regional Workshop for the Development of Packages of Adequate Learning Requirements in Population Education, the participants tackled the problem of non-institutionalization of population education into the formal and non-formal educational curricula in their countries. Based on their deliberations, several sets of guidelines and core messages were formulated to provide countries with a more definite direction that will hopefully ensure the functional and effective integration of population education in their respective national school and out-of-school curriculum system. Useful packages of learning materials in population education should help realize the country's population policy and goals within the broader framework of socioeconomic development, and the content of the package should comprehensively cover the core messages of the country's Population Information, Education and Communication (IEC) Program. The population knowledge base of the package should be accurate and relevant; the package should provide for graphic and visual presentation and for assessment of effects on the target groups. Proposed core messages in population education discuss the advantages of small family size and delayed marriage, and aspects of responsible parenthood. Other messages discuss population resource development and population-related beliefs and values.

Education and Learning for the Elderly: Why, How, What

ERIC Educational Resources Information Center

Boulton-Lewis, Gillian M.

2010-01-01

This paper is concerned with the general issues of ageing, learning, and education for the elderly. It also examines the more specific issues of why, how and what elders want to learn. The world's population is ageing rapidly. For example, it is estimated that by 2020 20% of the population in the USA will be 65 years old and over. It is predicted…

Analysis of the “naming game” with learning errors in communications

NASA Astrophysics Data System (ADS)

Lou, Yang; Chen, Guanrong

2015-07-01

Naming game simulates the process of naming an objective by a population of agents organized in a certain communication network. By pair-wise iterative interactions, the population reaches consensus asymptotically. We study naming game with communication errors during pair-wise conversations, with error rates in a uniform probability distribution. First, a model of naming game with learning errors in communications (NGLE) is proposed. Then, a strategy for agents to prevent learning errors is suggested. To that end, three typical topologies of communication networks, namely random-graph, small-world and scale-free networks, are employed to investigate the effects of various learning errors. Simulation results on these models show that 1) learning errors slightly affect the convergence speed but distinctively increase the requirement for memory of each agent during lexicon propagation; 2) the maximum number of different words held by the population increases linearly as the error rate increases; 3) without applying any strategy to eliminate learning errors, there is a threshold of the learning errors which impairs the convergence. The new findings may help to better understand the role of learning errors in naming game as well as in human language development from a network science perspective.

Analysis of the "naming game" with learning errors in communications.

PubMed

Lou, Yang; Chen, Guanrong

2015-07-16

Naming game simulates the process of naming an objective by a population of agents organized in a certain communication network. By pair-wise iterative interactions, the population reaches consensus asymptotically. We study naming game with communication errors during pair-wise conversations, with error rates in a uniform probability distribution. First, a model of naming game with learning errors in communications (NGLE) is proposed. Then, a strategy for agents to prevent learning errors is suggested. To that end, three typical topologies of communication networks, namely random-graph, small-world and scale-free networks, are employed to investigate the effects of various learning errors. Simulation results on these models show that 1) learning errors slightly affect the convergence speed but distinctively increase the requirement for memory of each agent during lexicon propagation; 2) the maximum number of different words held by the population increases linearly as the error rate increases; 3) without applying any strategy to eliminate learning errors, there is a threshold of the learning errors which impairs the convergence. The new findings may help to better understand the role of learning errors in naming game as well as in human language development from a network science perspective.

Reinforcement Learning of Two-Joint Virtual Arm Reaching in a Computer Model of Sensorimotor Cortex

PubMed Central

Neymotin, Samuel A.; Chadderdon, George L.; Kerr, Cliff C.; Francis, Joseph T.; Lytton, William W.

2014-01-01

Neocortical mechanisms of learning sensorimotor control involve a complex series of interactions at multiple levels, from synaptic mechanisms to cellular dynamics to network connectomics. We developed a model of sensory and motor neocortex consisting of 704 spiking model neurons. Sensory and motor populations included excitatory cells and two types of interneurons. Neurons were interconnected with AMPA/NMDA and GABAA synapses. We trained our model using spike-timing-dependent reinforcement learning to control a two-joint virtual arm to reach to a fixed target. For each of 125 trained networks, we used 200 training sessions, each involving 15 s reaches to the target from 16 starting positions. Learning altered network dynamics, with enhancements to neuronal synchrony and behaviorally relevant information flow between neurons. After learning, networks demonstrated retention of behaviorally relevant memories by using proprioceptive information to perform reach-to-target from multiple starting positions. Networks dynamically controlled which joint rotations to use to reach a target, depending on current arm position. Learning-dependent network reorganization was evident in both sensory and motor populations: learned synaptic weights showed target-specific patterning optimized for particular reach movements. Our model embodies an integrative hypothesis of sensorimotor cortical learning that could be used to interpret future electrophysiological data recorded in vivo from sensorimotor learning experiments. We used our model to make the following predictions: learning enhances synchrony in neuronal populations and behaviorally relevant information flow across neuronal populations, enhanced sensory processing aids task-relevant motor performance and the relative ease of a particular movement in vivo depends on the amount of sensory information required to complete the movement. PMID:24047323

Learning-by-catching: uncertain invasive-species populations and the value of information.

PubMed

D'Evelyn, Sean T; Tarui, Nori; Burnett, Kimberly; Roumasset, James A

2008-12-01

This paper develops a model of invasive species control when the species' population size is unknown. In the face of an uncertain population size, a resource manager's species-control efforts provide two potential benefits: (1) a direct benefit of possibly reducing the population of invasive species, and (2) an indirect benefit of information acquisition (due to learning about the population size, which reduces uncertainty). We provide a methodology that takes into account both of these benefits, and show how optimal management decisions are altered in the presence of the indirect benefit of learning. We then apply this methodology to the case of controlling the Brown Treesnake (Boiga irregularis) on the island of Saipan. We find that the indirect benefit--the value of information to reduce uncertainty--is likely to be quite large.

Combining population and patient-specific characteristics for prostate segmentation on 3D CT images

NASA Astrophysics Data System (ADS)

Ma, Ling; Guo, Rongrong; Tian, Zhiqiang; Venkataraman, Rajesh; Sarkar, Saradwata; Liu, Xiabi; Tade, Funmilayo; Schuster, David M.; Fei, Baowei

2016-03-01

Prostate segmentation on CT images is a challenging task. In this paper, we explore the population and patient-specific characteristics for the segmentation of the prostate on CT images. Because population learning does not consider the inter-patient variations and because patient-specific learning may not perform well for different patients, we are combining the population and patient-specific information to improve segmentation performance. Specifically, we train a population model based on the population data and train a patient-specific model based on the manual segmentation on three slice of the new patient. We compute the similarity between the two models to explore the influence of applicable population knowledge on the specific patient. By combining the patient-specific knowledge with the influence, we can capture the population and patient-specific characteristics to calculate the probability of a pixel belonging to the prostate. Finally, we smooth the prostate surface according to the prostate-density value of the pixels in the distance transform image. We conducted the leave-one-out validation experiments on a set of CT volumes from 15 patients. Manual segmentation results from a radiologist serve as the gold standard for the evaluation. Experimental results show that our method achieved an average DSC of 85.1% as compared to the manual segmentation gold standard. This method outperformed the population learning method and the patient-specific learning approach alone. The CT segmentation method can have various applications in prostate cancer diagnosis and therapy.

On the number of independent cultural traits carried by individuals and populations.

PubMed

Lehmann, Laurent; Aoki, Kenichi; Feldman, Marcus W

2011-02-12

In species subject to individual and social learning, each individual is likely to express a certain number of different cultural traits acquired during its lifetime. If the process of trait innovation and transmission reaches a steady state in the population, the number of different cultural traits carried by an individual converges to some stationary distribution. We call this the trait-number distribution. In this paper, we derive the trait-number distributions for both individuals and populations when cultural traits are independent of each other. Our results suggest that as the number of cultural traits becomes large, the trait-number distributions approach Poisson distributions so that their means characterize cultural diversity in the population. We then analyse how the mean trait number varies at both the individual and population levels as a function of various demographic features, such as population size and subdivision, and social learning rules, such as conformism and anti-conformism. Diversity at the individual and population levels, as well as at the level of cultural homogeneity within groups, depends critically on the details of population demography and the individual and social learning rules.

Changing students' perceptions of the homeless: A community service learning experience.

PubMed

Gardner, Janet; Emory, Jan

2018-03-01

The homeless are an underserved, local vulnerable population that can benefit from a service learning clinical practicum experience for baccalaureate prepared nursing students. Negative attitudes and disrespect among healthcare workers has been identified by the homeless as a barrier to healthcare. A service learning experience with a vulnerable population has been shown to change nursing students' attitudes and beliefs. A large university in a southern city partnered with a community based organization that provided services to the homeless to educate senior nursing students in a service learning experience. The goal of this project was to examine attitudes and perceptions of nursing students toward the homeless population before and after participation in a service learning clinical practicum experience. This case study utilized a pre and post experience questionnaire to collect qualitative data for the purposes of the project. The findings revealed students demonstrated a decrease in fear, an increase in empathy, and a deeper understanding of the advocacy role of nurses for people experiencing homelessness. Nurse educators are challenged to engage students with vulnerable populations to change the attitudes and perceptions for improvement in the overall health of communities served worldwide. Partnerships and service learning experiences can benefit all. Copyright © 2018 Elsevier Ltd. All rights reserved.

Domain learning naming game for color categorization.

PubMed

Li, Doujie; Fan, Zhongyan; Tang, Wallace K S

2017-01-01

Naming game simulates the evolution of vocabulary in a population of agents. Through pairwise interactions in the games, agents acquire a set of vocabulary in their memory for object naming. The existing model confines to a one-to-one mapping between a name and an object. Focus is usually put onto name consensus in the population rather than knowledge learning in agents, and hence simple learning model is usually adopted. However, the cognition system of human being is much more complex and knowledge is usually presented in a complicated form. Therefore, in this work, we extend the agent learning model and design a new game to incorporate domain learning, which is essential for more complicated form of knowledge. In particular, we demonstrate the evolution of color categorization and naming in a population of agents. We incorporate the human perceptive model into the agents and introduce two new concepts, namely subjective perception and subliminal stimulation, in domain learning. Simulation results show that, even without any supervision or pre-requisition, a consensus of a color naming system can be reached in a population solely via the interactions. Our work confirms the importance of society interactions in color categorization, which is a long debate topic in human cognition. Moreover, our work also demonstrates the possibility of cognitive system development in autonomous intelligent agents.

Domain learning naming game for color categorization

PubMed Central

2017-01-01

Naming game simulates the evolution of vocabulary in a population of agents. Through pairwise interactions in the games, agents acquire a set of vocabulary in their memory for object naming. The existing model confines to a one-to-one mapping between a name and an object. Focus is usually put onto name consensus in the population rather than knowledge learning in agents, and hence simple learning model is usually adopted. However, the cognition system of human being is much more complex and knowledge is usually presented in a complicated form. Therefore, in this work, we extend the agent learning model and design a new game to incorporate domain learning, which is essential for more complicated form of knowledge. In particular, we demonstrate the evolution of color categorization and naming in a population of agents. We incorporate the human perceptive model into the agents and introduce two new concepts, namely subjective perception and subliminal stimulation, in domain learning. Simulation results show that, even without any supervision or pre-requisition, a consensus of a color naming system can be reached in a population solely via the interactions. Our work confirms the importance of society interactions in color categorization, which is a long debate topic in human cognition. Moreover, our work also demonstrates the possibility of cognitive system development in autonomous intelligent agents. PMID:29136661

Reinforcement learning in complementarity game and population dynamics

NASA Astrophysics Data System (ADS)

Jost, Jürgen; Li, Wei

2014-02-01

We systematically test and compare different reinforcement learning schemes in a complementarity game [J. Jost and W. Li, Physica A 345, 245 (2005), 10.1016/j.physa.2004.07.005] played between members of two populations. More precisely, we study the Roth-Erev, Bush-Mosteller, and SoftMax reinforcement learning schemes. A modified version of Roth-Erev with a power exponent of 1.5, as opposed to 1 in the standard version, performs best. We also compare these reinforcement learning strategies with evolutionary schemes. This gives insight into aspects like the issue of quick adaptation as opposed to systematic exploration or the role of learning rates.

Predicting Virtual World User Population Fluctuations with Deep Learning

PubMed Central

Park, Nuri; Zhang, Qimeng; Kim, Jun Gi; Kang, Shin Jin; Kim, Chang Hun

2016-01-01

This paper proposes a system for predicting increases in virtual world user actions. The virtual world user population is a very important aspect of these worlds; however, methods for predicting fluctuations in these populations have not been well documented. Therefore, we attempt to predict changes in virtual world user populations with deep learning, using easily accessible online data, including formal datasets from Google Trends, Wikipedia, and online communities, as well as informal datasets collected from online forums. We use the proposed system to analyze the user population of EVE Online, one of the largest virtual worlds. PMID:27936009

Predicting Virtual World User Population Fluctuations with Deep Learning.

PubMed

Kim, Young Bin; Park, Nuri; Zhang, Qimeng; Kim, Jun Gi; Kang, Shin Jin; Kim, Chang Hun

2016-01-01

This paper proposes a system for predicting increases in virtual world user actions. The virtual world user population is a very important aspect of these worlds; however, methods for predicting fluctuations in these populations have not been well documented. Therefore, we attempt to predict changes in virtual world user populations with deep learning, using easily accessible online data, including formal datasets from Google Trends, Wikipedia, and online communities, as well as informal datasets collected from online forums. We use the proposed system to analyze the user population of EVE Online, one of the largest virtual worlds.

District Learning Tied to Student Learning

ERIC Educational Resources Information Center

McFadden, Ledyard

2009-01-01

Winners and finalists for the annual Broad Prize for Urban Education have consistently outperformed peer districts serving similar student populations. What makes the difference? These districts consistently demonstrate a learning loop that influences the district's ability to learn, which ultimately influences student opportunities to learn.…

Learned Vocal Variation Is Associated with Abrupt Cryptic Genetic Change in a Parrot Species Complex

PubMed Central

Ribot, Raoul F. H.; Buchanan, Katherine L.; Endler, John A.; Joseph, Leo; Bennett, Andrew T. D.; Berg, Mathew L.

2012-01-01

Contact zones between subspecies or closely related species offer valuable insights into speciation processes. A typical feature of such zones is the presence of clinal variation in multiple traits. The nature of these traits and the concordance among clines are expected to influence whether and how quickly speciation will proceed. Learned signals, such as vocalizations in species having vocal learning (e.g. humans, many birds, bats and cetaceans), can exhibit rapid change and may accelerate reproductive isolation between populations. Therefore, particularly strong concordance among clines in learned signals and population genetic structure may be expected, even among continuous populations in the early stages of speciation. However, empirical evidence for this pattern is often limited because differences in vocalisations between populations are driven by habitat differences or have evolved in allopatry. We tested for this pattern in a unique system where we may be able to separate effects of habitat and evolutionary history. We studied geographic variation in the vocalizations of the crimson rosella (Platycercus elegans) parrot species complex. Parrots are well known for their life-long vocal learning and cognitive abilities. We analysed contact calls across a ca 1300 km transect encompassing populations that differed in neutral genetic markers and plumage colour. We found steep clinal changes in two acoustic variables (fundamental frequency and peak frequency position). The positions of the two clines in vocal traits were concordant with a steep cline in microsatellite-based genetic variation, but were discordant with the steep clines in mtDNA, plumage and habitat. Our study provides new evidence that vocal variation, in a species with vocal learning, can coincide with areas of restricted gene flow across geographically continuous populations. Our results suggest that traits that evolve culturally can be strongly associated with reduced gene flow between populations, and therefore may promote speciation, even in the absence of other barriers. PMID:23227179

A combined learning algorithm for prostate segmentation on 3D CT images.

PubMed

Ma, Ling; Guo, Rongrong; Zhang, Guoyi; Schuster, David M; Fei, Baowei

2017-11-01

Segmentation of the prostate on CT images has many applications in the diagnosis and treatment of prostate cancer. Because of the low soft-tissue contrast on CT images, prostate segmentation is a challenging task. A learning-based segmentation method is proposed for the prostate on three-dimensional (3D) CT images. We combine population-based and patient-based learning methods for segmenting the prostate on CT images. Population data can provide useful information to guide the segmentation processing. Because of inter-patient variations, patient-specific information is particularly useful to improve the segmentation accuracy for an individual patient. In this study, we combine a population learning method and a patient-specific learning method to improve the robustness of prostate segmentation on CT images. We train a population model based on the data from a group of prostate patients. We also train a patient-specific model based on the data of the individual patient and incorporate the information as marked by the user interaction into the segmentation processing. We calculate the similarity between the two models to obtain applicable population and patient-specific knowledge to compute the likelihood of a pixel belonging to the prostate tissue. A new adaptive threshold method is developed to convert the likelihood image into a binary image of the prostate, and thus complete the segmentation of the gland on CT images. The proposed learning-based segmentation algorithm was validated using 3D CT volumes of 92 patients. All of the CT image volumes were manually segmented independently three times by two, clinically experienced radiologists and the manual segmentation results served as the gold standard for evaluation. The experimental results show that the segmentation method achieved a Dice similarity coefficient of 87.18 ± 2.99%, compared to the manual segmentation. By combining the population learning and patient-specific learning methods, the proposed method is effective for segmenting the prostate on 3D CT images. The prostate CT segmentation method can be used in various applications including volume measurement and treatment planning of the prostate. © 2017 American Association of Physicists in Medicine.

Structural drift: the population dynamics of sequential learning.

PubMed

Crutchfield, James P; Whalen, Sean

2012-01-01

We introduce a theory of sequential causal inference in which learners in a chain estimate a structural model from their upstream "teacher" and then pass samples from the model to their downstream "student". It extends the population dynamics of genetic drift, recasting Kimura's selectively neutral theory as a special case of a generalized drift process using structured populations with memory. We examine the diffusion and fixation properties of several drift processes and propose applications to learning, inference, and evolution. We also demonstrate how the organization of drift process space controls fidelity, facilitates innovations, and leads to information loss in sequential learning with and without memory.

Modeling eating behaviors: The role of environment and positive food association learning via a Ratatouille effect.

PubMed

Murillo, Anarina L; Safan, Muntaser; Castillo-Chavez, Carlos; Phillips, Elizabeth D Capaldi; Wadhera, Devina

2016-08-01

Eating behaviors among a large population of children are studied as a dynamic process driven by nonlinear interactions in the sociocultural school environment. The impact of food association learning on diet dynamics, inspired by a pilot study conducted among Arizona children in Pre-Kindergarten to 8th grades, is used to build simple population-level learning models. Qualitatively, mathematical studies are used to highlight the possible ramifications of instruction, learning in nutrition, and health at the community level. Model results suggest that nutrition education programs at the population-level have minimal impact on improving eating behaviors, findings that agree with prior field studies. Hence, the incorporation of food association learning may be a better strategy for creating resilient communities of healthy and non-healthy eaters. A Ratatouille effect can be observed when food association learners become food preference learners, a potential sustainable behavioral change, which in turn, may impact the overall distribution of healthy eaters. In short, this work evaluates the effectiveness of population-level intervention strategies and the importance of institutionalizing nutrition programs that factor in economical, social, cultural, and environmental elements that mesh well with the norms and values in the community.

Fermi field and Dirac oscillator in a Som-Raychaudhuri space-time

NASA Astrophysics Data System (ADS)

de Montigny, Marc; Zare, Soroush; Hassanabadi, Hassan

2018-05-01

We investigate the relativistic dynamics of a Dirac field in the Som-Raychaudhuri space-time, which is described by a Gödel-type metric and a stationary cylindrical symmetric solution of Einstein field equations for a charged dust distribution in rigid rotation. In order to analyze the effect of various physical parameters of this space-time, we solve the Dirac equation in the Som-Raychaudhuri space-time and obtain the energy levels and eigenfunctions of the Dirac operator by using the Nikiforov-Uvarov method. We also examine the behaviour of the Dirac oscillator in the Som-Raychaudhuri space-time, in particular, the effect of its frequency and the vorticity parameter.

Quantization with maximally degenerate Poisson brackets: the harmonic oscillator!

NASA Astrophysics Data System (ADS)

Nutku, Yavuz

2003-07-01

Nambu's construction of multi-linear brackets for super-integrable systems can be thought of as degenerate Poisson brackets with a maximal set of Casimirs in their kernel. By introducing privileged coordinates in phase space these degenerate Poisson brackets are brought to the form of Heisenberg's equations. We propose a definition for constructing quantum operators for classical functions, which enables us to turn the maximally degenerate Poisson brackets into operators. They pose a set of eigenvalue problems for a new state vector. The requirement of the single-valuedness of this eigenfunction leads to quantization. The example of the harmonic oscillator is used to illustrate this general procedure for quantizing a class of maximally super-integrable systems.

Theoretical L-shell Coster-Kronig energies 11 or equal to z or equal to 103

NASA Technical Reports Server (NTRS)

Chen, M. H.; Crasemann, B.; Huang, K. N.; Aoyagi, M.; Mark, H.

1976-01-01

Relativistic relaxed-orbital calculations of L-shell Coster-Kronig transition energies have been performed for all possible transitions in atoms with atomic numbers. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order approximation to the local approximation was thus included. Quantum-electrodynamic corrections were made. Each transition energy was computed as the difference between results of separate self-consistent-field calculations for the initial, singly ionized state and the final two-hole state. The following quantities are listed: total transition energy, 'electric' (Dirac-Hartree-Fock-Slater) contribution, magnetic and retardation contributions, and contributions due to vacuum polarization and self energy.

On the Nodal Lines of Eisenstein Series on Schottky Surfaces

NASA Astrophysics Data System (ADS)

Jakobson, Dmitry; Naud, Frédéric

2017-04-01

On convex co-compact hyperbolic surfaces {X=Γ backslash H2}, we investigate the behavior of nodal curves of real valued Eisenstein series {F_λ(z,ξ)}, where {λ} is the spectral parameter, {ξ} the direction at infinity. Eisenstein series are (non-{L^2}) eigenfunctions of the Laplacian {Δ_X} satisfying {Δ_X F_λ=(1/4+λ^2)F_λ}. As {λ} goes to infinity (the high energy limit), we show that, for generic {ξ}, the number of intersections of nodal lines with any compact segment of geodesic grows like {λ}, up to multiplicative constants. Applications to the number of nodal domains inside the convex core of the surface are then derived.

Quantization of the Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Kozlowski, K.; Sklyanin, E. K.; Torrielli, A.

2017-08-01

We propose a quantization of the Kadomtsev-Petviashvili equation on a cylinder equivalent to an infinite system of nonrelativistic one-dimensional bosons with the masses m = 1, 2,.... The Hamiltonian is Galilei-invariant and includes the split and merge terms Ψ _{{m_1}}^\\dag Ψ _{{m_2}}^\\dag {Ψ _{{m_1} + {m_2}}} and Ψ _{{m_1} + {m_2}}^\\dag {Ψ _{{m_1}}}{Ψ _{{m_2}}} for all combinations of particles with masses m 1, m 2, and m 1 + m 2 for a special choice of coupling constants. We construct the Bethe eigenfunctions for the model and verify the consistency of the coordinate Bethe ansatz and hence the quantum integrability of the model up to the mass M=8 sector.

Splitting of the Low Landau Levels into a Set of Positive Lebesgue Measure under Small Periodic Perturbations

NASA Astrophysics Data System (ADS)

Dinaburg, E. I.; Sinai, Ya. G.; Soshnikov, A. B.

We study the spectral properties of a two-dimensional Schrödinger operator with a uniform magnetic field and a small external periodic field: where and , are small parameters. Representing as the direct integral of one-dimensional quasi-periodic difference operators with long-range potential and employing recent results of E.I.Dinaburg about Anderson localization for such operators (we assume to be typical irrational) we construct the full set of generalised eigenfunctions for the low Landau bands. We also show that the Lebesgue measure of the low bands is positive and proportional in the main order to .

Dynamical Localization for Discrete and Continuous Random Schrödinger Operators

NASA Astrophysics Data System (ADS)

Germinet, F.; De Bièvre, S.

We show for a large class of random Schrödinger operators Ho on and on that dynamical localization holds, i.e. that, with probability one, for a suitable energy interval I and for q a positive real, Here ψ is a function of sufficiently rapid decrease, and PI(Ho) is the spectral projector of Ho corresponding to the interval I. The result is obtained through the control of the decay of the eigenfunctions of Ho and covers, in the discrete case, the Anderson tight-binding model with Bernoulli potential (dimension ν = 1) or singular potential (ν > 1), and in the continuous case Anderson as well as random Landau Hamiltonians.

A Novel Approach to Solve Linearized Stellar Pulsation Equations

NASA Astrophysics Data System (ADS)

Bard, Christopher; Teitler, S.

2011-01-01

We present a new approach to modeling linearized, non-radial pulsations in differentially rotating, massive stars. As a first step in this direction, we consider adiabatic pulsations and adopt the Cowling approximation that perturbations of the gravitational potential and its radial derivative are negligible. The angular dependence of the pulsation modes is expressed as a series expansion of associated Legendre polynomials; the resulting coupled system of differential equations is then solved by finding the eigenfrequencies at which the determinant of a characteristic matrix vanishes. Our method improves on previous treatments by removing the requirement that an arbitrary normalization be applied to the eigenfunctions; this brings the benefit of improved numerical robustness.

Transition Probabilities for Hydrogen-Like Atoms

NASA Astrophysics Data System (ADS)

Jitrik, Oliverio; Bunge, Carlos F.

2004-12-01

E1, M1, E2, M2, E3, and M3 transition probabilities for hydrogen-like atoms are calculated with point-nucleus Dirac eigenfunctions for Z=1-118 and up to large quantum numbers l=25 and n=26, increasing existing data more than a thousandfold. A critical evaluation of the accuracy shows a higher reliability with respect to previous works. Tables for hydrogen containing a subset of the results are given explicitly, listing the states involved in each transition, wavelength, term energies, statistical weights, transition probabilities, oscillator strengths, and line strengths. The complete results, including 1 863 574 distinct transition probabilities, lifetimes, and branching fractions are available at http://www.fisica.unam.mx/research/tables/spectra/1el

Relativistic Corrections to the Energy of the Electron in a Hydrogenlike Atom

NASA Astrophysics Data System (ADS)

Skobelev, V. V.

2017-11-01

Using the previously found solution of the Dirac equation for an electron in the field of the nucleus ( Ze), expressed in terms of the eigenfunction of the spin projection operator Σ3, in the expansion in the small parameter ( Zα), α = e 2/ ħc ≈ 1/137, relativistic and spin-orbit corrections to the energy of the electron in a hydrogenlike atom are calculated, where the latter, in our view, are represented in an easier to visualize form in comparison with previously known classical results. This work may be of methodological interest in the sense of some modification of the corresponding sections of the traditional course on quantum mechanics.

Level statistics of a noncompact cosmological billiard

NASA Astrophysics Data System (ADS)

Csordas, Andras; Graham, Robert; Szepfalusy, Peter

1991-08-01

A noncompact chaotic billiard on a two-dimensional space of constant negative curvature, the infinite equilateral triangle describing anisotropy oscillations in the very early universe, is studied quantum-mechanically. A Weyl formula with a logarithmic correction term is derived for the smoothed number of states function. For one symmetry class of the eigenfunctions, the level spacing distribution, the spectral rigidity Delta3, and the Sigma2 statistics are determined numerically using the finite matrix approximation. Systematic deviations are found both from the Gaussian orthogonal ensemble (GOE) and the Poissonian ensemble. However, good agreement with the GOE is found if the fundamental triangle is deformed in such a way that it no longer tiles the space.

Topology of the distribution of zeros of the Husimi function in the LiNC/LiCN molecular system.

PubMed

Arranz, F J; Benito, R M; Borondo, F

2004-04-08

Phase space representations of quantum mechanics constitute useful tools to study vibrations in molecular systems. Among all possibilities, the Husimi function or coherent state representation is very widely used, its maxima indicating which regions of phase space are relevant in the dynamics of the system. The corresponding zeros are also a good indicator to investigate the characteristics of the eigenstates, and it has been shown how the corresponding distributions can discriminate between regular, irregular, and scarred wave functions. In this paper, we discuss how this result can be understood in terms of the overlap between coherent states and system eigenfunctions. (c) 2004 American Institute of Physics

Electronic and optical properties of GaAs/AlGaAs Fibonacci ordered multiple quantum well systems

NASA Astrophysics Data System (ADS)

Amini, M.; Soleimani, M.; Ehsani, M. H.

2017-12-01

We numerically investigated the optical rectification coefficients (ORCs), transmission coefficient, energy levels and corresponding eigen-functions of GaAs/AlGaAs Fibonacci ordered multiple quantum well systems (FO-MQWs) in the presence of an external electric field. In our calculations, two different methods, including transfer matrix and finite-difference have been used. It has been illustrated that with three types of the FO-MQWs, presented here, localization of the wave-function in any position of the structure is possible. Therefore, managing the electron distribution within the system is easier now. Finally, using the presented structures we could tune the position and amplitude of the ORCs.

Exact Solution of Klein-Gordon and Dirac Equations with Snyder-de Sitter Algebra

NASA Astrophysics Data System (ADS)

Merad, M.; Hadj Moussa, M.

2018-01-01

In this paper, we present the exact solution of the (1+1)-dimensional relativistic Klein-Gordon and Dirac equations with linear vector and scalar potentials in the framework of deformed Snyder-de Sitter model. We introduce some changes of variables, we show that a one-dimensional linear potential for the relativistic system in a space deformed can be equivalent to the trigonometric Rosen-Morse potential in a regular space. In both cases, we determine explicitly the energy eigenvalues and their corresponding eigenfunctions expressed in terms of Romonovski polynomials. The limiting cases are analyzed for α 1 and α 2 → 0 and are compared with those of literature.

Learning of Grammar-Like Visual Sequences by Adults with and without Language-Learning Disabilities

ERIC Educational Resources Information Center

Aguilar, Jessica M.; Plante, Elena

2014-01-01

Purpose: Two studies examined learning of grammar-like visual sequences to determine whether a general deficit in statistical learning characterizes this population. Furthermore, we tested the hypothesis that difficulty in sustaining attention during the learning task might account for differences in statistical learning. Method: In Study 1,…

Ageing and Learning in Australia: Arguing an Evidence Base for Informed and Equitable Policy.

PubMed

Cuthill, Michael; Buys, Laurie; Wilson, Bruce; Kimberley, Helen; Reghenzani, Denise; Kearns, Peter; Thompson, Sally; Golding, Barry; Root, Jo; Weston, Rhonda

2016-01-01

Given Australia's population ageing and predicted impacts related to health, productivity, equity and enhancing quality of life outcomes for senior Australians, lifelong learning has been identified as a pathway for addressing the risks associated with an ageing population. To date Australian governments have paid little attention to addressing these needs and thus, there is an urgent need for policy development for lifelong learning as a national priority. The purpose of this article is to explore the current lifelong learning context in Australia and to propose a set of factors that are most likely to impact learning in later years. Evidence based policy that understands and incorporates learning opportunities for all citizens is required to meet emerging global challenges. Providing appropriate learning opportunities to seniors is one clear pathway for achieving diverse health, social and economic outcomes.

Instructional Utility and Learning Efficacy of Common Active Learning Strategies

ERIC Educational Resources Information Center

McConell, David A.; Chapman, LeeAnna; Czaijka, C. Douglas; Jones, Jason P.; Ryker, Katherine D.; Wiggen, Jennifer

2017-01-01

The adoption of active learning instructional practices in college science, technology, engineering, and mathematics (STEM) courses has been shown to result in improvements in student learning, contribute to increased retention rates, and reduce the achievement gap among different student populations. Descriptions of active learning strategies…

Projection specificity in heterogeneous locus coeruleus cell populations: implications for learning and memory

PubMed Central

Uematsu, Akira; Tan, Bao Zhen

2015-01-01

Noradrenergic neurons in the locus coeruleus (LC) play a critical role in many functions including learning and memory. This relatively small population of cells sends widespread projections throughout the brain including to a number of regions such as the amygdala which is involved in emotional associative learning and the medial prefrontal cortex which is important for facilitating flexibility when learning rules change. LC noradrenergic cells participate in both of these functions, but it is not clear how this small population of neurons modulates these partially distinct processes. Here we review anatomical, behavioral, and electrophysiological studies to assess how LC noradrenergic neurons regulate these different aspects of learning and memory. Previous work has demonstrated that subpopulations of LC noradrenergic cells innervate specific brain regions suggesting heterogeneity of function in LC neurons. Furthermore, noradrenaline in mPFC and amygdala has distinct effects on emotional learning and cognitive flexibility. Finally, neural recording data show that LC neurons respond during associative learning and when previously learned task contingencies change. Together, these studies suggest a working model in which distinct and potentially opposing subsets of LC neurons modulate particular learning functions through restricted efferent connectivity with amygdala or mPFC. This type of model may provide a general framework for understanding other neuromodulatory systems, which also exhibit cell type heterogeneity and projection specificity. PMID:26330494

Prevalence of Behavioural and Psychological Symptoms of Dementia in Individuals with Learning Disabilities.

PubMed

Devshi, Rajal; Shaw, Sarah; Elliott-King, Jordan; Hogervorst, Eef; Hiremath, Avinash; Velayudhan, Latha; Kumar, Satheesh; Baillon, Sarah; Bandelow, Stephan

2015-12-02

A review of 23 studies investigating the prevalence of Behavioural and psychological symptoms of dementia (BPSD) in the general and learning disability population and measures used to assess BPSD was carried out. BPSD are non-cognitive symptoms, which constitute as a major component of dementia regardless of its subtype Research has indicated that there is a high prevalence of BPSD in the general dementia population. There are limited studies, which investigate the prevalence of BPSD within individuals who have learning disabilities and dementia. Findings suggest BPSDs are present within individuals with learning disabilities and dementia. Future research should use updated tools for investigating the prevalence of BPSD within individuals with learning disabilities and dementia.

Teaching/learning strategies for the essentials of baccalaureate nursing education for entry-level community/public health nursing.

PubMed

Callen, Bonnie; Smith, Claudia M; Joyce, Barbara; Lutz, Jayne; Brown-Schott, Nancy; Block, Derryl

2013-01-01

The purpose of this article is to describe teaching/learning strategies for each of the 15 Essentials of Baccalaureate Nursing Education for Entry-Level Community/Public Health Nursing (ACHNE, 2009). Carper's ways of knowing serve as foundations for creating classroom and clinical experiences that focus on clinical action with community as client. Each community/public health essential is defined with relevance to community/public health nursing practice. Five teaching/learning strategies have been delineated for each essential with suggestions of teaching resources and/or target population application. Teaching/learning strategies that focus on community as client, population health, and the essential knowledge and competencies of C/PH nursing will help ensure preparation of baccalaureate prepared nurses with knowledge and skills to improve the health of populations. © 2013 Wiley Periodicals, Inc.

Genetic algorithm enhanced by machine learning in dynamic aperture optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Yongjun; Cheng, Weixing; Yu, Li Hua

With the aid of machine learning techniques, the genetic algorithm has been enhanced and applied to the multi-objective optimization problem presented by the dynamic aperture of the National Synchrotron Light Source II (NSLS-II) Storage Ring. During the evolution processes employed by the genetic algorithm, the population is classified into different clusters in the search space. The clusters with top average fitness are given “elite” status. Intervention on the population is implemented by repopulating some potentially competitive candidates based on the experience learned from the accumulated data. These candidates replace randomly selected candidates among the original data pool. The average fitnessmore » of the population is therefore improved while diversity is not lost. Maintaining diversity ensures that the optimization is global rather than local. The quality of the population increases and produces more competitive descendants accelerating the evolution process significantly. When identifying the distribution of optimal candidates, they appear to be located in isolated islands within the search space. Some of these optimal candidates have been experimentally confirmed at the NSLS-II storage ring. Furthermore, the machine learning techniques that exploit the genetic algorithm can also be used in other population-based optimization problems such as particle swarm algorithm.« less

Genetic algorithm enhanced by machine learning in dynamic aperture optimization

NASA Astrophysics Data System (ADS)

Li, Yongjun; Cheng, Weixing; Yu, Li Hua; Rainer, Robert

2018-05-01

With the aid of machine learning techniques, the genetic algorithm has been enhanced and applied to the multi-objective optimization problem presented by the dynamic aperture of the National Synchrotron Light Source II (NSLS-II) Storage Ring. During the evolution processes employed by the genetic algorithm, the population is classified into different clusters in the search space. The clusters with top average fitness are given "elite" status. Intervention on the population is implemented by repopulating some potentially competitive candidates based on the experience learned from the accumulated data. These candidates replace randomly selected candidates among the original data pool. The average fitness of the population is therefore improved while diversity is not lost. Maintaining diversity ensures that the optimization is global rather than local. The quality of the population increases and produces more competitive descendants accelerating the evolution process significantly. When identifying the distribution of optimal candidates, they appear to be located in isolated islands within the search space. Some of these optimal candidates have been experimentally confirmed at the NSLS-II storage ring. The machine learning techniques that exploit the genetic algorithm can also be used in other population-based optimization problems such as particle swarm algorithm.

Genetic algorithm enhanced by machine learning in dynamic aperture optimization

DOE PAGES

Li, Yongjun; Cheng, Weixing; Yu, Li Hua; ...

2018-05-29

With the aid of machine learning techniques, the genetic algorithm has been enhanced and applied to the multi-objective optimization problem presented by the dynamic aperture of the National Synchrotron Light Source II (NSLS-II) Storage Ring. During the evolution processes employed by the genetic algorithm, the population is classified into different clusters in the search space. The clusters with top average fitness are given “elite” status. Intervention on the population is implemented by repopulating some potentially competitive candidates based on the experience learned from the accumulated data. These candidates replace randomly selected candidates among the original data pool. The average fitnessmore » of the population is therefore improved while diversity is not lost. Maintaining diversity ensures that the optimization is global rather than local. The quality of the population increases and produces more competitive descendants accelerating the evolution process significantly. When identifying the distribution of optimal candidates, they appear to be located in isolated islands within the search space. Some of these optimal candidates have been experimentally confirmed at the NSLS-II storage ring. Furthermore, the machine learning techniques that exploit the genetic algorithm can also be used in other population-based optimization problems such as particle swarm algorithm.« less

Learning Enhances Sensory and Multiple Non-sensory Representations in Primary Visual Cortex

PubMed Central

Poort, Jasper; Khan, Adil G.; Pachitariu, Marius; Nemri, Abdellatif; Orsolic, Ivana; Krupic, Julija; Bauza, Marius; Sahani, Maneesh; Keller, Georg B.; Mrsic-Flogel, Thomas D.; Hofer, Sonja B.

2015-01-01

Summary We determined how learning modifies neural representations in primary visual cortex (V1) during acquisition of a visually guided behavioral task. We imaged the activity of the same layer 2/3 neuronal populations as mice learned to discriminate two visual patterns while running through a virtual corridor, where one pattern was rewarded. Improvements in behavioral performance were closely associated with increasingly distinguishable population-level representations of task-relevant stimuli, as a result of stabilization of existing and recruitment of new neurons selective for these stimuli. These effects correlated with the appearance of multiple task-dependent signals during learning: those that increased neuronal selectivity across the population when expert animals engaged in the task, and those reflecting anticipation or behavioral choices specifically in neuronal subsets preferring the rewarded stimulus. Therefore, learning engages diverse mechanisms that modify sensory and non-sensory representations in V1 to adjust its processing to task requirements and the behavioral relevance of visual stimuli. PMID:26051421

Learning That Makes a Difference: Pedagogy and Practice for Learning Abroad

ERIC Educational Resources Information Center

Benham Rennick, Joanne

2015-01-01

Society faces significant new challenges surrounding issues in human health; global security; environmental devastation; human rights violations; economic uncertainty; population explosion and regression; recognition of diversity, difference and special populations at home and abroad. In light of these challenges, there is a great opportunity, and…

Underserved Gifted Populations: Responding to Their Needs and Abilities. Perspectives on Creativity Research.

ERIC Educational Resources Information Center

Smutny, Joan Franklin, Ed.

Twenty-five papers address issues of the underserved gifted, including environmental influences, multicultural and global factors, special learning problems, and the highly gifted and creatively gifted. The papers are: "Twenty-five Teaching Strategies that Promote Learning Success for Underserved Gifted Populations" (Jerry Flack); "The Invisible…

Putting the Learning in Service Learning: From Soup Kitchen Models to the Black Metropolis Model

ERIC Educational Resources Information Center

Manley, Theodoric, Jr.; Buffa, Avery S.; Dube, Caleb; Reed, Lauren

2006-01-01

Results of the Black Metropolis Model (BMM) of service learning are analyzed and illustrated in this article to explain how to "put the learning in service learning." There are many soup kitchens or nontransforming models of service learning where students are asked to serve needy populations but internalize and learn little about the…

Stochastic gain in finite populations

NASA Astrophysics Data System (ADS)

Röhl, Torsten; Traulsen, Arne; Claussen, Jens Christian; Schuster, Heinz Georg

2008-08-01

Flexible learning rates can lead to increased payoffs under the influence of noise. In a previous paper [Traulsen , Phys. Rev. Lett. 93, 028701 (2004)], we have demonstrated this effect based on a replicator dynamics model which is subject to external noise. Here, we utilize recent advances on finite population dynamics and their connection to the replicator equation to extend our findings and demonstrate the stochastic gain effect in finite population systems. Finite population dynamics is inherently stochastic, depending on the population size and the intensity of selection, which measures the balance between the deterministic and the stochastic parts of the dynamics. This internal noise can be exploited by a population using an appropriate microscopic update process, even if learning rates are constant.

Tight-binding chains with off-diagonal disorder: Bands of extended electronic states induced by minimal quasi-one-dimensionality

NASA Astrophysics Data System (ADS)

Nandy, Atanu; Pal, Biplab; Chakrabarti, Arunava

2016-08-01

It is shown that an entire class of off-diagonally disordered linear lattices composed of two basic building blocks and described within a tight-binding model can be tailored to generate absolutely continuous energy bands. It can be achieved if linear atomic clusters of an appropriate size are side-coupled to a suitable subset of sites in the backbone, and if the nearest-neighbor hopping integrals, in the backbone and in the side-coupled cluster, bear a certain ratio. We work out the precise relationship between the number of atoms in one of the building blocks in the backbone and that in the side attachment. In addition, we also evaluate the definite correlation between the numerical values of the hopping integrals at different subsections of the chain, that can convert an otherwise point spectrum (or a singular continuous one for deterministically disordered lattices) with exponentially (or power law) localized eigenfunctions to an absolutely continuous spectrum comprising one or more bands (subbands) populated by extended, totally transparent eigenstates. The results, which are analytically exact, put forward a non-trivial variation of the Anderson localization (Anderson P. W., Phys. Rev., 109 (1958) 1492), pointing towards its unusual sensitivity to the numerical values of the system parameters and, go well beyond the other related models such as the Random Dimer Model (RDM) (Dunlap D. H. et al., Phys. Rev. Lett., 65 (1990) 88).

Effect of Kolb's Learning Styles under Inductive Guided-Inquiry Learning on Learning Outcomes

ERIC Educational Resources Information Center

Sudria, Ida Bagus Nyoman; Redhana, I. Wayan; Kirna, I. Made; Aini, Diah

2018-01-01

This study aimed to examine the effect of Kolb's learning styles on chemical learning activities and achievement of reaction rate taught by inductive guided inquiry learning. The population was eleventh grade Science students of a senior secondary school having relatively good academic input based on national testing results in Bali, Indonesia.…

Vertical transmission of learned signatures in a wild parrot

PubMed Central

Berg, Karl S.; Delgado, Soraya; Cortopassi, Kathryn A.; Beissinger, Steven R.; Bradbury, Jack W.

2012-01-01

Learned birdsong is a widely used animal model for understanding the acquisition of human speech. Male songbirds often learn songs from adult males during sensitive periods early in life, and sing to attract mates and defend territories. In presumably all of the 350+ parrot species, individuals of both sexes commonly learn vocal signals throughout life to satisfy a wide variety of social functions. Despite intriguing parallels with humans, there have been no experimental studies demonstrating learned vocal production in wild parrots. We studied contact call learning in video-rigged nests of a well-known marked population of green-rumped parrotlets (Forpus passerinus) in Venezuela. Both sexes of naive nestlings developed individually unique contact calls in the nest, and we demonstrate experimentally that signature attributes are learned from both primary care-givers. This represents the first experimental evidence for the mechanisms underlying the transmission of a socially acquired trait in a wild parrot population. PMID:21752824

Individual subject classification for Alzheimer's disease based on incremental learning using a spatial frequency representation of cortical thickness data.

PubMed

Cho, Youngsang; Seong, Joon-Kyung; Jeong, Yong; Shin, Sung Yong

2012-02-01

Patterns of brain atrophy measured by magnetic resonance structural imaging have been utilized as significant biomarkers for diagnosis of Alzheimer's disease (AD). However, brain atrophy is variable across patients and is non-specific for AD in general. Thus, automatic methods for AD classification require a large number of structural data due to complex and variable patterns of brain atrophy. In this paper, we propose an incremental method for AD classification using cortical thickness data. We represent the cortical thickness data of a subject in terms of their spatial frequency components, employing the manifold harmonic transform. The basis functions for this transform are obtained from the eigenfunctions of the Laplace-Beltrami operator, which are dependent only on the geometry of a cortical surface but not on the cortical thickness defined on it. This facilitates individual subject classification based on incremental learning. In general, methods based on region-wise features poorly reflect the detailed spatial variation of cortical thickness, and those based on vertex-wise features are sensitive to noise. Adopting a vertex-wise cortical thickness representation, our method can still achieve robustness to noise by filtering out high frequency components of the cortical thickness data while reflecting their spatial variation. This compromise leads to high accuracy in AD classification. We utilized MR volumes provided by Alzheimer's Disease Neuroimaging Initiative (ADNI) to validate the performance of the method. Our method discriminated AD patients from Healthy Control (HC) subjects with 82% sensitivity and 93% specificity. It also discriminated Mild Cognitive Impairment (MCI) patients, who converted to AD within 18 months, from non-converted MCI subjects with 63% sensitivity and 76% specificity. Moreover, it showed that the entorhinal cortex was the most discriminative region for classification, which is consistent with previous pathological findings. In comparison with other classification methods, our method demonstrated high classification performance in both categories, which supports the discriminative power of our method in both AD diagnosis and AD prediction. Copyright © 2011 Elsevier Inc. All rights reserved.

World Population: Facts in Focus. World Population Data Sheet Workbook. Population Learning Series.

ERIC Educational Resources Information Center

Crews, Kimberly A.

This workbook teaches population analysis using world population statistics. To complete the four student activity sheets, the students refer to the included "1988 World Population Data Sheet" which lists nations' statistical data that includes population totals, projected population, birth and death rates, fertility levels, and the…

Surface Wave Propagation on a Laterally Heterogeneous Earth

NASA Astrophysics Data System (ADS)

Tromp, Jeroen

1992-01-01

Love and Rayleigh waves propagating on the surface of the Earth exhibit path, phase and amplitude anomalies as a result of the lateral heterogeneity of the mantle. In the JWKB approximation, these anomalies can be determined by tracing surface wave trajectories, and calculating phase and amplitude anomalies along them. A time- or frequency -domain JWKB analysis yields local eigenfunctions, local dispersion relations, and conservation laws for the surface wave energy. The local dispersion relations determine the surface wave trajectories, and the energy equations determine the surface wave amplitudes. On an anisotrophic Earth model the local dispersion relation and the local vertical eigenfunctions depend explicitly on the direction of the local wavevector. Apart from the usual dynamical phase, which is the integral of the local wavevector along a raypath, there is an additional variation is phase. This additional phase, which is an analogue of the Berry phase in adiabatic quantum mechanics, vanishes in a waveguide with a local vertical two-fold symmetry axis or a local horizontal mirror plane. JWKB theory breaks down in the vicinity of caustics, where neighboring rays merge and the surface wave amplitude diverges. Based upon a potential representation of the surface wave field, a uniformly valid Maslov theory can be obtained. Surface wave trajectories are determined by a system of four ordinary differential equations which define a three-dimensional manifold in four-dimensional phase space (theta,phi,k_theta,k _phi), where theta is colatitude, phi is longitude, and k_theta and k _phi are the covariant components of the wavevector. There are no caustics in phase space; it is only when the rays in phase space are projected onto configuration space (theta,phi), the mixed spaces (k_theta,phi ) and (theta,k_phi), or onto momentum space (k_theta,k _phi), that caustics occur. The essential strategy is to employ a mixed or momentum space representation of the wavefield in the vicinity of a configuration space caustic.

Robust Seismic Normal Modes Computation in Radial Earth Models and A Novel Classification Based on Intersection Points of Waveguides

NASA Astrophysics Data System (ADS)

Ye, J.; Shi, J.; De Hoop, M. V.

2017-12-01

We develop a robust algorithm to compute seismic normal modes in a spherically symmetric, non-rotating Earth. A well-known problem is the cross-contamination of modes near "intersections" of dispersion curves for separate waveguides. Our novel computational approach completely avoids artificial degeneracies by guaranteeing orthonormality among the eigenfunctions. We extend Wiggins' and Buland's work, and reformulate the Sturm-Liouville problem as a generalized eigenvalue problem with the Rayleigh-Ritz Galerkin method. A special projection operator incorporating the gravity terms proposed by de Hoop and a displacement/pressure formulation are utilized in the fluid outer core to project out the essential spectrum. Moreover, the weak variational form enables us to achieve high accuracy across the solid-fluid boundary, especially for Stoneley modes, which have exponentially decaying behavior. We also employ the mixed finite element technique to avoid spurious pressure modes arising from discretization schemes and a numerical inf-sup test is performed following Bathe's work. In addition, the self-gravitation terms are reformulated to avoid computations outside the Earth, thanks to the domain decomposition technique. Our package enables us to study the physical properties of intersection points of waveguides. According to Okal's classification theory, the group velocities should be continuous within a branch of the same mode family. However, we have found that there will be a small "bump" near intersection points, which is consistent with Miropol'sky's observation. In fact, we can loosely regard Earth's surface and the CMB as independent waveguides. For those modes that are far from the intersection points, their eigenfunctions are localized in the corresponding waveguides. However, those that are close to intersection points will have physical features of both waveguides, which means they cannot be classified in either family. Our results improve on Okal's classification, demonstrating that dispersion curves from independent waveguides should be considered to break at intersection points.

SU-F-R-41: Regularized PCA Can Model Treatment-Related Changes in Head and Neck Patients Using Daily CBCTs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chetvertkov, M; Henry Ford Health System, Detroit, MI; Siddiqui, F

2016-06-15

Purpose: To use daily cone beam CTs (CBCTs) to develop regularized principal component analysis (PCA) models of anatomical changes in head and neck (H&N) patients, to guide replanning decisions in adaptive radiation therapy (ART). Methods: Known deformations were applied to planning CT (pCT) images of 10 H&N patients to model several different systematic anatomical changes. A Pinnacle plugin was used to interpolate systematic changes over 35 fractions, generating a set of 35 synthetic CTs for each patient. Deformation vector fields (DVFs) were acquired between the pCT and synthetic CTs and random fraction-to-fraction changes were superimposed on the DVFs. Standard non-regularizedmore » and regularized patient-specific PCA models were built using the DVFs. The ability of PCA to extract the known deformations was quantified. PCA models were also generated from clinical CBCTs, for which the deformations and DVFs were not known. It was hypothesized that resulting eigenvectors/eigenfunctions with largest eigenvalues represent the major anatomical deformations during the course of treatment. Results: As demonstrated with quantitative results in the supporting document regularized PCA is more successful than standard PCA at capturing systematic changes early in the treatment. Regularized PCA is able to detect smaller systematic changes against the background of random fraction-to-fraction changes. To be successful at guiding ART, regularized PCA should be coupled with models of when anatomical changes occur: early, late or throughout the treatment course. Conclusion: The leading eigenvector/eigenfunction from the both PCA approaches can tentatively be identified as a major systematic change during radiotherapy course when systematic changes are large enough with respect to random fraction-to-fraction changes. In all cases the regularized PCA approach appears to be more reliable at capturing systematic changes, enabling dosimetric consequences to be projected once trends are established early in the treatment course. This work is supported in part by a grant from Varian Medical Systems, Palo Alto, CA.« less

Improving Learning in Science and Basic Skills among Diverse Student Populations.

ERIC Educational Resources Information Center

Sutman, Francis X.; Guzman, Ana

This monograph is a rich resource of information designed to strengthen science and basic skills teaching, and improve learning for limited English proficient (LEP) minority student populations. It proposes the use of hands-on science investigations as the driving force for mathematics and English language development. The materials included in…

Adapting the ALP Model for Student and Institutional Needs

ERIC Educational Resources Information Center

Sides, Meredith

2016-01-01

With the increasing adoption of accelerated models of learning comes the necessary step of adapting these models to fit the unique needs of the student population at each individual institution. One such college adapted the ALP (Accelerated Learning Program) model and made specific changes to the target population, structure and scheduling, and…

The Geographic Accessibility and Inequality of Community-Based Elderly Learning Resources: A Remodeling Assessment, 2009-2017

ERIC Educational Resources Information Center

Tseng, Ming-Hseng; Wu, Hui-Ching

2018-01-01

Continuous elderly learning activities not only empower elderly populations' knowledge about health but also enhance these populations' social connections and social abilities, which can enhance their overall quality of life. Geographic accessibility is a determinant factor for elderly participation in social activities. In this study, we proposed…

A cholinergic feedback circuit to regulate striatal population uncertainty and optimize reinforcement learning.

PubMed

Franklin, Nicholas T; Frank, Michael J

2015-12-25

Convergent evidence suggests that the basal ganglia support reinforcement learning by adjusting action values according to reward prediction errors. However, adaptive behavior in stochastic environments requires the consideration of uncertainty to dynamically adjust the learning rate. We consider how cholinergic tonically active interneurons (TANs) may endow the striatum with such a mechanism in computational models spanning three Marr's levels of analysis. In the neural model, TANs modulate the excitability of spiny neurons, their population response to reinforcement, and hence the effective learning rate. Long TAN pauses facilitated robustness to spurious outcomes by increasing divergence in synaptic weights between neurons coding for alternative action values, whereas short TAN pauses facilitated stochastic behavior but increased responsiveness to change-points in outcome contingencies. A feedback control system allowed TAN pauses to be dynamically modulated by uncertainty across the spiny neuron population, allowing the system to self-tune and optimize performance across stochastic environments.

From primary care to public health: using Problem-based Learning and the ecological model to teach public health to first year medical students.

PubMed

Hoover, Cora R; Wong, Candice C; Azzam, Amin

2012-06-01

We investigated whether a public health-oriented Problem-Based Learning case presented to first-year medical students conveyed 12 "Population Health Competencies for Medical Students," as recommended by the Association of American Medical Colleges and the Regional Medicine-Public Health Education Centers. A public health-oriented Problem-Based Learning case guided by the ecological model paradigm was developed and implemented among two groups of 8 students at the University of California, Berkeley-UCSF Joint Medical Program, in the Fall of 2010. Using directed content analysis, student-generated written reports were coded for the presence of the 12 population health content areas. Students generated a total of 29 reports, of which 20 (69%) contained information relevant to at least one of the 12 population health competencies. Each of the 12 content areas was addressed by at least one report. As physicians-in-training prepare to confront the challenges of integrating prevention and population health with clinical practice, Problem-Based Learning is a promising tool to enhance medical students' engagement with public health.

Prevalence of Behavioural and Psychological Symptoms of Dementia in Individuals with Learning Disabilities

PubMed Central

Devshi, Rajal; Shaw, Sarah; Elliott-King, Jordan; Hogervorst, Eef; Hiremath, Avinash; Velayudhan, Latha; Kumar, Satheesh; Baillon, Sarah; Bandelow, Stephan

2015-01-01

A review of 23 studies investigating the prevalence of Behavioural and psychological symptoms of dementia (BPSD) in the general and learning disability population and measures used to assess BPSD was carried out. BPSD are non-cognitive symptoms, which constitute as a major component of dementia regardless of its subtype Research has indicated that there is a high prevalence of BPSD in the general dementia population. There are limited studies, which investigate the prevalence of BPSD within individuals who have learning disabilities and dementia. Findings suggest BPSDs are present within individuals with learning disabilities and dementia. Future research should use updated tools for investigating the prevalence of BPSD within individuals with learning disabilities and dementia. PMID:26854171

Attitudes toward Web-based distance learning among public health nurses in Taiwan: a questionnaire survey.

PubMed

Yu, Shu; Yang, Kuei-Feng

2006-08-01

Public health nurses (PHNs) often cannot receive in-service education due to limitations of time and space. Learning through the Internet has been a widely used technique in many professional and clinical nursing fields. The learner's attitude is the most important indicator that promotes learning. The purpose of this study was to investigate PHNs' attitude toward web-based learning and its determinants. This study conducted a cross-sectional research design. 369 health centers in Taiwan. The population involved this study was 2398 PHNs, and we used random sampling from this population. Finally, 329 PHNs completed the questionnaire, with a response rate of 84.0%. Data were collected by mailing the questionnaire. Most PHNs revealed a positive attitude toward web-based learning (mean+/-SD=55.02+/-6.39). PHNs who worked at village health centers, a service population less than 10,000, PHNs who had access to computer facility and on-line hardware in health centers and with better computer competence revealed more positive attitudes (p<0.01). Web-based learning is an important new way of in-service education; however, its success and hindering factors require further investigation. Individual computer competence is the main target for improvement, and educators should also consider how to establish a user-friendly learning environment on the Internet.

Relevance of a neurophysiological marker of attention allocation for children's learning-related behaviors and academic performance.

PubMed

Willner, Cynthia J; Gatzke-Kopp, Lisa M; Bierman, Karen L; Greenberg, Mark T; Segalowitz, Sidney J

2015-08-01

Learning-related behaviors are important for school success. Socioeconomic disadvantage confers risk for less adaptive learning-related behaviors at school entry, yet substantial variability in school readiness exists within socioeconomically disadvantaged populations. Investigation of neurophysiological systems associated with learning-related behaviors in high-risk populations could illuminate resilience processes. This study examined the relevance of a neurophysiological measure of controlled attention allocation, amplitude of the P3b event-related potential, for learning-related behaviors and academic performance in a sample of socioeconomically disadvantaged kindergarteners. The sample consisted of 239 children from an urban, low-income community, approximately half of whom exhibited behavior problems at school entry (45% aggressive/oppositional; 64% male; 69% African American, 21% Hispanic). Results revealed that higher P3b amplitudes to target stimuli in a go/no-go task were associated with more adaptive learning-related behaviors in kindergarten. Furthermore, children's learning-related behaviors in kindergarten mediated a positive indirect effect of P3b amplitude on growth in academic performance from kindergarten to 1st grade. Given that P3b amplitude reflects attention allocation processes, these findings build on the scientific justification for interventions targeting young children's attention skills in order to promote effective learning-related behaviors and academic achievement within socioeconomically disadvantaged populations. (c) 2015 APA, all rights reserved).

Structural Equation Modeling towards Online Learning Readiness, Academic Motivations, and Perceived Learning

ERIC Educational Resources Information Center

Horzum, Mehmet Baris; Kaymak, Zeliha Demir; Gungoren, Ozlem Canan

2015-01-01

The relationship between online learning readiness, academic motivations, and perceived learning was investigated via structural equation modeling in the research. The population of the research consisted of 750 students who studied using the online learning programs of Sakarya University. 420 of the students who volunteered for the research and…

Intergenerational Learning: A Valuable Learning Experience for Higher Education Students

ERIC Educational Resources Information Center

Corrigan, Trudy; McNamara, Gerry; O'Hara, Joe

2013-01-01

Problem Statement: This paper reports on the evaluation of a project rooted in the principles and practice of Intergenerational Learning. Intergenerational Learning is increasingly seen as a key strategy in providing learning opportunities for older people in societies where the profile of the population is ageing rapidly. No significant work has,…

Virtual Reality Rehabilitation from Social Cognitive and Motor Learning Theoretical Perspectives in Stroke Population

PubMed Central

Imam, Bita; Jarus, Tal

2014-01-01

Objectives. To identify the virtual reality (VR) interventions used for the lower extremity rehabilitation in stroke population and to explain their underlying training mechanisms using Social Cognitive (SCT) and Motor Learning (MLT) theoretical frameworks. Methods. Medline, Embase, Cinahl, and Cochrane databases were searched up to July 11, 2013. Randomized controlled trials that included a VR intervention for lower extremity rehabilitation in stroke population were included. The Physiotherapy Evidence Database (PEDro) scale was used to assess the quality of the included studies. The underlying training mechanisms involved in each VR intervention were explained according to the principles of SCT (vicarious learning, performance accomplishment, and verbal persuasion) and MLT (focus of attention, order and predictability of practice, augmented feedback, and feedback fading). Results. Eleven studies were included. PEDro scores varied from 3 to 7/10. All studies but one showed significant improvement in outcomes in favour of the VR group (P < 0.05). Ten VR interventions followed the principle of performance accomplishment. All the eleven VR interventions directed subject's attention externally, whereas nine provided training in an unpredictable and variable fashion. Conclusions. The results of this review suggest that VR applications used for lower extremity rehabilitation in stroke population predominantly mediate learning through providing a task-oriented and graduated learning under a variable and unpredictable practice. PMID:24523967

Modelling Social Learning in Monkeys

ERIC Educational Resources Information Center

Kendal, Jeremy R.

2008-01-01

The application of modelling to social learning in monkey populations has been a neglected topic. Recently, however, a number of statistical, simulation and analytical approaches have been developed to help examine social learning processes, putative traditions, the use of social learning strategies and the diffusion dynamics of socially…

Speciation: more likely through a genetic or through a learned habitat preference?

PubMed Central

Beltman, J.B; Metz, J.A.J

2005-01-01

A problem in understanding sympatric speciation is establishing how reproductive isolation can arise when there is disruptive selection on an ecological trait. One of the solutions that has been proposed is that a habitat preference evolves, and that mates are chosen within the preferred habitat. We present a model where the habitat preference can evolve either by means of a genetic mechanism or by means of learning. Employing an adaptive-dynamical analysis, we show that evolution proceeds either to a single population of specialists with a genetic preference for their optimal habitat, or to a population of generalists without a habitat preference. The generalist population subsequently experiences disruptive selection. Learning promotes speciation because it increases the intensity of disruptive selection. An individual-based version of the model shows that, when loci are completely unlinked and learning confers little cost, the presence of disruptive selection most probably leads to speciation via the simultaneous evolution of a learned habitat preference. For high costs of learning, speciation is most likely to occur via the evolution of a genetic habitat preference. However, the latter only happens when the effect of mutations is large, or when there is linkage between genes coding for the different traits. PMID:16011920

Learning, Attention/Hyperactivity, and Conduct Problems as Sequelae of Excessive Daytime Sleepiness in a General Population Study of Young Children

PubMed Central

Calhoun, Susan L.; Fernandez-Mendoza, Julio; Vgontzas, Alexandros N.; Mayes, Susan D.; Tsaoussoglou, Marina; Rodriguez-Muñoz, Alfredo; Bixler, Edward O.

2012-01-01

Study Objectives: Although excessive daytime sleepiness (EDS) is a common problem in children, with estimates of 15%; few studies have investigated the sequelae of EDS in young children. We investigated the association of EDS with objective neurocognitive measures and parent reported learning, attention/hyperactivity, and conduct problems in a large general population sample of children. Design: Cross-sectional. Setting: Population based. Participants: 508 children from The Penn State Child Cohort. Interventions: N/A. Measurements and Results: Children underwent a 9-h polysomnogram, comprehensive neurocognitive testing, and parent rating scales. Children were divided into 2 groups: those with and without parent-reported EDS. Structural equation modeling was used to examine whether processing speed and working memory performance would mediate the relationship between EDS and learning, attention/hyperactivity, and conduct problems. Logistic regression models suggest that parent-reported learning, attention/hyperactivity, and conduct problems, as well as objective measurement of processing speed and working memory are significant sequelae of EDS, even when controlling for AHI and objective markers of sleep. Path analysis demonstrates that processing speed and working memory performance are strong mediators of the association of EDS with learning and attention/hyperactivity problems, while to a slightly lesser degree are mediators from EDS to conduct problems. Conclusions: This study suggests that in a large general population sample of young children, parent-reported EDS is associated with neurobehavioral (learning, attention/hyperactivity, conduct) problems and poorer performance in processing speed and working memory. Impairment due to EDS in daytime cognitive and behavioral functioning can have a significant impact on children's development. Citation: Calhoun SL; Fernandez-Mendoza J; Vgontzas AN; Mayes SD; Tsaoussoglou M; Rodriguez-Muñoz A; Bixler EO. Learning, attention/hyperactivity, and conduct problems as sequelae of excessive daytime sleepiness in a general population study of young children. SLEEP 2012;35(5):627-632. PMID:22547888

Evolutionary Responses to Invasion: Cane Toad Sympatric Fish Show Enhanced Avoidance Learning

PubMed Central

Caller, Georgina; Brown, Culum

2013-01-01

The introduced cane toad (Bufo marinus) poses a major threat to biodiversity due to its lifelong toxicity. Several terrestrial native Australian vertebrates are adapting to the cane toad’s presence and lab trials have demonstrated that repeated exposure to B. marinus can result in learnt avoidance behaviour. Here we investigated whether aversion learning is occurring in aquatic ecosystems by comparing cane toad naïve and sympatric populations of crimson spotted rainbow fish (Melanotaenia duboulayi). The first experiment indicated that fish from the sympatric population had pre-existing aversion to attacking cane toad tadpoles but also showed reduced attacks on native tadpoles. The second experiment revealed that fish from both naïve and sympatric populations learned to avoid cane toad tadpoles following repeated, direct exposure. Allopatric fish also developed a general aversion to tadpoles. The aversion learning abilities of both groups was examined using an experiment involving novel distasteful prey items. While both populations developed a general avoidance of edible pellets in the presence of distasteful pellets, only the sympatric population significantly reduced the number of attacks on the novel distasteful prey item. These results indicate that experience with toxic prey items over multiple generations can enhance avoidance leaning capabilities via natural selection. PMID:23372788

Pediatric residents' learning styles and temperaments and their relationships to standardized test scores.

PubMed

Tuli, Sanjeev Y; Thompson, Lindsay A; Saliba, Heidi; Black, Erik W; Ryan, Kathleen A; Kelly, Maria N; Novak, Maureen; Mellott, Jane; Tuli, Sonal S

2011-12-01

Board certification is an important professional qualification and a prerequisite for credentialing, and the Accreditation Council for Graduate Medical Education (ACGME) assesses board certification rates as a component of residency program effectiveness. To date, research has shown that preresidency measures, including National Board of Medical Examiners scores, Alpha Omega Alpha Honor Medical Society membership, or medical school grades poorly predict postresidency board examination scores. However, learning styles and temperament have been identified as factors that 5 affect test-taking performance. The purpose of this study is to characterize the learning styles and temperaments of pediatric residents and to evaluate their relationships to yearly in-service and postresidency board examination scores. This cross-sectional study analyzed the learning styles and temperaments of current and past pediatric residents by administration of 3 validated tools: the Kolb Learning Style Inventory, the Keirsey Temperament Sorter, and the Felder-Silverman Learning Style test. These results were compared with known, normative, general and medical population data and evaluated for correlation to in-service examination and postresidency board examination scores. The predominant learning style for pediatric residents was converging 44% (33 of 75 residents) and the predominant temperament was guardian 61% (34 of 56 residents). The learning style and temperament distribution of the residents was significantly different from published population data (P  =  .002 and .04, respectively). Learning styles, with one exception, were found to be unrelated to standardized test scores. The predominant learning style and temperament of pediatric residents is significantly different than that of the populations of general and medical trainees. However, learning styles and temperament do not predict outcomes on standardized in-service and board examinations in pediatric residents.

Pediatric Residents' Learning Styles and Temperaments and Their Relationships to Standardized Test Scores

PubMed Central

Tuli, Sanjeev Y.; Thompson, Lindsay A.; Saliba, Heidi; Black, Erik W.; Ryan, Kathleen A.; Kelly, Maria N.; Novak, Maureen; Mellott, Jane; Tuli, Sonal S.

2011-01-01

Background Board certification is an important professional qualification and a prerequisite for credentialing, and the Accreditation Council for Graduate Medical Education (ACGME) assesses board certification rates as a component of residency program effectiveness. To date, research has shown that preresidency measures, including National Board of Medical Examiners scores, Alpha Omega Alpha Honor Medical Society membership, or medical school grades poorly predict postresidency board examination scores. However, learning styles and temperament have been identified as factors that 5 affect test-taking performance. The purpose of this study is to characterize the learning styles and temperaments of pediatric residents and to evaluate their relationships to yearly in-service and postresidency board examination scores. Methods This cross-sectional study analyzed the learning styles and temperaments of current and past pediatric residents by administration of 3 validated tools: the Kolb Learning Style Inventory, the Keirsey Temperament Sorter, and the Felder-Silverman Learning Style test. These results were compared with known, normative, general and medical population data and evaluated for correlation to in-service examination and postresidency board examination scores. Results The predominant learning style for pediatric residents was converging 44% (33 of 75 residents) and the predominant temperament was guardian 61% (34 of 56 residents). The learning style and temperament distribution of the residents was significantly different from published population data (P  =  .002 and .04, respectively). Learning styles, with one exception, were found to be unrelated to standardized test scores. Conclusions The predominant learning style and temperament of pediatric residents is significantly different than that of the populations of general and medical trainees. However, learning styles and temperament do not predict outcomes on standardized in-service and board examinations in pediatric residents. PMID:23205211

Supervised Machine Learning for Population Genetics: A New Paradigm

PubMed Central

Schrider, Daniel R.; Kern, Andrew D.

2018-01-01

As population genomic datasets grow in size, researchers are faced with the daunting task of making sense of a flood of information. To keep pace with this explosion of data, computational methodologies for population genetic inference are rapidly being developed to best utilize genomic sequence data. In this review we discuss a new paradigm that has emerged in computational population genomics: that of supervised machine learning (ML). We review the fundamentals of ML, discuss recent applications of supervised ML to population genetics that outperform competing methods, and describe promising future directions in this area. Ultimately, we argue that supervised ML is an important and underutilized tool that has considerable potential for the world of evolutionary genomics. PMID:29331490

Student Feedback in Elementary Online Learning: A Phenomenological Study Using Person-Centered Instruction

ERIC Educational Resources Information Center

Smistad, Kirsten E.

2013-01-01

Online learning is becoming increasingly attractive as an option for learning at the K-12 level. However, most research in online learning is done with adults or university participants-a population with a different developmental level and different reasons for learning than those still in compulsory schooling. This study examined the phenomenon…

Designing and Implementing Neighborhoods of Learning in Cork's UNESCO Learning City Project

ERIC Educational Resources Information Center

Ó Tuama, Séamus; O'Sullivan, Siobhán

2015-01-01

Cork, the Republic of Ireland's second most populous city, is one of 12 UNESCO Learning Cities globally. Becoming a learning city requires a sophisticated audit of education, learning and other socio-economic indicators. It also demands that cities become proactively engaged in delivering to the objectives set by the "Beijing Declaration on…

Framework for Quality Professional Development for Practitioners Working With Adult English Language Learners

ERIC Educational Resources Information Center

Center for Adult English Language Acquisition, 2008

2008-01-01

As a result of a growing immigrant population in the United States, many adult education programs are working with new populations of adult learners who need to learn English. There is a need for a strong workforce of trained and knowledgeable practitioners who can work effectively with adults learning English and facilitate transitions to…

Effects of Mastery Learning Approach on Secondary School Students' Physics Achievement

ERIC Educational Resources Information Center

Wambugu, Patriciah W.; Changeiywo, Johnson M.

2008-01-01

This study aimed at finding out the effects of Mastery Learning Approach (MLA) on students' achievement in Physics. The study was Quasi-experimental and Solomon Four Non-equivalent Control Group Design was used. The target population comprised of secondary school students in Kieni East Division of Nyeri District. The accessible population was Form…

A Study on the Progress toward Implementation of Learning-Centered Approaches at a Large Urban Community College

ERIC Educational Resources Information Center

Walters, Carmen Hawkins

2009-01-01

Faculty facing challenges of teaching students in a post-Katrina environment used learning-centered approaches to restore educational opportunities to its populations of hurricane-displaced students, the growing population of Hispanic students, and the business community. The study sought to determine if the faculty members had made progress…

The Impact of Aging on Education.

ERIC Educational Resources Information Center

Davis, Angela

The percentage of adults aged 65 years or older is expected to increase from 12 percent of the population in 1980 to more than 21 percent by the year 2030. Since many adults stay involved with learning activities well into their 80s and 90s, educational organizations have a great opportunity to supply learning activities to this population. To…

Scientific Value and Educational Goals: Balancing Priorities and Increasing Adult Engagement in a Citizen Science Project

ERIC Educational Resources Information Center

Sickler, Jessica; Cherry, Tammy Messick; Allee, Leslie; Smyth, Rebecca Rice; Losey, John

2014-01-01

The Lost Ladybug Project is a citizen science project that engages individuals and groups in research and learning about ladybug population dynamics. With a dual purpose of advancing scientists' research about ladybug populations and achieving learning outcomes with participants, the project's summative evaluation led to critical reflection on the…

The Middle-Aging 'Eighties in San Diego: Prospects for Lifelong Learning. AIR Forum 1979 Paper.

ERIC Educational Resources Information Center

Mason, Thomas R.

The processes and kinds of sources used in comprehensive educational planning employing institutional research are described to serve as a guide to provide recurrent education for a middle-aged population. The concept of lifelong learning has been addressed by postsecondary institutions because the traditional-aged college population has been…

Internet Access, Use and Sharing Levels among Students during the Teaching-Learning Process

ERIC Educational Resources Information Center

Tutkun, Omer F.

2011-01-01

The purpose of this study was to determine the awareness among students and levels regarding student access, use, and knowledge sharing during the teaching-learning process. The triangulation method was utilized in this study. The population of the research universe was 21,747. The student sample population was 1,292. Two different data collection…

Finite-difference solution of the compressible stability eigenvalue problem

NASA Technical Reports Server (NTRS)

Malik, M. R.

1982-01-01

A compressible stability analysis computer code is developed. The code uses a matrix finite difference method for local eigenvalue solution when a good guess for the eigenvalue is available and is significantly more computationally efficient than the commonly used initial value approach. The local eigenvalue search procedure also results in eigenfunctions and, at little extra work, group velocities. A globally convergent eigenvalue procedure is also developed which may be used when no guess for the eigenvalue is available. The global problem is formulated in such a way that no unstable spurious modes appear so that the method is suitable for use in a black box stability code. Sample stability calculations are presented for the boundary layer profiles of a Laminar Flow Control (LFC) swept wing.

Atomic electron energies including relativistic effects and quantum electrodynamic corrections

NASA Technical Reports Server (NTRS)

Aoyagi, M.; Chen, M. H.; Crasemann, B.; Huang, K. N.; Mark, H.

1977-01-01

Atomic electron energies have been calculated relativistically. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first order correction to the local approximation was thus included. Quantum-electrodynamic corrections were made. For all orbitals in all atoms with 2 less than or equal to Z less than or equal to 106, the following quantities are listed: total energies, electron kinetic energies, electron-nucleus potential energies, electron-electron potential energies consisting of electrostatic and Breit interaction (magnetic and retardation) terms, and vacuum polarization energies. These results will serve for detailed comparison of calculations based on other approaches. The magnitude of quantum electrodynamic corrections is exhibited quantitatively for each state.

Impact of nearest-neighbor repulsion on superconducting pairing in 2D extended Hubbard model

NASA Astrophysics Data System (ADS)

Jiang, Mi; Hahner, U. R.; Maier, T. A.; Schulthess, T. C.

Using dynamical cluster approximation (DCA) with an continuous-time QMC solver for the two-dimensional extended Hubbard model, we studied the impact of nearest-neighbor Coulomb repulsion V on d-wave superconducting pairing dynamics. By solving Bethe-Salpeter equation for particle-particle superconducting channel, we focused on the evolution of leading d-wave eigenvalue with V and the momentum and frequency dependence of the corresponding eigenfunction. The comparison with the evolution of both spin and charge susceptibilities versus V is presented showing the competition between spin and charge fluctuations. This research received generous support from the MARVEL NCCR and used resources of the Swiss National Supercomputing Center, as well as (INCITE) program in Oak Ridge Leadership Computing Facility.

Boundary-layer effects in composite laminates. I - Free-edge stress singularities. II - Free-edge stress solutions and basic characteristics

NASA Technical Reports Server (NTRS)

Wang, S. S.; Choi, I.

1982-01-01

The fundamental nature of the boundary-layer effect in fiber-reinforced composite laminates is formulated in terms of the theory of anisotropic elasticity. The basic structure of the boundary-layer field solution is obtained by using Lekhnitskii's stress potentials (1963). The boundary-layer stress field is found to be singular at composite laminate edges, and the exact order or strength of the boundary layer stress singularity is determined using an eigenfunction expansion method. A complete solution to the boundary-layer problem is then derived, and the convergence and accuracy of the solution are analyzed, comparing results with existing approximate numerical solutions. The solution method is demonstrated for a symmetric graphite-epoxy composite.

Irreducible projective representations and their physical applications

NASA Astrophysics Data System (ADS)

Yang, Jian; Liu, Zheng-Xin

2018-01-01

An eigenfunction method is applied to reduce the regular projective representations (Reps) of finite groups to obtain their irreducible projective Reps. Anti-unitary groups are treated specially, where the decoupled factor systems and modified Schur’s lemma are introduced. We discuss the applications of irreducible Reps in many-body physics. It is shown that in symmetry protected topological phases, geometric defects or symmetry defects may carry projective Rep of the symmetry group; while in symmetry enriched topological phases, intrinsic excitations (such as spinons or visons) may carry projective Rep of the symmetry group. We also discuss the applications of projective Reps in problems related to spectrum degeneracy, such as in search of models without sign problem in quantum Monte Carlo simulations.

Minimal analytical model for undular tidal bore profile; quantum and Hawking effect analogies

NASA Astrophysics Data System (ADS)

Berry, M. V.

2018-05-01

Waves travelling up-river, driven by high tides, often consist of a smooth front followed by a series of undulations. A simple approximate theory gives the rigidly travelling profile of such ‘undular hydraulic jumps’, up to scaling, as the integral of the Airy function; applying self-consistency fixes the scaling. The theory combines the standard hydraulic jump with ideas borrowed from quantum physics: Hamiltonian operators and zero-energy eigenfunctions. There is an analogy between undular bores and the Hawking effect in relativity: both concern waves associated with horizons. ‘Physics is not just Concerning the Nature of Things, but Concerning the Interconnectedness of all the Natures of Things’(Sir Charles Frank, retirement speech 1976).

Mathematical Methods for Physics and Engineering Third Edition Paperback Set

NASA Astrophysics Data System (ADS)

Riley, Ken F.; Hobson, Mike P.; Bence, Stephen J.

2006-06-01

Prefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.

A symmetric integral identity for Bessel functions with applications to integral geometry

NASA Astrophysics Data System (ADS)

Salman, Yehonatan

2017-12-01

In the article of Kunyansky (Inverse Probl 23(1):373-383, 2007) a symmetric integral identity for Bessel functions of the first and second kind was proved in order to obtain an explicit inversion formula for the spherical mean transform where our data is given on the unit sphere in Rn . The aim of this paper is to prove an analogous symmetric integral identity in case where our data for the spherical mean transform is given on an ellipse E in R2 . For this, we will use the recent results obtained by Cohl and Volkmer (J Phys A Math Theor 45:355204, 2012) for the expansions into eigenfunctions of Bessel functions of the first and second kind in elliptical coordinates.

Collisional dependence of Alfvén mode saturation in tokamaks

DOE PAGES

Zhou, Muni; White, Roscoe

2016-10-26

Saturation of Alfvén modes driven unstable by a distribution of high energy particles as a function of collisionality is investigated with a guiding center code, using numerical eigenfunctions produced by linear theory and numerical high energy particle distributions. The most important resonance is found and it is shown that when the resonance domain is bounded, not allowing particles to collisionlessly escape, the saturation amplitude is given by the balance of the resonance mixing time with the time for nearby particles to collisionally diffuse across the resonance width. Finally, saturation amplitudes are in agreement with theoretical predictions as long as themore » mode amplitude is not so large that it produces stochastic loss from the resonance domain.« less

Collisional dependence of Alfvén mode saturation in tokamaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Muni; White, Roscoe

Saturation of Alfvén modes driven unstable by a distribution of high energy particles as a function of collisionality is investigated with a guiding center code, using numerical eigenfunctions produced by linear theory and numerical high energy particle distributions. The most important resonance is found and it is shown that when the resonance domain is bounded, not allowing particles to collisionlessly escape, the saturation amplitude is given by the balance of the resonance mixing time with the time for nearby particles to collisionally diffuse across the resonance width. Finally, saturation amplitudes are in agreement with theoretical predictions as long as themore » mode amplitude is not so large that it produces stochastic loss from the resonance domain.« less

Rogue periodic waves of the focusing nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Chen, Jinbing; Pelinovsky, Dmitry E.

2018-02-01

Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn. Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov-Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine's breather). The magnification factor of the rogue periodic waves is computed as a function of the elliptic modulus. Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.

Rogue periodic waves of the focusing nonlinear Schrödinger equation.

PubMed

Chen, Jinbing; Pelinovsky, Dmitry E

2018-02-01

Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn . Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov-Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine's breather). The magnification factor of the rogue periodic waves is computed as a function of the elliptic modulus. Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.

Perturbations of Jacobi polynomials and piecewise hypergeometric orthogonal systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Neretin, Yu A

2006-12-31

A family of non-complete orthogonal systems of functions on the ray [0,{infinity}] depending on three real parameters {alpha}, {beta}, {theta} is constructed. The elements of this system are piecewise hypergeometric functions with singularity at x=1. For {theta}=0 these functions vanish on [1,{infinity}) and the system is reduced to the Jacobi polynomials P{sub n}{sup {alpha}}{sup ,{beta}} on the interval [0,1]. In the general case the functions constructed can be regarded as an interpretation of the expressions P{sub n+{theta}}{sup {alpha}}{sup ,{beta}}. They are eigenfunctions of an exotic Sturm-Liouville boundary-value problem for the hypergeometric differential operator. The spectral measure for this problem ismore » found.« less

Criticality in the quantum kicked rotor with a smooth potential.

PubMed

Dutta, Rina; Shukla, Pragya

2008-09-01

We investigate the possibility of an Anderson-type transition in the quantum kicked rotor with a smooth potential due to dynamical localization of the wave functions. Our results show the typical characteristics of a critical behavior, i.e., multifractal eigenfunctions and a scale-invariant level statistics at a critical kicking strength which classically corresponds to a mixed regime. This indicates the existence of a localization to delocalization transition in the quantum kicked rotor. Our study also reveals the possibility of other types of transition in the quantum kicked rotor, with a kicking strength well within the strongly chaotic regime. These transitions, driven by the breaking of exact symmetries, e.g., time reversal and parity, are similar to weak-localization transitions in disordered metals.

SEMICONDUCTOR PHYSICS: Properties of the two- and three-dimensional quantum dot qubit

NASA Astrophysics Data System (ADS)

Shihua, Chen

2010-05-01

On the condition of electric-longitudinal-optical (LO) phonon strong coupling in both two- and three-dimensional parabolic quantum dots (QDs), we obtain the eigenenergies of the ground state (GS) and the first excited state (ES), the eigenfunctions of the GS and the first ES by using a variational method of Pekar type. This system in QD may be employed as a quantum system-quantum bit (qubit). When the electron is in the superposition state of the GS and the first ES, we obtain the time evolution of the electron density. The relations of both the electron probability density and the period of oscillation with the electric-LO phonon coupling strength and confinement length are discussed.

Combining electromagnetic gyro-kinetic particle-in-cell simulations with collisions

NASA Astrophysics Data System (ADS)

Slaby, Christoph; Kleiber, Ralf; Könies, Axel

2017-09-01

It has been an open question whether for electromagnetic gyro-kinetic particle-in-cell (PIC) simulations pitch-angle collisions and the recently introduced pullback transformation scheme (Mishchenko et al., 2014; Kleiber et al., 2016) are consistent. This question is positively answered by comparing the PIC code EUTERPE with an approach based on an expansion of the perturbed distribution function in eigenfunctions of the pitch-angle collision operator (Legendre polynomials) to solve the electromagnetic drift-kinetic equation with collisions in slab geometry. It is shown how both approaches yield the same results for the frequency and damping rate of a kinetic Alfvén wave and how the perturbed distribution function is substantially changed by the presence of pitch-angle collisions.

The nonconforming virtual element method for eigenvalue problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gardini, Francesca; Manzini, Gianmarco; Vacca, Giuseppe

We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the L 2-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problems. The proposed schemes provide a correct approximation of the spectrum and we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numericalmore » tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.« less

Numerical analysis of spectral properties of coupled oscillator Schroedinger operators. I - Single and double well anharmonic oscillators

NASA Technical Reports Server (NTRS)

Isaacson, D.; Isaacson, E. L.; Paes-Leme, P. J.; Marchesin, D.

1981-01-01

Several methods for computing many eigenvalues and eigenfunctions of a single anharmonic oscillator Schroedinger operator whose potential may have one or two minima are described. One of the methods requires the solution of an ill-conditioned generalized eigenvalue problem. This method has the virtue of using a bounded amount of work to achieve a given accuracy in both the single and double well regions. Rigorous bounds are given, and it is proved that the approximations converge faster than any inverse power of the size of the matrices needed to compute them. The results of computations for the g:phi(4):1 theory are presented. These results indicate that the methods actually converge exponentially fast.

GLOBAL HELIOSEISMIC EVIDENCE FOR A DEEPLY PENETRATING SOLAR MERIDIONAL FLOW CONSISTING OF MULTIPLE FLOW CELLS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schad, A.; Roth, M.; Timmer, J., E-mail: ariane.schad@kis.uni-freiburg.de

2013-12-01

We use a novel global helioseismic analysis method to infer the meridional flow in the deep Solar interior. The method is based on the perturbation of eigenfunctions of Solar p modes due to meridional flow. We apply this method to time series obtained from Dopplergrams measured by the Michelson Doppler Imager aboard the Solar and Heliospheric Observatory covering the observation period 2004-2010. Our results show evidence that the meridional flow reaches down to the base of the convection zone. The flow profile has a complex spatial structure consisting of multiple flow cells distributed in depth and latitude. Toward the Solarmore » surface, our results are in good agreement with flow measurements from local helioseismology.« less

On numerical solutions to the QCD ’t Hooft equation in the limit of large quark mass

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zubov, Roman; Prokhvatilov, Evgeni

2016-01-22

First we give a short informal introduction to the theory behind the ’t Hooft equation. Then we consider numerical solutions to this equation in the limit of large fermion masses. It turns out that the spectrum of eigenvalues coincides with that of the Airy differential equation. Moreover when we take the Fourier transform of eigenfunctions, they look like the corresponding Airy functions with appropriate symmetry. It is known that these functions correspond to solutions of a one dimensional Schrodinger equation for a particle in a triangular potential well. So we find the analogy between this problem and the ’t Hooftmore » equation. We also present a simple intuition behind these results.« less

Computationally efficient finite-difference modal method for the solution of Maxwell's equations.

PubMed

Semenikhin, Igor; Zanuccoli, Mauro

2013-12-01

In this work, a new implementation of the finite-difference (FD) modal method (FDMM) based on an iterative approach to calculate the eigenvalues and corresponding eigenfunctions of the Helmholtz equation is presented. Two relevant enhancements that significantly increase the speed and accuracy of the method are introduced. First of all, the solution of the complete eigenvalue problem is avoided in favor of finding only the meaningful part of eigenmodes by using iterative methods. Second, a multigrid algorithm and Richardson extrapolation are implemented. Simultaneous use of these techniques leads to an enhancement in terms of accuracy, which allows a simple method such as the FDMM with a typical three-point difference scheme to be significantly competitive with an analytical modal method.

A linear shock cell model for non-circular jets using conformal mapping with a pseudo-spectral hybrid scheme

NASA Technical Reports Server (NTRS)

Bhat, Thonse R. S.; Baty, Roy S.; Morris, Philip J.

1990-01-01

The shock structure in non-circular supersonic jets is predicted using a linear model. This model includes the effects of the finite thickness of the mixing layer and the turbulence in the jet shear layer. A numerical solution is obtained using a conformal mapping grid generation scheme with a hybrid pseudo-spectral discretization method. The uniform pressure perturbation at the jet exit is approximated by a Fourier-Mathieu series. The pressure at downstream locations is obtained from an eigenfunction expansion that is matched to the pressure perturbation at the jet exit. Results are presented for a circular jet and for an elliptic jet of aspect ratio 2.0. Comparisons are made with experimental data.

Learning Profiles: The Learning Crisis Is Not (Mostly) about Enrollment

ERIC Educational Resources Information Center

Sandefur, Justin; Pritchett, Lant; Beatty, Amanda

2016-01-01

The differential patterns of grade progression have direct implications for the calculation of learning profiles. Researchers measure learning in primary school using survey data on reading and math skills of a nationally representative, population-based sample of children in India, Pakistan, Kenya, Tanzania, and Uganda. Research demonstrates that…

Psychosocial Functioning of Learning-Disabled Children: Replicability of Statistically Derived Subtypes.

ERIC Educational Resources Information Center

Fuerst, Darren R.; And Others

1989-01-01

Investigated Personality Inventory for Children scores of 132 learning-disabled children between ages of 6 and 12 years. Results indicated that learning-disabled children comprised heterogeneous population in terms of psychosocial functioning and that subtypes of learning-disabled children with similar patterns of socioemotional adjustment can be…

Distance Learning for Special Populations

ERIC Educational Resources Information Center

Bates, Rodger A.

2012-01-01

Distance education strategies for remotely deployed, highly mobile, or institutionalized populations are reviewed and critiqued. Specifically, asynchronous, offline responses for special military units, Native Americans on remote reservations, prison populations and other geographically, temporally or technologically isolated niche populations are…

Exploring student learning profiles in algebra-based studio physics: A person-centered approach

NASA Astrophysics Data System (ADS)

Pond, Jarrad W. T.; Chini, Jacquelyn J.

2017-06-01

In this study, we explore the strategic self-regulatory and motivational characteristics of students in studio-mode physics courses at three universities with varying student populations and varying levels of success in their studio-mode courses. We survey students using questions compiled from several existing questionnaires designed to measure students' study strategies, attitudes toward and motivations for learning physics, organization of scientific knowledge, experiences outside the classroom, and demographics. Using a person-centered approach, we utilize cluster analysis methods to group students into learning profiles based on their individual responses to better understand the strategies and motives of algebra-based studio physics students. Previous studies have identified five distinct learning profiles across several student populations using similar methods. We present results from first-semester and second-semester studio-mode introductory physics courses across three universities. We identify these five distinct learning profiles found in previous studies to be present within our population of introductory physics students. In addition, we investigate interactions between these learning profiles and student demographics. We find significant interactions between a student's learning profile and their experience with high school physics, major, gender, grade expectation, and institution. Ultimately, we aim to use this method of analysis to take the characteristics of students into account in the investigation of successful strategies for using studio methods of physics instruction within and across institutions.

Exploring Self-Directed Learning in the Online Learning Environment: Comparing Traditional versus Nontraditional Learner Populations a Qualitative Study

ERIC Educational Resources Information Center

Plews, Rachel Christine

2016-01-01

The purpose of this study was to explore self-directed learning in the online learning context. A sample of traditional and nontraditional learners, who were considered above average in their level of self-direction, participated in qualitative interviews to discuss their learning while engaged in an online course. The findings suggested no major…

Students' Perceptions and Readiness towards Mobile Learning in Colleges of Education: A Nigerian Perspective

ERIC Educational Resources Information Center

Chaka, John Gyang; Govender, Irene

2017-01-01

Access to quality education is becoming a huge challenge in Nigeria, in view of the exponential growth in its population, coupled with ethno-religious crises and other acts of terrorism. A large chunk of the country's population--about 26% have no access to education, as existing teaching and learning facilities have become inadequate. Some…

Process-Oriented Guided-Inquiry Learning in an Introductory Anatomy and Physiology Course with a Diverse Student Population

ERIC Educational Resources Information Center

Brown, Patrick J. P.

2010-01-01

Process-oriented guided-inquiry learning (POGIL), a pedagogical technique initially developed for college chemistry courses, has been implemented for 2 yr in a freshman-level anatomy and physiology course at a small private college. The course is populated with students with backgrounds ranging from no previous college-level science to junior and…

Teachers' Teaching Experience and Students' Learning Outcomes in Secondary Schools in Ondo State, Nigeria

ERIC Educational Resources Information Center

Adeyemi, T. O.

2008-01-01

This article examined teachers' teaching experience and students' learning outcomes in the secondary schools in Ondo State Nigeria. As a correlational survey, the study population comprised all the 257 secondary schools in the State. This population was made up of 147 rural schools and 110 urban schools. It was also made up of 12 single sex…

Project Recon

DTIC Science & Technology

2012-06-14

Management tool • Current Risk Recon functionality • Issues Recon & Opportunity Recon – Launching Fall 2012 • FMEA and Lessons Learned – Planned Future...Lessons learned UNCLASSIFIED Integrated Risk Management FMEA Failure Mode and Effects Analysis Risk Recon Fields from FMEA software pre...populate Risk Info sheet. Risk Mitigation from Risk Recon trace back and populate FMEA , new RPN numbers. Issues Recon When a risk becomes an issue

Population size vs. social connectedness - A gene-culture coevolutionary approach to cumulative cultural evolution.

PubMed

Kobayashi, Yutaka; Ohtsuki, Hisashi; Wakano, Joe Y

2016-10-01

It has long been debated if population size is a crucial determinant of the level of culture. While empirical results are mixed, recent theoretical studies suggest that social connectedness between people may be a more important factor than the size of the entire population. These models, however, do not take into account evolutionary responses of learning strategies determining the mode of transmission and innovation and are hence not suitable for predicting the long-term implications of parameters of interest. In the present paper, to address this issue, we provide a gene-culture coevolution model, in which the microscopic learning process of each individual is explicitly described as a continuous-time stochastic process and time allocation to social and individual learning is allowed to evolve. We have found that social connectedness has a larger impact on the equilibrium level of culture than population size especially when connectedness is weak and population size is large. This result, combined with those of previous culture-only models, points to the importance of studying separate effects of population size and internal social structure to better understand spatiotemporal variation in the level of culture. Copyright © 2016 Elsevier Inc. All rights reserved.

A paradox of cumulative culture.

PubMed

Kobayashi, Yutaka; Wakano, Joe Yuichiro; Ohtsuki, Hisashi

2015-08-21

Culture can grow cumulatively if socially learnt behaviors are improved by individual learning before being passed on to the next generation. Previous authors showed that this kind of learning strategy is unlikely to be evolutionarily stable in the presence of a trade-off between learning and reproduction. This is because culture is a public good that is freely exploited by any member of the population in their model (cultural social dilemma). In this paper, we investigate the effect of vertical transmission (transmission from parents to offspring), which decreases the publicness of culture, on the evolution of cumulative culture in both infinite and finite population models. In the infinite population model, we confirm that culture accumulates largely as long as transmission is purely vertical. It turns out, however, that introduction of even slight oblique transmission drastically reduces the equilibrium level of culture. Even more surprisingly, if the population size is finite, culture hardly accumulates even under purely vertical transmission. This occurs because stochastic extinction due to random genetic drift prevents a learning strategy from accumulating enough culture. Overall, our theoretical results suggest that introducing vertical transmission alone does not really help solve the cultural social dilemma problem. Copyright © 2015 Elsevier Ltd. All rights reserved.

Conditioning to colors: a population assay for visual learning in Drosophila.

PubMed

van Swinderen, Bruno

2011-11-01

Vision is a major sensory modality in Drosophila behavior, with more than one-half of the Drosophila brain devoted to visual processing. The mechanisms of vision in Drosophila can be studied in individuals and in populations of flies by using various paradigms. Although there has never been a widely used population assay for visual learning in Drosophila, some population paradigms have shown significant visual learning. These studies use colors as conditioned stimuli (CS) and shaking as the unconditioned stimulus (US). A simple version of the paradigm, conditioning to colors using a shaking device, is described here. A conditioning chamber, called a crab, is designed to center the flies after shaking by having them tumble down to the lowest point between joined glass tubes forming a V. Thus, vibration should be just strong enough to center most flies. After shaking, flies display a geotactic response and climb up either side of the V, and their choice of which side to climb is influenced by color displays on either side. The proportion of flies on either side determines the flies' natural preference or their learned avoidance of a color associated with shaking.

Novel Spoken Word Learning in Adults with Developmental Dyslexia

ERIC Educational Resources Information Center

Conner, Peggy S.

2013-01-01

A high percentage of individuals with dyslexia struggle to learn unfamiliar spoken words, creating a significant obstacle to foreign language learning after early childhood. The origin of spoken-word learning difficulties in this population, generally thought to be related to the underlying literacy deficit, is not well defined (e.g., Di Betta…

Analysis of the Learning Styles of Diverse Student Populations and Implications for Higher Education Instructional Change

ERIC Educational Resources Information Center

Novogrodsky, Dorothy

2012-01-01

Higher education is one of the last institutions of learning to embrace the challenge of learner diversity that exists everywhere today (Dunn & Griggs, 2000; Rowley, Lujan, Dolence, 1998). This investigation explored the relationships between perceived preferred instructional strategies and student learning styles of learning-style aware…

Learning to Reflect and to Attribute Constructively as Basic Components of Self-Regulated Learning

ERIC Educational Resources Information Center

Masui, Chris; De Corte, Erik

2005-01-01

Background: Higher education is facing a number of problems: adjusting to larger and more heterogeneous student populations, increasing the number of graduating students, and preparing for lifelong learning. Improving learning competence can make a substantial contribution to solving each of these major concerns. The growing knowledge base on…

Considering a Voice of the Body for Adult Transformative Learning Theory

ERIC Educational Resources Information Center

Boleyn, Elizabeth C.

2013-01-01

Unknowingly, much of the population of the Western World are thinking machines who live and learn isolated from somatic experiences. They distrust their bodies in the learning process and are stuck living out unquestioned realities of embodied socioculturalism and rationalism which guide decision making, learning and ways of being. Considering a…

Making the Transition to E-Learning: Strategies and Issues

ERIC Educational Resources Information Center

Bullen, Mark, Ed.; Janes, Diane, Ed.

2007-01-01

Higher education institutions around the world are increasingly turning to e-learning as a way of dealing with growing and changing student populations. Education for the knowledge society means new skills and knowledge are needed and it means that lifelong learning has become a necessity. Higher education institutions are looking to e-learning to…

Identification of Learning Mechanisms in a Wild Meerkat Population

PubMed Central

Hoppitt, Will; Samson, Jamie; Laland, Kevin N.; Thornton, Alex

2012-01-01

Vigorous debates as to the evolutionary origins of culture remain unresolved due to an absence of methods for identifying learning mechanisms in natural populations. While laboratory experiments on captive animals have revealed evidence for a number of mechanisms, these may not necessarily reflect the processes typically operating in nature. We developed a novel method that allows social and asocial learning mechanisms to be determined in animal groups from the patterns of interaction with, and solving of, a task. We deployed it to analyse learning in groups of wild meerkats (Suricata suricatta) presented with a novel foraging apparatus. We identify nine separate learning processes underlying the meerkats’ foraging behaviour, in each case precisely quantifying their strength and duration, including local enhancement, emulation, and a hitherto unrecognized form of social learning, which we term ‘observational perseverance’. Our analysis suggests a key factor underlying the stability of behavioural traditions is a high ratio of specific to generalized social learning effects. The approach has widespread potential as an ecologically valid tool to investigate learning mechanisms in natural groups of animals, including humans. PMID:22905113

Social learning in humans and other animals

PubMed Central

Gariépy, Jean-François; Watson, Karli K.; Du, Emily; Xie, Diana L.; Erb, Joshua; Amasino, Dianna; Platt, Michael L.

2014-01-01

Decisions made by individuals can be influenced by what others think and do. Social learning includes a wide array of behaviors such as imitation, observational learning of novel foraging techniques, peer or parental influences on individual preferences, as well as outright teaching. These processes are believed to underlie an important part of cultural variation among human populations and may also explain intraspecific variation in behavior between geographically distinct populations of animals. Recent neurobiological studies have begun to uncover the neural basis of social learning. Here we review experimental evidence from the past few decades showing that social learning is a widespread set of skills present in multiple animal species. In mammals, the temporoparietal junction, the dorsomedial, and dorsolateral prefrontal cortex, as well as the anterior cingulate gyrus, appear to play critical roles in social learning. Birds, fish, and insects also learn from others, but the underlying neural mechanisms remain poorly understood. We discuss the evolutionary implications of these findings and highlight the importance of emerging animal models that permit precise modification of neural circuit function for elucidating the neural basis of social learning. PMID:24765063

A cholinergic feedback circuit to regulate striatal population uncertainty and optimize reinforcement learning

PubMed Central

Franklin, Nicholas T; Frank, Michael J

2015-01-01

Convergent evidence suggests that the basal ganglia support reinforcement learning by adjusting action values according to reward prediction errors. However, adaptive behavior in stochastic environments requires the consideration of uncertainty to dynamically adjust the learning rate. We consider how cholinergic tonically active interneurons (TANs) may endow the striatum with such a mechanism in computational models spanning three Marr's levels of analysis. In the neural model, TANs modulate the excitability of spiny neurons, their population response to reinforcement, and hence the effective learning rate. Long TAN pauses facilitated robustness to spurious outcomes by increasing divergence in synaptic weights between neurons coding for alternative action values, whereas short TAN pauses facilitated stochastic behavior but increased responsiveness to change-points in outcome contingencies. A feedback control system allowed TAN pauses to be dynamically modulated by uncertainty across the spiny neuron population, allowing the system to self-tune and optimize performance across stochastic environments. DOI: http://dx.doi.org/10.7554/eLife.12029.001 PMID:26705698

Service-Learning and Mathematics

ERIC Educational Resources Information Center

Roemer, Cynthia Anne

2009-01-01

Contemporary educational theory has given increased attention to service-learning as valuable pedagogy. Ever-changing technology progress and applications demand a quantitatively literate population, supporting the need for experiential activities in mathematics. This study addresses service-learning pedagogy in mathematics through a study of the…

Zebra Finch Song Phonology and Syntactical Structure across Populations and Continents-A Computational Comparison.

PubMed

Lachlan, Robert F; van Heijningen, Caroline A A; Ter Haar, Sita M; Ten Cate, Carel

2016-01-01

Learned bird songs are often characterized by a high degree of variation between individuals and sometimes between populations, while at the same time maintaining species specificity. The evolution of such songs depends on the balance between plasticity and constraints. Captive populations provide an opportunity to examine signal variation and differentiation in detail, so we analyzed adult male zebra finch (Taeniopygia guttata) songs recorded from 13 populations across the world, including one sample of songs from wild-caught males in their native Australia. Cluster analysis suggested some, albeit limited, evidence that zebra finch song units belonged to universal, species-wide categories, linked to restrictions in vocal production and non-song parts of the vocal repertoire. Across populations, songs also showed some syntactical structure, although any song unit could be placed anywhere within the song. On the other hand, there was a statistically significant differentiation between populations, but the effect size was very small, and its communicative significance dubious. Our results suggest that variation in zebra finch songs within a population is largely determined by species-wide constraints rather than population-specific features. Although captive zebra finch populations have been sufficiently isolated to allow them to genetically diverge, there does not appear to have been any divergence in the genetically determined constraints that underlie song learning. Perhaps more surprising is the lack of locally diverged cultural traditions. Zebra finches serve as an example of a system where frequent learning errors may rapidly create within-population diversity, within broad phonological and syntactical constraints, and prevent the formation of long-term cultural traditions that allow populations to diverge.

Learning, climate and the evolution of cultural capacity.

PubMed

Whitehead, Hal

2007-03-21

Patterns of environmental variation influence the utility, and thus evolution, of different learning strategies. I use stochastic, individual-based evolutionary models to assess the relative advantages of 15 different learning strategies (genetic determination, individual learning, vertical social learning, horizontal/oblique social learning, and contingent combinations of these) when competing in variable environments described by 1/f noise. When environmental variation has little effect on fitness, then genetic determinism persists. When environmental variation is large and equal over all time-scales ("white noise") then individual learning is adaptive. Social learning is advantageous in "red noise" environments when variation over long time-scales is large. Climatic variability increases with time-scale, so that short-lived organisms should be able to rely largely on genetic determination. Thermal climates usually are insufficiently red for social learning to be advantageous for species whose fitness is very determined by temperature. In contrast, population trajectories of many species, especially large mammals and aquatic carnivores, are sufficiently red to promote social learning in their predators. The ocean environment is generally redder than that on land. Thus, while individual learning should be adaptive for many longer-lived organisms, social learning will often be found in those dependent on the populations of other species, especially if they are marine. This provides a potential explanation for the evolution of a prevalence of social learning, and culture, in humans and cetaceans.

Learning about population-health through a community practice learning project: An evaluation study.

PubMed

Davenport, Maggie; Ooms, Ann; Marks-Maran, Di

2016-03-01

Increasing student nurse numbers requiring community placement learning opportunities has led to insufficient numbers of community nurses being available to support student nurses in the community. Although the study presented in the article is based in the UK this issue is reported widely in the literature across the globe. Universities in many countries have had to find innovative ways of providing community health learning opportunities for student nurses. This article reports on how one university in the UK has approached this challenge through students engaging in a population-based study in the community through group work. A research study was undertaken into this innovation which found that the student nurses engaged well with the project and with their groups and undertaking the project had positive value and impact on them and their understanding of population-health. Issues that arose for them largely focused on unequal participation in the group work by some with many participants perceiving that they had done more work on the group project and presentation than others in their group. However, working in this way was perceived to be a good learning experience for the majority of participants. Copyright © 2016 Elsevier Ltd. All rights reserved.

An Evaluation of the Effectiveness of a "Five Ways to Well-Being" Group Run with People with Learning Disabilities

ERIC Educational Resources Information Center

Mahoney-Davies, Gerwyn; Dixon, Clare; Tynan, Hannah; Mann, Sian

2017-01-01

Background: The "Five Ways to Well-being" document presents five ways in which people in the general population may be able to improve their well-being. This study evaluates the use of a "Five Ways to Well-being" group in a population of people with learning disabilities. Materials and Methods: Twelve participants who attend a…

The Use of Structured Social Interaction with the Culture-General Assimilator To Increase Cognitive Problem Solving about Intercultural Interactions in an Ethnically Diverse Population.

ERIC Educational Resources Information Center

Ilola, Lisa Marie

This study describes an intercultural learning program combining cooperative learning with critical incidents drawn from the culture-general assimilator developed by Brislin. The training program was adapted to school teachers, a population already identified as a high-risk group because of the frequency and unpredictability of the intercultural…

Distance Learning: A Game Changer

ERIC Educational Resources Information Center

Bates, Rodger; LaBrecque, Bryan

2017-01-01

Previous research identified a variety of special populations which may be serviced through online learning activities. These have included the military, Native Americans, prisoners, remote occupations, and others. This paper focuses the growing role of distance learning opportunities for student and professional athletes. Special attention is…

A Facilitating Effective Teaching through Learning Based on Learning Styles and Ways of Thinking

ERIC Educational Resources Information Center

Ginting, Siti Aisyah

2017-01-01

The study deals with learning styles and ways of thinking in facilitating effective teaching. The objective of this study was to investigate the relationship between students' learning style and ways of thinking toward effective teaching. This study was conducted by using correlational design. The population of the study were 360 university…

Captivating Lifelong Learners in the Third Age: Lessons Learned from a University-Based Institute

ERIC Educational Resources Information Center

Talmage, Craig A.; Lacher, R. Geoffrey; Pstross, Mikulas; Knopf, Richard C.; Burkhart, Karla A.

2015-01-01

The prevalence of learning providers for third agers continues to expand alongside the growth of the older adult population, yet there remains little empirical evidence on what types of learning experiences are most desired by lifelong learners. This article examines the effects that different learning topics have on attendance at classes hosted…

Impediments of E-Learning Adoption in Higher Learning Institutions of Tanzania: An Empirical Review

ERIC Educational Resources Information Center

Mwakyusa, Wilson Pholld; Mwalyagile, Neema Venance

2016-01-01

It is experienced that most of the Higher Learning Institutions (HLIs) in developing countries including Tanzania fails to fully implement e-learning system as a an alternative method of delivering education to a large population in the universities. However, some of HLIs are practicing the blended method by which both elearning and traditional…

Relevance of IT Integration into Teaching to Learning Satisfaction and Learning Effectiveness

ERIC Educational Resources Information Center

Huang, Shiuab-Ying

2014-01-01

The main purpose of this study is to verify and understand the effects of IT integration into teaching by colleges and vocational schools in Taiwan on learning effectiveness, with learning satisfaction as a mediator. This paper adopts stratified sampling on the administrative supervisors and teachers (i.e. population) in Taiwanese colleges and…

Cooperative Learning Instructional Methods for CS1: Design, Implementation, and Evaluation

ERIC Educational Resources Information Center

Beck, Leland; Chizhik, Alexander

2013-01-01

Cooperative learning is a well-known instructional technique that has been applied with a wide variety of subject matter and a broad spectrum of populations. This article briefly reviews the principles of cooperative learning, and describes how these principles were incorporated into a comprehensive set of cooperative learning activities for a CS1…

What's It Like to Work with a Clinical Psychologist of a Specialist Learning Disabilities Service? Views from People with Learning Disabilities

ERIC Educational Resources Information Center

Gifford, Clive; Evers, Catherine; Walden, Sarah

2013-01-01

Clinical psychologists are well placed to work with people with learning disabilities given the high prevalence of psychiatric disorders in this population and the specialist training undertaken by psychologists. The evidence for psychological interventions in learning disabilities is scarce compared to the evidence for mainstream psychological…

Designing instruction to support mechanical reasoning: Three alternatives in the simple machines learning environment

NASA Astrophysics Data System (ADS)

McKenna, Ann Frances

2001-07-01

Creating a classroom environment that fosters a productive learning experience and engages students in the learning process is a complex endeavor. A classroom environment is dynamic and requires a unique synergy among students, teacher, classroom artifacts and events to achieve robust understanding and knowledge integration. This dissertation addresses this complex issue by developing, implementing, and investigating the simple machines learning environment (SIMALE) to support students' mechanical reasoning and understanding. SIMALE was designed to support reflection, collaborative learning, and to engage students in generative learning through multiple representations of concepts and successive experimentation and design activities. Two key components of SIMALE are an original web-based software tool and hands-on Lego activities. A research study consisting of three treatment groups was created to investigate the benefits of hands-on and web-based computer activities on students' analytic problem solving ability, drawing/modeling ability, and conceptual understanding. The study was conducted with two populations of students that represent a diverse group with respect to gender, ethnicity, academic achievement and social/economic status. One population of students in this dissertation study participated from the Mathematics, Engineering, and Science Achievement (MESA) program that serves minorities and under-represented groups in science and mathematics. The second group was recruited from the Academic Talent Development Program (ATDP) that is an academically competitive outreach program offered through the University of California at Berkeley. Results from this dissertation show success of the SIMALE along several dimensions. First, students in both populations achieved significant gains in analytic problem solving ability, drawing/modeling ability, and conceptual understanding. Second, significant differences that were found on pre-test measures were eliminated on post-test measures. Specifically, female students scored significantly lower than males on the overall pre-tests but scored as well as males on the same post-test measures. MESA students also scored significantly lower than ATDP students on pre-test measures but both populations scored equally well on the post-tests. This dissertation has therefore shown the SIMALE to support a collaborative, reflective, and generative learning environment. Furthermore, the SIMALE clearly contributes to students' mechanical reasoning and understanding of simple machines concepts for a diverse population of students.

Collaborative Testing as a Model for Addressing Equity in Student Success in STEM Classes

NASA Astrophysics Data System (ADS)

Dileonardo, C.; James, B. R.

2016-12-01

Introductory Earth science classes at two-year colleges play a critical role as "gateway courses" for underrepresented student populations into undergraduate STEM programs. Students entering college underprepared in math and science typically receive their only exposure to science at the undergraduate level in introductory courses in the Earth and space sciences. In many colleges a huge disparity exists in these classes between success rates amongst students from groups traditionally represented in the STEM fields and those from underrepresented populations. Closing the equity gap in success in these courses is a major focus of many pilot projects nationally. This concern has also led to the adoption of new teaching and learning practices, based on research in learning, in introductory Earth science pedagogy. Models of teaching practices including greater engagement, active learning approaches, and collaborative learning structures seem to help with student achievement in introductory courses. But, whereas these practices might increase overall student success they have not proven to close the equity gap in achievement. De Anza a two-year college in the San Francisco bay area has a long history in the geology department of incorporating and testing teaching practices developed out of research in learning. Collaborative learning has infused every aspect of our learning approaches in the Earth sciences, including laboratory, fieldwork, and test preparation. Though these approaches seemed to have educational benefit the huge equity gap department-wide persisted between targeted and non-targeted populations. Three years ago collaborative testing models were introduced into our geology and meteorology classes. The mechanism included methods for directly comparing collaborative to individual testing. The net result was that targeted populations including African Americans, Latinos, and Filipinos increased steadily at around 3.5% per year from 66% to 73%. The overall success rates of the non-targeted groups remained between 84% and 86%. Preliminary analysis suggests that for disengaged students in the targeted populations the opportunity to collaborate on a portion of the actual test got them more involved in the collaborative process as it offers immediate tangible return on in-class success.

Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex.

PubMed

Bressloff, P C; Cowan, J D; Golubitsky, M; Thomas, P J; Wiener, M C

2001-03-29

This paper is concerned with a striking visual experience: that of seeing geometric visual hallucinations. Hallucinatory images were classified by Klüver into four groups called form constants comprising (i) gratings, lattices, fretworks, filigrees, honeycombs and chequer-boards, (ii) cobwebs, (iii) tunnels, funnels, alleys, cones and vessels, and (iv) spirals. This paper describes a mathematical investigation of their origin based on the assumption that the patterns of connection between retina and striate cortex (henceforth referred to as V1)-the retinocortical map-and of neuronal circuits in V1, both local and lateral, determine their geometry. In the first part of the paper we show that form constants, when viewed in V1 coordinates, essentially correspond to combinations of plane waves, the wavelengths of which are integral multiples of the width of a human Hubel-Wiesel hypercolumn, ca. 1.33-2 mm. We next introduce a mathematical description of the large-scale dynamics of V1 in terms of the continuum limit of a lattice of interconnected hypercolumns, each of which itself comprises a number of interconnected iso-orientation columns. We then show that the patterns of interconnection in V1 exhibit a very interesting symmetry, i.e. they are invariant under the action of the planar Euclidean group E(2)-the group of rigid motions in the plane-rotations, reflections and translations. What is novel is that the lateral connectivity of V1 is such that a new group action is needed to represent its properties: by virtue of its anisotropy it is invariant with respect to certain shifts and twists of the plane. It is this shift-twist invariance that generates new representations of E(2). Assuming that the strength of lateral connections is weak compared with that of local connections, we next calculate the eigenvalues and eigenfunctions of the cortical dynamics, using Rayleigh-Schrödinger perturbation theory. The result is that in the absence of lateral connections, the eigenfunctions are degenerate, comprising both even and odd combinations of sinusoids in straight phi, the cortical label for orientation preference, and plane waves in r, the cortical position coordinate. 'Switching-on' the lateral interactions breaks the degeneracy and either even or else odd eigenfunctions are selected. These results can be shown to follow directly from the Euclidean symmetry we have imposed. In the second part of the paper we study the nature of various even and odd combinations of eigenfunctions or planforms, the symmetries of which are such that they remain invariant under the particular action of E(2) we have imposed. These symmetries correspond to certain subgroups of E(2), the so-called axial subgroups. Axial subgroups are important in that the equivariant branching lemma indicates that when a symmetrical dynamical system becomes unstable, new solutions emerge which have symmetries corresponding to the axial subgroups of the underlying symmetry group. This is precisely the case studied in this paper. Thus we study the various planforms that emerge when our model V1 dynamics become unstable under the presumed action of hallucinogens or flickering lights. We show that the planforms correspond to the axial subgroups of E(2), under the shift-twist action. We then compute what such planforms would look like in the visual field, given an extension of the retinocortical map to include its action on local edges and contours. What is most interesting is that, given our interpretation of the correspondence between V1 planforms and perceived patterns, the set of planforms generates representatives of all the form constants. It is also noteworthy that the planforms derived from our continuum model naturally divide V1 into what are called linear regions, in which the pattern has a near constant orientation, reminiscent of the iso-orientation patches constructed via optical imaging. The boundaries of such regions form fractures whose points of intersection correspond to the well-known 'pinwheels'. To complete the study we then investigate the stability of the planforms, using methods of nonlinear stability analysis, including Liapunov-Schmidt reduction and Poincaré-Lindstedt perturbation theory. We find a close correspondence between stable planforms and form constants. The results are sensitive to the detailed specification of the lateral connectivity and suggest an interesting possibility, that the cortical mechanisms by which geometric visual hallucinations are generated, if sited mainly in V1, are closely related to those involved in the processing of edges and contours.

Reduced Fokker-Planck models for fast particle distribution across a transition layer of disparate plasma temperatures

NASA Astrophysics Data System (ADS)

Tang, Xian-Zhu; Berk, H. L.; Guo, Zehua; McDevitt, C. J.

2014-03-01

Across a transition layer of disparate plasma temperatures, the high energy tail of the plasma distribution can have appreciable deviations from the local Maxwellian distribution due to the Knudson layer effect. The Fokker-Planck equation for the tail particle population can be simplified in a series of practically useful limiting cases. The first is the approximation of background Maxwellian distribution for linearizing the collision operator. The second is the supra-thermal particle speed ordering of vTi ≪ v ≪ vTe for the tail ions and vTi ≪ vTe ≪ v for the tail electrons. Keeping both the collisional drag and energy scattering is essential for the collision operator to produce a Maxwellian tail distribution. The Fokker-Planck model for following the tail ion distribution for a given background plasma profile is explicitly worked out for systems of one spatial dimension, in both slab and spherical geometry. A third simplification is an expansion of the tail particle distribution using the spherical harmonics, which are eigenfunctions of the pitch angle scattering operator. This produces a set of coupled Fokker-Planck equations that contain energy-dependent spatial diffusion terms in two coordinates (position and energy), which originate from pitch angle scattering in the original Fokker-Planck equation. It is shown that the well-known diffusive Fokker-Planck model is a poor approximation of the two-mode truncation model, which itself has fundamental deficiency compared with the three-mode truncation model. The cause is the lack of even-symmetry representation in pitch dependence in the two-mode truncation model.

From cultural traditions to cumulative culture: parameterizing the differences between human and nonhuman culture.

PubMed

Kempe, Marius; Lycett, Stephen J; Mesoudi, Alex

2014-10-21

Diverse species exhibit cultural traditions, i.e. population-specific profiles of socially learned traits, from songbird dialects to primate tool-use behaviours. However, only humans appear to possess cumulative culture, in which cultural traits increase in complexity over successive generations. Theoretically, it is currently unclear what factors give rise to these phenomena, and consequently why cultural traditions are found in several species but cumulative culture in only one. Here, we address this by constructing and analysing cultural evolutionary models of both phenomena that replicate empirically attestable levels of cultural variation and complexity in chimpanzees and humans. In our model of cultural traditions (Model 1), we find that realistic cultural variation between populations can be maintained even when individuals in different populations invent the same traits and migration between populations is frequent, and under a range of levels of social learning accuracy. This lends support to claims that putative cultural traditions are indeed cultural (rather than genetic) in origin, and suggests that cultural traditions should be widespread in species capable of social learning. Our model of cumulative culture (Model 2) indicates that both the accuracy of social learning and the number of cultural demonstrators interact to determine the complexity of a trait that can be maintained in a population. Combining these models (Model 3) creates two qualitatively distinct regimes in which there are either a few, simple traits, or many, complex traits. We suggest that these regimes correspond to nonhuman and human cultures, respectively. The rarity of cumulative culture in nature may result from this interaction between social learning accuracy and number of demonstrators. Copyright © 2014 Elsevier Ltd. All rights reserved.

Learning from experience: three community health population-based outreach projects for graduate and undergraduate students.

PubMed

D'Lugoff, Marion Isaacs; McCarter, Jeanne

2005-01-01

Three outreach activities by a school of nursing, in partnership with community agencies, provided learning experiences in primary and secondary preventive health care for graduate and undergraduate nursing students while addressing health needs in the community. The activities included administration of immunizations to a newly arrived Somali Bantu refugee population, targeted screening of an African-American population at risk for diabetic retinopathy, and general health screening for an underserved Hispanic immigrant population. These activities lend insight and depth to a community health curriculum by allowing students to provide needed services while engaging with culturally diverse clients of varying socioeconomic status. Learner objectives, resources, processes and outcomes are provided for each example.

Improving Student Engagement in Learning Activities.

ERIC Educational Resources Information Center

Adams, Nancy; And Others

Engaging students seriously in their own academic learning is a persistent difficulty for teachers. The goal of this action research project was to actively involve elementary school students in their learning. The program was implemented at three elementary schools in northern Illinois serving multicultural populations; special education…

A Brick and Mortar Approach

ERIC Educational Resources Information Center

Tretter, Thomas; Ardasheva, Yuliya; Bookstrom, Eric

2014-01-01

Literacy skills are critical for building science knowledge. For English Language Learners (ELLs)--the fastest growing population in U.S. schools (Goldenberg 2008)--learning English compounds the challenge of learning complex science concepts. This challenge is particularly acute for learning academic, science-specific English words and language…

WA10 Working in partnership with people with learning disabilities: academics and people with learning disabilities working together to disseminate the findings of a confidential inquiry into deaths of people with learning disabilities through film.

PubMed

Russ, Lesley

2015-04-01

In England, between 2010-2013, a Confidential Inquiry into premature Deaths of People with Learning Disabilities was commissioned by the Department of Health. This took place in SW England led by Norah Fry Research Centre at Bristol University. Findings from the investigations into 247 deaths included that men with learning disabilities die, on average 13 years sooner and women, on average 20 years sooner, than the general population. Over 1/3 (37%) were found to be avoidable, being amenable to good quality healthcare. A number of key recommendations were made which required understanding by a range of audiences including people with learning disabilities and their carers. This workshop will demonstrate how academics can work with actors with learning disabilities to disseminate research findings about a sensitive subject in a thought provoking and accessible way. Academics worked with the MISFITs theatre company to make a DVD about the findings and recommendations of the Confidential Inquiry. The DVD presents the findings of the Confidential Inquiry through the stories of John, Bill, Karen and Emily. It powerfully illustrates the importance of diagnosing and treating illness of people with learning disabilities in a timely and appropriate manner and highlights the measures that could be taken to reduce premature deaths in this population. The session provides an example of how the voices of people with learning disabilities can communicate research messages effectively to people with learning disabilities, health and social care practitioners and others who support the learning disability population. © 2015, Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions.

Learning style preferences of nursing students at two universities in Iran and Malaysia

PubMed Central

Abdollahimohammad, Abdolghani; Ja’afar, Rogayah

2014-01-01

Purpose: Learning style preferences vary within the nursing field and there is no consensus on a predominant learning style preference in nursing students. The current study compared the learning style preferences of nursing students at two universities in Iran and Malaysia. Methods: A purposive sampling method was used to collect data from the two study populations. Data were collected using the Learning Style Scale (LSS), which is a valid and reliable inventory. The LSS consists of 22 items with five subscales including perceptive, solitary, analytic, imaginative, and competitive. The questionnaires were distributed at the end of the academic year during regular class time for optimum response. The Mann-Whitney U-test was used to compare the learning style preferences between the two study populations. Results: A significant difference was found in perceptive, solitary, and analytic learning styles between two groups of nursing students. However, there was no significant difference in imaginative and competitive learning styles between the two groups. Most of the students were in the middle range of the learning styles. Conclusion: There were similarities and differences in learning style preferences between Zabol Medical Sciences University (ZBMU) and University Sains Malaysia (USM) nursing students. The USM nursing students were more sociable and analytic learners, whereas the ZBMU nursing students were more solitary and perceptive learners. PMID:25417864

Learning style preferences of nursing students at two universities in Iran and Malaysia.

PubMed

Abdollahimohammad, Abdolghani; Ja'afar, Rogayah

2014-01-01

Learning style preferences vary within the nursing field and there is no consensus on a predominant learning style preference in nursing students. The current study compared the learning style preferences of nursing students at two universities in Iran and Malaysia. A purposive sampling method was used to collect data from the two study populations. Data were collected using the Learning Style Scale (LSS), which is a valid and reliable inventory. The LSS consists of 22 items with five subscales including perceptive, solitary, analytic, imaginative, and competitive. The questionnaires were distributed at the end of the academic year during regular class time for optimum response. The Mann-Whitney U-test was used to compare the learning style preferences between the two study populations. A significant difference was found in perceptive, solitary, and analytic learning styles between two groups of nursing students. However, there was no significant difference in imaginative and competitive learning styles between the two groups. Most of the students were in the middle range of the learning styles. There were similarities and differences in learning style preferences between Zabol Medical Sciences University (ZBMU) and University Sains Malaysia (USM) nursing students. The USM nursing students were more sociable and analytic learners, whereas the ZBMU nursing students were more solitary and perceptive learners.

Observations Of General Learning Patterns In An Upper-Level Thermal Physics Course

NASA Astrophysics Data System (ADS)

Meltzer, David E.

2009-11-01

I discuss some observations from using interactive-engagement instructional methods in an upper-level thermal physics course over a two-year period. From the standpoint of the subject matter knowledge of the upper-level students, there was a striking persistence of common learning difficulties previously observed in students enrolled in the introductory course, accompanied, however, by some notable contrasts between the groups. More broadly, I comment on comparisons and contrasts regarding general pedagogical issues among different student sub-populations, for example: differences in the receptivity of lower- and upper-level students to diagrammatic representations; varying receptivity to tutorial-style instructional approach within the upper-level population; and contrasting approaches to learning among physics and engineering sub-populations in the upper-level course with regard to use of symbolic notation, mathematical equations, and readiness to employ verbal explanations.

Observational learning from tool using models by human-reared and mother-reared capuchin monkeys (Cebus apella).

PubMed

Fredman, Tamar; Whiten, Andrew

2008-04-01

Studies of wild capuchins suggest an important role for social learning, but experiments with captive subjects have generally not supported this. Here we report social learning in two quite different populations of capuchin monkeys (Cebus apella). In experiment 1, human-raised monkeys observed a familiar human model open a foraging box using a tool in one of two alternative ways: levering versus poking. In experiment 2, mother-raised monkeys viewed similar techniques demonstrated by monkey models. A control group in each population saw no model. In both experiments, independent coders detected which technique experimental subjects had seen, thus confirming social learning. Further analyses examined fidelity of copying at three levels of resolution. The human-raised monkeys exhibited fidelity at the highest level, the specific tool use technique witnessed. The lever technique was seen only in monkeys exposed to a levering model, by contrast with controls and those witnessing poke. Mother-reared monkeys instead typically ignored the tool and exhibited fidelity at a lower level, tending only to re-create whichever result the model had achieved by either levering or poking. Nevertheless this level of social learning was associated with significantly greater levels of success in monkeys witnessing a model than in controls, an effect absent in the human-reared population. Results in both populations are consistent with a process of canalization of the repertoire in the direction of the approach witnessed, producing a narrower, socially shaped behavioural profile than among controls who saw no model.

Generative inference for cultural evolution.

PubMed

Kandler, Anne; Powell, Adam

2018-04-05

One of the major challenges in cultural evolution is to understand why and how various forms of social learning are used in human populations, both now and in the past. To date, much of the theoretical work on social learning has been done in isolation of data, and consequently many insights focus on revealing the learning processes or the distributions of cultural variants that are expected to have evolved in human populations. In population genetics, recent methodological advances have allowed a greater understanding of the explicit demographic and/or selection mechanisms that underlie observed allele frequency distributions across the globe, and their change through time. In particular, generative frameworks-often using coalescent-based simulation coupled with approximate Bayesian computation (ABC)-have provided robust inferences on the human past, with no reliance on a priori assumptions of equilibrium. Here, we demonstrate the applicability and utility of generative inference approaches to the field of cultural evolution. The framework advocated here uses observed population-level frequency data directly to establish the likely presence or absence of particular hypothesized learning strategies. In this context, we discuss the problem of equifinality and argue that, in the light of sparse cultural data and the multiplicity of possible social learning processes, the exclusion of those processes inconsistent with the observed data might be the most instructive outcome. Finally, we summarize the findings of generative inference approaches applied to a number of case studies.This article is part of the theme issue 'Bridging cultural gaps: interdisciplinary studies in human cultural evolution'. © 2018 The Author(s).

Machine Learning for Treatment Assignment: Improving Individualized Risk Attribution

PubMed Central

Weiss, Jeremy; Kuusisto, Finn; Boyd, Kendrick; Liu, Jie; Page, David

2015-01-01

Clinical studies model the average treatment effect (ATE), but apply this population-level effect to future individuals. Due to recent developments of machine learning algorithms with useful statistical guarantees, we argue instead for modeling the individualized treatment effect (ITE), which has better applicability to new patients. We compare ATE-estimation using randomized and observational analysis methods against ITE-estimation using machine learning, and describe how the ITE theoretically generalizes to new population distributions, whereas the ATE may not. On a synthetic data set of statin use and myocardial infarction (MI), we show that a learned ITE model improves true ITE estimation and outperforms the ATE. We additionally argue that ITE models should be learned with a consistent, nonparametric algorithm from unweighted examples and show experiments in favor of our argument using our synthetic data model and a real data set of D-penicillamine use for primary biliary cirrhosis. PMID:26958271

Machine Learning for Treatment Assignment: Improving Individualized Risk Attribution.

PubMed

Weiss, Jeremy; Kuusisto, Finn; Boyd, Kendrick; Liu, Jie; Page, David

2015-01-01

Clinical studies model the average treatment effect (ATE), but apply this population-level effect to future individuals. Due to recent developments of machine learning algorithms with useful statistical guarantees, we argue instead for modeling the individualized treatment effect (ITE), which has better applicability to new patients. We compare ATE-estimation using randomized and observational analysis methods against ITE-estimation using machine learning, and describe how the ITE theoretically generalizes to new population distributions, whereas the ATE may not. On a synthetic data set of statin use and myocardial infarction (MI), we show that a learned ITE model improves true ITE estimation and outperforms the ATE. We additionally argue that ITE models should be learned with a consistent, nonparametric algorithm from unweighted examples and show experiments in favor of our argument using our synthetic data model and a real data set of D-penicillamine use for primary biliary cirrhosis.

Physical isolation with virtual support: Registrars' learning via remote supervision.

PubMed

Wearne, Susan M; Teunissen, Pim W; Dornan, Tim; Skinner, Timothy

2014-08-26

Abstract Purpose: Changing the current geographical maldistribution of the medical workforce is important for global health. Research regarding programs that train doctors for work with disadvantaged, rural populations is needed. This paper explores one approach of remote supervision of registrars in isolated rural practice. Researching how learning occurs without on-site supervision may also reveal other key elements of postgraduate education. Methods: Thematic analysis of in-depth interviews exploring 11 respondents' experiences of learning via remote supervision. Results: Remote supervision created distinctive learning environments. Respondents' attributes interacted with external supports to influence whether and how their learning was promoted or impeded. Registrars with clinical and/or life experience, who were insightful and motivated to direct their learning, turned the challenges of isolated practice into opportunities that accelerated their professional development. Discussion: Remote supervision was not necessarily problematic but instead provided rich learning for doctors training in and for the context where they were needed. Registrars learnt through clinical responsibility for defined populations and longitudinal, supportive supervisory relationships. Responsibility and continuity may be as important as supervisory proximity for experienced registrars.

Learning to be different: Acquired skills, social learning, frequency dependence, and environmental variation can cause behaviourally mediated foraging specializations

USGS Publications Warehouse

Tinker, M.T.; Mangel, M.; Estes, J.A.

2009-01-01

Question: How does the ability to improve foraging skills by learning, and to transfer that learned knowledge, affect the development of intra-population foraging specializations? Features of the model: We use both a state-dependent life-history model implemented by stochastic dynamic programming (SDPM) and an individual-based model (IBM) to capture the dynamic nature of behavioural preferences in feeding. Variables in the SDPM include energy reserves, skill levels, energy and handling time per single prey item, metabolic rate, the rates at which skills are learned and forgotten, the effect of skills on handling time, and the relationship between energy reserves and fitness. Additional variables in the IBM include the probability of successful weaning, the logistic dynamics of the prey species with stochastic recruitment, the intensity of top-down control of prey by predators, the mean and variance in skill levels of new recruits, and the extent to which learned Information can be transmitted via matrilineal social learning. Key range of variables: We explore the effects of approaching the time horizon in the SDPM, changing the extent to which skills can improve with experience, increasing the rates of learning or forgetting of skills, changing whether the learning curve is constant, accelerating (T-shaped) or decelerating ('r'-shaped), changing both mean and maximum possible energy reserves, changing metabolic costs of foraging, and changing the rate of encounter with prey. Conclusions: The model results show that the following factors increase the degree of prey specialization observed in a predator population: (1) Experience handling a prey type can substantially improve foraging skills for that prey. (2) There is limited ability to retain complex learned skills for multiple prey types. (3) The learning curve for acquiring new foraging skills is accelerating, or J-shaped. (4) The metabolic costs of foraging are high relative to available energy reserves. (5) Offspring can learn foraging skills from their mothers (matrilineal social learning). (6) Food abundance is limited, such that average individual energy reserves are low Additionally, the following factors increase the likelihood of alternative specializations co-occurring in a predator population: (1) The predator exerts effective top-down control of prey abundance, resulting in frequency-dependent dynamics. (2) There is stochastic Variation in prey population dynamics, but this Variation is neither too extreme in magnitude nor too 'slow' with respect to the time required for an individual forager to learn new foraging skills. For a given predator population, we deduce that the degree of specialization will be highest for those prey types requiring complex capture or handling skills, while prey species that are both profitable and easy to capture and handle will be included in the diet of all individuals. Frequency-dependent benefits of selecting alternative prey types, combined with the ability of foragers to improve their foraging skills by learning, and transmit learned skills to offspring, can result in behaviourally mediated foraging specialization, and also lead to the co-existence of alternative specializations. The extent of such specialization is predicted to be a variable trait, increasing in locations or years when intra-specific competition is high relative to inter-specific competition. ?? 2009 M. Tim Tinker.

Development of a Late-Life Dementia Prediction Index with Supervised Machine Learning in the Population-Based CAIDE Study.

PubMed

Pekkala, Timo; Hall, Anette; Lötjönen, Jyrki; Mattila, Jussi; Soininen, Hilkka; Ngandu, Tiia; Laatikainen, Tiina; Kivipelto, Miia; Solomon, Alina

2017-01-01

This study aimed to develop a late-life dementia prediction model using a novel validated supervised machine learning method, the Disease State Index (DSI), in the Finnish population-based CAIDE study. The CAIDE study was based on previous population-based midlife surveys. CAIDE participants were re-examined twice in late-life, and the first late-life re-examination was used as baseline for the present study. The main study population included 709 cognitively normal subjects at first re-examination who returned to the second re-examination up to 10 years later (incident dementia n = 39). An extended population (n = 1009, incident dementia 151) included non-participants/non-survivors (national registers data). DSI was used to develop a dementia index based on first re-examination assessments. Performance in predicting dementia was assessed as area under the ROC curve (AUC). AUCs for DSI were 0.79 and 0.75 for main and extended populations. Included predictors were cognition, vascular factors, age, subjective memory complaints, and APOE genotype. The supervised machine learning method performed well in identifying comprehensive profiles for predicting dementia development up to 10 years later. DSI could thus be useful for identifying individuals who are most at risk and may benefit from dementia prevention interventions.

Nonlinear stability of Halley comethosheath with transverse plasma motion

NASA Technical Reports Server (NTRS)

Srivastava, Krishna M.; Tsurutani, Bruce T.

1994-01-01

Weakly nonlinear Magneto Hydrodynamic (MHD) stability of the Halley cometosheath determined by the balance between the outward ion-neutral drag force and the inward Lorentz force is investigated including the transverse plasma motion as observed in the flanks with the help of the method of multiple scales. The eigenvalues and the eigenfunctions are obtained for the linear problem and the time evolution of the amplitude is obtained using the solvability condition for the solution of the second order problem. The diamagnetic cavity boundary and the adjacent layer of about 100 km thickness is found unstable for the travelling waves of certain wave numbers. Halley ionopause has been observed to have strong ripples with a wavelength of several hundred kilometers. It is found that nonlinear effects have stabilizing effect.

Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation.

PubMed

Hu, Xiao-Rui; Lou, Sen-Yue; Chen, Yong

2012-05-01

In nonlinear science, it is very difficult to find exact interaction solutions among solitons and other kinds of complicated waves such as cnoidal waves and Painlevé waves. Actually, even if for the most well-known prototypical models such as the Kortewet-de Vries (KdV) equation and the Kadomtsev-Petviashvili (KP) equation, this kind of problem has not yet been solved. In this paper, the explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetries which are related to Darboux transformation for the well-known KdV equation. The same approach also yields some other types of interaction solutions among different types of solutions such as solitary waves, rational solutions, Bessel function solutions, and/or general Painlevé II solutions.

Propagation of eigenmodes and transfer functions in waveguide WDM structures

NASA Astrophysics Data System (ADS)

Mashkov, Vladimir A.; Francoeur, S.; Geuss, U.; Neiser, K.; Temkin, Henryk

1998-02-01

A method of propagation functions and transfer amplitudes suitable for the design of integrated optical circuits is presented. The method is based on vectorial formulation of electrodynamics: the distributions and propagation of electromagnetic fields in optical circuits is described by equivalent surface sources. This approach permits a division of complex optical waveguide structures into sets of primitive blocks and to separately calculate the transfer function and the transfer amplitude for each block. The transfer amplitude of the entire optical system is represented by a convolution of transfer amplitudes of its primitive blocks. The eigenvalues and eigenfunctions of arbitrary waveguide structure are obtained in the WKB approximation and compared with other methods. The general approach is illustrated with the transfer amplitude calculations for Dragone's star coupler and router.

Application of polynomial su(1, 1) algebra to Pöschl-Teller potentials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Hong-Biao, E-mail: zhanghb017@nenu.edu.cn; Lu, Lu

2013-12-15

Two novel polynomial su(1, 1) algebras for the physical systems with the first and second Pöschl-Teller (PT) potentials are constructed, and their specific representations are presented. Meanwhile, these polynomial su(1, 1) algebras are used as an algebraic technique to solve eigenvalues and eigenfunctions of the Hamiltonians associated with the first and second PT potentials. The algebraic approach explores an appropriate new pair of raising and lowing operators K-circumflex{sub ±} of polynomial su(1, 1) algebra as a pair of shift operators of our Hamiltonians. In addition, two usual su(1, 1) algebras associated with the first and second PT potentials are derivedmore » naturally from the polynomial su(1, 1) algebras built by us.« less

Effect of turbulent eddy viscosity on the unstable surface mode above an acoustic liner

NASA Astrophysics Data System (ADS)

Marx, David; Aurégan, Yves

2013-07-01

Lined ducts are used to reduce noise radiation from ducts in turbofan engines. In certain conditions they may sustain hydrodynamic instabilities. A local linear stability analysis of the flow in a 2D lined channel is performed using a numerical integration of the governing equations. Several model equations are used, one of them taking into account turbulent eddy viscosity, and a realistic turbulent mean flow profile is used that vanishes at the wall. The stability analysis results are compared to published experimental results. Both the model and the experiments show the existence of an unstable mode, and the importance of taking into account eddy viscosity in the model is shown. When this is done, quantities such as the growth rate and the velocity eigenfunctions are shown to agree correctly.

Stabilization of Taylor-Couette flow due to time-periodic outer cylinder oscillation

NASA Technical Reports Server (NTRS)

Murray, B. T.; Mcfadden, G. B.; Coriell, S. R.

1990-01-01

The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case when the inner cylinder is rotated at a constant angular velocity and the outer cylinder is driven sinusoidally in time with zero mean rotation. This configuration was studied experimentally by Walsh and Donnelly. The critical Reynolds numbers calculated from linear stability theory agree well with the experimental values, except at large modulation amplitudes and small frequencies. The theoretical values are obtained using Floquet theory implemented in two distinct approaches: a truncated Fourier series representation in time, and a fundamental solution matrix based on a Chebyshev pseudospectral representation in space. For large amplitude, low frequency modulation, the linear eigenfunctions are temporally complex, consisting of a quiescent region followed by rapid change in the perturbed flow velocities.

I-cored Coil Probe Located Above a Conductive Plate with a Surface Hole

NASA Astrophysics Data System (ADS)

Tytko, Grzegorz; Dziczkowski, Leszek

2018-02-01

This work presents an axially symmetric mathematical model of an I-cored coil placed over a two-layered conductive material with a cylindrical surface hole. The problem was divided into regions for which the magnetic vector potential of a filamentary coil was established applying the truncated region eigenfunction expansion method. Then the final formula was developed to calculate impedance changes for a cylindrical coil with reference to both the air and to a material with no hole. The influence of a surface flaw in the conductive material on the components of coil impedance was examined. Calculations were made in Matlab for a hole with various radii and the results thereof were verified with the finite element method in COMSOL Multiphysics package. Very good consistency was achieved in all cases.

The Darboux transformation of the derivative nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Xu, Shuwei; He, Jingsong; Wang, Lihong

2011-07-01

The n-fold Darboux transformation (DT) is a 2 × 2 matrix for the Kaup-Newell (KN) system. In this paper, each element of this matrix is expressed by a ratio of the (n + 1) × (n + 1) determinant and n × n determinant of eigenfunctions. Using these formulae, the expressions of the q[n] and r[n] in the KN system are generated by the n-fold DT. Further, under the reduction condition, the rogue wave, rational traveling solution, dark soliton, bright soliton, breather solution and periodic solution of the derivative nonlinear Schrödinger equation are given explicitly by different seed solutions. In particular, the rogue wave and rational traveling solution are two kinds of new solutions. The complete classification of these solutions generated by one-fold DT is given.

Student Solution Manual for Mathematical Methods for Physics and Engineering Third Edition

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2006-03-01

Preface; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics.

Magnonic qudit and algebraic Bethe Ansatz

NASA Astrophysics Data System (ADS)

Lulek, B.; Lulek, T.

2010-03-01

A magnonic qudit is proposed as the memory unit of a register of a quantum computer. It is the N-dimensional space, extracted from the 2N-dimensional space of all quantum states of the magnetic Heisenberg ring of N spins 1/2, as the space of all states of a single magnon. Three bases: positional, momentum, and that of Weyl duality are described, together with appropriate Fourier and Kostka transforms. It is demonstrated how exact Bethe Ansatz (BA) eigenfunctions, classified in terms of rigged string configurations, can be coded using a collection of magnonic qudits. To this aim, the algebraic BA is invoked, such that a single magnonic qudit is prepared in a state corresponding to a magnon in one of the states provided by spectral parameters emerging from the corresponding BA equations.

Anisotropic Laplace-Beltrami Eigenmaps: Bridging Reeb Graphs and Skeletons*

PubMed Central

Shi, Yonggang; Lai, Rongjie; Krishna, Sheila; Sicotte, Nancy; Dinov, Ivo; Toga, Arthur W.

2010-01-01

In this paper we propose a novel approach of computing skeletons of robust topology for simply connected surfaces with boundary by constructing Reeb graphs from the eigenfunctions of an anisotropic Laplace-Beltrami operator. Our work brings together the idea of Reeb graphs and skeletons by incorporating a flux-based weight function into the Laplace-Beltrami operator. Based on the intrinsic geometry of the surface, the resulting Reeb graph is pose independent and captures the global profile of surface geometry. Our algorithm is very efficient and it only takes several seconds to compute on neuroanatomical structures such as the cingulate gyrus and corpus callosum. In our experiments, we show that the Reeb graphs serve well as an approximate skeleton with consistent topology while following the main body of conventional skeletons quite accurately. PMID:21339850

Pattern formation in nonextensive thermodynamics: selection criterion based on the Renyi entropy production.

PubMed

Cybulski, Olgierd; Matysiak, Daniel; Babin, Volodymyr; Holyst, Robert

2005-05-01

We analyze a system of two different types of Brownian particles confined in a cubic box with periodic boundary conditions. Particles of different types annihilate when they come into close contact. The annihilation rate is matched by the birth rate, thus the total number of each kind of particles is conserved. When in a stationary state, the system is divided by an interface into two subregions, each occupied by one type of particles. All possible stationary states correspond to the Laplacian eigenfunctions. We show that the system evolves towards those stationary distributions of particles which minimize the Renyi entropy production. In all cases, the Renyi entropy production decreases monotonically during the evolution despite the fact that the topology and geometry of the interface exhibit abrupt and violent changes.

First-passage time of Brownian motion with dry friction.

PubMed

Chen, Yaming; Just, Wolfram

2014-02-01

We provide an analytic solution to the first-passage time (FPT) problem of a piecewise-smooth stochastic model, namely Brownian motion with dry friction, using two different but closely related approaches which are based on eigenfunction decompositions on the one hand and on the backward Kolmogorov equation on the other. For the simple case containing only dry friction, a phase-transition phenomenon in the spectrum is found which relates to the position of the exit point, and which affects the tail of the FPT distribution. For the model containing as well a driving force and viscous friction the impact of the corresponding stick-slip transition and of the transition to ballistic exit is evaluated quantitatively. The proposed model is one of the very few cases where FPT properties are accessible by analytical means.

The eigenvalue problem in phase space.

PubMed

Cohen, Leon

2018-06-30

We formulate the standard quantum mechanical eigenvalue problem in quantum phase space. The equation obtained involves the c-function that corresponds to the quantum operator. We use the Wigner distribution for the phase space function. We argue that the phase space eigenvalue equation obtained has, in addition to the proper solutions, improper solutions. That is, solutions for which no wave function exists which could generate the distribution. We discuss the conditions for ascertaining whether a position momentum function is a proper phase space distribution. We call these conditions psi-representability conditions, and show that if these conditions are imposed, one extracts the correct phase space eigenfunctions. We also derive the phase space eigenvalue equation for arbitrary phase space distributions functions. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Unsteady seepage flow over sloping beds in response to multiple localized recharge

NASA Astrophysics Data System (ADS)

Bansal, Rajeev K.

2017-05-01

New generalized solutions of linearized Boussinesq equation are derived to approximate the dynamic behavior of subsurface seepage flow induced by multiple localized time-varying recharges over sloping ditch-drain aquifer system. The mathematical model is based on extended Dupuit-Forchheimer assumption and treats the spatial location of recharge basins as additional parameter. Closed form analytic expressions for spatio-temporal variations in water head distribution and discharge rate into the drains are obtained by solving the governing flow equation using eigenvalue-eigenfunction method. Downward and zero-sloping aquifers are treated as special cases of main results. A numerical example is used for illustration of combined effects of various parameters such as spatial coordinates of the recharge basin, aquifer's bed slope, and recharge rate on the dynamic profiles of phreatic surface.

Analytical solutions for the dynamics of two trapped interacting ultracold atoms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Idziaszek, Zbigniew; Calarco, Tommaso; CNR-INFM BEC Center, I-38050 Povo

2006-08-15

We discuss exact solutions of the Schroedinger equation for the system of two ultracold atoms confined in an axially symmetric harmonic potential. We investigate different geometries of the trapping potential, in particular we study the properties of eigenenergies and eigenfunctions for quasi-one-dimensional and quasi-two-dimensional traps. We show that the quasi-one-dimensional and the quasi-two-dimensional regimes for two atoms can be already realized in the traps with moderately large (or small) ratios of the trapping frequencies in the axial and the transverse directions. Finally, we apply our theory to Feshbach resonances for trapped atoms. Introducing in our description an energy-dependent scattering lengthmore » we calculate analytically the eigenenergies for two trapped atoms in the presence of a Feshbach resonance.« less

On the rational monodromy-free potentials with sextic growth

NASA Astrophysics Data System (ADS)

Gibbons, J.; Veselov, A. P.

2009-01-01

We study the rational potentials V(x ), with sextic growth at infinity, such that the corresponding one-dimensional Schrödinger equation has no monodromy in the complex domain for all values of the spectral parameter. We investigate in detail the subclass of such potentials which can be constructed by the Darboux transformations from the well-known class of quasiexactly solvable potentials V =x6-νx2+l(l +1)/x2. We show that, in contrast with the case of quadratic growth, there are monodromy-free potentials which have quasirational eigenfunctions, but which cannot be given by this construction. We discuss the relations between the corresponding algebraic varieties and present some elementary solutions of the Calogero-Moser problem in the external field with sextic potential.

Hermitian Hamiltonian equivalent to a given non-Hermitian one: manifestation of spectral singularity.

PubMed

Samsonov, Boris F

2013-04-28

One of the simplest non-Hermitian Hamiltonians, first proposed by Schwartz in 1960, that may possess a spectral singularity is analysed from the point of view of the non-Hermitian generalization of quantum mechanics. It is shown that the η operator, being a second-order differential operator, has supersymmetric structure. Asymptotic behaviour of the eigenfunctions of a Hermitian Hamiltonian equivalent to the given non-Hermitian one is found. As a result, the corresponding scattering matrix and cross section are given explicitly. It is demonstrated that the possible presence of a spectral singularity in the spectrum of the non-Hermitian Hamiltonian may be detected as a resonance in the scattering cross section of its Hermitian counterpart. Nevertheless, just at the singular point, the equivalent Hermitian Hamiltonian becomes undetermined.

Localization or tunneling in asymmetric double-well potentials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Dae-Yup, E-mail: dsong@sunchon.ac.kr

An asymmetric double-well potential is considered, assuming that the wells are parabolic around the minima. The WKB wave function of a given energy is constructed inside the barrier between the wells. By matching the WKB function to the exact wave functions of the parabolic wells on both sides of the barrier, for two almost degenerate states, we find a quantization condition for the energy levels which reproduces the known energy splitting formula between the two states. For the other low-lying non-degenerate states, we show that the eigenfunction should be primarily localized in one of the wells with negligible magnitude inmore » the other. Using Dekker’s method (Dekker, 1987), the present analysis generalizes earlier results for weakly biased double-well potentials to systems with arbitrary asymmetry.« less

Non-polynomial extensions of solvable potentials à la Abraham-Moses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Odake, Satoru; Sasaki, Ryu; Center for Theoretical Sciences, National Taiwan University, Taipei 10617, Taiwan

2013-10-15

Abraham-Moses transformations, besides Darboux transformations, are well-known procedures to generate extensions of solvable potentials in one-dimensional quantum mechanics. Here we present the explicit forms of infinitely many seed solutions for adding eigenstates at arbitrary real energy through the Abraham-Moses transformations for typical solvable potentials, e.g., the radial oscillator, the Darboux-Pöschl-Teller, and some others. These seed solutions are simple generalisations of the virtual state wavefunctions, which are obtained from the eigenfunctions by discrete symmetries of the potentials. The virtual state wavefunctions have been an essential ingredient for constructing multi-indexed Laguerre and Jacobi polynomials through multiple Darboux-Crum transformations. In contrast to themore » Darboux transformations, the virtual state wavefunctions generate non-polynomial extensions of solvable potentials through the Abraham-Moses transformations.« less

Approaches for assessing risks to sensitive populations: Lessons learned from evaluating risks in the pediatric populations*

EPA Science Inventory

Assessing the risk profiles of potentially sensitive populations requires a 'tool chest' of methodological approaches to adequately characterize and evaluate these populations. At present, there is an extensive body of literature on methodologies that apply to the evaluation of...

Population Education: A Knowledge Base.

ERIC Educational Resources Information Center

Jacobson, Willard J.

To aid junior high and high school educators and curriculum planners as they develop population education programs, the book provides an overview of the population education knowledge base. In addition, it suggests learning activities, discussion questions, and background information which can be integrated into courses dealing with population,…

Impromptu Learning: Unplanned Occurrences, Intended Outcomes

ERIC Educational Resources Information Center

Jefferies, Julián; Nguyen, Angela-MinhTu

2014-01-01

During a study abroad experience on the island of Vieques, Puerto Rico, participants found themselves in an "impromptu learning experience" that extended their learning beyond Puerto Rican culture to real-world debates of tourist development, environmental issues, and the struggles of the native population. In this paper, we introduce…

Individual Learning Accounts: Honourable Intentions, Ignoble Utility?

ERIC Educational Resources Information Center

Thursfield, Denise; Smith, Vikki; Holden, Rick; Hamblett, John

2002-01-01

Evaluation of the implementation of Individual Learning Accounts in Britain revealed five themes that may explain the program's lack of success: individualistic approach to adult education, conflict of individualism with partnership, ineffective targeting of low-skilled populations, lack of linkage with a lifelong commitment to learning, and…

Handbook of Research on Collaborative Teaching Practice in Virtual Learning Environments

ERIC Educational Resources Information Center

Panconesi, Gianni, Ed.; Guida, Maria, Ed.

2017-01-01

Modern technology has enhanced many aspects of life, including classroom education. By offering virtual learning experiences, educational systems can become more efficient and effective at teaching the student population. The "Handbook of Research on Collaborative Teaching Practice in Virtual Learning Environments" highlights program…

Using Project-Based Learning and Google Docs to Support Diversity

ERIC Educational Resources Information Center

Leh, Amy

2014-01-01

A graduate course, ETEC543 ("Technology and Learning I"), was revised to better serve increasing new student population, international students, in an academic program. Project-based learning, Google Docs, and instructional strategies fostering diversity and critical thinking were incorporated into the course redesign. Observations,…

When Does Fading Enhance Perceptual Category Learning?

ERIC Educational Resources Information Center

Pashler, Harold; Mozer, Michael C.

2013-01-01

Training that uses exaggerated versions of a stimulus discrimination (fading) has sometimes been found to enhance category learning, mostly in studies involving animals and impaired populations. However, little is known about whether and when fading facilitates learning for typical individuals. This issue was explored in 7 experiments. In…