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.

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.

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.

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.

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.

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.

Improved statistical power with a sparse shape model in detecting an aging effect in the hippocampus and amygdala

NASA Astrophysics Data System (ADS)

Chung, Moo K.; Kim, Seung-Goo; Schaefer, Stacey M.; van Reekum, Carien M.; Peschke-Schmitz, Lara; Sutterer, Matthew J.; Davidson, Richard J.

2014-03-01

The sparse regression framework has been widely used in medical image processing and analysis. However, it has been rarely used in anatomical studies. We present a sparse shape modeling framework using the Laplace- Beltrami (LB) eigenfunctions of the underlying shape and show its improvement of statistical power. Tradition- ally, the LB-eigenfunctions are used as a basis for intrinsically representing surface shapes as a form of Fourier descriptors. To reduce high frequency noise, only the first few terms are used in the expansion and higher frequency terms are simply thrown away. However, some lower frequency terms may not necessarily contribute significantly in reconstructing the surfaces. Motivated by this idea, we present a LB-based method to filter out only the significant eigenfunctions by imposing a sparse penalty. For dense anatomical data such as deformation fields on a surface mesh, the sparse regression behaves like a smoothing process, which will reduce the error of incorrectly detecting false negatives. Hence the statistical power improves. The sparse shape model is then applied in investigating the influence of age on amygdala and hippocampus shapes in the normal population. The advantage of the LB sparse framework is demonstrated by showing the increased statistical power.

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.

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

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Squared eigenfunctions for the Sasa-Satsuma equation

NASA Astrophysics Data System (ADS)

Yang, Jianke; Kaup, D. J.

2009-02-01

Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. They are needed for various studies related to integrable equations, such as the development of its soliton perturbation theory. In this article, squared eigenfunctions are derived for the Sasa-Satsuma equation whose spectral operator is a 3×3 system, while its linearized operator is a 2×2 system. It is shown that these squared eigenfunctions are sums of two terms, where each term is a product of a Jost function and an adjoint Jost function. The procedure of this derivation consists of two steps: First is to calculate the variations of the potentials via variations of the scattering data by the Riemann-Hilbert method. The second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations. While this procedure has been used before on other integrable equations, it is shown here, for the first time, that for a general integrable equation, the functions appearing in these variation relations are precisely the squared eigenfunctions and adjoint squared eigenfunctions satisfying, respectively, the linearized equation and the adjoint linearized equation of the integrable system. This proof clarifies this procedure and provides a unified explanation for previous results of squared eigenfunctions on individual integrable equations. This procedure uses primarily the spectral operator of the Lax pair. Thus two equations in the same integrable hierarchy will share the same squared eigenfunctions (except for a time-dependent factor). In the Appendix, the squared eigenfunctions are presented for the Manakov equations whose spectral operator is closely related to that of the Sasa-Satsuma equation.

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.

Stability analysis of the Peregrine solution via squared eigenfunctions

NASA Astrophysics Data System (ADS)

Schober, C. M.; Strawn, M.

2017-10-01

A preliminary numerical investigation involving ensembles of perturbed initial data for the Peregrine soliton (the lowest order rational solution of the nonlinear Schrödinger equation) indicates that it is unstable [16]. In this paper we analytically investigate the linear stability of the Peregrine soliton, appealing to the fact that the Peregrine solution can be viewed as the singular limit of a single mode spatially periodic breathers (SPB). The "squared eigenfunction" connection between the Zakharov-Shabat (Z-S) system and the linearized NLS equation is employed in the stability analysis. Specifically, we determine the eigenfunctions of the Z-S system associated with the Peregrine soliton and construct a family of solutions of the associated linearized NLS (about the Peregrine) in terms of quadratic products of components of the eigenfunctions (i.e., the squared eigenfunction). We find there exist solutions of the linearization that grow exponentially in time, thus showing the Peregrine soliton is linearly unstable.

Measurements of the eigenfunction of reversed shear Alfvén eigenmodes that sweep downward in frequency

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

Heidbrink, W. W.; Austin, M. E.; Spong, D. A.

2013-08-15

Reversed shear Alfvén eigenmodes (RSAEs) usually sweep upward in frequency when the minimum value of the safety factor q{sub min} decreases in time. On rare occasions, RSAEs sweep downward prior to the upward sweep. Electron cyclotron emission measurements show that the radial eigenfunction during the downsweeping phase is similar to the eigenfunction of normal, upsweeping RSAEs.

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.

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.

Stability analysis of confined V-shaped flames in high-velocity streams.

PubMed

El-Rabii, Hazem; Joulin, Guy; Kazakov, Kirill A

2010-06-01

The problem of linear stability of confined V-shaped flames with arbitrary gas expansion is addressed. Using the on-shell description of flame dynamics, a general equation governing propagation of disturbances of an anchored flame is obtained. This equation is solved analytically for V-flames anchored in high-velocity channel streams. It is demonstrated that dynamics of the flame disturbances in this case is controlled by the memory effects associated with vorticity generated by the perturbed flame. The perturbation growth rate spectrum is determined, and explicit analytical expressions for the eigenfunctions are given. It is found that the piecewise linear V structure is unstable for all values of the gas expansion coefficient. Despite the linearity of the basic pattern, however, evolutions of the V-flame disturbances are completely different from those found for freely propagating planar flames or open anchored flames. The obtained results reveal strong influence of the basic flow and the channel walls on the stability properties of confined V-flames.

Averages of Eigenfunctions Over Hypersurfaces

NASA Astrophysics Data System (ADS)

Canzani, Yaiza; Galkowski, Jeffrey; Toth, John A.

2018-06-01

Let ( M, g) be a compact, smooth, Riemannian manifold and φ_h an L 2-normalized sequence of Laplace eigenfunctions with defect measure {μ}. Let H be a smooth hypersurface with unit exterior normal ν. Our main result says that when μ is not concentrated conormally to H, the eigenfunction restrictions to H satisfy \\int_H φ_h dσ_H = o(1) \\quad and \\quad \\int_H h D_{ν} φ_h dσ_H = o(1), {h \\to 0^+}.

Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation.

PubMed

Marcotte, Christopher D; Grigoriev, Roman O

2016-09-01

This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes (response functions) demonstrate the strongest localization. We also discuss the implications of the localization for the dynamics and control of unstable spiral waves. In particular, the interaction with no-flux boundaries leads to a drift of spiral waves which can be understood with the help of the response functions.

Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation

NASA Astrophysics Data System (ADS)

Marcotte, Christopher D.; Grigoriev, Roman O.

2016-09-01

This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes (response functions) demonstrate the strongest localization. We also discuss the implications of the localization for the dynamics and control of unstable spiral waves. In particular, the interaction with no-flux boundaries leads to a drift of spiral waves which can be understood with the help of the response functions.

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.

Quantum Ergodicity and L p Norms of Restrictions of Eigenfunctions

NASA Astrophysics Data System (ADS)

Hezari, Hamid

2018-02-01

We prove an analogue of Sogge's local L p estimates for L p norms of restrictions of eigenfunctions to submanifolds, and use it to show that for quantum ergodic eigenfunctions one can get improvements of the results of Burq-Gérard-Tzvetkov, Hu, and Chen-Sogge. The improvements are logarithmic on negatively curved manifolds (without boundary) and by o(1) for manifolds (with or without boundary) with ergodic geodesic flows. In the case of ergodic billiards with piecewise smooth boundary, we get o(1) improvements on L^∞ estimates of Cauchy data away from a shrinking neighborhood of the corners, and as a result using the methods of Ghosh et al., Jung and Zelditch, Jung and Zelditch, we get that the number of nodal domains of 2-dimensional ergodic billiards tends to infinity as λ \\to ∞. These results work only for a full density subsequence of any given orthonormal basis of eigenfunctions. We also present an extension of the L p estimates of Burq-Gérard-Tzvetkov, Hu, Chen-Sogge for the restrictions of Dirichlet and Neumann eigenfunctions to compact submanifolds of the interior of manifolds with piecewise smooth boundary. This part does not assume ergodicity on the manifolds.

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.

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.

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.

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.

A Computer Program for the Computation of Running Gear Temperatures Using Green's Function

NASA Technical Reports Server (NTRS)

Koshigoe, S.; Murdock, J. W.; Akin, L. S.; Townsend, D. P.

1996-01-01

A new technique has been developed to study two dimensional heat transfer problems in gears. This technique consists of transforming the heat equation into a line integral equation with the use of Green's theorem. The equation is then expressed in terms of eigenfunctions that satisfy the Helmholtz equation, and their corresponding eigenvalues for an arbitrarily shaped region of interest. The eigenfunction are obtalned by solving an intergral equation. Once the eigenfunctions are found, the temperature is expanded in terms of the eigenfunctions with unknown time dependent coefficients that can be solved by using Runge Kutta methods. The time integration is extremely efficient. Therefore, any changes in the time dependent coefficients or source terms in the boundary conditions do not impose a great computational burden on the user. The method is demonstrated by applying it to a sample gear tooth. Temperature histories at representative surface locatons are given.

Free and constrained expansion of fire ant aggregations

NASA Astrophysics Data System (ADS)

Fernandez-Nieves, Alberto; Anderson, Caleb

We revisit the classical free and constrained expansion of ideal gases with fire ant aggregations. We use rectangular parallel plates to confine fire ants to two-dimensions and watch how these expand when the plates are horizontal or when these are vertical. In the first case, the ants expand in a rather disorganized fashion, while in the second case, when there is work involved, the expansion is rather organized. The behavior is reminiscent of what is expected from the so called reversible process theorems of classical thermodynamics despite the ant aggregation is intrinsically out of equilibrium. This talk will focus on these results and in related observations in the same experimental setting.

A nodal domain theorem for integrable billiards in two dimensions

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

Samajdar, Rhine; Jain, Sudhir R., E-mail: srjain@barc.gov.in

Eigenfunctions of integrable planar billiards are studied — in particular, the number of nodal domains, ν of the eigenfunctions with Dirichlet boundary conditions are considered. The billiards for which the time-independent Schrödinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and non-separable integrable billiards, ν satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of mmodkn, given a particular k, for a set of quantum numbers, m,n. Further, we observe that the patterns in a familymore » are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations. - Highlights: • We find that the number of nodal domains of eigenfunctions of integrable, planar billiards satisfy a class of difference equations. • The eigenfunctions labelled by quantum numbers (m,n) can be classified in terms of mmodkn. • A theorem is presented, realising algebraic representations of geometrical patterns exhibited by the domains. • This work presents a connection between integrable systems and difference equations.« less

Late time cosmology with LISA: Probing the cosmic expansion with massive black hole binary mergers as standard sirens

NASA Astrophysics Data System (ADS)

Tamanini, Nicola

2017-05-01

This paper summarises the potential of the LISA mission to constrain the expansion history of the universe using massive black hole binary mergers as gravitational wave standard sirens. After briefly reviewing the concept of standard siren, the analysis and methodologies of Ref [1] are briefly outlined to show how LISA can be used as a cosmological probe, while a selection of results taken from Refs. [1, 2] is presented in order to estimate the power of LISA in constraining cosmological parameters.

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.

Improved Critical Eigenfunction Restriction Estimates on Riemannian Surfaces with Nonpositive Curvature

NASA Astrophysics Data System (ADS)

Xi, Yakun; Zhang, Cheng

2017-03-01

We show that one can obtain improved L 4 geodesic restriction estimates for eigenfunctions on compact Riemannian surfaces with nonpositive curvature. We achieve this by adapting Sogge's strategy in (Improved critical eigenfunction estimates on manifolds of nonpositive curvature, Preprint). We first combine the improved L 2 restriction estimate of Blair and Sogge (Concerning Toponogov's Theorem and logarithmic improvement of estimates of eigenfunctions, Preprint) and the classical improved {L^∞} estimate of Bérard to obtain an improved weak-type L 4 restriction estimate. We then upgrade this weak estimate to a strong one by using the improved Lorentz space estimate of Bak and Seeger (Math Res Lett 18(4):767-781, 2011). This estimate improves the L 4 restriction estimate of Burq et al. (Duke Math J 138:445-486, 2007) and Hu (Forum Math 6:1021-1052, 2009) by a power of {(log logλ)^{-1}}. Moreover, in the case of compact hyperbolic surfaces, we obtain further improvements in terms of {(logλ)^{-1}} by applying the ideas from (Chen and Sogge, Commun Math Phys 329(3):435-459, 2014) and (Blair and Sogge, Concerning Toponogov's Theorem and logarithmic improvement of estimates of eigenfunctions, Preprint). We are able to compute various constants that appeared in (Chen and Sogge, Commun Math Phys 329(3):435-459, 2014) explicitly, by proving detailed oscillatory integral estimates and lifting calculations to the universal cover H^2.

Freshwater Institute: Focused on improving recirculating aquaculture system technology

USDA-ARS?s Scientific Manuscript database

Recirculating aquaculture system (RAS) technologies help to overcome barriers to domestic aquaculture expansion and enhance the sustainability of the modern fish farming industry through reduction in environmental impacts. With RAS, fish farm expansion is no longer highly constrained by competition ...

Vector-valued Jack polynomials and wavefunctions on the torus

NASA Astrophysics Data System (ADS)

Dunkl, Charles F.

2017-06-01

The Hamiltonian of the quantum Calogero-Sutherland model of N identical particles on the circle with 1/r 2 interactions has eigenfunctions consisting of Jack polynomials times the base state. By use of the generalized Jack polynomials taking values in modules of the symmetric group and the matrix solution of a system of linear differential equations one constructs novel eigenfunctions of the Hamiltonian. Like the usual wavefunctions each eigenfunction determines a symmetric probability density on the N-torus. The construction applies to any irreducible representation of the symmetric group. The methods depend on the theory of generalized Jack polynomials due to Griffeth, and the Yang-Baxter graph approach of Luque and the author.

Refined and Microlocal Kakeya-Nikodym Bounds of Eigenfunctions in Higher Dimensions

NASA Astrophysics Data System (ADS)

Blair, Matthew D.; Sogge, Christopher D.

2017-12-01

We prove a Kakeya-Nikodym bound on eigenfunctions and quasimodes, which sharpens a result of the authors (Blair and Sogge in Anal PDE 8:747-764, 2015) and extends it to higher dimensions. As in the prior work, the key intermediate step is to prove a microlocal version of these estimates, which involves a phase space decomposition of these modes that is essentially invariant under the bicharacteristic/geodesic flow. In a companion paper (Blair and Sogge in J Differ Geom, 2015), it will be seen that these sharpened estimates yield improved L q ( M) bounds on eigenfunctions in the presence of nonpositive curvature when {2 < q < 2(d+1)/d-1}.

Automated generation of influence functions for planar crack problems

NASA Technical Reports Server (NTRS)

Sire, Robert A.; Harris, David O.; Eason, Ernest D.

1989-01-01

A numerical procedure for the generation of influence functions for Mode I planar problems is described. The resulting influence functions are in a form for convenient evaluation of stress-intensity factors for complex stress distributions. Crack surface displacements are obtained by a least-squares solution of the Williams eigenfunction expansion for displacements in a cracked body. Discrete values of the influence function, evaluated using the crack surface displacements, are curve fit using an assumed functional form. The assumed functional form includes appropriate limit-behavior terms for very deep and very shallow cracks. Continuous representation of the influence function provides a convenient means for evaluating stress-intensity factors for arbitrary stress distributions by numerical integration. The procedure is demonstrated for an edge-cracked strip and a radially cracked disk. Comparisons with available published results demonstrate the accuracy of the procedure.

Edge delamination in angle-ply composite laminates, part 5

NASA Technical Reports Server (NTRS)

Wang, S. S.

1981-01-01

A theoretical method was developed for describing the edge delamination stress intensity characteristics in angle-ply composite laminates. The method is based on the theory of anisotropic elasticity. The edge delamination problem is formulated using Lekhnitskii's complex-variable stress potentials and an especially developed eigenfunction expansion method. The method predicts exact orders of the three-dimensional stress singularity in a delamination crack tip region. With the aid of boundary collocation, the method predicts the complete stress and displacement fields in a finite-dimensional, delaminated composite. Fracture mechanics parameters such as the mixed-mode stress intensity factors and associated energy release rates for edge delamination can be calculated explicity. Solutions are obtained for edge delaminated (theta/-theta theta/-theta) angle-ply composites under uniform axial extension. Effects of delamination lengths, fiber orientations, lamination and geometric variables are studied.

Banana regime pressure anisotropy in a bumpy cylinder magnetic field

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

Garcia-Perciante, A.L.; Callen, J.D.; Shaing, K.C.

The pressure anisotropy is calculated for a plasma in a bumpy cylindrical magnetic field in the low collisionality (banana) regime for small magnetic-field modulations ({epsilon}{identical_to}{delta}B/2B<<1). Solutions are obtained by integrating the drift-kinetic equation along field lines in steady state. A closure for the local value of the parallel viscous force B{center_dot}{nabla}{center_dot}{pi}{sub parallel} is then calculated and is shown to exceed the flux-surface-averaged parallel viscous force by a factor of O(1/{epsilon}). A high-frequency limit ({omega}>>{nu}) for the pressure anisotropy is also determined and the calculation is then extended to include the full frequency dependence by using an expansion inmore » Cordey eigenfunctions.« less

Effect of Swirl on Turbulent Structures in Supersonic Jets

NASA Technical Reports Server (NTRS)

Rao, Ram Mohan; Lundgren, Thomas S.

1998-01-01

Direct Numerical Simulation (DNS) is used to study the mechanism of generation and evolution of turbulence structures in a temporally evolving supersonic swirling round jet and also to examine the resulting acoustic radiations. Fourier spectral expansions are used in the streamwise and azimuthal directions and a 1-D b-spline Galerkin representation is used in the radial direction. Spectral-like accuracy is achieved using this numerical scheme. Direct numerical simulations, using the b-spline spectral method, are carried out starting from mean flow initial conditions which are perturbed by the most unstable linear stability eigenfunctions. It is observed that the initial helical instability waves evolve into helical vortices which eventually breakdown into smaller scales of turbulence. 'Rib' structures similar to those seen in incompressible mixing layer flow of Rogers and Moserl are observed. The jet core breakdown stage exhibits increased acoustic radiations.

Surface loading of a viscoelastic earth-I. General theory

NASA Astrophysics Data System (ADS)

Tromp, Jeroen; Mitrovica, Jerry X.

1999-06-01

We present a new normal-mode formalism for computing the response of an aspherical, self-gravitating, linear viscoelastic earth model to an arbitrary surface load. The formalism makes use of recent advances in the theory of the Earth's free oscillations, and is based upon an eigenfunction expansion methodology, rather than the tradi-tional Love-number approach to surface-loading problems. We introduce a surface-load representation theorem analogous to Betti's reciprocity relation in seismology. Taking advantage of this theorem and the biorthogonality of the viscoelastic modes, we determine the complete response to a surface load in the form of a Green's function. We also demonstrate that each viscoelastic mode has its own unique energy partitioning, which can be used to characterize it. In subsequent papers, we apply the theory to spherically symmetric and aspherical earth models.

Filter method without boundary-value condition for simultaneous calculation of eigenfunction and eigenvalue of a stationary Schrödinger equation on a grid.

PubMed

Nurhuda, M; Rouf, A

2017-09-01

The paper presents a method for simultaneous computation of eigenfunction and eigenvalue of the stationary Schrödinger equation on a grid, without imposing boundary-value condition. The method is based on the filter operator, which selects the eigenfunction from wave packet at the rate comparable to δ function. The efficacy and reliability of the method are demonstrated by comparing the simulation results with analytical or numerical solutions obtained by using other methods for various boundary-value conditions. It is found that the method is robust, accurate, and reliable. Further prospect of filter method for simulation of the Schrödinger equation in higher-dimensional space will also be highlighted.

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.

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.

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.

Stochastic uncertainty analysis for unconfined flow systems

USGS Publications Warehouse

Liu, Gaisheng; Zhang, Dongxiao; Lu, Zhiming

2006-01-01

A new stochastic approach proposed by Zhang and Lu (2004), called the Karhunen‐Loeve decomposition‐based moment equation (KLME), has been extended to solving nonlinear, unconfined flow problems in randomly heterogeneous aquifers. This approach is on the basis of an innovative combination of Karhunen‐Loeve decomposition, polynomial expansion, and perturbation methods. The random log‐transformed hydraulic conductivity field (lnKS) is first expanded into a series in terms of orthogonal Gaussian standard random variables with their coefficients obtained as the eigenvalues and eigenfunctions of the covariance function of lnKS. Next, head h is decomposed as a perturbation expansion series Σh(m), where h(m) represents the mth‐order head term with respect to the standard deviation of lnKS. Then h(m) is further expanded into a polynomial series of m products of orthogonal Gaussian standard random variables whose coefficients hi1,i2,...,im(m) are deterministic and solved sequentially from low to high expansion orders using MODFLOW‐2000. Finally, the statistics of head and flux are computed using simple algebraic operations on hi1,i2,...,im(m). A series of numerical test results in 2‐D and 3‐D unconfined flow systems indicated that the KLME approach is effective in estimating the mean and (co)variance of both heads and fluxes and requires much less computational effort as compared to the traditional Monte Carlo simulation technique.

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

Analytical modeling of drug dynamics induced by eluting stents in the coronary multi-layered curved domain.

PubMed

d'Errico, Michele; Sammarco, Paolo; Vairo, Giuseppe

2015-09-01

Pharmacokinetics induced by drug eluting stents (DES) in coronary walls is modeled by means of a one-dimensional multi-layered model, accounting for vessel curvature and non-homogeneous properties of the arterial tissues. The model includes diffusion mechanisms, advection effects related to plasma filtration through the walls, and bio-chemical drug reactions. A non-classical Sturm-Liouville problem with discontinuous coefficients is derived, whose closed-form analytical solution is obtained via an eigenfunction expansion. Soundness and consistency of the proposed approach are shown by numerical computations based on possible clinical treatments involving both hydrophilic and hydrophobic drugs. The influence of the main model parameters on drug delivery mechanisms is analyzed, highlighting the effects induced by vessel curvature and yielding comparative indications and useful insights into the concurring mechanisms governing the pharmacokinetics. Copyright © 2015. Published by Elsevier Inc.

Numerical analysis of two-fluid tearing mode instability in a finite aspect ratio cylinder

NASA Astrophysics Data System (ADS)

Ito, Atsushi; Ramos, Jesús J.

2018-01-01

The two-fluid resistive tearing mode instability in a periodic plasma cylinder of finite aspect ratio is investigated numerically for parameters such that the cylindrical aspect ratio and two-fluid effects are of order unity, hence the real and imaginary parts of the mode eigenfunctions and growth rate are comparable. Considering a force-free equilibrium, numerical solutions of the complete eigenmode equations for general aspect ratios and ion skin depths are compared and found to be in very good agreement with the corresponding analytic solutions derived by means of the boundary layer theory [A. Ito and J. J. Ramos, Phys. Plasmas 24, 072102 (2017)]. Scaling laws for the growth rate and the real frequency of the mode are derived from the analytic dispersion relation by using Taylor expansions and Padé approximations. The cylindrical finite aspect ratio effect is inferred from the scaling law for the real frequency of the mode.

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.

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.

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.

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.

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

Dynamics of Compressible Convection and Thermochemical Mantle Convection

NASA Astrophysics Data System (ADS)

Liu, Xi

The Earth's long-wavelength geoid anomalies have long been used to constrain the dynamics and viscosity structure of the mantle in an isochemical, whole-mantle convection model. However, there is strong evidence that the seismically observed large low shear velocity provinces (LLSVPs) in the lowermost mantle are chemically distinct and denser than the ambient mantle. In this thesis, I investigated how chemically distinct and dense piles influence the geoid. I formulated dynamically self-consistent 3D spherical convection models with realistic mantle viscosity structure which reproduce Earth's dominantly spherical harmonic degree-2 convection. The models revealed a compensation effect of the chemically dense LLSVPs. Next, I formulated instantaneous flow models based on seismic tomography to compute the geoid and constrain mantle viscosity assuming thermochemical convection with the compensation effect. Thermochemical models reconcile the geoid observations. The viscosity structure inverted for thermochemical models is nearly identical to that of whole-mantle models, and both prefer weak transition zone. Our results have implications for mineral physics, seismic tomographic studies, and mantle convection modelling. Another part of this thesis describes analyses of the influence of mantle compressibility on thermal convection in an isoviscous and compressible fluid with infinite Prandtl number. A new formulation of the propagator matrix method is implemented to compute the critical Rayleigh number and the corresponding eigenfunctions for compressible convection. Heat flux and thermal boundary layer properties are quantified in numerical models and scaling laws are developed.

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

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.

The WHO/PEPFAR collaboration to prepare an operations manual for HIV prevention, care, and treatment at primary health centers in high-prevalence, resource-constrained settings: defining laboratory services.

PubMed

Spira, Thomas; Lindegren, Mary Lou; Ferris, Robert; Habiyambere, Vincent; Ellerbrock, Tedd

2009-06-01

The expansion of HIV/AIDS care and treatment in resource-constrained countries, especially in sub-Saharan Africa, has generally developed in a top-down manner. Further expansion will involve primary health centers where human and other resources are limited. This article describes the World Health Organization/President's Emergency Plan for AIDS Relief collaboration formed to help scale up HIV services in primary health centers in high-prevalence, resource-constrained settings. It reviews the contents of the Operations Manual developed, with emphasis on the Laboratory Services chapter, which discusses essential laboratory services, both at the center and the district hospital level, laboratory safety, laboratory testing, specimen transport, how to set up a laboratory, human resources, equipment maintenance, training materials, and references. The chapter provides specific information on essential tests and generic job aids for them. It also includes annexes containing a list of laboratory supplies for the health center and sample forms.

Colonization behaviors of mountain pine beetle on novel hosts: Implications for range expansion into northeastern North America

Treesearch

Derek W. Rosenberger; Robert C. Venette; Mitchell P. Maddox; Brian H. Aukema; Gadi V.P. Reddy

2017-01-01

As climates change, thermal limits may no longer constrain some native herbivores within their historical ranges. The mountain pine beetle, Dendroctonus ponderosae Hopkins, is a tree-killing bark beetle native to western North America that is currently expanding its range. Continued eastward expansion through the newly invaded and novel jack pine...

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.

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.

Science with the space-based interferometer eLISA. III: probing the expansion of the universe using gravitational wave standard sirens

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

Tamanini, Nicola; Caprini, Chiara; Barausse, Enrico

We investigate the capability of various configurations of the space interferometer eLISA to probe the late-time background expansion of the universe using gravitational wave standard sirens. We simulate catalogues of standard sirens composed by massive black hole binaries whose gravitational radiation is detectable by eLISA, and which are likely to produce an electromagnetic counterpart observable by future surveys. The main issue for the identification of a counterpart resides in the capability of obtaining an accurate enough sky localisation with eLISA. This seriously challenges the capability of four-link (2 arm) configurations to successfully constrain the cosmological parameters. Conversely, six-link (3 arm)more » configurations have the potential to provide a test of the expansion of the universe up to z ∼ 8 which is complementary to other cosmological probes based on electromagnetic observations only. In particular, in the most favourable scenarios, they can provide a significant constraint on H{sub 0} at the level of 0.5%. Furthermore, (Ω{sub M}, Ω{sub Λ}) can be constrained to a level competitive with present SNIa results. On the other hand, the lack of massive black hole binary standard sirens at low redshift allows to constrain dark energy only at the level of few percent.« less

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

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.

Boundary layer thermal stresses in angle-ply composite laminates, part 1. [graphite-epoxy composites

NASA Technical Reports Server (NTRS)

Wang, S. S.; Choi, I.

1981-01-01

Thermal boundary-layer stresses (near free edges) and displacements were determined by a an eigenfunction expansion technique and the establishment of an appropriate particular solution. Current solutions in the region away from the singular domain (free edge) are found to be excellent agreement with existing approximate numerical results. As the edge is approached, the singular term controls the near field behavior of the boundary layer. Results are presented for cases of various angle-ply graphite/epoxy laminates with (theta/-theta/theta/theta) configurations. These results show high interlaminar (through-the-thickness) stresses. Thermal boundary-layer thicknesses of different composite systems are determined by examining the strain energy density distribution in composites. It is shown that the boundary-layer thickness depends on the degree of anisotropy of each individual lamina, thermomechanical properties of each ply, and the relative thickness of adjacent layers. The interlaminar thermal stresses are compressive with increasing temperature. The corresponding residual stresses are tensile and may enhance interply delaminations.

Planar dynamics of a uniform beam with rigid bodies affixed to the ends

NASA Technical Reports Server (NTRS)

Storch, J.; Gates, S.

1983-01-01

The planar dynamics of a uniform elastic beam subject to a variety of geometric and natural boundary conditions and external excitations were analyzed. The beams are inextensible and capable of small transverse bending deformations only. Classical beam vibration eigenvalue problems for a cantilever with tip mass, a cantilever with tip body and an unconstrained beam with rigid bodies at each are examined. The characteristic equations, eigenfunctions and orthogonality relations for each are derived. The forced vibration of a cantilever with tip body subject to base acceleration is analyzed. The exact solution of the governing nonhomogeneous partial differential equation with time dependent boundary conditions is presented and compared with a Rayleigh-Ritz approximate solution. The arbitrary planar motion of an elastic beam with rigid bodies at the ends is addressed. Equations of motion are derived for two modal expansions of the beam deflection. The motion equations are cast in a first order form suitable for numerical integration. Selected FORTRAN programs are provided.

A Squeeze-film Damping Model for the Circular Torsion Micro-resonators

NASA Astrophysics Data System (ADS)

Yang, Fan; Li, Pu

2017-07-01

In recent years, MEMS devices are widely used in many industries. The prediction of squeeze-film damping is very important for the research of high quality factor resonators. In the past, there have been many analytical models predicting the squeeze-film damping of the torsion micro-resonators. However, for the circular torsion micro-plate, the works over it is very rare. The only model presented by Xia et al[7] using the method of eigenfunction expansions. In this paper, The Bessel series solution is used to solve the Reynolds equation under the assumption of the incompressible gas of the gap, the pressure distribution of the gas between two micro-plates is obtained. Then the analytical expression for the damping constant of the device is derived. The result of the present model matches very well with the finite element method (FEM) solutions and the result of Xia’s model, so the present models’ accuracy is able to be validated.

Transverse cracking and stiffness reduction in composite laminates

NASA Technical Reports Server (NTRS)

Yuan, F. G.; Selek, M. C.

1993-01-01

A study of transverse cracking mechanism in composite laminates is presented using a singular hybrid finite element model. The model provides the global structural response as well as the precise local crack-tip stress fields. An elasticity basis for the problem is established by employing Lekhnitskii's complex variable potentials and method of eigenfunction expansion. Stress singularities associated with the transverse crack are obtained by decomposing the deformation into the symmetric and antisymmetric modes and proper boundary conditions. A singular hybrid element is thereby formulated based on the variational principle of a modified hybrid functional to incorporate local crack singularities. Axial stiffness reduction due to transverse cracking is studied. The results are shown to be in very good agreement with the existing experimental data. Comparison with simple shear lag analysis is also given. The effects of stress intensity factors and strain energy density on the increase of crack density are analyzed. The results reveal that the parameters approach definite limits when crack densities are saturated, an evidence of the existence of characteristic damage state.

Scattering Cross Section of Sound Waves by the Modal Element Method

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1994-01-01

#he modal element method has been employed to determine the scattered field from a plane acoustic wave impinging on a two dimensional body. In the modal element method, the scattering body is represented by finite elements, which are coupled to an eigenfunction expansion representing the acoustic pressure in the infinite computational domain surrounding the body. The present paper extends the previous work by developing the algorithm necessary to calculate the acoustics scattering cross section by the modal element method. The scattering cross section is the acoustical equivalent to the Radar Cross Section (RCS) in electromagnetic theory. Since the scattering cross section is evaluated at infinite distance from the body, an asymptotic approximation is used in conjunction with the standard modal element method. For validation, the scattering cross section of the rigid circular cylinder is computed for the frequency range 0.1 is less than or equal to ka is less than or equal to 100. Results show excellent agreement with the analytic solution.

Oblique wave trapping by vertical permeable membrane barriers located near a wall

NASA Astrophysics Data System (ADS)

Koley, Santanu; Sahoo, Trilochan

2017-12-01

The effectiveness of a vertical partial flexible porous membrane wave barrier located near a rigid vertical impermeable seawall for trapping obliquely incident surface gravity waves are analyzed in water of uniform depth under the assumption of linear water wave theory and small amplitude membrane barrier response. From the general formulation of the submerged membrane barrier, results for bottom-standing and surface-piercing barriers are computed and analyzed in special cases. Using the eigenfunction expansion method, the boundary-value problems are converted into series relations and then the required unknowns are obtained using the least squares approximation method. Various physical quantities of interests like reflection coefficient, wave energy dissipation, wave forces acting on the membrane barrier and the seawall are computed and analyzed for different values of the wave and structural parameters. The study will be useful in the design of the membrane wave barrier for the creation of tranquility zone in the lee side of the barrier to protect the seawall.

Low-dimensional and Data Fusion Techniques Applied to a Rectangular Supersonic Multi-stream Jet

NASA Astrophysics Data System (ADS)

Berry, Matthew; Stack, Cory; Magstadt, Andrew; Ali, Mohd; Gaitonde, Datta; Glauser, Mark

2017-11-01

Low-dimensional models of experimental and simulation data for a complex supersonic jet were fused to reconstruct time-dependent proper orthogonal decomposition (POD) coefficients. The jet consists of a multi-stream rectangular single expansion ramp nozzle, containing a core stream operating at Mj , 1 = 1.6 , and bypass stream at Mj , 3 = 1.0 with an underlying deck. POD was applied to schlieren and PIV data to acquire the spatial basis functions. These eigenfunctions were projected onto their corresponding time-dependent large eddy simulation (LES) fields to reconstruct the temporal POD coefficients. This reconstruction was able to resolve spectral peaks that were previously aliased due to the slower sampling rates of the experiments. Additionally, dynamic mode decomposition (DMD) was applied to the experimental and LES datasets, and the spatio-temporal characteristics were compared to POD. The authors would like to acknowledge AFOSR, program manager Dr. Doug Smith, for funding this research, Grant No. FA9550-15-1-0435.

Reduction by symmetries in singular quantum-mechanical problems: General scheme and application to Aharonov-Bohm model

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

Smirnov, A. G., E-mail: smirnov@lpi.ru

2015-12-15

We develop a general technique for finding self-adjoint extensions of a symmetric operator that respects a given set of its symmetries. Problems of this type naturally arise when considering two- and three-dimensional Schrödinger operators with singular potentials. The approach is based on constructing a unitary transformation diagonalizing the symmetries and reducing the initial operator to the direct integral of a suitable family of partial operators. We prove that symmetry preserving self-adjoint extensions of the initial operator are in a one-to-one correspondence with measurable families of self-adjoint extensions of partial operators obtained by reduction. The general scheme is applied to themore » three-dimensional Aharonov-Bohm Hamiltonian describing the electron in the magnetic field of an infinitely thin solenoid. We construct all self-adjoint extensions of this Hamiltonian, invariant under translations along the solenoid and rotations around it, and explicitly find their eigenfunction expansions.« less

A quasi-spectral method for Cauchy problem of 2/D Laplace equation on an annulus

NASA Astrophysics Data System (ADS)

Saito, Katsuyoshi; Nakada, Manabu; Iijima, Kentaro; Onishi, Kazuei

2005-01-01

Real numbers are usually represented in the computer as a finite number of digits hexa-decimal floating point numbers. Accordingly the numerical analysis is often suffered from rounding errors. The rounding errors particularly deteriorate the precision of numerical solution in inverse and ill-posed problems. We attempt to use a multi-precision arithmetic for reducing the rounding error evil. The use of the multi-precision arithmetic system is by the courtesy of Dr Fujiwara of Kyoto University. In this paper we try to show effectiveness of the multi-precision arithmetic by taking two typical examples; the Cauchy problem of the Laplace equation in two dimensions and the shape identification problem by inverse scattering in three dimensions. It is concluded from a few numerical examples that the multi-precision arithmetic works well on the resolution of those numerical solutions, as it is combined with the high order finite difference method for the Cauchy problem and with the eigenfunction expansion method for the inverse scattering problem.

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.

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.

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.

Constrained variation in Jastrow method at high density

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

Owen, J.C.; Bishop, R.F.; Irvine, J.M.

1976-11-01

A method is derived for constraining the correlation function in a Jastrow variational calculation which permits the truncation of the cluster expansion after two-body terms, and which permits exact minimization of the two-body cluster by functional variation. This method is compared with one previously proposed by Pandharipande and is found to be superior both theoretically and practically. The method is tested both on liquid /sup 3/He, by using the Lennard--Jones potential, and on the model system of neutrons treated as Boltzmann particles (''homework'' problem). Good agreement is found both with experiment and with other calculations involving the explicit evaluation ofmore » higher-order terms in the cluster expansion. The method is then applied to a more realistic model of a neutron gas up to a density of 4 neutrons per F/sup 3/, and is found to give ground-state energies considerably lower than those of Pandharipande. (AIP)« less

Limits on radial differential rotation in Sun-like stars from parametric fits to oscillation power spectra

NASA Astrophysics Data System (ADS)

Nielsen, M. B.; Schunker, H.; Gizon, L.; Schou, J.; Ball, W. H.

2017-06-01

Context. Rotational shear in Sun-like stars is thought to be an important ingredient in models of stellar dynamos. Thanks to helioseismology, rotation in the Sun is characterized well, but the interior rotation profiles of other Sun-like stars are not so well constrained. Until recently, measurements of rotation in Sun-like stars have focused on the mean rotation, but little progress has been made on measuring or even placing limits on differential rotation. Aims: Using asteroseismic measurements of rotation we aim to constrain the radial shear in five Sun-like stars observed by the NASA Kepler mission: KIC 004914923, KIC 005184732, KIC 006116048, KIC 006933899, and KIC 010963065. Methods: We used stellar structure models for these five stars from previous works. These models provide the mass density, mode eigenfunctions, and the convection zone depth, which we used to compute the sensitivity kernels for the rotational frequency splitting of the modes. We used these kernels as weights in a parametric model of the stellar rotation profile of each star, where we allowed different rotation rates for the radiative interior and the convective envelope. This parametric model was incorporated into a fit to the oscillation power spectrum of each of the five Kepler stars. This fit included a prior on the rotation of the envelope, estimated from the rotation of surface magnetic activity measured from the photometric variability. Results: The asteroseismic measurements without the application of priors are unable to place meaningful limits on the radial shear. Using a prior on the envelope rotation enables us to constrain the interior rotation rate and thus the radial shear. In the five cases that we studied, the interior rotation rate does not differ from the envelope by more than approximately ± 30%. Uncertainties in the rotational splittings are too large to unambiguously determine the sign of the radial shear.

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.

The Funnel Geometry of Open Flux Tubes in the Low Solar Corona Constrained by O VI and Ne VIII Outflow

NASA Technical Reports Server (NTRS)

Byhring, Hanne S.; Esser, Ruth; Lie-Svendsen, Oystein

2008-01-01

Model calculations show that observed outflow velocities of order 7-10 km/s of C IV and O VI ions, and 15-20 km/s of Ne VIII ions, are not only consistent with models of the solar wind from coronas holes, but also place unique constraints on the degree of flow tube expansion as well as the location of the expansion in the transition region/lower corona.

Supercritical flow characteristics at abrupt expansion structure

NASA Astrophysics Data System (ADS)

Lim, Jia Jun; Puay, How Tion; Zakaria, Nor Azazi

2017-10-01

When dealing with the design of a hydraulic structure, lateral expansion is often necessary for flow emerging at high velocity served as a cross-sectional transition. If the abrupt expansion structure is made to diverge rapidly, it will cause the major part of the flow fail to follow the boundaries. If the transition is too gradual, it will result in a waste of structural material. A preliminary study on the flow structure near the expansion and its relationship with flow parameter is carried out in this study. A two-dimensional depth-averaged model is developed to simulate the supercritical flow at the abrupt expansion structure. Constrained Interpolation Profile (CIP) scheme (which is of third order accuracy) is adopted in the numerical model. Results show that the flow structure and flow characteristics at the abrupt expansion can be reproduced numerically. The validation of numerical result is done against analytical studies. The result from numerical simulation showed good agreement with the analytical solution.

The effect of imperfections on the vertical buckling of railroad tracks

DOT National Transportation Integrated Search

1976-06-30

This report deals with an analytical prediction of the effect of geometric imperfections on the post-buckling characteristics of railroad tracks. The analysis is restricted to the case of vertical track buckling due to constrained thermal expansion i...

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.

Computation of resistive instabilities by matched asymptotic expansions

DOE PAGES

Glasser, A. H.; Wang, Z. R.; Park, J. -K.

2016-11-17

Here, we present a method for determining the linear resistive magnetohydrodynamic (MHD) stability of an axisymmetric toroidal plasma, based on the method of matched asymptotic expansions. The plasma is partitioned into a set of ideal MHD outer regions, connected through resistive MHD inner regions about singular layers where q = m/n, with m and n toroidal mode numbers, respectively, and q the safety factor. The outer regions satisfy the ideal MHD equations with zero-frequency, which are identical to the Euler-Lagrange equations for minimizing the potential energy delta W. The solutions to these equations go to infinity at the singular surfaces.more » The inner regions satisfy the equations of motion of resistive MHD with a finite eigenvalue, resolving the singularity. Both outer and inner regions are solved numerically by newly developed singular Galerkin methods, using specialized basis functions. These solutions are matched asymptotically, providing a complex dispersion relation which is solved for global eigenvalues and eigenfunctions in full toroidal geometry. The dispersion relation may have multiple complex unstable roots, which are found by advanced root-finding methods. These methods are much faster and more robust than the previous numerical methods. The new methods are applicable to more challenging high-pressure and strongly shaped plasma equilibria and generalizable to more realistic inner region dynamics. In the thermonuclear regime, where the outer and inner regions overlap, they are also much faster and more accurate than the straight-through methods, which treat the resistive MHD equations in the whole plasma volume.« less

Linear analysis using secants for materials with temperature dependent nonlinear elastic modulus and thermal expansion properties

NASA Astrophysics Data System (ADS)

Pepi, John W.

2017-08-01

Thermally induced stress is readily calculated for linear elastic material properties using Hooke's law in which, for situations where expansion is constrained, stress is proportional to the product of the material elastic modulus and its thermal strain. When material behavior is nonlinear, one needs to make use of nonlinear theory. However, we can avoid that complexity in some situations. For situations in which both elastic modulus and coefficient of thermal expansion vary with temperature, solutions can be formulated using secant properties. A theoretical approach is thus presented to calculate stresses for nonlinear, neo-Hookean, materials. This is important for high acuity optical systems undergoing large temperature extremes.

Modal ring method for the scattering of sound

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1993-01-01

The modal element method for acoustic scattering can be simplified when the scattering body is rigid. In this simplified method, called the modal ring method, the scattering body is represented by a ring of triangular finite elements forming the outer surface. The acoustic pressure is calculated at the element nodes. The pressure in the infinite computational region surrounding the body is represented analytically by an eigenfunction expansion. The two solution forms are coupled by the continuity of pressure and velocity on the body surface. The modal ring method effectively reduces the two-dimensional scattering problem to a one-dimensional problem capable of handling very high frequency scattering. In contrast to the boundary element method or the method of moments, which perform a similar reduction in problem dimension, the model line method has the added advantage of having a highly banded solution matrix requiring considerably less computer storage. The method shows excellent agreement with analytic results for scattering from rigid circular cylinders over a wide frequency range (1 is equal to or less than ka is less than or equal to 100) in the near and far fields.

Modal element method for scattering of sound by absorbing bodies

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1992-01-01

The modal element method for acoustic scattering from 2-D body is presented. The body may be acoustically soft (absorbing) or hard (reflecting). The infinite computational region is divided into two subdomains - the bounded finite element domain, which is characterized by complicated geometry and/or variable material properties, and the surrounding unbounded homogeneous domain. The acoustic pressure field is represented approximately in the finite element domain by a finite element solution, and is represented analytically by an eigenfunction expansion in the homogeneous domain. The two solutions are coupled by the continuity of pressure and velocity across the interface between the two subdomains. Also, for hard bodies, a compact modal ring grid system is introduced for which computing requirements are drastically reduced. Analysis for 2-D scattering from solid and coated (acoustically treated) bodies is presented, and several simple numerical examples are discussed. In addition, criteria are presented for determining the number of modes to accurately resolve the scattered pressure field from a solid cylinder as a function of the frequency of the incoming wave and the radius of the cylinder.

Different approach to the modeling of nonfree particle diffusion

NASA Astrophysics Data System (ADS)

Buhl, Niels

2018-03-01

A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore networks to general geometric domains can be considered and that the (free random walk) central limit theorem can be generalized to cover also the nonfree case. The latter gives rise to a continuum-limit description of the diffusive motion where the effect of partially absorbing barriers is accounted for in a natural and non-Markovian way that, in contrast to the traditional approach, quantifies the absorptivity of a barrier in terms of a dimensionless parameter in the range 0 to 1. The generalized theorem gives two general analytic expressions for the continuum-limit propagator: an infinite sum of Gaussians and an infinite sum of plane waves. These expressions entail the known method-of-images and Laplace eigenfunction expansions as special cases and show how the presence of partially absorbing barriers can lead to phenomena such as line splitting and band gap formation in the plane wave wave-number spectrum.

Quantum Model of a Charged Black Hole

NASA Astrophysics Data System (ADS)

Gladush, V. D.

A canonical approach for constructing of the classical and quantum description spherically-symmetric con guration gravitational and electromagnetic elds is considered. According to the sign of the square of the Kodama vector, space-time is divided into R-and T-regions. By virtue of the generalized Birkho theorem, one can choose coordinate systems such that the desired metric functions in the T-region depend on the time, and in the R-domain on the space coordinate. Then, the initial action for the con guration breaks up into terms describing the elds in the T- and R-regions with the time and space evolutionary variable, respectively. For these regions, Lagrangians of the con guration are constructed, which contain dynamic and non-dynamic degrees of freedom, leading to constrains. We concentrate our attention on dynamic T-regions. There are two additional conserved physical quantities: the charge and the total mass of the system. The Poisson bracket of the total mass with the Hamiltonian function vanishes in the weak sense. A classical solution of the eld equations in the con guration space (minisuperspace) is constructed without xing non-dynamic variable. In the framework of the canonical approach to the quantum mechanics of the system under consideration, physical states are found by solving the Hamiltonian constraint in the operator form (the DeWitt equation) for the system wave function Ψ. It also requires that Ψ is an eigenfunction of the operators of charge and total mass. For the symmetric of the mass operator the corresponding ordering of operators is carried out. Since the total mass operator commutes with the Hamiltonian in the weak sense, its eigenfunctions must be constructed in conjunction with the solution of the DeWitt equation. The consistency condition leads to the ansatz, with the help of which the solution of the DeWitt equation for the state Ψem with a defined total mass and charge is constructed, taking into account the regularity condition on the horizon. The mass and charge spectra of the con guration in this approach turn out to be continuous. It is interesting that formal quantization in the R-region with a space evolutionary coordinate leads to a similar result.

Simultaneous Constraints on the Mass and Radius of Aql X–1 from Quiescence and X-Ray Burst Observations

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

Li, Zhaosheng; Falanga, Maurizio; Chen, Li

The measurement of neutron star mass and radius is one of the most direct ways to distinguish between various dense matter equations of state. The mass and radius of accreting neutron stars hosted in low-mass X-ray binaries can be constrained by several methods, including photospheric radius expansion from type I X-ray bursts and from quiescent spectra. In this paper, we apply for the first time these two methods simultaneously to constrain the mass and radius of Aql X–1. The quiescent spectra from Chandra and XMM-Newton , and photospheric radius expansion bursts from RXTE are used. The determination of the massmore » and radius of Aql X–1 is also used to verify the consistency between the two methods and to narrow down the uncertainties of the neutron star mass and radius. It is found that the distance to Aql X–1 should be in the range of 4.0–5.75 kpc, based on the overlapping confidence regions between photospheric radius expansion burst and quiescent spectra methods. In addition, we show that the mass and radius determined for the compact star in Aql X–1 are compatible with strange star equations of state and conventional neutron star models.« less

Constraining a Possible Variation of G with Type Ia Supernovae

NASA Astrophysics Data System (ADS)

Mould, Jeremy; Uddin, Syed A.

2014-03-01

Astrophysical cosmology constrains the variation of Newton's Constant in a manner complementary to laboratory experiments, such as the celebrated lunar laser ranging campaign. Supernova cosmology is an example of the former and has attained campaign status, following planning by a Dark Energy Task Force in 2005. In this paper, we employ the full SNIa data set to the end of 2013 to set a limit on G variation. In our approach, we adopt the standard candle delineation of the redshift distance relation. We set an upper limit on its rate of change |dot{G}/G| of 0.1 parts per billion per year over 9 Gyrs. By contrast, lunar laser ranging tests variation of G over the last few decades. Conversely, one may adopt the laboratory result as a prior and constrain the effect of variable G in dark energy equation of state experiments to δw < 0.02. We also examine the parameterisation G 1 + z. Its short expansion age conflicts with the measured values of the expansion rate and the density in a flat Universe. In conclusion, supernova cosmology complements other experiments in limiting G variation. An important caveat is that it rests on the assumption that the same mass of 56Ni is burned to create the standard candle regardless of redshift. These two quantities, f and G, where f is the Chandrasekhar mass fraction burned, are degenerate. Constraining f variation alone requires more understanding of the SNIa mechanism.

Laplace-Beltrami Eigenvalues and Topological Features of Eigenfunctions for Statistical Shape Analysis

PubMed Central

Reuter, Martin; Wolter, Franz-Erich; Shenton, Martha; Niethammer, Marc

2009-01-01

This paper proposes the use of the surface based Laplace-Beltrami and the volumetric Laplace eigenvalues and -functions as shape descriptors for the comparison and analysis of shapes. These spectral measures are isometry invariant and therefore allow for shape comparisons with minimal shape pre-processing. In particular, no registration, mapping, or remeshing is necessary. The discriminatory power of the 2D surface and 3D solid methods is demonstrated on a population of female caudate nuclei (a subcortical gray matter structure of the brain, involved in memory function, emotion processing, and learning) of normal control subjects and of subjects with schizotypal personality disorder. The behavior and properties of the Laplace-Beltrami eigenvalues and -functions are discussed extensively for both the Dirichlet and Neumann boundary condition showing advantages of the Neumann vs. the Dirichlet spectra in 3D. Furthermore, topological analyses employing the Morse-Smale complex (on the surfaces) and the Reeb graph (in the solids) are performed on selected eigenfunctions, yielding shape descriptors, that are capable of localizing geometric properties and detecting shape differences by indirectly registering topological features such as critical points, level sets and integral lines of the gradient field across subjects. The use of these topological features of the Laplace-Beltrami eigenfunctions in 2D and 3D for statistical shape analysis is novel. PMID:20161035

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

The Analytical Diffusion-Expansion Model for Forbush Decreases Caused by Flux Ropes

NASA Astrophysics Data System (ADS)

Dumbovic, M.; Temmer, M.

2017-12-01

Identification and tracking of interplanetary coronal mass ejections (ICMEs) throughout the heliosphere is a growingly important aspect of space weather research. One of the "signatures" of ICME passage is the corresponding Forbush decrease (FD), a short term decrease in the galactic cosmic ray flux. These depressions are observed at the surface of the Earth for over 50 years, by several spacecraft in interplanetary space in the past couple of decades, and recently also on Mars' surface with Curiosity rover. In order to use FDs as ICME signatures efficiently, it is important to model ICME interaction with energetic particles by taking into account ICME evolution and constraining the model with observational data. We present an analytical diffusion-expansion FD model ForbMod which is based on the widely used approach of the initially empty, closed magnetic structure (i.e. flux rope) which fills up slowly with particles by perpendicular diffusion. The model is restricted to explain only the depression caused by the magnetic structure of the ICME and not of the associated shock. We use remote CME observations and a 3D reconstruction method (the Graduated Cylindrical Shell method) to constrain initial and boundary conditions of the FD model and take into account CME evolutionary properties by incorporating flux rope expansion. Several options of flux rope expansion are regarded as the competing mechanism to diffusion which can lead to different FD characteristics. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 745782.

Whither Thee, Educational Technology? Suggesting a Critical Expansion of Our Epistemology for Emerging Leaders

ERIC Educational Resources Information Center

Kowch, Eugene G.

2013-01-01

It is possible that some outdated ideas about "management" in our field are constraining our preparation of new educational technologists to lead education organizations in the Knowledge Age? This paper takes an interdisciplinary stance to examine educational administration, education technology and complexivist thinking about leadership…

Spectral algorithms for multiple scale localized eigenfunctions in infinitely long, slightly bent quantum waveguides

NASA Astrophysics Data System (ADS)

Boyd, John P.; Amore, Paolo; Fernández, Francisco M.

2018-03-01

A "bent waveguide" in the sense used here is a small perturbation of a two-dimensional rectangular strip which is infinitely long in the down-channel direction and has a finite, constant width in the cross-channel coordinate. The goal is to calculate the smallest ("ground state") eigenvalue of the stationary Schrödinger equation which here is a two-dimensional Helmholtz equation, ψxx +ψyy + Eψ = 0 where E is the eigenvalue and homogeneous Dirichlet boundary conditions are imposed on the walls of the waveguide. Perturbation theory gives a good description when the "bending strength" parameter ɛ is small as described in our previous article (Amore et al., 2017) and other works cited therein. However, such series are asymptotic, and it is often impractical to calculate more than a handful of terms. It is therefore useful to develop numerical methods for the perturbed strip to cover intermediate ɛ where the perturbation series may be inaccurate and also to check the pertubation expansion when ɛ is small. The perturbation-induced change-in-eigenvalue, δ ≡ E(ɛ) - E(0) , is O(ɛ2) . We show that the computation becomes very challenging as ɛ → 0 because (i) the ground state eigenfunction varies on both O(1) and O(1 / ɛ) length scales and (ii) high accuracy is needed to compute several correct digits in δ, which is itself small compared to the eigenvalue E. The multiple length scales are not geographically separate, but rather are inextricably commingled in the neighborhood of the boundary deformation. We show that coordinate mapping and immersed boundary strategies both reduce the computational domain to the uniform strip, allowing application of pseudospectral methods on tensor product grids with tensor product basis functions. We compared different basis sets; Chebyshev polynomials are best in the cross-channel direction. However, sine functions generate rather accurate analytical approximations with just a single basis function. In the down-channel coordinate, X ∈ [ - ∞ , ∞ ] , Fourier domain truncation using the change of coordinate X = sinh(Lt) is considerably more efficient than rational Chebyshev functions TBn(X ; L) . All the spectral methods, however, yielded the required accuracy on a desktop computer.

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.

Efficient modeling of photonic crystals with local Hermite polynomials

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

Boucher, C. R.; Li, Zehao; Albrecht, J. D.

2014-04-21

Developing compact algorithms for accurate electrodynamic calculations with minimal computational cost is an active area of research given the increasing complexity in the design of electromagnetic composite structures such as photonic crystals, metamaterials, optical interconnects, and on-chip routing. We show that electric and magnetic (EM) fields can be calculated using scalar Hermite interpolation polynomials as the numerical basis functions without having to invoke edge-based vector finite elements to suppress spurious solutions or to satisfy boundary conditions. This approach offers several fundamental advantages as evidenced through band structure solutions for periodic systems and through waveguide analysis. Compared with reciprocal space (planemore » wave expansion) methods for periodic systems, advantages are shown in computational costs, the ability to capture spatial complexity in the dielectric distributions, the demonstration of numerical convergence with scaling, and variational eigenfunctions free of numerical artifacts that arise from mixed-order real space basis sets or the inherent aberrations from transforming reciprocal space solutions of finite expansions. The photonic band structure of a simple crystal is used as a benchmark comparison and the ability to capture the effects of spatially complex dielectric distributions is treated using a complex pattern with highly irregular features that would stress spatial transform limits. This general method is applicable to a broad class of physical systems, e.g., to semiconducting lasers which require simultaneous modeling of transitions in quantum wells or dots together with EM cavity calculations, to modeling plasmonic structures in the presence of EM field emissions, and to on-chip propagation within monolithic integrated circuits.« less

Model-independent cosmological constraints from growth and expansion

NASA Astrophysics Data System (ADS)

L'Huillier, Benjamin; Shafieloo, Arman; Kim, Hyungjin

2018-05-01

Reconstructing the expansion history of the Universe from Type Ia supernovae data, we fit the growth rate measurements and put model-independent constraints on some key cosmological parameters, namely, Ωm, γ, and σ8. The constraints are consistent with those from the concordance model within the framework of general relativity, but the current quality of the data is not sufficient to rule out modified gravity models. Adding the condition that dark energy density should be positive at all redshifts, independently of its equation of state, further constrains the parameters and interestingly supports the concordance model.

A Constrained Scheme for High Precision Downward Continuation of Potential Field Data

NASA Astrophysics Data System (ADS)

Wang, Jun; Meng, Xiaohong; Zhou, Zhiwen

2018-04-01

To further improve the accuracy of the downward continuation of potential field data, we present a novel constrained scheme in this paper combining the ideas of the truncated Taylor series expansion, the principal component analysis, the iterative continuation and the prior constraint. In the scheme, the initial downward continued field on the target plane is obtained from the original measured field using the truncated Taylor series expansion method. If the original field was with particularly low signal-to-noise ratio, the principal component analysis is utilized to suppress the noise influence. Then, the downward continued field is upward continued to the plane of the prior information. If the prior information was on the target plane, it should be upward continued over a short distance to get the updated prior information. Next, the difference between the calculated field and the updated prior information is calculated. The cosine attenuation function is adopted to get the scope of constraint and the corresponding modification item. Afterward, a correction is performed on the downward continued field on the target plane by adding the modification item. The correction process is iteratively repeated until the difference meets the convergence condition. The accuracy of the proposed constrained scheme is tested on synthetic data with and without noise. Numerous model tests demonstrate that downward continuation using the constrained strategy can yield more precise results compared to other downward continuation methods without constraints and is relatively insensitive to noise even for downward continuation over a large distance. Finally, the proposed scheme is applied to real magnetic data collected within the Dapai polymetallic deposit from the Fujian province in South China. This practical application also indicates the superiority of the presented scheme.

Super-Eddington accreting massive black holes explore high-z cosmology: Monte-Carlo simulations

NASA Astrophysics Data System (ADS)

Cai, Rong-Gen; Guo, Zong-Kuan; Huang, Qing-Guo; Yang, Tao

2018-06-01

In this paper, we simulate Super-Eddington accreting massive black holes (SEAMBHs) as the candles to probe cosmology for the first time. SEAMBHs have been demonstrated to be able to provide a new tool for estimating cosmological distance. Thus, we create a series of mock data sets of SEAMBHs, especially in the high redshift region, to check their abilities to probe the cosmology. To fulfill the potential of the SEAMBHs on the cosmology, we apply the simulated data to three projects. The first is the exploration of their abilities to constrain the cosmological parameters, in which we combine different data sets of current observations such as the cosmic microwave background from Planck and type Ia supernovae from Joint Light-curve Analysis (JLA). We find that the high redshift SEAMBHs can help to break the degeneracies of the background cosmological parameters constrained by Planck and JLA, thus giving much tighter constraints of the cosmological parameters. The second uses the high redshift SEAMBHs as the complements of the low redshift JLA to constrain the early expansion rate and the dark energy density evolution in the cold dark matter frame. Our results show that these high redshift SEAMBHs are very powerful on constraining the early Hubble rate and the evolution of the dark energy density; thus they can give us more information about the expansion history of our Universe, which is also crucial for testing the Λ CDM model in the high redshift region. Finally, we check the SEAMBH candles' abilities to reconstruct the equation of state for dark energy at high redshift. In summary, our results show that the SEAMBHs, as the rare candles in the high redshift region, can provide us a new and independent observation to probe cosmology in the future.

A viable dark fluid model

NASA Astrophysics Data System (ADS)

Elkhateeb, Esraa

2018-01-01

We consider a cosmological model based on a generalization of the equation of state proposed by Nojiri and Odintsov (2004) and Štefančić (2005, 2006). We argue that this model works as a dark fluid model which can interpolate between dust equation of state and the dark energy equation of state. We show how the asymptotic behavior of the equation of state constrained the parameters of the model. The causality condition for the model is also studied to constrain the parameters and the fixed points are tested to determine different solution classes. Observations of Hubble diagram of SNe Ia supernovae are used to further constrain the model. We present an exact solution of the model and calculate the luminosity distance and the energy density evolution. We also calculate the deceleration parameter to test the state of the universe expansion.

Densification behavior of ceramic and crystallizable glass materials constrained on a rigid substrate

NASA Astrophysics Data System (ADS)

Calata, Jesus N.

2005-11-01

Constrained sintering is an important process for many applications. The sintering process almost always involves some form of constraint, both internal and external, such as rigid particles, reinforcing fibers and substrates to which the porous body adheres. The densification behavior of zinc oxide and cordierite-base crystallizable glass constrained on a rigid substrate was studied to add to the understanding of the behavior of various materials undergoing sintering when subjected to external substrate constraint. Porous ZnO films were isothermally sintered at temperatures between 900°C and 1050°C. The results showed that the densification of films constrained on substrates is severely reduced. This was evident in the sintered microstructures where the particles are joined together by narrower necks forming a more open structure, instead of the equiaxed grains with wide grain boundaries observed in the freestanding films. The calculated activation energies of densification were also different. For the density range of 60 to 64%, the constrained film had an activation energy of 391 +/- 34 kJ/mole compared to 242 +/- 21 kJ/mole for the freestanding film, indicating a change in the densification mechanism. In-plane stresses were observed during the sintering of the constrained films. Yielding of the films, in which the stresses dropped slight or remained unchanged, occurred at relative densities below 60% before the stresses climbed linearly with increasing density followed by a gradual relaxation. A substantial amount of the stresses remained after cooling. Free and constrained films of the cordierite-base crystallizable glass (glass-ceramic) were sintered between 900°C and 1000°C. The substrate constraint did not have a significant effect on the densification rate but the constrained films eventually underwent expansion. Calculations of the densification activation energy showed that, on average, it was close to 1077 kJ/mole, the activation energy of the glass, indicating that the prevailing mechanism was still viscous flow. The films expanded earlier and faster with increasing sintering temperature. The expansion was traced to the formation of pores at the interface with the silicon substrate and to a lesser extent on aluminum nitride. It was significantly reduced when the silicon substrate was pre-oxidized at 900°C, leading to the conclusion that the pore formation at the interface was due to poor wetting, which in turn was caused by the loss of the thin oxide layer through a reaction with the glass.

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.

Peace Economics and Program Change in Undergraduate Peace Studies Programs

ERIC Educational Resources Information Center

Reuschlein, Robert W.

2009-01-01

The purpose of this study was to create knowledge about peace economics content of Midwest undergraduate peace studies programs, barriers that constrain economic content expansion, and strategies to overcome these barriers. A 40 question survey of directors and 4 director interviews were used to gather data to test hypotheses on the curriculum…

Constrained range expansion and climate change assessments

Treesearch

Yohay Carmel; Curtis H. Flather

2006-01-01

Modeling the future distribution of keystone species has proved to be an important approach to assessing the potential ecological consequences of climate change (Loehle and LeBlanc 1996; Hansen et al. 2001). Predictions of range shifts are typically based on empirical models derived from simple correlative relationships between climatic characteristics of occupied and...

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

Li, Xiao-Dong; Park, Changbom; Forero-Romero, J. E.

We propose a method based on the redshift dependence of the Alcock-Paczynski (AP) test to measure the expansion history of the universe. It uses the isotropy of the galaxy density gradient field to constrain cosmological parameters. If the density parameter Ω {sub m} or the dark energy equation of state w are incorrectly chosen, the gradient field appears to be anisotropic with the degree of anisotropy varying with redshift. We use this effect to constrain the cosmological parameters governing the expansion history of the universe. Although redshift-space distortions (RSD) induced by galaxy peculiar velocities also produce anisotropies in the gradientmore » field, these effects are close to uniform in magnitude over a large range of redshift. This makes the redshift variation of the gradient field anisotropy relatively insensitive to the RSD. By testing the method on mock surveys drawn from the Horizon Run 3 cosmological N-body simulations, we demonstrate that the cosmological parameters can be estimated without bias. Our method is complementary to the baryon acoustic oscillation or topology methods as it depends on D{sub AH} , the product of the angular diameter distance and the Hubble parameter.« less

Dendritic cells control fibroblastic reticular network tension and lymph node expansion.

PubMed

Acton, Sophie E; Farrugia, Aaron J; Astarita, Jillian L; Mourão-Sá, Diego; Jenkins, Robert P; Nye, Emma; Hooper, Steven; van Blijswijk, Janneke; Rogers, Neil C; Snelgrove, Kathryn J; Rosewell, Ian; Moita, Luis F; Stamp, Gordon; Turley, Shannon J; Sahai, Erik; Reis e Sousa, Caetano

2014-10-23

After immunogenic challenge, infiltrating and dividing lymphocytes markedly increase lymph node cellularity, leading to organ expansion. Here we report that the physical elasticity of lymph nodes is maintained in part by podoplanin (PDPN) signalling in stromal fibroblastic reticular cells (FRCs) and its modulation by CLEC-2 expressed on dendritic cells. We show in mouse cells that PDPN induces actomyosin contractility in FRCs via activation of RhoA/C and downstream Rho-associated protein kinase (ROCK). Engagement by CLEC-2 causes PDPN clustering and rapidly uncouples PDPN from RhoA/C activation, relaxing the actomyosin cytoskeleton and permitting FRC stretching. Notably, administration of CLEC-2 protein to immunized mice augments lymph node expansion. In contrast, lymph node expansion is significantly constrained in mice selectively lacking CLEC-2 expression in dendritic cells. Thus, the same dendritic cells that initiate immunity by presenting antigens to T lymphocytes also initiate remodelling of lymph nodes by delivering CLEC-2 to FRCs. CLEC-2 modulation of PDPN signalling permits FRC network stretching and allows for the rapid lymph node expansion--driven by lymphocyte influx and proliferation--that is the critical hallmark of adaptive immunity.

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.

Constrained State Estimation for Individual Localization in Wireless Body Sensor Networks

PubMed Central

Feng, Xiaoxue; Snoussi, Hichem; Liang, Yan; Jiao, Lianmeng

2014-01-01

Wireless body sensor networks based on ultra-wideband radio have recently received much research attention due to its wide applications in health-care, security, sports and entertainment. Accurate localization is a fundamental problem to realize the development of effective location-aware applications above. In this paper the problem of constrained state estimation for individual localization in wireless body sensor networks is addressed. Priori knowledge about geometry among the on-body nodes as additional constraint is incorporated into the traditional filtering system. The analytical expression of state estimation with linear constraint to exploit the additional information is derived. Furthermore, for nonlinear constraint, first-order and second-order linearizations via Taylor series expansion are proposed to transform the nonlinear constraint to the linear case. Examples between the first-order and second-order nonlinear constrained filters based on interacting multiple model extended kalman filter (IMM-EKF) show that the second-order solution for higher order nonlinearity as present in this paper outperforms the first-order solution, and constrained IMM-EKF obtains superior estimation than IMM-EKF without constraint. Another brownian motion individual localization example also illustrates the effectiveness of constrained nonlinear iterative least square (NILS), which gets better filtering performance than NILS without constraint. PMID:25390408

Electro-osmotic flow in a rotating rectangular microchannel

PubMed Central

Ng, Chiu-On; Qi, Cheng

2015-01-01

An analytical model is presented for low-Rossby-number electro-osmotic flow in a rectangular channel rotating about an axis perpendicular to its own. The flow is driven under the combined action of Coriolis, pressure, viscous and electric forces. Analytical solutions in the form of eigenfunction expansions are developed for the problem, which is controlled by the rotation parameter (or the inverse Ekman number), the Debye parameter, the aspect ratio of the channel and the distribution of zeta potentials on the channel walls. Under the conditions of fast rotation and a thin electric double layer (EDL), an Ekman–EDL develops on the horizontal walls. This is essentially an Ekman layer subjected to electrokinetic effects. The flow structure of this boundary layer as a function of the Ekman layer thickness normalized by the Debye length is investigated in detail in this study. It is also shown that the channel rotation may have qualitatively different effects on the flow rate, depending on the channel width and the zeta potential distributions. Axial and secondary flows are examined in detail to reveal how the development of a geostrophic core may lead to a rise or fall of the mean flow. PMID:26345088

Anderson Localization for Schrödinger Operators on with Strongly Mixing Potentials

NASA Astrophysics Data System (ADS)

Bourgain, Jean; Schlag, Wilhelm

In this paper we show that for a.e. x∈[ 0,2 π) the operators defined on as and with Dirichlet condition ψ- 1= 0, have pure point spectrum in with exponentially decaying eigenfunctions where δ > 0 and are small. As it is a simple consequence of known techniques that for small λ one has [- 2 +δ, 2-δ]⊂ spectrum (H(x)) for a.e.x∈[ 0, 2 π), we thus established Anderson localization on the spectrum up to the edges and the center. More general potentials than cosine can be treated, but only those energies with nonzero spectral density are allowed. Finally, we prove the same result for operators on the whole line with potential , where A:?2-->?2 is a hyperbolic toral automorphism, F∈C1(?2), ∫F= 0, and λ small. The basis for our analysis is an asymptotic formula for the Lyapunov exponent for λ--> 0 by Figotin-Pastur, and generalized by Chulaevski-Spencer. We combine this asymptotic expansion with certain martingale large deviation estimates in order to apply the methods developed by Bourgain and Goldstein in the quasi-periodic case.

Recent advances in computational-analytical integral transforms for convection-diffusion problems

NASA Astrophysics Data System (ADS)

Cotta, R. M.; Naveira-Cotta, C. P.; Knupp, D. C.; Zotin, J. L. Z.; Pontes, P. C.; Almeida, A. P.

2017-10-01

An unifying overview of the Generalized Integral Transform Technique (GITT) as a computational-analytical approach for solving convection-diffusion problems is presented. This work is aimed at bringing together some of the most recent developments on both accuracy and convergence improvements on this well-established hybrid numerical-analytical methodology for partial differential equations. Special emphasis is given to novel algorithm implementations, all directly connected to enhancing the eigenfunction expansion basis, such as a single domain reformulation strategy for handling complex geometries, an integral balance scheme in dealing with multiscale problems, the adoption of convective eigenvalue problems in formulations with significant convection effects, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Then, selected examples are presented that illustrate the improvement achieved in each class of extension, in terms of convergence acceleration and accuracy gain, which are related to conjugated heat transfer in complex or multiscale microchannel-substrate geometries, multidimensional Burgers equation model, and diffusive metal extraction through polymeric hollow fiber membranes. Numerical results are reported for each application and, where appropriate, critically compared against the traditional GITT scheme without convergence enhancement schemes and commercial or dedicated purely numerical approaches.

Photoionization and Recombination

NASA Technical Reports Server (NTRS)

Nahar, Sultana N.

2000-01-01

Theoretically self-consistent calculations for photoionization and (e + ion) recombination are described. The same eigenfunction expansion for the ion is employed in coupled channel calculations for both processes, thus ensuring consistency between cross sections and rates. The theoretical treatment of (e + ion) recombination subsumes both the non-resonant recombination ("radiative recombination"), and the resonant recombination ("di-electronic recombination") processes in a unified scheme. In addition to the total, unified recombination rates, level-specific recombination rates and photoionization cross sections are obtained for a large number of atomic levels. Both relativistic Breit-Pauli, and non-relativistic LS coupling, calculations are carried out in the close coupling approximation using the R-matrix method. Although the calculations are computationally intensive, they yield nearly all photoionization and recombination parameters needed for astrophysical photoionization models with higher precision than hitherto possible, estimated at about 10-20% from comparison with experimentally available data (including experimentally derived DR rates). Results are electronically available for over 40 atoms and ions. Photoionization and recombination of He-, and Li-like C and Fe are described for X-ray modeling. The unified method yields total and complete (e+ion) recombination rate coefficients, that can not otherwise be obtained theoretically or experimentally.

The extended Fourier pseudospectral time-domain method for atmospheric sound propagation.

PubMed

Hornikx, Maarten; Waxler, Roger; Forssén, Jens

2010-10-01

An extended Fourier pseudospectral time-domain (PSTD) method is presented to model atmospheric sound propagation by solving the linearized Euler equations. In this method, evaluation of spatial derivatives is based on an eigenfunction expansion. Evaluation on a spatial grid requires only two spatial points per wavelength. Time iteration is done using a low-storage optimized six-stage Runge-Kutta method. This method is applied to two-dimensional non-moving media models, one with screens and one for an urban canyon, with generally high accuracy in both amplitude and phase. For a moving atmosphere, accurate results have been obtained in models with both a uniform and a logarithmic wind velocity profile over a rigid ground surface and in the presence of a screen. The method has also been validated for three-dimensional sound propagation over a screen. For that application, the developed method is in the order of 100 times faster than the second-order-accurate FDTD solution to the linearized Euler equations. The method is found to be well suited for atmospheric sound propagation simulations where effects of complex meteorology and straight rigid boundary surfaces are to be investigated.

Generalized moment analysis of magnetic field correlations for accumulations of spherical and cylindrical magnetic pertubers

NASA Astrophysics Data System (ADS)

Kurz, Felix; Kampf, Thomas; Buschle, Lukas; Schlemmer, Heinz-Peter; Bendszus, Martin; Heiland, Sabine; Ziener, Christian

2016-12-01

In biological tissue, an accumulation of similarly shaped objects with a susceptibility difference to the surrounding tissue generates a local distortion of the external magnetic field in magnetic resonance imaging. It induces stochastic field fluctuations that characteristically influence proton spin diffusion in the vicinity of these magnetic perturbers. The magnetic field correlation that is associated with such local magnetic field inhomogeneities can be expressed in the form of a dynamic frequency autocorrelation function that is related to the time evolution of the measured magnetization. Here, an eigenfunction expansion for two simple magnetic perturber shapes, that of spheres and cylinders, is considered for restricted spin diffusion in a simple model geometry. Then, the concept of generalized moment analysis, an approximation technique that is applied in the study of (non-)reactive processes that involve Brownian motion, allows to provide analytical expressions for the correlation function for different exponential decay forms. Results for the biexponential decay for both spherical and cylindrical magnetized objects are derived and compared with the frequently used (less accurate) monoexponential decay forms. They are in asymptotic agreement with the numerically exact value of the correlation function for long and short times.

Variation of Time Domain Failure Probabilities of Jack-up with Wave Return Periods

NASA Astrophysics Data System (ADS)

Idris, Ahmad; Harahap, Indra S. H.; Ali, Montassir Osman Ahmed

2018-04-01

This study evaluated failure probabilities of jack up units on the framework of time dependent reliability analysis using uncertainty from different sea states representing different return period of the design wave. Surface elevation for each sea state was represented by Karhunen-Loeve expansion method using the eigenfunctions of prolate spheroidal wave functions in order to obtain the wave load. The stochastic wave load was propagated on a simplified jack up model developed in commercial software to obtain the structural response due to the wave loading. Analysis of the stochastic response to determine the failure probability in excessive deck displacement in the framework of time dependent reliability analysis was performed by developing Matlab codes in a personal computer. Results from the study indicated that the failure probability increases with increase in the severity of the sea state representing a longer return period. Although the results obtained are in agreement with the results of a study of similar jack up model using time independent method at higher values of maximum allowable deck displacement, it is in contrast at lower values of the criteria where the study reported that failure probability decreases with increase in the severity of the sea state.

Vibroacoustic study of a point-constrained plate mounted in a duct

NASA Astrophysics Data System (ADS)

Sapkale, Swapnil L.; Sucheendran, Mahesh M.; Gupta, Shakti S.; Kanade, Shantanu V.

2018-04-01

The vibroacoustic study of the interaction of sound with a point-constrained, simply-supported square plate is considered in this paper. The plate is mounted flush on one of the walls of an infinite duct of rectangular cross section and is backed by a cavity. The plate response and the acoustic field is predicted by solving the coupled governing equations using modal expansion with the relevant eigenmodes of the plate dynamics and acoustic fields in the duct and cavity. By varying the location of the point constraint, the frequency characteristics of the transmission loss in the duct can be tuned. The point constraint can also alter the amplitude and spectral characteristics of the plate's response. Interestingly, some new peaks are observed in the response because of the excitation of unsymmetric modes which are otherwise dormant. Mode-localization phenomenon, which is the localization of vibration in specific regions of the plate, is observed for selected constrained points.

Characterizing and modeling the free recovery and constrained recovery behavior of a polyurethane shape memory polymer

NASA Astrophysics Data System (ADS)

Volk, Brent L.; Lagoudas, Dimitris C.; Maitland, Duncan J.

2011-09-01

In this work, tensile tests and one-dimensional constitutive modeling were performed on a high recovery force polyurethane shape memory polymer that is being considered for biomedical applications. The tensile tests investigated the free recovery (zero load) response as well as the constrained displacement recovery (stress recovery) response at extension values up to 25%, and two consecutive cycles were performed during each test. The material was observed to recover 100% of the applied deformation when heated at zero load in the second thermomechanical cycle, and a stress recovery of 1.5-4.2 MPa was observed for the constrained displacement recovery experiments. After the experiments were performed, the Chen and Lagoudas model was used to simulate and predict the experimental results. The material properties used in the constitutive model—namely the coefficients of thermal expansion, shear moduli, and frozen volume fraction—were calibrated from a single 10% extension free recovery experiment. The model was then used to predict the material response for the remaining free recovery and constrained displacement recovery experiments. The model predictions match well with the experimental data.

Dynamic analysis of a hollow cylinder subject to a dual traveling force imposed on its inner surface

NASA Astrophysics Data System (ADS)

Lee, Sooyoung; Seok, Jongwon

2015-03-01

The dynamic behavior of a hollow cylinder under a dual traveling force applied to the inner surface is investigated in this study. The cylinder is constrained at both the top and bottom surfaces not to move in the length direction but free in other directions. And a dual force travels at a constant velocity along the length direction on the inner surface of the hollow cylinder. The resulting governing field equations and the associated boundary conditions are ruled by the general Hooke's law. Due to the nature of the field equations, proper adjoint system of equations and biorthogonality conditions were derived in a precise and detailed manner. To solve these field equations in this study, the method of separation of variable is used and the method of Fro¨benius is employed for the differential equations in the radial direction. Using the field equations, the eigenanalyses on both the original and its adjoint system were performed with great care, which results in the eigenfunction sets of both systems. The biorthogonality conditions were applied to the field equations to obtain the discretized equation for each mode. Using the solutions of the discretized equations that account for the boundary forcing terms, the critical speed for a dual traveling force for each mode could be computed.

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.

Data-driven discovery of Koopman eigenfunctions using deep learning

NASA Astrophysics Data System (ADS)

Lusch, Bethany; Brunton, Steven L.; Kutz, J. Nathan

2017-11-01

Koopman operator theory transforms any autonomous non-linear dynamical system into an infinite-dimensional linear system. Since linear systems are well-understood, a mapping of non-linear dynamics to linear dynamics provides a powerful approach to understanding and controlling fluid flows. However, finding the correct change of variables remains an open challenge. We present a strategy to discover an approximate mapping using deep learning. Our neural networks find this change of variables, its inverse, and a finite-dimensional linear dynamical system defined on the new variables. Our method is completely data-driven and only requires measurements of the system, i.e. it does not require derivatives or knowledge of the governing equations. We find a minimal set of approximate Koopman eigenfunctions that are sufficient to reconstruct and advance the system to future states. We demonstrate the method on several dynamical systems.

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.

An Analytical Diffusion–Expansion Model for Forbush Decreases Caused by Flux Ropes

NASA Astrophysics Data System (ADS)

Dumbović, Mateja; Heber, Bernd; Vršnak, Bojan; Temmer, Manuela; Kirin, Anamarija

2018-06-01

We present an analytical diffusion–expansion Forbush decrease (FD) model ForbMod, which is based on the widely used approach of an initially empty, closed magnetic structure (i.e., flux rope) that fills up slowly with particles by perpendicular diffusion. The model is restricted to explaining only the depression caused by the magnetic structure of the interplanetary coronal mass ejection (ICME). We use remote CME observations and a 3D reconstruction method (the graduated cylindrical shell method) to constrain initial boundary conditions of the FD model and take into account CME evolutionary properties by incorporating flux rope expansion. Several flux rope expansion modes are considered, which can lead to different FD characteristics. In general, the model is qualitatively in agreement with observations, whereas quantitative agreement depends on the diffusion coefficient and the expansion properties (interplay of the diffusion and expansion). A case study was performed to explain the FD observed on 2014 May 30. The observed FD was fitted quite well by ForbMod for all expansion modes using only the diffusion coefficient as a free parameter, where the diffusion parameter was found to correspond to an expected range of values. Our study shows that, in general, the model is able to explain the global properties of an FD caused by a flux rope and can thus be used to help understand the underlying physics in case studies.

Thermodynamic properties of hydrate phases immersed in ice phase

NASA Astrophysics Data System (ADS)

Belosludov, V. R.; Subbotin, O. S.; Krupskii, D. S.; Ikeshoji, T.; Belosludov, R. V.; Kawazoe, Y.; Kudoh, J.

2006-01-01

Thermodynamic properties and the pressure of hydrate phases immersed in the ice phase with the aim to understand the nature of self-preservation effect of methane hydrate in the framework of macroscopic and microscopic molecular models was studied. It was show that increasing of pressure is happen inside methane hydrate phases immersed in the ice phase under increasing temperature and if the ice structure does not destroy, the methane hydrate will have larger pressure than ice phase. This is because of the thermal expansion of methane hydrate in a few times larger than ice one. The thermal expansion of the hydrate is constrained by the thermal expansion of ice because it can remain in a region of stability within the methane hydrate phase diagram. The utter lack of preservation behavior in CS-II methane- ethane hydrate can be explain that the thermal expansion of ethane-methane hydrate coincide with than ice one it do not pent up by thermal expansion of ice. The pressure and density during the crossing of interface between ice and hydrate was found and dynamical and thermodynamic stability of this system are studied in accordance with relation between ice phase and hydrate phase.

Theoretical Limits of Energy Density in Silicon-Carbon Composite Anode Based Lithium Ion Batteries.

PubMed

Dash, Ranjan; Pannala, Sreekanth

2016-06-17

Silicon (Si) is under consideration as a potential next-generation anode material for the lithium ion battery (LIB). Experimental reports of up to 40% increase in energy density of Si anode based LIBs (Si-LIBs) have been reported in literature. However, this increase in energy density is achieved when the Si-LIB is allowed to swell (volumetrically expand) more than graphite based LIB (graphite-LIB) and beyond practical limits. The volume expansion of LIB electrodes should be negligible for applications such as automotive or mobile devices. We determine the theoretical bounds of Si composition in a Si-carbon composite (SCC) based anode to maximize the volumetric energy density of a LIB by constraining the external dimensions of the anode during charging. The porosity of the SCC anode is adjusted to accommodate the volume expansion during lithiation. The calculated threshold value of Si was then used to determine the possible volumetric energy densities of LIBs with SCC anode (SCC-LIBs) and the potential improvement over graphite-LIBs. The level of improvement in volumetric and gravimetric energy density of SCC-LIBs with constrained volume is predicted to be less than 10% to ensure the battery has similar power characteristics of graphite-LIBs.

Communication: Density functional theory embedding with the orthogonality constrained basis set expansion procedure

NASA Astrophysics Data System (ADS)

Culpitt, Tanner; Brorsen, Kurt R.; Hammes-Schiffer, Sharon

2017-06-01

Density functional theory (DFT) embedding approaches have generated considerable interest in the field of computational chemistry because they enable calculations on larger systems by treating subsystems at different levels of theory. To circumvent the calculation of the non-additive kinetic potential, various projector methods have been developed to ensure the orthogonality of molecular orbitals between subsystems. Herein the orthogonality constrained basis set expansion (OCBSE) procedure is implemented to enforce this subsystem orbital orthogonality without requiring a level shifting parameter. This scheme is a simple alternative to existing parameter-free projector-based schemes, such as the Huzinaga equation. The main advantage of the OCBSE procedure is that excellent convergence behavior is attained for DFT-in-DFT embedding without freezing any of the subsystem densities. For the three chemical systems studied, the level of accuracy is comparable to or higher than that obtained with the Huzinaga scheme with frozen subsystem densities. Allowing both the high-level and low-level DFT densities to respond to each other during DFT-in-DFT embedding calculations provides more flexibility and renders this approach more generally applicable to chemical systems. It could also be useful for future extensions to embedding approaches combining wavefunction theories and DFT.

Constraining f(R) theories with cosmography

NASA Astrophysics Data System (ADS)

Anabella Teppa Pannia, Florencia; Esteban Perez Bergliaffa, Santiago

2013-08-01

A method to set constraints on the parameters of extended theories of gravitation is presented. It is based on the comparison of two series expansions of any observable that depends on H(z). The first expansion is of the cosmographical type, while the second uses the dependence of H with z furnished by a given type of extended theory. When applied to f(R) theories together with the redshift drift, the method yields limits on the parameters of two examples (the theory of Hu and Sawicki [1], and the exponential gravity introduced by Linder [2]) that are compatible with or more stringent than the existing ones, as well as a limit for a previously unconstrained parameter.

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.

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.

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.

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.

Constraining the dark energy models with H (z ) data: An approach independent of H0

NASA Astrophysics Data System (ADS)

Anagnostopoulos, Fotios K.; Basilakos, Spyros

2018-03-01

We study the performance of the latest H (z ) data in constraining the cosmological parameters of different cosmological models, including that of Chevalier-Polarski-Linder w0w1 parametrization. First, we introduce a statistical procedure in which the chi-square estimator is not affected by the value of the Hubble constant. As a result, we find that the H (z ) data do not rule out the possibility of either nonflat models or dynamical dark energy cosmological models. However, we verify that the time varying equation-of-state parameter w (z ) is not constrained by the current expansion data. Combining the H (z ) and the Type Ia supernova data, we find that the H (z )/SNIa overall statistical analysis provides a substantial improvement of the cosmological constraints with respect to those of the H (z ) analysis. Moreover, the w0-w1 parameter space provided by the H (z )/SNIa joint analysis is in very good agreement with that of Planck 2015, which confirms that the present analysis with the H (z ) and supernova type Ia (SNIa) probes correctly reveals the expansion of the Universe as found by the team of Planck. Finally, we generate sets of Monte Carlo realizations in order to quantify the ability of the H (z ) data to provide strong constraints on the dark energy model parameters. The Monte Carlo approach shows significant improvement of the constraints, when increasing the sample to 100 H (z ) measurements. Such a goal can be achieved in the future, especially in the light of the next generation of surveys.

Dendritic Cells Control Fibroblastic Reticular Network Tension and Lymph Node Expansion

PubMed Central

Acton, Sophie E.; Farrugia, Aaron J.; Astarita, Jillian L.; Mourão-Sá, Diego; Jenkins, Robert P.; Nye, Emma; Hooper, Steven; van Blijswijk, Janneke; Rogers, Neil C.; Snelgrove, Kathryn J.; Rosewell, Ian; Moita, Luis F.; Stamp, Gordon; Turley, Shannon J.; Sahai, Erik; Sousa, Caetano Reis e

2014-01-01

Following immunogenic challenge, infiltrating and dividing lymphocytes significantly increase lymph node (LN) cellularity leading to organ expansion1,2. Here we report that the physical elasticity of LNs is maintained in part by podoplanin (PDPN) signalling in stromal fibroblastic reticular cells (FRCs) and its modulation by CLEC-2 expressed on dendritic cells (DCs). We show that PDPN induces actomyosin contractility in FRCs via activation of RhoA/C and downstream Rho-kinase. Engagement by CLEC-2 causes PDPN clustering and rapidly uncouples PDPN from RhoA/C activation, relaxing the actomyosin cytoskeleton and permitting FRC stretching. Notably, administration of CLEC-2 protein to immunised mice augments LN expansion. In contrast, the latter is significantly constrained in mice selectively lacking CLEC-2 expression in DCs. Thus, the same DCs that initiate immunity by presenting antigens to T lymphocytes3 also initiate remodeling of LNs by delivering CLEC-2 to FRCs. CLEC-2 modulation of PDPN signalling permits FRC network stretching and allows for the rapid LN expansion driven by lymphocyte influx and proliferation that is the critical hallmark of adaptive immunity. PMID:25341788

Ion flux enhancements and oscillations in spatially confined laser produced aluminum plasmas

NASA Astrophysics Data System (ADS)

Singh, S. C.; Fallon, C.; Hayden, P.; Mujawar, M.; Yeates, P.; Costello, J. T.

2014-09-01

Ion signals from laser produced plasmas (LPPs) generated inside aluminum rectangular cavities at a fixed depth d = 2 mm and varying width, x = 1.0, 1.6, and 2.75 mm were obtained by spatially varying the position of a negatively biased Langmuir probe. Damped oscillatory features superimposed on Maxwellian distributed ion signals were observed. Depending on the distance of the probe from the target surface, three to twelve fold enhancements in peak ion density were observed via confinement of the LPP, generated within rectangular cavities of varying width which constrained the plasma plume to near one dimensional expansion in the vertical plane. The effects of lateral spatial confinement on the expansion velocity of the LPP plume front, the temperature, density and expansion velocity of ions, enhancement of ion flux, and ion energy distribution were recorded. The periodic behavior of ion signals was analyzed and found to be related to the electron plasma frequency and electron-ion collision frequency. The effects of confinement and enhancement of various ion parameters and expansion velocities of the LPP ion plume are explained on the basis of shock wave theory.

Colonization and demographic expansion of freshwater fauna across the Hawaiian archipelago.

PubMed

Alda, F; Gagne, R B; Walter, R P; Hogan, J D; Moody, K N; Zink, F; McIntyre, P B; Gilliam, J F; Blum, M J

2016-10-01

It is widely accepted that insular terrestrial biodiversity progresses with island age because colonization and diversification proceed over time. Here, we assessed whether this principle extends to oceanic island streams. We examined rangewide mtDNA sequence variation in four stream-dwelling species across the Hawaiian archipelago to characterize the relationship between colonization and demographic expansion, and to determine whether either factor reflects island age. We found that colonization and demographic expansion are not related and that neither corresponds to island age. The snail Neritina granosa exhibited the oldest colonization time (~2.713 mya) and time since demographic expansion (~282 kya), likely reflecting a preference for lotic habitats most prevalent on young islands. Conversely, gobioid fishes (Awaous stamineus, Eleotris sandwicensis and Sicyopterus stimpsoni) colonized the archipelago only ~0.411-0.935 mya, suggesting ecological opportunities for colonization in this group were temporally constrained. These findings indicate that stream communities form across colonization windows, underscoring the importance of ecological opportunities in shaping island freshwater diversity. © 2016 European Society For Evolutionary Biology. Journal of Evolutionary Biology © 2016 European Society For Evolutionary Biology.

Conjoined constraints on modified gravity from the expansion history and cosmic growth

NASA Astrophysics Data System (ADS)

Basilakos, Spyros; Nesseris, Savvas

2017-09-01

In this paper we present conjoined constraints on several cosmological models from the expansion history H (z ) and cosmic growth f σ8. The models we study include the CPL w0wa parametrization, the holographic dark energy (HDE) model, the time-varying vacuum (ΛtCDM ) model, the Dvali, Gabadadze and Porrati (DGP) and Finsler-Randers (FRDE) models, a power-law f (T ) model, and finally the Hu-Sawicki f (R ) model. In all cases we perform a simultaneous fit to the SnIa, CMB, BAO, H (z ) and growth data, while also following the conjoined visualization of H (z ) and f σ8 as in Linder (2017). Furthermore, we introduce the figure of merit (FoM) in the H (z )-f σ8 parameter space as a way to constrain models that jointly fit both probes well. We use both the latest H (z ) and f σ8 data, but also LSST-like mocks with 1% measurements, and we find that the conjoined method of constraining the expansion history and cosmic growth simultaneously is able not only to place stringent constraints on these parameters, but also to provide an easy visual way to discriminate cosmological models. Finally, we confirm the existence of a tension between the growth-rate and Planck CMB data, and we find that the FoM in the conjoined parameter space of H (z )-f σ8(z ) can be used to discriminate between the Λ CDM model and certain classes of modified gravity models, namely the DGP and f (T ).

Kin competition and the evolution of cooperation

PubMed Central

Platt, Thomas G.; Bever, James D.

2017-01-01

Kin and multilevel selection theories predict that genetic structure is required for the evolution of cooperation. However, local competition among relatives can limit cooperative benefits, antagonizing the evolution of cooperation. We show that several ecological factors determine the extent to which kin competition constrains cooperative benefits. In addition, we argue that cooperative acts that expand local carrying capacity are less constrained by kin competition than other cooperative traits, and are therefore more likely to evolve. These arguments are particularly relevant to microbial cooperation, which often involves the production of public goods that promote population expansion. The challenge now is to understand how an organism’s ecology influences how much cooperative groups contribute to future generations and thereby the evolution of cooperation. PMID:19409651

Scaling the universe: Gravitational lenses and the Hubble constant

PubMed Central

Myers, Steven T.

1999-01-01

Gravitational lenses, besides being interesting in their own right, have been demonstrated to be suitable as “gravitational standard rulers” for the measurement of the rate of expansion of the Universe (Ho), as well as to constrain the values of the cosmological parameters such as Ωo and Λo that control the evolution of the volume of the Universe with cosmic time. PMID:10200245

Characterizing and modeling the free recovery and constrained recovery behavior of a polyurethane shape memory polymer

PubMed Central

Volk, Brent L; Lagoudas, Dimitris C; Maitland, Duncan J

2011-01-01

In this work, tensile tests and one-dimensional constitutive modeling are performed on a high recovery force polyurethane shape memory polymer that is being considered for biomedical applications. The tensile tests investigate the free recovery (zero load) response as well as the constrained displacement recovery (stress recovery) response at extension values up to 25%, and two consecutive cycles are performed during each test. The material is observed to recover 100% of the applied deformation when heated at zero load in the second thermomechanical cycle, and a stress recovery of 1.5 MPa to 4.2 MPa is observed for the constrained displacement recovery experiments. After performing the experiments, the Chen and Lagoudas model is used to simulate and predict the experimental results. The material properties used in the constitutive model – namely the coefficients of thermal expansion, shear moduli, and frozen volume fraction – are calibrated from a single 10% extension free recovery experiment. The model is then used to predict the material response for the remaining free recovery and constrained displacement recovery experiments. The model predictions match well with the experimental data. PMID:22003272

LITHO1.0: An Updated Crust and Lithosphere Model of the Earth

NASA Astrophysics Data System (ADS)

Masters, G.; Ma, Z.; Laske, G.; Pasyanos, M. E.

2011-12-01

We are developing LITHO1.0: an updated crust and lithosphere model of the Earth. The overall plan is to take the popular CRUST2.0 model - a global model of crustal structure with a relatively poor representation of the uppermost mantle - and improve its nominal resolution to 1 degree and extend the model to include lithospheric structure. The new model, LITHO1.0, will be constrained by many different datasets including extremely large new datasets of relatively short period group velocity data. Other data sets include (but are not limited to) compilations of receiver function constraints and active source studies. To date, we have completed the compilation of extremely large global datasets of group velocity for Rayleigh and Love waves from 10mHz to 40mHz using a cluster analysis technique. We have also extended the method to measure phase velocity and are complementing the group velocity with global data sets of longer period phase data that help to constrain deep lithosphere properties. To model these data, we require a starting model for the crust at a nominal resolution of 1 degree. This has been developed by constructing a map of crustal thickness using data from receiver function and active source experiments where available, and by using CRUST2.0 where other constraints are not available. Particular care has been taken to make sure that the locations of sharp changes in crustal thickness are accurately represented. This map is then used as a template to extend CRUST2.0 to 1 degree nominal resolution and to develop starting maps of all crustal properties. We are currently modeling the data using two techniques. The first is a linearized inversion about the 3D crustal starting model. Note that it is important to use local eigenfunctions to compute Frechet derivatives due to the extreme variations in crustal structure. Another technique uses a targeted grid search method. A preliminary model for the crustal part of the model will be presented.

Electromagnetic scattering from two-dimensional thick material junctions

NASA Technical Reports Server (NTRS)

Ricoy, M. A.; Volakis, John L.

1990-01-01

The problem of the plane wave diffraction is examined by an arbitrary symmetric two dimensional junction, where Generalized Impedance Boundary Conditions (GIBCs) and Generalized Sheet Transition Conditions (GSTCs) are employed to simulate the slabs. GIBCs and GSTCs are constructed for multilayer planar slabs of arbitrary thickness and the resulting GIBC/GSTC reflection coefficients are compared with exact counterparts to evaluate the GIBCs/GSTCs. The plane wave diffraction by a multilayer material slab recessed in a perfectly conducting ground plane is formulated and solved via the Generalized Scattering Matrix Formulation (GDMF) in conjunction with the dual integral equation approach. Various scattering patterns are computed and validated with exact results where possible. The diffraction by a material discontinuity in a thick dielectric/ferrite slab is considered by modelling the constituent slabs with GSTCs. A non-unique solution in terms of unknown constants is obtained, and these constants are evaluated for the recessed slab geometry by comparison with the solution obtained therein. Several other simplified cases are also presented and discussed. An eigenfunction expansion method is introduced to determine the unknown solution constants in the general case. This procedure is applied to the non-unique solution in terms of unknown constants; and scattering patterns are presented for various slab junctions and compared with alternative results where possible.

Effect of wall pattern configurations on Stokes flow through a microchannel with superhydrophobic slip

NASA Astrophysics Data System (ADS)

Mak, H. M.; Ng, C. O.

2010-11-01

The present work aims to study low-Reynolds-number flow through a microchannel with superhydrophobic surfaces, which contain a periodic array of parallel ribs on the upper and lower walls. Mimicking impregnation, the liquid is allowed to penetrate the grooves between the ribs which are filled with an inviscid gas. The array of ribs and grooves gives a heterogeneous wall boundary condition to the channel flow, with partial-slip boundary condition on the solid surface and no-shear boundary condition on the liquid-gas interface. Using the method of eigenfunction expansions and domain decomposition, semi-analytical models are developed for four configurations. Two of them are for longitudinal flow and the others are for transverse flow. For each flow orientation, in-phase and out-phase alignments of ribs between the upper and lower walls are analyzed. The effect of the phase alignments of ribs is appreciable when the channel height is sufficiently small. In-phase alignment gives rise to a larger effective slip length in longitudinal flow. On the contrary, out-phase alignment will yield a larger effective slip length in transverse flow. This work was supported by the Research Grants Council of the Hong Kong Special Administrative Region, China, through Project HKU 7156/09E.

Electrokinetic flows through a parallel-plate channel with slipping stripes on walls

NASA Astrophysics Data System (ADS)

Chu, Henry C. W.; Ng, Chiu-On

2011-11-01

Electrohydrodynamic flows through a periodically-micropatterned plane channel are considered. One unit of wall pattern consists of a slipping and non-slipping stripe, each with a distinct zeta potential. The problems are solved semi-analytically by eigenfunction expansion and point collocation. In the regime of linear response, the Onsager relation for the fluid and current fluxes are deduced as linear functions of the hydrodynamic and electric forcings. The phenomenological coefficients are explicitly expressed as functions of the channel height, the Debye parameter, the slipping area fraction of the wall, the intrinsic slip length, and the zeta potentials. We generalize the theoretical limits made in previous studies on electrokinetic flow over an inhomogeneously slipping surface. One should be cautious when applying these limits. First, when a surface is not 100% uniformly slipping but has a small fraction of area being covered by no-slip slots, the electroosmotic enhancement can be appreciably reduced. Second, when the electric double layer is only moderately thin, slipping-uncharged regions on a surface will have finite inhibition effect on the electroosmotic flow. Financial support by the RGC of the HKSAR, China: Project Nos. HKU715609E, HKU715510E; and the HKU under the Seed Funding Programme for Basic Research: Project Code 200911159024.

Inverse problem analysis for identification of reaction kinetics constants in microreactors for biodiesel synthesis

NASA Astrophysics Data System (ADS)

Pontes, P. C.; Naveira-Cotta, C. P.

2016-09-01

The theoretical analysis for the design of microreactors in biodiesel production is a complicated task due to the complex liquid-liquid flow and mass transfer processes, and the transesterification reaction that takes place within these microsystems. Thus, computational simulation is an important tool that aids in understanding the physical-chemical phenomenon and, consequently, in determining the suitable conditions that maximize the conversion of triglycerides during the biodiesel synthesis. A diffusive-convective-reactive coupled nonlinear mathematical model, that governs the mass transfer process during the transesterification reaction in parallel plates microreactors, under isothermal conditions, is here described. A hybrid numerical-analytical solution via the Generalized Integral Transform Technique (GITT) for this partial differential system is developed and the eigenfunction expansions convergence rates are extensively analyzed and illustrated. The heuristic method of Particle Swarm Optimization (PSO) is applied in the inverse analysis of the proposed direct problem, to estimate the reaction kinetics constants, which is a critical step in the design of such microsystems. The results present a good agreement with the limited experimental data in the literature, but indicate that the GITT methodology combined with the PSO approach provide a reliable computational algorithm for direct-inverse analysis in such reactive mass transfer problems.

Analytical and experimental studies of an optimum multisegment phased liner noise suppression concept

NASA Technical Reports Server (NTRS)

Sawdy, D. T.; Beckemeyer, R. J.; Patterson, J. D.

1976-01-01

Results are presented from detailed analytical studies made to define methods for obtaining improved multisegment lining performance by taking advantage of relative placement of each lining segment. Properly phased liner segments reflect and spatially redistribute the incident acoustic energy and thus provide additional attenuation. A mathematical model was developed for rectangular ducts with uniform mean flow. Segmented acoustic fields were represented by duct eigenfunction expansions, and mode-matching was used to ensure continuity of the total field. Parametric studies were performed to identify attenuation mechanisms and define preliminary liner configurations. An optimization procedure was used to determine optimum liner impedance values for a given total lining length, Mach number, and incident modal distribution. Optimal segmented liners are presented and it is shown that, provided the sound source is well-defined and flow environment is known, conventional infinite duct optimum attenuation rates can be improved. To confirm these results, an experimental program was conducted in a laboratory test facility. The measured data are presented in the form of analytical-experimental correlations. Excellent agreement between theory and experiment verifies and substantiates the analytical prediction techniques. The results indicate that phased liners may be of immediate benefit in the development of improved aircraft exhaust duct noise suppressors.

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.

Structure of edge-state inner products in the fractional quantum Hall effect

NASA Astrophysics Data System (ADS)

Fern, R.; Bondesan, R.; Simon, S. H.

2018-04-01

We analyze the inner products of edge state wave functions in the fractional quantum Hall effect, specifically for the Laughlin and Moore-Read states. We use an effective description for these inner products given by a large-N expansion ansatz proposed in a recent work by J. Dubail, N. Read, and E. Rezayi [Phys. Rev. B 86, 245310 (2012), 10.1103/PhysRevB.86.245310]. As noted by these authors, the terms in this ansatz can be constrained using symmetry, a procedure we perform to high orders. We then check this conjecture by calculating the overlaps exactly for small system sizes and compare the numerics with our high-order expansion. We find the effective description to be very accurate.

Constraining inverse-curvature gravity with supernovae.

PubMed

Mena, Olga; Santiago, José; Weller, Jochen

2006-02-03

We show that models of generalized modified gravity, with inverse powers of the curvature, can explain the current accelerated expansion of the Universe without resorting to dark energy and without conflicting with solar system experiments. We have solved the Friedmann equations for the full dynamical range of the evolution of the Universe and performed a detailed analysis of supernovae data in the context of such models that results in an excellent fit. If we further include constraints on the current expansion of the Universe and on its age, we obtain that the matter content of the Universe is 0.07

Curvature of the freeze-out line in heavy ion collisions

DOE PAGES

Bazavov, A.; Ding, H. -T.; Hegde, P.; ...

2016-01-28

Here, we calculate the mean and variance of net-baryon number and net-electric charge distributions from quantum chromodynamics (QCD) using a next-to-leading order Taylor expansion in terms of temperature and chemical potentials. Moreover, these expansions with experimental data from STAR and PHENIX are compared, we determine the freeze-out temperature in the limit of vanishing baryon chemical potential, and, for the first time, constrain the curvature of the freeze-out line through a direct comparison between experimental data on net-charge fluctuations and a QCD calculation. We obtain a bound on the curvature coefficient, κmore » $^f$$_2$$<0.011, that is compatible with lattice QCD results on the curvature of the QCD transition line.« less

Solitons on Noncommutative Torus as Elliptic Calogero-Gaudin Models, Branes and Laughlin Wave Functions

NASA Astrophysics Data System (ADS)

Hou, Bo-Yu; Peng, Dan-Tao; Shi, Kang-Jie; Yue, Rui-Hong

For the noncommutative torus T, in the case of the noncommutative parameter θ = (Z)/(n), we construct the basis of Hilbert space Hn in terms of θ functions of the positions zi of n solitons. The wrapping around the torus generates the algebra An, which is the Zn × Zn Heisenberg group on θ functions. We find the generators g of a local elliptic su(n), which transform covariantly by the global gauge transformation of An. By acting on Hn we establish the isomorphism of An and g. We embed this g into the L-matrix of the elliptic Gaudin and Calogero-Moser models to give the dynamics. The moment map of this twisted cotangent sunT) bundle is matched to the D-equation with the Fayet-Illiopoulos source term, so the dynamics of the noncommutative solitons become that of the brane. The geometric configuration (k, u) of the spectral curve det|L(u) - k| = 0 describes the brane configuration, with the dynamical variables zi of the noncommutative solitons as the moduli T⊗ n/Sn. Furthermore, in the noncommutative Chern-Simons theory for the quantum Hall effect, the constrain equation with quasiparticle source is identified also with the moment map equation of the noncommutative sunT cotangent bundle with marked points. The eigenfunction of the Gaudin differential L-operators as the Laughlin wave function is solved by Bethe ansatz.

Carbon-shell-constrained silicon cluster derived from Al-Si alloy as long-cycling life lithium ion batteries anode

NASA Astrophysics Data System (ADS)

Su, Junming; Zhang, Congcong; Chen, Xiang; Liu, Siyang; Huang, Tao; Yu, Aishui

2018-03-01

Although silicon is the most promising anode material for Li-ion batteries, large volume expansion during lithiation and delithiation is the main obstacle limiting the commercial application of silicon anodes. There are two ways to alleviate volume expansion and prevent further pulverization of a Si anode: fabrication of a rational nanostructure possessing void spaces and uniform distribution of the conducting sites, without a good balance effect in mitigating the limiting factors and enhancing battery performance. In this paper, we propose a novel nanostructure - a carbon-shell-constrained Si cluster (Si/C shell) with both adequate void space and good distribution of electrical contact sites to guarantee homogeneous lithiation in the initial cycle. Benefiting from the ability to maintain electrical conductivity of the outer carbon shell, even after cluster fragmentation, the Si/C shell synthesized from low-cost commercial Al-Si alloy spheres can deliver 0.03% capacity loss from 100th to 1000th cycles at a current density of 1 A g-1. The Si/C shell sample with the dual functional structure mentioned above can also maintain its own nanostructure during cycling and deliver excellent rate performance. It is a concise and scalable strategy which can simplify the preparation of other alloy anode materials for Li-ion batteries.

Theoretical Limits of Energy Density in Silicon-Carbon Composite Anode Based Lithium Ion Batteries

PubMed Central

Dash, Ranjan; Pannala, Sreekanth

2016-01-01

Silicon (Si) is under consideration as a potential next-generation anode material for the lithium ion battery (LIB). Experimental reports of up to 40% increase in energy density of Si anode based LIBs (Si-LIBs) have been reported in literature. However, this increase in energy density is achieved when the Si-LIB is allowed to swell (volumetrically expand) more than graphite based LIB (graphite-LIB) and beyond practical limits. The volume expansion of LIB electrodes should be negligible for applications such as automotive or mobile devices. We determine the theoretical bounds of Si composition in a Si–carbon composite (SCC) based anode to maximize the volumetric energy density of a LIB by constraining the external dimensions of the anode during charging. The porosity of the SCC anode is adjusted to accommodate the volume expansion during lithiation. The calculated threshold value of Si was then used to determine the possible volumetric energy densities of LIBs with SCC anode (SCC-LIBs) and the potential improvement over graphite-LIBs. The level of improvement in volumetric and gravimetric energy density of SCC-LIBs with constrained volume is predicted to be less than 10% to ensure the battery has similar power characteristics of graphite-LIBs. PMID:27311811

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.

Extended Plefka expansion for stochastic dynamics

NASA Astrophysics Data System (ADS)

Bravi, B.; Sollich, P.; Opper, M.

2016-05-01

We propose an extension of the Plefka expansion, which is well known for the dynamics of discrete spins, to stochastic differential equations with continuous degrees of freedom and exhibiting generic nonlinearities. The scenario is sufficiently general to allow application to e.g. biochemical networks involved in metabolism and regulation. The main feature of our approach is to constrain in the Plefka expansion not just first moments akin to magnetizations, but also second moments, specifically two-time correlations and responses for each degree of freedom. The end result is an effective equation of motion for each single degree of freedom, where couplings to other variables appear as a self-coupling to the past (i.e. memory term) and a coloured noise. This constitutes a new mean field approximation that should become exact in the thermodynamic limit of a large network, for suitably long-ranged couplings. For the analytically tractable case of linear dynamics we establish this exactness explicitly by appeal to spectral methods of random matrix theory, for Gaussian couplings with arbitrary degree of symmetry.

Generalized framework for testing gravity with gravitational-wave propagation. II. Constraints on Horndeski theory

NASA Astrophysics Data System (ADS)

Arai, Shun; Nishizawa, Atsushi

2018-05-01

Gravitational waves (GW) are generally affected by modification of a gravity theory during propagation at cosmological distances. We numerically perform a quantitative analysis on Horndeski theory at the cosmological scale to constrain the Horndeski theory by GW observations in a model-independent way. We formulate a parametrization for a numerical simulation based on the Monte Carlo method and obtain the classification of the models that agrees with cosmic accelerating expansion within observational errors of the Hubble parameter. As a result, we find that a large group of the models in the Horndeski theory that mimic cosmic expansion of the Λ CDM model can be excluded from the simultaneous detection of a GW and its electromagnetic transient counterpart. Based on our result and the latest detection of GW170817 and GRB170817A, we conclude that the subclass of Horndeski theory including arbitrary functions G4 and G5 can hardly explain cosmic accelerating expansion without fine-tuning.

Redshift Space Distortion on the Small Scale Clustering of Structure

NASA Astrophysics Data System (ADS)

Park, Hyunbae; Sabiu, Cristiano; Li, Xiao-dong; Park, Changbom; Kim, Juhan

2018-01-01

The positions of galaxies in comoving Cartesian space varies under different cosmological parameter choices, inducing a redshift-dependent scaling in the galaxy distribution. The shape of the two-point correlation of galaxies exhibits a significant redshift evolution when the galaxy sample is analyzed under a cosmology differing from the true, simulated one. In our previous works, we can made use of this geometrical distortion to constrain the values of cosmological parameters governing the expansion history of the universe. This current work is a continuation of our previous works as a strategy to constrain cosmological parameters using redshift-invariant physical quantities. We now aim to understand the redshift evolution of the full shape of the small scale, anisotropic galaxy clustering and give a firmer theoretical footing to our previous works.

In situ TEM observation of heterogeneous phase transition of a constrained single-crystalline Ag2Te nanowire.

PubMed

In, Juneho; Yoo, Youngdong; Kim, Jin-Gyu; Seo, Kwanyong; Kim, Hyunju; Ihee, Hyotchel; Oh, Sang Ho; Kim, Bongsoo

2010-11-10

Laterally epitaxial single crystalline Ag2Te nanowires (NWs) are synthesized on sapphire substrates by the vapor transport method. We observed the phase transitions of these Ag2Te NWs via in situ transmission electron microscopy (TEM) after covering them with Pt layers. The constrained NW shows phase transition from monoclinic to a body-centered cubic (bcc) structure near the interfaces, which is ascribed to the thermal stress caused by differences in the thermal expansion coefficients. Furthermore, we observed the nucleation and growth of bcc phase penetrating into the face-centered cubic matrix at 200 °C by high-resolution TEM in real time. Our results would provide valuable insight into how compressive stresses imposed by overlayers affect behaviors of nanodevices.

Influence of Parallel Dark Matter Sectors on Big Bang Nucleosynthesis

NASA Astrophysics Data System (ADS)

Challa, Venkata Sai Sreeharsha

Big Bang Nucleosynthesis (BBN) is a phenomenological theory that describes the synthesis of light nuclei after a few seconds of the cosmic time in the primordial universe. The twelve nuclear reactions in the first few seconds of the cosmic history are constrained by factors such as baryon to photon ratio, number of neutrino families, and present day element abundances. The belief that the expansion of the universe must be slowed down by gravity, was defeated by the recent observation of an accelerated expansion of the universe. Friedmann equations, which describe the cosmic dynamics, need to be revised considering also the existence of dark matter, another recent astronomical observation. The effects of multiple parallel universes of dark matter (dark sectors) on the accelerated expansion of the universe are studied. Collectively, these additional effects will lead to a new cosmological model. We had developed a numerical code on BBN to address the effects of such dark sectors on the abundances of all the light elements. We have studied the effect of degrees of freedom of dark-matter in the early universe on primordial abundances of light elements. The predicted abundances of light elements are compared with observed constraints to obtain bounds on the number of dark sectors, NDM. Comparison of the obtained results with the observations during the BBN epoch shows that the number of dark matter sectors are only loosely constrained, and the dark matter sectors are colder than the ordinary matter sectors. Also, we verified that the existence of parallel dark matter sectors with colder temperatures does not affect the constraints set by observations on the number of neutrino families, Nnu .

Hominin expansion into Central Asia during the last interglacial

NASA Astrophysics Data System (ADS)

Asmerom, Yemane; Polyak, Victor J.; Wagner, Jennifer D. M.; Jonathan Patchett, P.

2018-07-01

Central Asia was a likely gateway for hominin expansion. Obi-Rakhmat Grotto, northeastern Uzbekistan, has a deposit that contains the remains of a hominin child (OR-1) and more than 60,000 Paleolithic artifacts, making it one of the most important archaeological sites in Central Asia. Regionally, genetic data suggest hominin presence and human-Neanderthal interbreeding as far back as 100 ka, although, to date, absolute ages of hominin remains that old have not been known in the region. We present new uranium-series dates that constrain the age of the Obi-Rakhmat deposit to 98 ka towards the top and 109 ka for the layer containing OR-1, pushing hominin expansion into Central Asia minimally to 109 ± 2 ka, to a time, based on the genetic clock, of Neanderthal-modern human interbreeding. Our chronology establishes a minimum age of 98 ka for the well-developed lithic industry in Central Asia. The period covering the deposition of the sediments containing the artifacts and specimen OR-1 coincides with a warm and one of the most humid intervals of Marine Isotope Stage (MIS) 5 and last glacial period in the region, providing support for climate-driven hominin expansion.

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.

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.

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…

On the fate of laser-produced NH 2 in a constrained pulsed expansion of trimethylamine alane and NH 3

NASA Astrophysics Data System (ADS)

Demchuk, Alexander; Cahill, John J.; Simpson, Steven; Koplitz, Brent

2001-11-01

The effects of both 193 nm radiation and NH 3 on an expansion of trimethylamine alane (TMAA) have been studied. In neat TMAA, 193 nm radiation induces small but significant clustering. When NH 3 is introduced in the absence of 193 nm photons, no visible reaction occurs. However, when NH 3 is introduced along with 193 nm photons, the H 3Al:N(CH 3) 3 parent molecule is completely replaced by H 3AlNH 2. Moreover, the clustering channels observed with neat TMAA disappear. The apparent stability or inertness of the R 3MNH 2 (R=H, CH 3 or C 2H 5; M=Ga or Al) species in a variety of metal nitride reactive environments is discussed.

Spectator electric fields, de Sitter spacetime, and the Schwinger effect

NASA Astrophysics Data System (ADS)

Giovannini, Massimo

2018-03-01

During a de Sitter stage of expansion, the spectator fields of different spin are constrained by the critical density bound and by further requirements determined by their specific physical nature. The evolution of spectator electric fields in conformally flat background geometries is occasionally concocted by postulating the existence of ad hoc currents, but this apparently innocuous trick violates the second law of thermodynamics. Such a problem occurs, in particular, for those configurations (customarily employed for the analysis of the Schwinger effect in four-dimensional de Sitter backgrounds) leading to an electric energy density which is practically unaffected by the expansion of the underlying geometry. The obtained results are compared with more mundane situations where Joule heating develops in the early stages of a quasi-de Sitter phase.

Global Solar Magnetic Field Organization in the Outer Corona: Influence on the Solar Wind Speed and Mass Flux Over the Cycle

NASA Astrophysics Data System (ADS)

Réville, Victor; Brun, Allan Sacha

2017-11-01

The dynamics of the solar wind depends intrinsically on the structure of the global solar magnetic field, which undergoes fundamental changes over the 11-year solar cycle. For instance, the wind terminal velocity is thought to be anti-correlated with the expansion factor, a measure of how the magnetic field varies with height in the solar corona, usually computed at a fixed height (≈ 2.5 {R}⊙ , the source surface radius that approximates the distance at which all magnetic field lines become open). However, the magnetic field expansion affects the solar wind in a more detailed way, its influence on the solar wind properties remaining significant well beyond the source surface. We demonstrate this using 3D global magnetohydrodynamic (MHD) simulations of the solar corona, constrained by surface magnetograms over half a solar cycle (1989-2001). A self-consistent expansion beyond the solar wind critical point (even up to 10 {R}⊙ ) makes our model comply with observed characteristics of the solar wind, namely, that the radial magnetic field intensity becomes latitude independent at some distance from the Sun, and that the mass flux is mostly independent of the terminal wind speed. We also show that near activity minimum, the expansion in the higher corona has more influence on the wind speed than the expansion below 2.5 {R}⊙ .

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)

Integrating Levels of Analysis in Systems and Cognitive Neurosciences: Selective Attention as a Case Study.

PubMed

Itthipuripat, Sirawaj; Serences, John T

2016-06-01

Neuroscience is inherently interdisciplinary, rapidly expanding beyond its roots in biological sciences to many areas of the social and physical sciences. This expansion has led to more sophisticated ways of thinking about the links between brains and behavior and has inspired the development of increasingly advanced tools to characterize the activity of large populations of neurons. However, along with these advances comes a heightened risk of fostering confusion unless efforts are made to better integrate findings across different model systems and to develop a better understanding about how different measurement techniques provide mutually constraining information. Here we use selective visuospatial attention as a case study to highlight the importance of these issues, and we suggest that exploiting multiple measures can better constrain models that relate neural activity to animal behavior. © The Author(s) 2015.

A Semi-Analytical Model for Dispersion Modelling Studies in the Atmospheric Boundary Layer

NASA Astrophysics Data System (ADS)

Gupta, A.; Sharan, M.

2017-12-01

The severe impact of harmful air pollutants has always been a cause of concern for a wide variety of air quality analysis. The analytical models based on the solution of the advection-diffusion equation have been the first and remain the convenient way for modeling air pollutant dispersion as it is easy to handle the dispersion parameters and related physics in it. A mathematical model describing the crosswind integrated concentration is presented. The analytical solution to the resulting advection-diffusion equation is limited to a constant and simple profiles of eddy diffusivity and wind speed. In practice, the wind speed depends on the vertical height above the ground and eddy diffusivity profiles on the downwind distance from the source as well as the vertical height. In the present model, a method of eigen-function expansion is used to solve the resulting partial differential equation with the appropriate boundary conditions. This leads to a system of first order ordinary differential equations with a coefficient matrix depending on the downwind distance. The solution of this system, in general, can be expressed in terms of Peano-baker series which is not easy to compute, particularly when the coefficient matrix becomes non-commutative (Martin et al., 1967). An approach based on Taylor's series expansion is introduced to find the numerical solution of first order system. The method is applied to various profiles of wind speed and eddy diffusivities. The solution computed from the proposed methodology is found to be efficient and accurate in comparison to those available in the literature. The performance of the model is evaluated with the diffusion datasets from Copenhagen (Gryning et al., 1987) and Hanford (Doran et al., 1985). In addition, the proposed method is used to deduce three dimensional concentrations by considering the Gaussian distribution in crosswind direction, which is also evaluated with diffusion data corresponding to a continuous point source.

Growth rate in the dynamical dark energy models.

PubMed

Avsajanishvili, Olga; Arkhipova, Natalia A; Samushia, Lado; Kahniashvili, Tina

Dark energy models with a slowly rolling cosmological scalar field provide a popular alternative to the standard, time-independent cosmological constant model. We study the simultaneous evolution of background expansion and growth in the scalar field model with the Ratra-Peebles self-interaction potential. We use recent measurements of the linear growth rate and the baryon acoustic oscillation peak positions to constrain the model parameter [Formula: see text] that describes the steepness of the scalar field potential.

Geographically structured host specificity is caused by the range expansions and host shifts of a symbiotic fungus.

PubMed

Wolfe, Benjamin E; Pringle, Anne

2012-04-01

The inability to associate with local species may constrain the spread of mutualists arriving to new habitats, but the fates of introduced, microbial mutualists are largely unknown. The deadly poisonous ectomycorrhizal fungus Amanita phalloides (the death cap) is native to Europe and introduced to the East and West Coasts of North America. By cataloging host associations across the two continents, we record dramatic changes in specificity among the three ranges. On the East Coast, where the fungus is restricted in its distribution, it associates almost exclusively with pines, which are rarely hosts of A. phalloides in its native range. In California, where the fungus is widespread and locally abundant, it associates almost exclusively with oaks, mirroring the host associations observed in Europe. The most common host of the death cap in California is the endemic coast live oak (Quercus agrifolia), and the current distribution of A. phalloides appears constrained within the distribution of Q. agrifolia. In California, host shifts to native plants are also associated with a near doubling in the resources allocated to sexual reproduction and a prolonged fruiting period; mushrooms are twice as large as they are elsewhere and mushrooms are found throughout the year. Host and niche shifts are likely to shape the continuing range expansion of A. phalloides and other ectomycorrhizal fungi introduced across the world.

Geographically structured host specificity is caused by the range expansions and host shifts of a symbiotic fungus

PubMed Central

Wolfe, Benjamin E; Pringle, Anne

2012-01-01

The inability to associate with local species may constrain the spread of mutualists arriving to new habitats, but the fates of introduced, microbial mutualists are largely unknown. The deadly poisonous ectomycorrhizal fungus Amanita phalloides (the death cap) is native to Europe and introduced to the East and West Coasts of North America. By cataloging host associations across the two continents, we record dramatic changes in specificity among the three ranges. On the East Coast, where the fungus is restricted in its distribution, it associates almost exclusively with pines, which are rarely hosts of A. phalloides in its native range. In California, where the fungus is widespread and locally abundant, it associates almost exclusively with oaks, mirroring the host associations observed in Europe. The most common host of the death cap in California is the endemic coast live oak (Quercus agrifolia), and the current distribution of A. phalloides appears constrained within the distribution of Q. agrifolia. In California, host shifts to native plants are also associated with a near doubling in the resources allocated to sexual reproduction and a prolonged fruiting period; mushrooms are twice as large as they are elsewhere and mushrooms are found throughout the year. Host and niche shifts are likely to shape the continuing range expansion of A. phalloides and other ectomycorrhizal fungi introduced across the world. PMID:22134645

Few-body semiclassical approach to nucleon transfer and emission reactions

NASA Astrophysics Data System (ADS)

Sultanov, Renat A.; Guster, D.

2014-04-01

A three-body semiclassical model is proposed to describe the nucleon transfer and emission reactions in a heavy-ion collision. In this model the two heavy particles, i.e. nuclear cores A1(ZA1, MA1) and A2(ZA2, MA2), move along classical trajectories {{R}_1}( t ) and {{R}_2}( t ) respectively, while the dynamics of the lighter neutron (n) is considered from a quantum mechanical point of view. Here, Mi are the nucleon masses and Zi are the Coulomb charges of the heavy nuclei (i = 1, 2). A Faddeev-type semiclassical formulation using realistic paired nuclear-nuclear potentials is applied so that all three channels (elastic, rearrangement and break-up) are described in a unified manner. In order to solve the time-dependent equations the Faddeev components of the total three-body wave-function are expanded in terms of the input and output channel target eigenfunctions. In the special case, when the nuclear cores are identical (A1 ≡ A2) and also the two-level approximation in the expansion over the target (subsystem) functions is used, the time-dependent semiclassical Faddeev equations are resolved in an explicit way. To determine the realistic {{R}_1}( t ) and {{R}_2}( t ) trajectories of the nuclear cores, a self-consistent approach based on the Feynman path integral theory is applied.

A Reduced-Order Successive Linear Estimator for Geostatistical Inversion and its Application in Hydraulic Tomography

NASA Astrophysics Data System (ADS)

Zha, Yuanyuan; Yeh, Tian-Chyi J.; Illman, Walter A.; Zeng, Wenzhi; Zhang, Yonggen; Sun, Fangqiang; Shi, Liangsheng

2018-03-01

Hydraulic tomography (HT) is a recently developed technology for characterizing high-resolution, site-specific heterogeneity using hydraulic data (nd) from a series of cross-hole pumping tests. To properly account for the subsurface heterogeneity and to flexibly incorporate additional information, geostatistical inverse models, which permit a large number of spatially correlated unknowns (ny), are frequently used to interpret the collected data. However, the memory storage requirements for the covariance of the unknowns (ny × ny) in these models are prodigious for large-scale 3-D problems. Moreover, the sensitivity evaluation is often computationally intensive using traditional difference method (ny forward runs). Although employment of the adjoint method can reduce the cost to nd forward runs, the adjoint model requires intrusive coding effort. In order to resolve these issues, this paper presents a Reduced-Order Successive Linear Estimator (ROSLE) for analyzing HT data. This new estimator approximates the covariance of the unknowns using Karhunen-Loeve Expansion (KLE) truncated to nkl order, and it calculates the directional sensitivities (in the directions of nkl eigenvectors) to form the covariance and cross-covariance used in the Successive Linear Estimator (SLE). In addition, the covariance of unknowns is updated every iteration by updating the eigenvalues and eigenfunctions. The computational advantages of the proposed algorithm are demonstrated through numerical experiments and a 3-D transient HT analysis of data from a highly heterogeneous field site.

New formulations for tsunami runup estimation

NASA Astrophysics Data System (ADS)

Kanoglu, U.; Aydin, B.; Ceylan, N.

2017-12-01

We evaluate shoreline motion and maximum runup in two folds: One, we use linear shallow water-wave equations over a sloping beach and solve as initial-boundary value problem similar to the nonlinear solution of Aydın and Kanoglu (2017, Pure Appl. Geophys., https://doi.org/10.1007/s00024-017-1508-z). Methodology we present here is simple; it involves eigenfunction expansion and, hence, avoids integral transform techniques. We then use several different types of initial wave profiles with and without initial velocity, estimate shoreline properties and confirm classical runup invariance between linear and nonlinear theories. Two, we use the nonlinear shallow water-wave solution of Kanoglu (2004, J. Fluid Mech. 513, 363-372) to estimate maximum runup. Kanoglu (2004) presented a simple integral solution for the nonlinear shallow water-wave equations using the classical Carrier and Greenspan transformation, and further extended shoreline position and velocity to a simpler integral formulation. In addition, Tinti and Tonini (2005, J. Fluid Mech. 535, 33-64) defined initial condition in a very convenient form for near-shore events. We use Tinti and Tonini (2005) type initial condition in Kanoglu's (2004) shoreline integral solution, which leads further simplified estimates for shoreline position and velocity, i.e. algebraic relation. We then use this algebraic runup estimate to investigate effect of earthquake source parameters on maximum runup and present results similar to Sepulveda and Liu (2016, Coast. Eng. 112, 57-68).

On the optical properties of carbon nanotubes. Part I. A general formula for the dynamical optical conductivity

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

Rasmussen, Morten Grud, E-mail: morteng@math.aau.dk; Ricaud, Benjamin, E-mail: benjamin.ricaud@epfl.ch; Savoie, Baptiste, E-mail: baptiste.savoie@gmail.com

2016-02-15

This paper is the first one in a series of two articles in which we revisit the optical properties of single-walled carbon nanotubes (SWNTs). Produced by rolling up a graphene sheet, SWNTs owe their intriguing properties to their cylindrical quasi-one-dimensional (quasi-1D) structure (the ratio length/radius is experimentally of order of 10{sup 3}). We model SWNT by circular cylinders of small diameters on the surface of which the conduction electron gas is confined by the electric field generated by the fixed carbon ions. The pair-interaction potential considered is the 3D Coulomb potential restricted to the cylinder. To reflect the quasi-1D structure,more » we introduce a 1D effective many-body Hamiltonian which is the starting-point of our analysis. To investigate the optical properties, we consider a perturbation by a uniform time-dependent electric field modeling an incident light beam along the longitudinal direction. By using Kubo’s method, we derive within the linear response theory an asymptotic expansion in the low-temperature regime for the dynamical optical conductivity at fixed density of particles. The leading term only involves the eigenvalues and associated eigenfunctions of the (unperturbed) 1D effective many-body Hamiltonian and allows us to account for the sharp peaks observed in the optical absorption spectrum of SWNT.« less

Acoustic plane wave diffraction from a truncated semi-infinite cone in axial irradiation

NASA Astrophysics Data System (ADS)

Kuryliak, Dozyslav; Lysechko, Victor

2017-11-01

The diffraction problem of the plane acoustic wave on the semi-infinite truncated soft and rigid cones in the case of axial incidence is solved. The problem is formulated as a boundary-value problem in terms of Helmholtz equation, with Dirichlet and Neumann boundary conditions, for scattered velocity potential. The incident field is taken to be the total field of semi-infinite cone, the expression of which is obtained by solving the auxiliary diffraction problem by the use of Kontorovich-Lebedev integral transformation. The diffracted field is sought via the expansion in series of the eigenfunctions for subdomains of the Helmholtz equation taking into account the edge condition. The corresponding diffraction problem is reduced to infinite system of linear algebraic equations (ISLAE) making use of mode matching technique and orthogonality properties of the Legendre functions. The method of analytical regularization is applied in order to extract the singular part in ISLAE, invert it exactly and reduce the problem to ISLAE of the second kind, which is readily amenable to calculation. The numerical solution of this system relies on the reduction method; and its accuracy depends on the truncation order. The case of degeneration of the truncated semi-infinite cone into an aperture in infinite plane is considered. Characteristic features of diffracted field in near and far fields as functions of cone's parameters are examined.

The initial-value problem for viscous channel flows

NASA Technical Reports Server (NTRS)

Criminale, W. O.; Jackson, T. L.; Lasseigne, D. G.

1995-01-01

Plane viscous channel flows are perturbed and the ensuing initial-value problems are investigated in detail. Unlike traditional methods where traveling wave normal modes are assumed for solution, this works offers a means whereby completely arbitrary initial input can be specified without having to resort to eigenfunction expansions. The full temporal behavior, including both early time transients and the long time asymptotics, can be determined for any initial disturbance. Effects of three-dimensionality can be assessed. The bases for the analysis are: (a) linearization of the governing equations; (b) Fourier decomposition in the spanwise and streamwise directions of the flow; and (c) direct numerical integration of the resulting partial differential equations. All of the stability data that are known for such flows can be reproduced. Also, the optimal initial condition can be determined in a straight forward manner and such optimal conditions clearly reflect transient growth data that is easily determined by a rational choice of a basis for the initial conditions. Although there can be significant transient growth for subcritical values of the Reynolds number using this approach it does not appear possible that arbitrary initial conditions will lead to the exceptionally large transient amplitudes that have been determined by optimization of normal modes. The approach is general and can be applied to other classes of problems where only a finite discrete spectrum exists, such as the boundary layer for example.

A conserved pattern of differential expansion of cortical areas in simian primates.

PubMed

Chaplin, Tristan A; Yu, Hsin-Hao; Soares, Juliana G M; Gattass, Ricardo; Rosa, Marcello G P

2013-09-18

The layout of areas in the cerebral cortex of different primates is quite similar, despite significant variations in brain size. However, it is clear that larger brains are not simply scaled up versions of smaller brains: some regions of the cortex are disproportionately large in larger species. It is currently debated whether these expanded areas arise through natural selection pressures for increased cognitive capacity or as a result of the application of a common developmental sequence on different scales. Here, we used computational methods to map and quantify the expansion of the cortex in simian primates of different sizes to investigate whether there is any common pattern of cortical expansion. Surface models of the marmoset, capuchin, and macaque monkey cortex were registered using the software package CARET and the spherical landmark vector difference algorithm. The registration was constrained by the location of identified homologous cortical areas. When comparing marmosets with both capuchins and macaques, we found a high degree of expansion in the temporal parietal junction, the ventrolateral prefrontal cortex, and the dorsal anterior cingulate cortex, all of which are high-level association areas typically involved in complex cognitive and behavioral functions. These expanded maps correlated well with previously published macaque to human registrations, suggesting that there is a general pattern of primate cortical scaling.

Bergmann's rule is maintained during a rapid range expansion in a damselfly.

PubMed

Hassall, Christopher; Keat, Simon; Thompson, David J; Watts, Phillip C

2014-02-01

Climate-induced range shifts result in the movement of a sample of genotypes from source populations to new regions. The phenotypic consequences of those shifts depend upon the sample characteristics of the dispersive genotypes, which may act to either constrain or promote phenotypic divergence, and the degree to which plasticity influences the genotype-environment interaction. We sampled populations of the damselfly Erythromma viridulum from northern Europe to quantify the phenotypic (latitude-body size relationship based on seven morphological traits) and genetic (variation at microsatellite loci) patterns that occur during a range expansion itself. We find a weak spatial genetic structure that is indicative of high gene flow during a rapid range expansion. Despite the potentially homogenizing effect of high gene flow, however, there is extensive phenotypic variation among samples along the invasion route that manifests as a strong, positive correlation between latitude and body size consistent with Bergmann's rule. This positive correlation cannot be explained by variation in the length of larval development (voltinism). While the adaptive significance of latitudinal variation in body size remains obscure, geographical patterns in body size in odonates are apparently underpinned by phenotypic plasticity and this permits a response to one or more environmental correlates of latitude during a range expansion. © 2013 John Wiley & Sons Ltd.

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…

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.

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.

Robust numerical electromagnetic eigenfunction expansion algorithms

NASA Astrophysics Data System (ADS)

Sainath, Kamalesh

This thesis summarizes developments in rigorous, full-wave, numerical spectral-domain (integral plane wave eigenfunction expansion [PWE]) evaluation algorithms concerning time-harmonic electromagnetic (EM) fields radiated by generally-oriented and positioned sources within planar and tilted-planar layered media exhibiting general anisotropy, thickness, layer number, and loss characteristics. The work is motivated by the need to accurately and rapidly model EM fields radiated by subsurface geophysical exploration sensors probing layered, conductive media, where complex geophysical and man-made processes can lead to micro-laminate and micro-fractured geophysical formations exhibiting, at the lower (sub-2MHz) frequencies typically employed for deep EM wave penetration through conductive geophysical media, bulk-scale anisotropic (i.e., directional) electrical conductivity characteristics. When the planar-layered approximation (layers of piecewise-constant material variation and transversely-infinite spatial extent) is locally, near the sensor region, considered valid, numerical spectral-domain algorithms are suitable due to their strong low-frequency stability characteristic, and ability to numerically predict time-harmonic EM field propagation in media with response characterized by arbitrarily lossy and (diagonalizable) dense, anisotropic tensors. If certain practical limitations are addressed, PWE can robustly model sensors with general position and orientation that probe generally numerous, anisotropic, lossy, and thick layers. The main thesis contributions, leading to a sensor and geophysical environment-robust numerical modeling algorithm, are as follows: (1) Simple, rapid estimator of the region (within the complex plane) containing poles, branch points, and branch cuts (critical points) (Chapter 2), (2) Sensor and material-adaptive azimuthal coordinate rotation, integration contour deformation, integration domain sub-region partition and sub-region-dependent integration order (Chapter 3), (3) Integration partition-extrapolation-based (Chapter 3) and Gauss-Laguerre Quadrature (GLQ)-based (Chapter 4) evaluations of the deformed, semi-infinite-length integration contour tails, (4) Robust in-situ-based (i.e., at the spectral-domain integrand level) direct/homogeneous-medium field contribution subtraction and analytical curbing of the source current spatial spectrum function's ill behavior (Chapter 5), and (5) Analytical re-casting of the direct-field expressions when the source is embedded within a NBAM, short for non-birefringent anisotropic medium (Chapter 6). The benefits of these contributions are, respectively, (1) Avoiding computationally intensive critical-point location and tracking (computation time savings), (2) Sensor and material-robust curbing of the integrand's oscillatory and slow decay behavior, as well as preventing undesirable critical-point migration within the complex plane (computation speed, precision, and instability-avoidance benefits), (3) sensor and material-robust reduction (or, for GLQ, elimination) of integral truncation error, (4) robustly stable modeling of scattered fields and/or fields radiated from current sources modeled as spatially distributed (10 to 1000-fold compute-speed acceleration also realized for distributed-source computations), and (5) numerically stable modeling of fields radiated from sources within NBAM layers. Having addressed these limitations, are PWE algorithms applicable to modeling EM waves in tilted planar-layered geometries too? This question is explored in Chapter 7 using a Transformation Optics-based approach, allowing one to model wave propagation through layered media that (in the sensor's vicinity) possess tilted planar interfaces. The technique leads to spurious wave scattering however, whose induced computation accuracy degradation requires analysis. Mathematical exhibition, and exhaustive simulation-based study and analysis of the limitations of, this novel tilted-layer modeling formulation is Chapter 7's main contribution.

Tunable PhoXonic Band Gap Materials from Self-Assembly of Block Copolymers and Colloidal Nanocrystals (NBIT Phase II)

DTIC Science & Technology

2013-12-12

their application in sensors and as displays. We found that the thermochromic behavior of a lamellar block copolymer poly(styrene-b-2-vinylpyridine...the solution pH. The findings of this work provide the basis for understanding and controlling the properties of thermochromic block copolymers...by the glassy PS layers . The glassy layers completely constrain the lateral expansion of the P2VP gel block and the dislocation defect network that

Analytical approximation and numerical simulations for periodic travelling water waves

NASA Astrophysics Data System (ADS)

Kalimeris, Konstantinos

2017-12-01

We present recent analytical and numerical results for two-dimensional periodic travelling water waves with constant vorticity. The analytical approach is based on novel asymptotic expansions. We obtain numerical results in two different ways: the first is based on the solution of a constrained optimization problem, and the second is realized as a numerical continuation algorithm. Both methods are applied on some examples of non-constant vorticity. This article is part of the theme issue 'Nonlinear water waves'.

Potential-field sounding using Euler's homogeneity equation and Zidarov bubbling

USGS Publications Warehouse

Cordell, Lindrith

1994-01-01

Potential-field (gravity) data are transformed into a physical-property (density) distribution in a lower half-space, constrained solely by assumed upper bounds on physical-property contrast and data error. A two-step process is involved. The data are first transformed to an equivalent set of line (2-D case) or point (3-D case) sources, using Euler's homogeneity equation evaluated iteratively on the largest residual data value. Then, mass is converted to a volume-density product, constrained to an upper density bound, by 'bubbling,' which exploits circular or radial expansion to redistribute density without changing the associated gravity field. The method can be developed for gravity or magnetic data in two or three dimensions. The results can provide a beginning for interpretation of potential-field data where few independent constraints exist, or more likely, can be used to develop models and confirm or extend interpretation of other geophysical data sets.

Probing dark energy in the scope of a Bianchi type I spacetime

NASA Astrophysics Data System (ADS)

Amirhashchi, Hassan

2018-03-01

It is well known that the flat Friedmann-Robertson-Walker metric is a special case of Bianchi type I spacetime. In this paper, we use 38 Hubble parameter, H (z ), measurements at intermediate redshifts 0.07 ≤z ≤2.36 and its joint combination with the latest "joint light curves" (JLA) sample, comprising 740 type Ia supernovae in the redshift range of z ɛ [0.01 ,1.30 ] to constrain the parameters of the Bianchi type I dark energy model. We also use the same datasets to constrain flat a Λ CDM model. In both cases, we specifically address the expansion rate H0 as well as the transition redshift zt determinations out of these measurements. In both models, we found that using joint combination of datasets gives rise to lower values for model parameters. Also to compare the considered cosmologies, we have made Akaike information criterion and Bayes factor (Ψ ) tests.

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.

Biophysical constraints on leaf expansion in a tall conifer.

PubMed

Meinzer, Frederick C; Bond, Barbara J; Karanian, Jennifer A

2008-02-01

The physiological mechanisms responsible for reduced extension growth as trees increase in height remain elusive. We evaluated biophysical constraints on leaf expansion in old-growth Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) trees. Needle elongation rates, plastic and elastic extensibility, bulk leaf water (Psi(L)) and osmotic (Psi(pi)) potential, bulk tissue yield threshold and final needle length were characterized along a height gradient in crowns of > 50-m-tall trees during the period between bud break and full expansion (May to June). Although needle length decreased with increasing height, there was no height-related trend in leaf plastic extensibility, which was highest immediately after bud break (2.9%) and declined rapidly to a stable minimum value (0.3%) over a 3-week period during which leaf expansion was completed. There was a significant positive linear relationship between needle elongation rates and plastic extensibility. Yield thresholds were consistently lower at the upper and middle crown sampling heights. The mean yield threshold across all sampling heights was 0.12 +/- 0.03 MPa on June 8, rising to 0.34 +/- 0.03 MPa on June 15 and 0.45 +/- 0.05 MPa on June 24. Bulk leaf Psi(pi) decreased linearly with increasing height at a rate of 0.004 MPa m(-1) during the period of most rapid needle elongation, but the vertical osmotic gradient was not sufficient to fully compensate for the 0.015 MPa m(-1) vertical gradient in Psi(L), implying that bulk leaf turgor declined at a rate of about 0.011 MPa m(-1) increase in height. Although height-dependent reductions in turgor appeared to constrain leaf expansion, it is possible that the impact of reduced turgor was mitigated by delayed phenological development with increasing height, which resulted in an increase with height in the temperature during leaf expansion.

Optimizing future imaging survey of galaxies to confront dark energy and modified gravity models

NASA Astrophysics Data System (ADS)

Yamamoto, Kazuhiro; Parkinson, David; Hamana, Takashi; Nichol, Robert C.; Suto, Yasushi

2007-07-01

We consider the extent to which future imaging surveys of galaxies can distinguish between dark energy and modified gravity models for the origin of the cosmic acceleration. Dynamical dark energy models may have similar expansion rates as models of modified gravity, yet predict different growth of structure histories. We parametrize the cosmic expansion by the two parameters, w0 and wa, and the linear growth rate of density fluctuations by Linder’s γ, independently. Dark energy models generically predict γ≈0.55, while the Dvali-Gabadadze-Porrati (DGP) model γ≈0.68. To determine if future imaging surveys can constrain γ within 20% (or Δγ<0.1), we perform the Fisher matrix analysis for a weak-lensing survey such as the ongoing Hyper Suprime-Cam (HSC) project. Under the condition that the total observation time is fixed, we compute the figure of merit (FoM) as a function of the exposure time texp. We find that the tomography technique effectively improves the FoM, which has a broad peak around texp≃several˜10min; a shallow and wide survey is preferred to constrain the γ parameter. While Δγ<0.1 cannot be achieved by the HSC weak-lensing survey alone, one can improve the constraints by combining with a follow-up spectroscopic survey like Wide-field Fiber-fed Multi-Object Spectrograph (WFMOS) and/or future cosmic microwave background (CMB) observations.

Empirical Model of Precipitating Ion Oval

NASA Astrophysics Data System (ADS)

Goldstein, Jerry

2017-10-01

In this brief technical report published maps of ion integral flux are used to constrain an empirical model of the precipitating ion oval. The ion oval is modeled as a Gaussian function of ionospheric latitude that depends on local time and the Kp geomagnetic index. The three parameters defining this function are the centroid latitude, width, and amplitude. The local time dependences of these three parameters are approximated by Fourier series expansions whose coefficients are constrained by the published ion maps. The Kp dependence of each coefficient is modeled by a linear fit. Optimization of the number of terms in the expansion is achieved via minimization of the global standard deviation between the model and the published ion map at each Kp. The empirical model is valid near the peak flux of the auroral oval; inside its centroid region the model reproduces the published ion maps with standard deviations of less than 5% of the peak integral flux. On the subglobal scale, average local errors (measured as a fraction of the point-to-point integral flux) are below 30% in the centroid region. Outside its centroid region the model deviates significantly from the H89 integral flux maps. The model's performance is assessed by comparing it with both local and global data from a 17 April 2002 substorm event. The model can reproduce important features of the macroscale auroral region but none of its subglobal structure, and not immediately following a substorm.

Construction of ground-state preserving sparse lattice models for predictive materials simulations

NASA Astrophysics Data System (ADS)

Huang, Wenxuan; Urban, Alexander; Rong, Ziqin; Ding, Zhiwei; Luo, Chuan; Ceder, Gerbrand

2017-08-01

First-principles based cluster expansion models are the dominant approach in ab initio thermodynamics of crystalline mixtures enabling the prediction of phase diagrams and novel ground states. However, despite recent advances, the construction of accurate models still requires a careful and time-consuming manual parameter tuning process for ground-state preservation, since this property is not guaranteed by default. In this paper, we present a systematic and mathematically sound method to obtain cluster expansion models that are guaranteed to preserve the ground states of their reference data. The method builds on the recently introduced compressive sensing paradigm for cluster expansion and employs quadratic programming to impose constraints on the model parameters. The robustness of our methodology is illustrated for two lithium transition metal oxides with relevance for Li-ion battery cathodes, i.e., Li2xFe2(1-x)O2 and Li2xTi2(1-x)O2, for which the construction of cluster expansion models with compressive sensing alone has proven to be challenging. We demonstrate that our method not only guarantees ground-state preservation on the set of reference structures used for the model construction, but also show that out-of-sample ground-state preservation up to relatively large supercell size is achievable through a rapidly converging iterative refinement. This method provides a general tool for building robust, compressed and constrained physical models with predictive power.

Oil Palm Expansion in the Brazilian Amazon (2006-2014): Effects of the 2010 Sustainable Oil Palm Production Program

NASA Astrophysics Data System (ADS)

Benami, E.; Curran, L. M.

2017-12-01

Brazil has the world's largest suitable land area for oil palm (Elaeis guineensis) establishment, with estimates as high as 238 million ha. To promote oil palm development, Brazil launched the Sustainable Palm Oil Production Program (SPOPP) in 2010 and delineated 30 million ha for its growth that excluded forested areas and indigenous reserves. Here we examine oil palm expansion (2006-2014) as well as the SPOPP's effectiveness in Pará, the major oil palm producing state in Brazil. By combining analyses of satellite imagery, land registration data, and site based interviews, we found that oil palm area expanded 205%. Although >50% of oil palm parcels were located within 0.5 km of intact forests, <5% of intact forests were converted by direct deforestation. In contrast, 15-90% of oil palm expansion in Asia and other Latin American countries came from directly converting forested lands. Direct intact forest conversion pre- and post-SPOPP declined from 4% to <1%; however, <1% of the 30 million ha promoted for oil palm was developed by 2014. To explore the major factors that may have constrained oil palm expansion under the SPOPP, we conducted microeconomic simulations of oil palm production, combined with interviews with actors/individuals from oil palm companies, civil society, researchers at universities and NGOs, and governmental agencies. Brazil's oil palm-deforestation dynamics, policies, and economic conditions will be discussed.

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.

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.

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.

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.

Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth

NASA Astrophysics Data System (ADS)

Chakrabarti, Aloknath; Mohapatra, Smrutiranjan

2013-09-01

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates, separated by a gap of finite width, floating horizontally on water of finite depth, are investigated in the present work for a two-dimensional time-harmonic case. Within the frame of linear water wave theory, the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions. Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem. In both the problems, the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates. Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations. The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration. The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

Wave trapping by dual porous barriers near a wall in the presence of bottom undulation

NASA Astrophysics Data System (ADS)

Kaligatla, R. B.; Manisha; Sahoo, T.

2017-09-01

Trapping of oblique surface gravity waves by dual porous barriers near a wall is studied in the presence of step type varying bottom bed that is connected on both sides by water of uniform depths. The porous barriers are assumed to be fixed at a certain distance in front of a vertical rigid wall. Using linear water wave theory and Darcy's law for flow past porous structure, the physical problem is converted into a boundary value problem. Using eigenfunction expansion in the uniform bottom bed region and modified mild-slope equation in the varying bottom bed region, the mathematical problem is handled for solution. Moreover, certain jump conditions are used to account for mass conservation at slope discontinuities in the bottom bed profile. To understand the effect of dual porous barriers in creating tranquility zone and minimum load on the sea wall, reflection coefficient, wave forces acting on the barrier and the wall, and surface wave elevation are computed and analyzed for different values of depth ratio, porous-effect parameter, incident wave angle, gap between the barriers and wall and slope length of undulated bottom. The study reveals that with moderate porosity and suitable gap between barriers and sea wall, using dual barriers an effective wave trapping system can be developed which will exert less wave force on the barriers and the rigid wall. The proposed wave trapping system is likely to be of immense help for protecting various facilities/ infrastructures in coastal environment.

Wave interactions with multiple semi-immersed Jarlan-type perforated breakwaters

NASA Astrophysics Data System (ADS)

Elbisy, Moussa S.

2017-06-01

This study examines wave interactions with multiple semi-immersed Jarlan-type perforated breakwaters. A numerical model based on linear wave theory and an eigenfunction expansion method has been developed to study the hydrodynamic characteristics of breakwaters. The numerical results show a good agreement with previous analytical results and experimental data for limiting cases of double partially immersed impermeable walls and double and triple Jarlan-type breakwaters. The wave transmission coefficient C T; reflection coefficient C R, and energy dissipation coefficient C E coefficients and the horizontal wave force exerted on the front and rear walls are examined. The results show that C R reaches the maximum value when B/L = 0.46 n while it is smallest when B/L=0.46 n+0.24 ( n=0, 1, 2,...). An economical triple semi-immersed Jarlan-type perforated breakwater can be designed with B/L = 0.25 and C R and C T ranging from 0.25 to 0.32 by choosing a relative draft d/h of 0.35 and a permeability parameter of the perforated front walls being 0.5 for an incident wave number kh nearly equal to 2.0. The triple semi-immersed Jarlan-type perforated breakwaters with significantly reduced C R, will enhance the structure's wave absorption ability, and lead to smaller wave forces compared with the double one. The proposed model may be used to predict the response of a structure in the preliminary design stage for practical engineering.

Baryon interactions in lattice QCD: the direct method vs. the HAL QCD potential method

NASA Astrophysics Data System (ADS)

Iritani, T.; HAL QCD Collaboration

We make a detailed comparison between the direct method and the HAL QCD potential method for the baryon-baryon interactions, taking the $\\Xi\\Xi$ system at $m_\\pi= 0.51$ GeV in 2+1 flavor QCD and using both smeared and wall quark sources. The energy shift $\\Delta E_\\mathrm{eff}(t)$ in the direct method shows the strong dependence on the choice of quark source operators, which means that the results with either (or both) source are false. The time-dependent HAL QCD method, on the other hand, gives the quark source independent $\\Xi\\Xi$ potential, thanks to the derivative expansion of the potential, which absorbs the source dependence to the next leading order correction. The HAL QCD potential predicts the absence of the bound state in the $\\Xi\\Xi$($^1$S$_0$) channel at $m_\\pi= 0.51$ GeV, which is also confirmed by the volume dependence of finite volume energy from the potential. We also demonstrate that the origin of the fake plateau in the effective energy shift $\\Delta E_\\mathrm{eff}(t)$ at $t \\sim 1$ fm can be clarified by a few low-lying eigenfunctions and eigenvalues on the finite volume derived from the HAL QCD potential, which implies that the ground state saturation of $\\Xi\\Xi$($^1$S$_0$) requires $t \\sim 10$ fm in the direct method for the smeared source on $(4.3 \\ \\mathrm{fm})^3$ lattice, while the HAL QCD method does not suffer from such a problem.

Simultaneous constraint and phase conversion processing of oxide superconductors

DOEpatents

Li, Qi; Thompson, Elliott D.; Riley, Jr., Gilbert N.; Hellstrom, Eric E.; Larbalestier, David C.; DeMoranville, Kenneth L.; Parrell, Jeffrey A.; Reeves, Jodi L.

2003-04-29

A method of making an oxide superconductor article includes subjecting an oxide superconductor precursor to a texturing operation to orient grains of the oxide superconductor precursor to obtain a highly textured precursor; and converting the textured oxide superconducting precursor into an oxide superconductor, while simultaneously applying a force to the precursor which at least matches the expansion force experienced by the precursor during phase conversion to the oxide superconductor. The density and the degree of texture of the oxide superconductor precursor are retained during phase conversion. The constraining force may be applied isostatically.

Quantum mechanics of conformally and minimally coupled Friedmann-Robertson-Walker cosmology

NASA Astrophysics Data System (ADS)

Kim, Sang Pyo

1992-10-01

The expansion method by a time-dependent basis of the eigenfunctions for the space-coordinate-dependent sub-Hamiltonian is one of the most natural frameworks for quantum systems, relativistic as well as nonrelativistic. The complete set of wave functions is found in the product integral formulation, whose constants of integration are fixed by Cauchy initial data. The wave functions for the Friedmann-Robertson-Walker (FRW) cosmology conformally and minimally coupled to a scalar field with a power-law potential or a polynomial potential are expanded in terms of the eigenfunctions of the scalar field sub-Hamiltonian part. The resultant gravitational field part which is an ``intrinsic'' timelike variable-dependent matrix-valued differential equation is solved again in the product integral formulation. There are classically allowed regions for the ``intrinsic'' timelike variable depending on the scalar field quantum numbers and these regions increase accordingly as the quantum numbers increase. For a fixed large three-geometry the wave functions corresponding to the low excited (small quantum number) states of the scalar field are exponentially damped or diverging and the wave functions corresponding to the high excited (large quantum number) states are still oscillatory but become eventually exponential as the three-geometry becomes larger. Furthermore, a proposal is advanced that the wave functions exponentially damped for a large three-geometry may be interpreted as ``tunneling out'' wave functions into, and the wave functions exponentially diverging as ``tunneling in'' from, different universes with the same or different topologies, the former being interpreted as the recently proposed Hawking-Page wormhole wave functions. It is observed that there are complex as well as Euclidean actions depending on the quantum numbers of the scalar field part outside the classically allowed region both of the gravitational and scalar fields, suggesting the usefulness of complex geometry and complex trajectories. From the most general wave functions for the FRW cosmology conformally coupled to scalar field, the boundary conditions for the wormhole wave functions are modified so that the modulus of wave functions, instead of the wave functions themselves, should be exponentially damped for a large three-geometry and be regular up to some negative power of the three-geometry as the three-geometry collapses. The wave functions for the FRW cosmology minimally coupled to an inhomogeneous scalar field are similarly found in the product integral formulation. The role of a large number of the inhomogeneous modes of the scalar field is not only to increase the classically allowed regions for the gravitational part but also to provide a mechanism of the decoherence of quantum interferences between the different sizes of the universe.

Hydrothermal Alteration of Open Fractures in Prospective Geothermal Drill Cores, Akutan Island, Alaska

NASA Astrophysics Data System (ADS)

Kent, T.

2011-12-01

The goal of this study is to constrain the most recent thermal alteration of two drill cores (HSB2/HSB4) from the Island of Akutan in the Aleutian Islands of Alaska. These cores are characterized by identifying mineralogy using x-ray diffraction spectra, energy dispersive spectroscopy with a scanning electron microscope and optical mineralogy. This is then compared with the coincident thermal data gathered on site in order to help constrain the most recent thermal activity of this dynamic resource. Using multiple temperature diagnostic minerals and their paragenesis, a relative thermal history is produced of expansive propylitic alteration. When combined with the wireline temperature gradients of the cores a model of downward migration emerges. Shallow occurrences of high temperature minerals that lie above the boiling point to depth curve indicate higher hydrostatic pressures in the past which can be attributed to a combination of glacial effects, including a significant amount of glacial erosion that is recognized due to a lack of significant clay cap to the geothermal resource.

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

Recent developments in SWL physics research.

PubMed

Zhong, P; Xi, X; Zhu, S; Cocks, F H; Preminger, G M

1999-11-01

Two projects in our laboratory highlight some recent developments in shockwave lithotripsy (SWL) physics research. In the first project, we developed a prototype of a piezoelectric annular array (PEAA) shockwave generator that can be retrofitted on a Dornier HM-3 lithotripter for active control of cavitation during SWL. The PEAA generator, operating at 15 kV, produces a peak positive pressure of approximately 8 MPa with a -6-dB beam diameter of 5 mm. The shockwave generated by the PEAA was used to control and force the collapse of cavitation bubbles induced by a laboratory electrohydraulic shockwave lithotripter with a truncated HM-3 reflector. With optimal time delay between the lithotripter pulse and the PEAA-generated shockwave, the collapse of cavitation bubbles near the stone surface could be intensified, and the resultant stone fragmentation in vitro could be significantly improved. In the second project, high-speed shadowgraph imaging was used to visualize the dynamics of lithotripter-induced bubble oscillation in a vascular phantom. Compared with the free bubble oscillation in water, the expansion of cavitation bubble(s) produced in silicone tubes and a 200-microm cellulose hollow fiber by either a Nortech EHL or a Dornier XL-1 lithotripter was found to be significantly constrained. Rupture of the cellulose hollow fiber was observed consistently after about 20 shocks from the XL-1 lithotripter at an output voltage of 20 kV. These results confirm experimentally that SWL-induced cavitation in vivo can be significantly constrained by the surrounding tissue, and large intraluminal bubble expansions could cause rupture of capillaries and small blood vessels.

Dynamics and Control of Articulated Anisotropic Timoshenko Beams

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1996-01-01

The paper illustrates the use of continuum models in control design for stabilizing flexible structures. A 6-DOF anisotropic Timoshenko beam with discrete nodes where lumped masses or actuators are located provides a sufficiently rich model to be of interest for mathematical theory as well as practical application. We develop concepts and tools to help answer engineering questions without having to resort to ad hoc heuristic ("physical") arguments or faith. In this sense the paper is more mathematically oriented than engineering papers and vice versa at the same time. For instance we make precise time-domain solutions using the theory of semigroups of operators rather than formal "inverse Laplace transforms." We show that the modes arise as eigenvalues of the generator of the semigroup, which are then related to the eigenvalues of the stiffness operator. With the feedback control, the modes are no longer orthogonal and the question naturally arises as to whether there is still a modal expansion. Here we prove that the eigenfunctions yield a biorthogonal Riesz basis and indicate the corresponding expansion. We prove mathematically that the number of eigenvalues is nonfinite, based on the theory of zeros of entire functions. We make precise the notion of asymptotic modes and indicate how to calculate them. Although limited by space, we do consider the root locus problem and show for instance that the damping at first increases as the control gain increases but starts to decrease at a critical value, and goes to zero as the gain increases without bound. The undamped oscillatory modes remain oscillatory and the rigid-body modes go over into deadbeat modes. The Timoshenko model dynamics are translated into a canonical wave equation in a Hilbert space. The solution is shown to require the use of an "energy" norm which is no more than the total energy: potential plus kinetic. We show that, under an appropriate extension of the notion of controllability, rate feedback with a collocated sensor can stabilize the structure in the sense that all modes are damped and the energy decays to zero. An example, non-numeric, is worked out in some detail illustrating the concepts and theory developed.

Cosmology with gamma-ray bursts. II. Cosmography challenges and cosmological scenarios for the accelerated Universe

NASA Astrophysics Data System (ADS)

Demianski, Marek; Piedipalumbo, Ester; Sawant, Disha; Amati, Lorenzo

2017-02-01

Context. Explaining the accelerated expansion of the Universe is one of the fundamental challenges in physics today. Cosmography provides information about the evolution of the universe derived from measured distances, assuming only that the space time geometry is described by the Friedman-Lemaitre-Robertson-Walker metric, and adopting an approach that effectively uses only Taylor expansions of basic observables. Aims: We perform a high-redshift analysis to constrain the cosmographic expansion up to the fifth order. It is based on the Union2 type Ia supernovae data set, the gamma-ray burst Hubble diagram, a data set of 28 independent measurements of the Hubble parameter, baryon acoustic oscillations measurements from galaxy clustering and the Lyman-α forest in the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS), and some Gaussian priors on h and ΩM. Methods: We performed a statistical analysis and explored the probability distributions of the cosmographic parameters. By building up their regions of confidence, we maximized our likelihood function using the Markov chain Monte Carlo method. Results: Our high-redshift analysis confirms that the expansion of the Universe currently accelerates; the estimation of the jerk parameter indicates a possible deviation from the standard ΛCDM cosmological model. Moreover, we investigate implications of our results for the reconstruction of the dark energy equation of state (EOS) by comparing the standard technique of cosmography with an alternative approach based on generalized Padé approximations of the same observables. Because these expansions converge better, is possible to improve the constraints on the cosmographic parameters and also on the dark matter EOS. Conclusions: The estimation of the jerk and the DE parameters indicates at 1σ a possible deviation from the ΛCDM cosmological model.

Constraints on Cosmology and Gravity from the Growth of X-ray Luminous Galaxy Clusters

NASA Astrophysics Data System (ADS)

Mantz, Adam; Allen, S. W.; Rapetti, D.; Ebeling, H.; Drlica-Wagner, A.

2010-03-01

I will present simultaneous constraints on galaxy cluster X-ray scaling relations and models of cosmology and gravity obtained from observations of the growth of massive clusters. The data set consists of 238 flux-selected clusters at redshifts z≤0.5 drawn from the ROSAT All-Sky Survey, and incorporates extensive Chandra follow-up observations. Our results on the scaling relations are consistent with excess heating of the intracluster medium, although the evolution of the relations remains consistent with the predictions of simple gravitational collapse models. For spatially flat, constant-w cosmological models, the cluster data yield Ωm=0.23±0.04, σ8=0.82±0.05, and w=-1.01±0.20, including conservative allowances for systematic uncertainties. Our results are consistent and competitive with a variety of independent cosmological data. In evolving-w models, marginalizing over transition redshifts in the range 0.05-1, the combination of the growth of structure data with the cosmic microwave background, supernovae, cluster gas mass fractions and baryon acoustic oscillations constrains the dark energy equation of state at late and early times to be respectively w0=-0.88±0.21 and wet=-1.05+0.20-0.36. Applying this combination of data to the problem of determining fundamental neutrino properties, we place an upper limit on the species-summed neutrino mass at 0.33eV (95% CL) and constrain the effective number of relativistic species to 3.4±0.6. In addition to dark energy and related problems, such data can be used to test the predictions of General Relativity. Introducing the standard Peebles/Linder parametrization of the linear growth rate, we use the cluster data to constrain the growth of structure, independent of the expansion of the Universe. Our analysis provides a tight constraint on the combination γ(σ8/0.8)6.8=0.55+0.13-0.10, and is simultaneously consistent with the predictions of relativity (γ=0.55) and the cosmological constant expansion model. This work was funded by NASA, the U.S. Department of Energy, and Stanford University.

Computation in Dynamically Bounded Asymmetric Systems

PubMed Central

Rutishauser, Ueli; Slotine, Jean-Jacques; Douglas, Rodney

2015-01-01

Previous explanations of computations performed by recurrent networks have focused on symmetrically connected saturating neurons and their convergence toward attractors. Here we analyze the behavior of asymmetrical connected networks of linear threshold neurons, whose positive response is unbounded. We show that, for a wide range of parameters, this asymmetry brings interesting and computationally useful dynamical properties. When driven by input, the network explores potential solutions through highly unstable ‘expansion’ dynamics. This expansion is steered and constrained by negative divergence of the dynamics, which ensures that the dimensionality of the solution space continues to reduce until an acceptable solution manifold is reached. Then the system contracts stably on this manifold towards its final solution trajectory. The unstable positive feedback and cross inhibition that underlie expansion and divergence are common motifs in molecular and neuronal networks. Therefore we propose that very simple organizational constraints that combine these motifs can lead to spontaneous computation and so to the spontaneous modification of entropy that is characteristic of living systems. PMID:25617645

Implicitly causality enforced solution of multidimensional transient photon transport equation.

PubMed

Handapangoda, Chintha C; Premaratne, Malin

2009-12-21

A novel method for solving the multidimensional transient photon transport equation for laser pulse propagation in biological tissue is presented. A Laguerre expansion is used to represent the time dependency of the incident short pulse. Owing to the intrinsic causal nature of Laguerre functions, our technique automatically always preserve the causality constrains of the transient signal. This expansion of the radiance using a Laguerre basis transforms the transient photon transport equation to the steady state version. The resulting equations are solved using the discrete ordinates method, using a finite volume approach. Therefore, our method enables one to handle general anisotropic, inhomogeneous media using a single formulation but with an added degree of flexibility owing to the ability to invoke higher-order approximations of discrete ordinate quadrature sets. Therefore, compared with existing strategies, this method offers the advantage of representing the intensity with a high accuracy thus minimizing numerical dispersion and false propagation errors. The application of the method to one, two and three dimensional geometries is provided.

Endosperm turgor pressure decreases during early Arabidopsis seed development.

PubMed

Beauzamy, Léna; Fourquin, Chloé; Dubrulle, Nelly; Boursiac, Yann; Boudaoud, Arezki; Ingram, Gwyneth

2016-09-15

In Arabidopsis, rapid expansion of the coenocytic endosperm after fertilisation has been proposed to drive early seed growth, which is in turn constrained by the seed coat. This hypothesis implies physical heterogeneity between the endosperm and seed coat compartments during early seed development, which to date has not been demonstrated. Here, we combine tissue indentation with modelling to show that the physical properties of the developing seed are consistent with the hypothesis that elevated endosperm-derived turgor pressure drives early seed expansion. We provide evidence that whole-seed turgor is generated by the endosperm at early developmental stages. Furthermore, we show that endosperm cellularisation and seed growth arrest are associated with a drop in endosperm turgor pressure. Finally, we demonstrate that this decrease is perturbed when the function of POLYCOMB REPRESSIVE COMPLEX 2 is lost, suggesting that turgor pressure changes could be a target of genomic imprinting. Our results indicate a developmental role for changes in endosperm turgor pressure in the Arabidopsis seed. © 2016. Published by The Company of Biologists Ltd.

In situ X-ray and neutron diffraction of the Ruddlesden–Popper compounds (RE 2–xSr x)₀.₉₈(Fe₀.₈Co₀.₂) 1–yMg yO 4–δ (RE=La, Pr): Structure and CO₂ stability

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

Chatzichristodoulou, C., E-mail: ccha@dtu.dk; Hauback, B.C.; Hendriksen, P.V.

2013-05-01

The crystal structure of the Ruddlesden–Popper compounds (La₁.₀Sr₁.₀)₀.₈Fe₁.₀Co₀.₂O 4–δ and (La₁.₂Sr₀.₈)₀.₉₈(Fe₀.₈Co₀.₂)₀.₈Mg₀.₂O 4–δ was investigated at 1000 °C in N₂ (a O₂=1×10₋₄ by in-situ powder neutron diffraction. In-situ powder X-ray diffraction (PXD) was also employed to investigate the temperature dependence of the lattice parameters of the compounds in air and the oxygen activity dependence of the lattice parameters at 800 °C and 1000 °C. The thermal and chemical expansion coefficients, determined along the two crystallographic directions of the tetragonal unit cell, are highly anisotropic. The equivalent pseudo-cubic thermal and chemical expansion coefficients are in agreement with values determined by dilatometry. Themore » chemical stability in CO₂ containing environments of various Ruddlesden–Popper compounds with chemical formula (RE 2-xSr x)₀.₉₈(Fe₀.₈Co₀.₂) 1-yMg yO 4–δ (RE=La, Pr), as well as their stability limit in H₂/H₂O=4.5 were also determined by in-situ PXD for x=0.9, 1.0 and y=0, 0.2. - Graphical abstract: Influence of electronic configuration on bond length, lattice parameters and anisotropic thermal and chemical expansion. Highlights: • The thermal and chemical expansion coefficients are largely anisotropic. • The expansion of the perovskite layers is constrained along the a direction. • The studied compositions show remarkable thermodynamic stability upon reduction. • The thermal and chemical expansion coefficients are lower than related perovskites. • The investigated materials decompose in CO₂ containing atmospheres.« less

The expansion rate of the intermediate universe in light of Planck

NASA Astrophysics Data System (ADS)

Verde, Licia; Protopapas, Pavlos; Jimenez, Raul

2014-12-01

We use cosmology-independent measurements of the expansion history in the redshift range 0.1 ≲ z < 1.2 and compare them with the Cosmic Microwave Background-derived expansion history predictions. The motivation is to investigate if the tension between the local (cosmology independent) Hubble constant H0 value and the Planck-derived H0 is also present at other redshifts. We conclude that there is no tension between Planck and cosmology independent-measurements of the Hubble parameter H(z) at 0.1 ≲ z < 1.2 for the ΛCDM model (odds of tension are only 1:15, statistically not significant). Considering extensions of the ΛCDM model does not improve these odds (actually makes them worse), thus favouring the simpler model over its extensions. On the other hand the H(z) data are also not in tension with the local H0 measurements but the combination of all three data-sets shows a highly significant tension (odds ∼1:400). Thus the new data deepen the mystery of the mismatch between Planck and local H0 measurements, and cannot univocally determine whether it is an effect localised at a particular redshift. Having said this, we find that assuming the NGC4258 maser distance as the correct anchor for H0, brings the odds to comfortable values. Further, using only the expansion history measurements we constrain, within the ΛCDM model, H0 = 68.5 ± 3.5 and Ωm = 0.32 ± 0.05 (at 68% confidence) without relying on any CMB prior. We also address the question of how smooth the expansion history of the Universe is given the cosmology independent data and conclude that there is no evidence for deviations from smoothness on the expansion history, neither variations with time in the value of the equation of state of dark energy.

Massive expansion and differential evolution of small heat shock proteins with wheat (Triticum aestivum L.) polyploidization.

PubMed

Wang, Xiaoming; Wang, Ruochen; Ma, Chuang; Shi, Xue; Liu, Zhenshan; Wang, Zhonghua; Sun, Qixin; Cao, Jun; Xu, Shengbao

2017-05-31

Wheat (Triticum aestivum), one of the world's most important crops, is facing unprecedented challenges due to global warming. To evaluate the gene resources for heat adaptation in hexaploid wheat, small heat shock proteins (sHSPs), the key plant heat protection genes, were comprehensively analysed in wheat and related species. We found that the sHSPs of hexaploid wheat were massively expanded in A and B subgenomes with intrachromosomal duplications during polyploidization. These expanded sHSPs were under similar purifying selection and kept the expressional patterns with the original copies. Generally, a strong purifying selection acted on the α-crystallin domain (ACD) and theoretically constrain conserved function. Meanwhile, weaker purifying selection and strong positive selection acted on the N-terminal region, which conferred sHSP flexibility, allowing adjustments to a wider range of substrates in response to genomic and environmental changes. Notably, in CI, CV, ER, MI and MII subfamilies, gene duplications, expression variations and functional divergence occurred before wheat polyploidization. Our results indicate the massive expansion of active sHSPs in hexaploid wheat may also provide more raw materials for evolving functional novelties and generating genetic diversity to face future global climate changes, and highlight the expansion of stress response genes with wheat polyploidization.

(2, 2) superconformal bootstrap in two dimensions

DOE PAGES

Lin, Ying -Hsuan; Shao, Shu -Heng; Wang, Yifan; ...

2017-05-19

We find a simple relation between two-dimensional BPS N = 2 superconformal blocks and bosonic Virasoro conformal blocks, which allows us to analyze the crossing equations for BPS 4-point functions in unitary (2, 2) superconformal theories numerically with semidefinite programming. Here, we constrain gaps in the non-BPS spectrum through the operator product expansion of BPS operators, in ways that depend on the moduli of exactly marginal deformations through chiral ring coefficients. In some cases, our bounds on the spectral gaps are observed to be saturated by free theories, by N = 2 Liouville theory, and by certain Landau-Ginzburg models.

Comment on ‘A novel method for fast and robust estimation of fluorescence decay dynamics using constrained least-square deconvolution with Laguerre expansion’

NASA Astrophysics Data System (ADS)

Zhang, Yongliang; Day-Uei Li, David

2017-02-01

This comment is to clarify that Poisson noise instead of Gaussian noise shall be included to assess the performances of least-squares deconvolution with Laguerre expansion (LSD-LE) for analysing fluorescence lifetime imaging data obtained from time-resolved systems. Moreover, we also corrected an equation in the paper. As the LSD-LE method is rapid and has the potential to be widely applied not only for diagnostic but for wider bioimaging applications, it is desirable to have precise noise models and equations.

Effect of load introduction on graphite epoxy compression specimens

NASA Technical Reports Server (NTRS)

Reiss, R.; Yao, T. M.

1981-01-01

Compression testing of modern composite materials is affected by the manner in which the compressive load is introduced. Two such effects are investigated: (1) the constrained edge effect which prevents transverse expansion and is common to all compression testing in which the specimen is gripped in the fixture; and (2) nonuniform gripping which induces bending into the specimen. An analytical model capable of quantifying these foregoing effects was developed which is based upon the principle of minimum complementary energy. For pure compression, the stresses are approximated by Fourier series. For pure bending, the stresses are approximated by Legendre polynomials.

Constraints on operator ordering from third quantization

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

Ohkuwa, Yoshiaki; Faizal, Mir, E-mail: f2mir@uwaterloo.ca; Ezawa, Yasuo

2016-02-15

In this paper, we analyse the Wheeler–DeWitt equation in the third quantized formalism. We will demonstrate that for certain operator ordering, the early stages of the universe are dominated by quantum fluctuations, and the universe becomes classical at later stages during the cosmic expansion. This is physically expected, if the universe is formed from quantum fluctuations in the third quantized formalism. So, we will argue that this physical requirement can be used to constrain the form of the operator ordering chosen. We will explicitly demonstrate this to be the case for two different cosmological models.

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

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.

The Analytical Solution of the Transient Radial Diffusion Equation with a Nonuniform Loss Term.

NASA Astrophysics Data System (ADS)

Loridan, V.; Ripoll, J. F.; De Vuyst, F.

2017-12-01

Many works have been done during the past 40 years to perform the analytical solution of the radial diffusion equation that models the transport and loss of electrons in the magnetosphere, considering a diffusion coefficient proportional to a power law in shell and a constant loss term. Here, we propose an original analytical method to address this challenge with a nonuniform loss term. The strategy is to match any L-dependent electron losses with a piecewise constant function on M subintervals, i.e., dealing with a constant lifetime on each subinterval. Applying an eigenfunction expansion method, the eigenvalue problem becomes presently a Sturm-Liouville problem with M interfaces. Assuming the continuity of both the distribution function and its first spatial derivatives, we are able to deal with a well-posed problem and to find the full analytical solution. We further show an excellent agreement between both the analytical solutions and the solutions obtained directly from numerical simulations for different loss terms of various shapes and with a diffusion coefficient DLL L6. We also give two expressions for the required number of eigenmodes N to get an accurate snapshot of the analytical solution, highlighting that N is proportional to 1/√t0, where t0 is a time of interest, and that N increases with the diffusion power. Finally, the equilibrium time, defined as the time to nearly reach the steady solution, is estimated by a closed-form expression and discussed. Applications to Earth and also Jupiter and Saturn are discussed.

Measurement of Kirchhoff's stress intensity factors in bending plates

NASA Astrophysics Data System (ADS)

Bäcker, D.; Kuna, M.; Häusler, C.

2014-03-01

A measurement method of the stress intensity factors defined by KIRCHHOFF's theory for a crack in a bending plate is shown. For this purpose, a thin piezoelectric polyvinylidene fluoride film (PVDF) is attached to the surface of the cracked plate. The measured electrical voltages are coupled with the load type and the crack tip position relative to the sensor film. Stress intensity factors and the crack tip position can be determined by solving the non-linear inverse problem based on the measured signals. To guarantee solvability of the problem, more measuring electrodes on the film have to be taken in to account. To the developed sensor concept the KIRCHHOFF's plate theory has been applied. In order to connect the electrical signals and the stress intensity factors the stresses near the crack tip have to be written in eigenfunctions (see WILLIAMS [1]). The presented method was verified by means of the example of a straight crack of the length 2a in an infinite isotropic plate under all- side bending. It was found that the positioning of the electrodes is delimited by two radii. On one hand, the measurement points should not be too close to the crack tip. In this area, the Kirchhoff's plate theory cannot be used effectively. On the other hand, the measuring electrodes should be placed at a smaller distance to each other and not too far from the crack tip regarding the convergence radius of the WILLIAMS series expansion. Test calculations on a straight crack in an infinite isotropic plate showed the general applicability of the measurement method.

Stratified wakes, the high Froude number approximation, and potential flow

NASA Astrophysics Data System (ADS)

Vasholz, David P.

2011-12-01

Properties of a steady wake generated by a body moving uniformly at constant depth through a stratified fluid are studied as a function of two parameters inserted into the linearized equations of motion. The first parameter, μ, multiplies the along-track gradient term in the source equation. When formal solutions for an arbitrary buoyancy frequency profile are written as eigenfunction expansions, one finds that the limit μ → 0 corresponds to a high Froude number approximation accompanied by a substantial reduction in the complexity of the calculation. For μ = 1, upstream effects are present and the eigenvalues correspond to critical speeds above which transverse waves disappear for any given mode. For sufficiently high modes, the high Froude number approximation is valid. The second tracer multiplies the square of the buoyancy frequency term in the linearized conservation of mass equation and enables direct comparisons with the limit of potential flow. Detailed results are given for the simplest possible profile, in which the buoyancy frequency is independent of depth; emphasis is placed upon quantities that can, in principle, be experimentally measured in a laboratory experiment. The vertical displacement field is written in terms of a stratified wake form factor {{H}} , which is the sum of a wavelike contribution that is non-zero downstream and an evanescent contribution that appears symmetrically upstream and downstream. First- and second-order cross-track moments of {{H}} are analyzed. First-order results predict enhanced upstream vertical displacements. Second-order results expand upon previous predictions of wavelike resonances and also predict evanescent resonance effects.

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.

Hydrodynamic analysis and shape optimization for vertical axisymmetric wave energy converters

NASA Astrophysics Data System (ADS)

Zhang, Wan-chao; Liu, Heng-xu; Zhang, Liang; Zhang, Xue-wei

2016-12-01

The absorber is known to be vertical axisymmetric for a single-point wave energy converter (WEC). The shape of the wetted surface usually has a great influence on the absorber's hydrodynamic characteristics which are closely linked with the wave power conversion ability. For complex wetted surface, the hydrodynamic coefficients have been predicted traditionally by hydrodynamic software based on the BEM. However, for a systematic study of various parameters and geometries, they are too multifarious to generate so many models and data grids. This paper examines a semi-analytical method of decomposing the complex axisymmetric boundary into several ring-shaped and stepped surfaces based on the boundary discretization method (BDM) which overcomes the previous difficulties. In such case, by using the linear wave theory based on eigenfunction expansion matching method, the expressions of velocity potential in each domain, the added mass, radiation damping and wave excitation forces of the oscillating absorbers are obtained. The good astringency of the hydrodynamic coefficients and wave forces are obtained for various geometries when the discrete number reaches a certain value. The captured wave power for a same given draught and displacement for various geometries are calculated and compared. Numerical results show that the geometrical shape has great effect on the wave conversion performance of the absorber. For absorbers with the same outer radius and draught or displacement, the cylindrical type shows fantastic wave energy conversion ability at some given frequencies, while in the random sea wave, the parabolic and conical ones have better stabilization and applicability in wave power conversion.

Detection, modeling and matching of pleural thickenings from CT data towards an early diagnosis of malignant pleural mesothelioma

NASA Astrophysics Data System (ADS)

Chaisaowong, Kraisorn; Kraus, Thomas

2014-03-01

Pleural thickenings can be caused by asbestos exposure and may evolve into malignant pleural mesothelioma. While an early diagnosis plays the key role to an early treatment, and therefore helping to reduce morbidity, the growth rate of a pleural thickening can be in turn essential evidence to an early diagnosis of the pleural mesothelioma. The detection of pleural thickenings is today done by a visual inspection of CT data, which is time-consuming and underlies the physician's subjective judgment. Computer-assisted diagnosis systems to automatically assess pleural mesothelioma have been reported worldwide. But in this paper, an image analysis pipeline to automatically detect pleural thickenings and measure their volume is described. We first delineate automatically the pleural contour in the CT images. An adaptive surface-base smoothing technique is then applied to the pleural contours to identify all potential thickenings. A following tissue-specific topology-oriented detection based on a probabilistic Hounsfield Unit model of pleural plaques specify then the genuine pleural thickenings among them. The assessment of the detected pleural thickenings is based on the volumetry of the 3D model, created by mesh construction algorithm followed by Laplace-Beltrami eigenfunction expansion surface smoothing technique. Finally, the spatiotemporal matching of pleural thickenings from consecutive CT data is carried out based on the semi-automatic lung registration towards the assessment of its growth rate. With these methods, a new computer-assisted diagnosis system is presented in order to assure a precise and reproducible assessment of pleural thickenings towards the diagnosis of the pleural mesothelioma in its early stage.

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.

Dynamic patterns of cortical expansion during folding of the preterm human brain.

PubMed

Garcia, Kara E; Robinson, Emma C; Alexopoulos, Dimitrios; Dierker, Donna L; Glasser, Matthew F; Coalson, Timothy S; Ortinau, Cynthia M; Rueckert, Daniel; Taber, Larry A; Van Essen, David C; Rogers, Cynthia E; Smyser, Christopher D; Bayly, Philip V

2018-03-20

During the third trimester of human brain development, the cerebral cortex undergoes dramatic surface expansion and folding. Physical models suggest that relatively rapid growth of the cortical gray matter helps drive this folding, and structural data suggest that growth may vary in both space (by region on the cortical surface) and time. In this study, we propose a unique method to estimate local growth from sequential cortical reconstructions. Using anatomically constrained multimodal surface matching (aMSM), we obtain accurate, physically guided point correspondence between younger and older cortical reconstructions of the same individual. From each pair of surfaces, we calculate continuous, smooth maps of cortical expansion with unprecedented precision. By considering 30 preterm infants scanned two to four times during the period of rapid cortical expansion (28-38 wk postmenstrual age), we observe significant regional differences in growth across the cortical surface that are consistent with the emergence of new folds. Furthermore, these growth patterns shift over the course of development, with noninjured subjects following a highly consistent trajectory. This information provides a detailed picture of dynamic changes in cortical growth, connecting what is known about patterns of development at the microscopic (cellular) and macroscopic (folding) scales. Since our method provides specific growth maps for individual brains, we are also able to detect alterations due to injury. This fully automated surface analysis, based on tools freely available to the brain-mapping community, may also serve as a useful approach for future studies of abnormal growth due to genetic disorders, injury, or other environmental variables.

Tensor non-Gaussianity from axion-gauge-fields dynamics: parameter search

NASA Astrophysics Data System (ADS)

Agrawal, Aniket; Fujita, Tomohiro; Komatsu, Eiichiro

2018-06-01

We calculate the bispectrum of scale-invariant tensor modes sourced by spectator SU(2) gauge fields during inflation in a model containing a scalar inflaton, a pseudoscalar axion and SU(2) gauge fields. A large bispectrum is generated in this model at tree-level as the gauge fields contain a tensor degree of freedom, and its production is dominated by self-coupling of the gauge fields. This is a unique feature of non-Abelian gauge theory. The shape of the tensor bispectrum is approximately an equilateral shape for 3lesssim mQlesssim 4, where mQ is an effective dimensionless mass of the SU(2) field normalised by the Hubble expansion rate during inflation. The amplitude of non-Gaussianity of the tensor modes, characterised by the ratio Bh/P2h, is inversely proportional to the energy density fraction of the gauge field. This ratio can be much greater than unity, whereas the ratio from the vacuum fluctuation of the metric is of order unity. The bispectrum is effective at constraining large mQ regions of the parameter space, whereas the power spectrum constrains small mQ regions.

The determinants of dentists' productivity and the measurement of output.

PubMed

Gutacker, Nils; Harris, Anthony; Brennan, David; Hollingsworth, Bruce

2015-01-01

Improving the productivity of the healthcare system, for example by taking advantage of scale economies or encouraging substitution of expensive specialist personnel with less expensive workers, is often seen as an attractive way to meet increasing demand within a constrained budget. Using data on 558 dentists participating in the Longitudinal Study of Dentists' Practice Activity (LSDPA) survey between 1993 and 2003 linked to patient data and average fee schedules, we estimate production functions for private dental services in Australia to quantify the contribution of different capital and labour inputs and identify economies of scale in the production of dental care. Given the challenges in measuring output in the healthcare setting, we discuss three different output measures (raw activity, time-, and price-weighted activity) and test the sensitivity of results to the choice of measure. Our results suggest that expansion of the scale of dental services is unlikely to be constrained by decreasing returns to scale. We note that conclusions about the contribution of individual input factors and the estimated returns to scale are sensitive to the choice of output measure employed. Copyright © 2014 Elsevier Ltd. All rights reserved.

Isoprene emissions over Asia 1979-2012 : impact of climate and land use changes

NASA Astrophysics Data System (ADS)

Stavrakou, Trissevgeni; Müller, Jean-Francois; Bauwens, Maite; Guenther, Alex; De Smedt, Isabelle; Van Roozendael, Michel

2014-05-01

Due to the scarcity of observational contraints and the rapidly changing environment in East and Southeast Asia, isoprene emissions predicted by models are expected to bear substantial uncertainties. This study aims at improving upon current bottom-up estimates, and investigate the temporal evolution of isoprene fluxes in Asia over 1979-2012. For that, we use the MEGAN model and incorporate (i) changes in land use, including the rapid expansion of oil palms, (ii) meteorological variability, (iii) long-term changes in solar radiation constrained by surface network measurements, and (iv) recent experimental evidence that South Asian forests are much weaker isoprene emitters than previously assumed. These effects lead to a significant reduction of the total isoprene fluxes over the studied domain compared to the standard simulation. The bottom-up emissions are evaluated using satellite-based emission estimates derived from inverse modelling constrained by GOME-2/MetOp-A formaldehyde columns through 2007-2012. The top-down estimates support our assumptions and confirm the lower isoprene emission rate in tropical forests of Indonesia and Malaysia.

On the BV formalism of open superstring field theory in the large Hilbert space

NASA Astrophysics Data System (ADS)

Matsunaga, Hiroaki; Nomura, Mitsuru

2018-05-01

We construct several BV master actions for open superstring field theory in the large Hilbert space. First, we show that a naive use of the conventional BV approach breaks down at the third order of the antifield number expansion, although it enables us to define a simple "string antibracket" taking the Darboux form as spacetime antibrackets. This fact implies that in the large Hilbert space, "string fields-antifields" should be reassembled to obtain master actions in a simple manner. We determine the assembly of the string anti-fields on the basis of Berkovits' constrained BV approach, and give solutions to the master equation defined by Dirac antibrackets on the constrained string field-antifield space. It is expected that partial gauge-fixing enables us to relate superstring field theories based on the large and small Hilbert spaces directly: reassembling string fields-antifields is rather natural from this point of view. Finally, inspired by these results, we revisit the conventional BV approach and construct a BV master action based on the minimal set of string fields-antifields.

Effect of the chameleon scalar field on brane cosmological evolution

NASA Astrophysics Data System (ADS)

Bisabr, Y.; Ahmadi, F.

2017-11-01

We have investigated a brane world model in which the gravitational field in the bulk is described both by a metric tensor and a minimally coupled scalar field. This scalar field is taken to be a chameleon with an appropriate potential function. The scalar field interacts with matter and there is an energy transfer between the two components. We find a late-time asymptotic solution which exhibits late-time accelerating expansion. We also show that the Universe recently crosses the phantom barrier without recourse to any exotic matter. We provide some thermodynamic arguments which constrain both the direction of energy transfer and dynamics of the extra dimension.

Estimation of the full marginal costs of port related truck traffic.

PubMed

Berechman, Joseph

2009-11-01

NY region is expected to grow by additional 1 million people by 2020, which translates into roughly 70 million more tons of goods to be delivered annually. Due to lack of rail capacity, mainly trucks will haul this volume of freight, challenging an already much constrained highway network. What are the total costs associated with this additional traffic, in particular, congestion, safety and emission? Since a major source of this expected flow is the Port of New York-New Jersey, this paper focuses on the estimation of the full marginal costs of truck traffic resulting from the further expansion of the port's activities.

Charge of the right brigade? Communities, coverage, and care for the uninsured.

PubMed

Brown, Lawrence D; Stevens, Beth

2006-01-01

The Robert Wood Johnson Foundation's Communities in Charge (CIC) program funded projects in fourteen communities that aimed to expand health insurance coverage and improve care for their uninsured residents. Our examination of seven program sites suggests that despite solid community leadership and carefully crafted plans, political, economic, and organizational obstacles precluded much expansion of coverage and constrained reforms. Redistribution of financial and organizational resources among both mainstream and safety-net institutions in these communities was hard to achieve. CIC's record offers little evidence that communities are better equipped than are other sectors of U.S. society to solve the problem of uninsurance.

Is pulsar timing a hopeful tool for detection of relic gravitational waves by using GW150914 data?

NASA Astrophysics Data System (ADS)

Ghayour, Basem

2018-04-01

The inflation stage has a behaviour as power law expansion like S(η )∝ η ^{1+β } where β constrained on the 1+β <0. If the inflation were preceded by a radiation era, then there would be thermal spectrum of relic gravitational waves at the time of inflation. Based on this idea we find new upper bound on β by comparison the thermal spectrum with strain sensitivity of single pulsar timing. Also we show that sensitivity curve of single pulsar timing may be hopeful tool for detection of the spectrum in usual and thermal case by using the GW150914 data.

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

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.

Three-dimensional, two-species magnetohydrodynamic studies of the early time behaviors of the Combined Release and Radiation Effects Satellite G2 barium release

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

Xie, Lianghai, E-mail: xielh@nssc.ac.cn; Li, Lei; Wang, Jingdong

2014-04-15

We present a three-dimensional, two-species (Ba{sup +} and H{sup +}) MHD model to study the early time behaviors of a barium release at about 1 R{sub E} like Combined Release and Radiation Effects Satellite G2, with emphasis placed on the three-dimensional evolution of the barium cloud and its effects on the ambient plasma environment. We find that the perturbations caused by the cloud are the combined results of the initial injection, the radial expansion, and the diamagnetic effect and propagate as fast MHD waves in the magnetosphere. In return, the transverse expansion and the cross-B motion of barium ions aremore » constrained by the magnetic force, which lead to a field-aligned striation of ions and the decoupling of these ions from the neutrals. Our simulation shows the formation and collapse of the diamagnetic cavity in the barium cloud. The estimated time scale for the cavity evolution might be much shorter if photoionization time scale and field aligned expansion of barium ions are considered. In addition, our two species MHD simulation also finds the snowplow effect resulting from the momentum coupling between barium ions and background H{sup +}, which creates density hole and bumps in the background H{sup +} when barium ions expanding along the magnetic field lines.« less

Land cover change or land-use intensification: simulating land system change with a global-scale land change model.

PubMed

van Asselen, Sanneke; Verburg, Peter H

2013-12-01

Land-use change is both a cause and consequence of many biophysical and socioeconomic changes. The CLUMondo model provides an innovative approach for global land-use change modeling to support integrated assessments. Demands for goods and services are, in the model, supplied by a variety of land systems that are characterized by their land cover mosaic, the agricultural management intensity, and livestock. Land system changes are simulated by the model, driven by regional demand for goods and influenced by local factors that either constrain or promote land system conversion. A characteristic of the new model is the endogenous simulation of intensification of agricultural management versus expansion of arable land, and urban versus rural settlements expansion based on land availability in the neighborhood of the location. Model results for the OECD Environmental Outlook scenario show that allocation of increased agricultural production by either management intensification or area expansion varies both among and within world regions, providing useful insight into the land sparing versus land sharing debate. The land system approach allows the inclusion of different types of demand for goods and services from the land system as a driving factor of land system change. Simulation results are compared to observed changes over the 1970-2000 period and projections of other global and regional land change models. © 2013 John Wiley & Sons Ltd.

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.

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

Topography and tectonics of mid-oceanic ridge axes

NASA Technical Reports Server (NTRS)

Sleep, N. H.; Rosendahl, B. R.

1979-01-01

Numerical fluid dynamic models of mid-oceanic ridge axes were constructed using distributions of material properties constrained by seismic studies and thermal calculations. The calculations indicate that spreading is passive except for forces caused by density differences due to thermal expansion and partial melt. Except for geometric differences due to temperature distribution, one set of mechanical properties can adequately explain central rifts of slow ridges and central peaks of fast ridges. Viscous head loss in the upwelling material dominates at low spreading rates where material ascends through a narrow conduit. Thermal expansion and partial melting dominate at high spreading rates where a wide low viscosity crustal magma chamber is present. The preferred rheology is 10 to the 20th poise for the upwelling lithosphere; less than 5 x 10 to the 17th for the crustal magma chamber and axial intrusion zone at fast ridges, and a yield stress of 200 bars for the lithosphere. The calculation correctly predicts the existence of central peaks at 'hot-spot' ridges, where seismic evidence indicates a large magma chamber.

Finite-element modelling of thermal micracking in fresh and consolidated marbles

NASA Astrophysics Data System (ADS)

Weiss, T.; Fuller, E.; Siegesmund, S.

2003-04-01

The initial stage of marble weathering is supposed to be controlled by thermal microcracking. Due to the anisotropy of the thermal expansion coefficients of calcite, the main rock forming mineral in marble, stresses are caused which lead to thermally-induced microcracking, especially along the grain boundaries. The so-called "granular disintegration" is a frequent weathering phenomenon observed for marbles. The controlling parameters are the grain size, grain shape and grain orientation. We use a finite-element approach to constrain magnitude and directional dependence of thermal degradation. Therefore, different assumptions are validated including the fracture toughness of the grain boundaries, the effects of the grain-to-grain orientation and bulk lattice preferred orientation (here referred to as texture). The resulting thermal microcracking and bulk rock thermal expansion anisotropy are validated. It is evident that thermal degradation depends on the texture. Strongly textured marbles exhibit a clear directional dependence of thermal degradation and a smaller bulk thermal degradation than randomly oriented ones. The effect of different stone consolidants in the pore space of degraded marble is simulated and its influence on mechanical properties such as tensile strength are evaluated.

Precision growth index using the clustering of cosmic structures and growth data

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

Pouri, Athina; Basilakos, Spyros; Plionis, Manolis, E-mail: athpouri@phys.uoa.gr, E-mail: svasil@academyofathens.gr, E-mail: mplionis@physics.auth.gr

2014-08-01

We use the clustering properties of Luminous Red Galaxies (LRGs) and the growth rate data provided by the various galaxy surveys in order to constrain the growth index γ) of the linear matter fluctuations. We perform a standard χ{sup 2}-minimization procedure between theoretical expectations and data, followed by a joint likelihood analysis and we find a value of γ=0.56± 0.05, perfectly consistent with the expectations of the ΛCDM model, and Ω{sub m0} =0.29± 0.01, in very good agreement with the latest Planck results. Our analysis provides significantly more stringent growth index constraints with respect to previous studies, as indicated by the fact thatmore » the corresponding uncertainty is only ∼ 0.09 γ. Finally, allowing γ to vary with redshift in two manners (Taylor expansion around z=0, and Taylor expansion around the scale factor), we find that the combined statistical analysis between our clustering and literature growth data alleviates the degeneracy and obtain more stringent constraints with respect to other recent studies.« less

Evaluation of thermal expansion coefficient of carbon fiber reinforced composites using electronic speckle interferometry.

PubMed

Dong, Chengzhi; Li, Kai; Jiang, Yuxi; Arola, Dwayne; Zhang, Dongsheng

2018-01-08

An optical system for measuring the coefficient of thermal expansion (CTE) of materials has been developed based on electronic speckle interferometry. In this system, the temperature can be varied from -60°C to 180°C with a Peltier device. A specific specimen geometry and an optical arrangement based on the Michelson interferometer are proposed to measure the deformation along two orthogonal axes due to temperature changes. The advantages of the system include its high sensitivity and stability over the whole range of measurement. The experimental setup and approach for estimating the CTE was validated using an Aluminum alloy. Following this validation, the system was applied for characterizing the CTE of carbon fiber reinforced composite (CFRP) laminates. For the unidirectional fiber reinforced composites, the CTE varied with fiber orientation and exhibits anisotropic behavior. By stacking the plies with specific angles and order, the CTE of a specific CFRP was constrained to a low level with minimum variation temperature. The optical system developed in this study can be applied to CTE measurement for engineering and natural materials with high accuracy.

Global niche of marine anaerobic metabolisms expanded by particle microenvironments

NASA Astrophysics Data System (ADS)

Bianchi, Daniele; Weber, Thomas S.; Kiko, Rainer; Deutsch, Curtis

2018-04-01

In ocean waters, anaerobic microbial respiration should be confined to the anoxic waters found in coastal regions and tropical oxygen minimum zones, where it is energetically favourable. However, recent molecular and geochemical evidence has pointed to a much broader distribution of denitrifying and sulfate-reducing microbes. Anaerobic metabolisms are thought to thrive in microenvironments that develop inside sinking organic aggregates, but the global distribution and geochemical significance of these microenvironments is poorly understood. Here, we develop a new size-resolved particle model to predict anaerobic respiration from aggregate properties and seawater chemistry. Constrained by observations of the size spectrum of sinking particles, the model predicts that denitrification and sulfate reduction can be sustained throughout vast, hypoxic expanses of the ocean, and could explain the trace metal enrichment observed in particles due to sulfide precipitation. Globally, the expansion of the anaerobic niche due to particle microenvironments doubles the rate of water column denitrification compared with estimates based on anoxic zones alone, and changes the sensitivity of the marine nitrogen cycle to deoxygenation in a warming climate.

A 6% measurement of the Hubble parameter at z ∼0.45: direct evidence of the epoch of cosmic re-acceleration

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

Moresco, Michele; Cimatti, Andrea; Citro, Annalisa

2016-05-01

Deriving the expansion history of the Universe is a major goal of modern cosmology. To date, the most accurate measurements have been obtained with Type Ia Supernovae (SNe) and Baryon Acoustic Oscillations (BAO), providing evidence for the existence of a transition epoch at which the expansion rate changes from decelerated to accelerated. However, these results have been obtained within the framework of specific cosmological models that must be implicitly or explicitly assumed in the measurement. It is therefore crucial to obtain measurements of the accelerated expansion of the Universe independently of assumptions on cosmological models. Here we exploit the unprecedentedmore » statistics provided by the Baryon Oscillation Spectroscopic Survey (BOSS, [1-3]) Data Release 9 to provide new constraints on the Hubble parameter H ( z ) using the cosmic chronometers approach. We extract a sample of more than 130000 of the most massive and passively evolving galaxies, obtaining five new cosmology-independent H ( z ) measurements in the redshift range 0.3 < z < 0.5, with an accuracy of ∼11–16% incorporating both statistical and systematic errors. Once combined, these measurements yield a 6% accuracy constraint of H ( z = 0.4293) = 91.8 ± 5.3 km/s/Mpc. The new data are crucial to provide the first cosmology-independent determination of the transition redshift at high statistical significance, measuring z {sub t} = 0.4 ± 0.1, and to significantly disfavor the null hypothesis of no transition between decelerated and accelerated expansion at 99.9% confidence level. This analysis highlights the wide potential of the cosmic chronometers approach: it permits to derive constraints on the expansion history of the Universe with results competitive with standard probes, and most importantly, being the estimates independent of the cosmological model, it can constrain cosmologies beyond—and including—the ΛCDM model.« less

Inverse problem to constrain the controlling parameters of large-scale heat transport processes: The Tiberias Basin example

NASA Astrophysics Data System (ADS)

Goretzki, Nora; Inbar, Nimrod; Siebert, Christian; Möller, Peter; Rosenthal, Eliyahu; Schneider, Michael; Magri, Fabien

2015-04-01

Salty and thermal springs exist along the lakeshore of the Sea of Galilee, which covers most of the Tiberias Basin (TB) in the northern Jordan- Dead Sea Transform, Israel/Jordan. As it is the only freshwater reservoir of the entire area, it is important to study the salinisation processes that pollute the lake. Simulations of thermohaline flow along a 35 km NW-SE profile show that meteoric and relic brines are flushed by the regional flow from the surrounding heights and thermally induced groundwater flow within the faults (Magri et al., 2015). Several model runs with trial and error were necessary to calibrate the hydraulic conductivity of both faults and major aquifers in order to fit temperature logs and spring salinity. It turned out that the hydraulic conductivity of the faults ranges between 30 and 140 m/yr whereas the hydraulic conductivity of the Upper Cenomanian aquifer is as high as 200 m/yr. However, large-scale transport processes are also dependent on other physical parameters such as thermal conductivity, porosity and fluid thermal expansion coefficient, which are hardly known. Here, inverse problems (IP) are solved along the NW-SE profile to better constrain the physical parameters (a) hydraulic conductivity, (b) thermal conductivity and (c) thermal expansion coefficient. The PEST code (Doherty, 2010) is applied via the graphical interface FePEST in FEFLOW (Diersch, 2014). The results show that both thermal and hydraulic conductivity are consistent with the values determined with the trial and error calibrations. Besides being an automatic approach that speeds up the calibration process, the IP allows to cover a wide range of parameter values, providing additional solutions not found with the trial and error method. Our study shows that geothermal systems like TB are more comprehensively understood when inverse models are applied to constrain coupled fluid flow processes over large spatial scales. References Diersch, H.-J.G., 2014. FEFLOW Finite Element Modeling of Flow, Mass and Heat Transport in Porous and Fractured Media. Springer- Verlag Berlin Heidelberg ,996p. Doherty J., 2010, PEST: Model-Independent Parameter Estimation. user manual 5th Edition. Watermark, Brisbane, Australia Magri, F., Inbar, N., Siebert C., Rosenthal, E., Guttman, J., Möller, P., 2015. Transient simulations of large-scale hydrogeological processes causing temperature and salinity anomalies in the Tiberias Basin. Journal of Hydrology, 520(0), 342-355.

The hippocampal system as the cortical resource manager: a model connecting psychology, anatomy and physiology.

PubMed

Coward, L Andrew

2010-01-01

A model is described in which the hippocampal system functions as resource manager for the neocortex. This model is developed from an architectural concept for the brain as a whole within which the receptive fields of neocortical columns can gradually expand but with some limited exceptions tend not to contract. The definition process for receptive fields is constrained so that they overlap as little as possible, and change as little as possible, but at least a minimum number of columns detect their fields within every sensory input state. Below this minimum, the receptive fields of some columns are expanded slightly until the minimum level is reached. The columns in which this expansion occurs are selected by a competitive process in the hippocampal system that identifies those in which only a relatively small expansion is required, and sends signals to those columns that trigger the expansion. These expansions in receptive fields are the information record that forms the declarative memory of the input state. Episodic memory activates a set of columns in which receptive fields expanded simultaneously at some point in the past, and the hippocampal system is therefore the appropriate source for information guiding access to such memories. Semantic memory associates columns that are often active (with or without expansions in receptive fields) simultaneously. Initially, the hippocampus can guide access to such memories on the basis of initial information recording, but to avoid corruption of the information needed for ongoing resource management, access control shifts to other parts of the neocortex. The roles of the mammillary bodies, amygdala and anterior thalamic nucleus can be understood as modulating information recording in accordance with various behavioral priorities. During sleep, provisional physical connectivity is created that supports receptive field expansions in the subsequent wake period, but previously created memories are not affected. This model matches a wide range of neuropsychological observation better than alternative hippocampal models. The information mechanisms required by the model are consistent with known brain anatomy and neuron physiology.

How CMB and large-scale structure constrain chameleon interacting dark energy

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

Boriero, Daniel; Das, Subinoy; Wong, Yvonne Y.Y., E-mail: boriero@physik.uni-bielefeld.de, E-mail: subinoy@iiap.res.in, E-mail: yvonne.y.wong@unsw.edu.au

2015-07-01

We explore a chameleon type of interacting dark matter-dark energy scenario in which a scalar field adiabatically traces the minimum of an effective potential sourced by the dark matter density. We discuss extensively the effect of this coupling on cosmological observables, especially the parameter degeneracies expected to arise between the model parameters and other cosmological parameters, and then test the model against observations of the cosmic microwave background (CMB) anisotropies and other cosmological probes. We find that the chameleon parameters α and β, which determine respectively the slope of the scalar field potential and the dark matter-dark energy coupling strength,more » can be constrained to α < 0.17 and β < 0.19 using CMB data and measurements of baryon acoustic oscillations. The latter parameter in particular is constrained only by the late Integrated Sachs-Wolfe effect. Adding measurements of the local Hubble expansion rate H{sub 0} tightens the bound on α by a factor of two, although this apparent improvement is arguably an artefact of the tension between the local measurement and the H{sub 0} value inferred from Planck data in the minimal ΛCDM model. The same argument also precludes chameleon models from mimicking a dark radiation component, despite a passing similarity between the two scenarios in that they both delay the epoch of matter-radiation equality. Based on the derived parameter constraints, we discuss possible signatures of the model for ongoing and future large-scale structure surveys.« less

Functional morphology of the feeding apparatus, feeding constraints, and suction performance in the nurse shark Ginglymostoma cirratum.

PubMed

Motta, Philip J; Hueter, Robert E; Tricas, Timothy C; Summers, Adam P; Huber, Daniel R; Lowry, Dayv; Mara, Kyle R; Matott, Michael P; Whitenack, Lisa B; Wintzer, Alpa P

2008-09-01

The nurse shark, Ginglymostoma cirratum, is an obligate suction feeder that preys on benthic invertebrates and fish. Its cranial morphology exhibits a suite of structural and functional modifications that facilitate this mode of prey capture. During suction-feeding, subambient pressure is generated by the ventral expansion of the hyoid apparatus and the floor of its buccopharyngeal cavity. As in suction-feeding bony fishes, the nurse shark exhibits expansive, compressive, and recovery kinematic phases that produce posterior-directed water flow through the buccopharyngeal cavity. However, there is generally neither a preparatory phase nor cranial elevation. Suction is generated by the rapid depression of the buccopharyngeal floor by the coracoarcualis, coracohyoideus, and coracobranchiales muscles. Because the hyoid arch of G. cirratum is loosely connected to the mandible, contraction of the rectus cervicis muscle group can greatly depress the floor of the buccopharyngeal cavity below the depressed mandible, resulting in large volumetric expansion. Suction pressures in the nurse shark vary greatly, but include the greatest subambient pressures reported for an aquatic-feeding vertebrate. Maximum suction pressure does not appear to be related to shark size, but is correlated with the rate of buccopharyngeal expansion. As in suction-feeding bony fishes, suction in the nurse shark is only effective within approximately 3 cm in front of the mouth. The foraging behavior of this shark is most likely constrained to ambushing or stalking due to the exponential decay of effective suction in front of the mouth. Prey capture may be facilitated by foraging within reef confines and close to the substrate, which can enhance the effective suction distance, or by foraging at night when it can more closely approach prey.

Global solar magetic field organization in the extended corona: influence on the solar wind speed and density over the cycle.

NASA Astrophysics Data System (ADS)

Réville, V.; Velli, M.; Brun, S.

2017-12-01

The dynamics of the solar wind depends intrinsically on the structure of the global solar magnetic field, which undergoes fundamental changes over the 11yr solar cycle. For instance, the wind terminal velocity is thought to be anti-correlated with the expansion factor, a measure of how the magnetic field varies with height in the solar corona, usually computed at a fixed height (≈ 2.5 Rȯ, the source surface radius which approximates the distance at which all magnetic field lines become open). However, the magnetic field expansion affects the solar wind in a more detailed way, its influence on the solar wind properties remaining significant well beyond the source surface: we demonstrate this using 3D global MHD simulations of the solar corona, constrained by surface magnetograms over half a solar cycle (1989-2001). For models to comply with the constraints provided by observed characteristics of the solar wind, namely, that the radial magnetic field intensity becomes latitude independent at some distance from the Sun (Ulysses observations beyond 1 AU), and that the terminal wind speed is anti-correlated with the mass flux, they must accurately describe expansion beyond the solar wind critical point (even up to 10Rȯ and higher in our model). We also show that near activity minimum, expansion in the higher corona beyond 2.5 Rȯ is actually the dominant process affecting the wind speed. We discuss the consequences of this result on the necessary acceleration profile of the solar wind, the location of the sonic point and of the energy deposition by Alfvén waves.

The undatables: Quantifying uncertainty in a highly expanded Late Glacial-Holocene sediment sequence recovered from the deepest Baltic Sea basin—IODP Site M0063

NASA Astrophysics Data System (ADS)

Obrochta, S. P.; Andrén, T.; Fazekas, S. Z.; Lougheed, B. C.; Snowball, I.; Yokoyama, Y.; Miyairi, Y.; Kondo, R.; Kotilainen, A. T.; Hyttinen, O.; Fehr, A.

2017-03-01

Laminated, organic-rich silts and clays with high dissolved gas content characterize sediments at IODP Site M0063 in the Landsort Deep, which at 459 m is the deepest basin in the Baltic Sea. Cores recovered from Hole M0063A experienced significant expansion as gas was released during the recovery process, resulting in high sediment loss. Therefore, during operations at subsequent holes, penetration was reduced to 2 m per 3.3 m core, permitting expansion into 1.3 m of initially empty liner. Fully filled liners were recovered from Holes B through E, indicating that the length of recovered intervals exceeded the penetrated distance by a factor of >1.5. A typical down-core logarithmic trend in gamma density profiles, with anomalously low-density values within the upper ˜1 m of each core, suggests that expansion primarily occurred in this upper interval. Thus, we suggest that a simple linear correction is inappropriate. This interpretation is supported by anisotropy of magnetic susceptibility data that indicate vertical stretching in the upper ˜1.5 m of expanded cores. Based on the mean gamma density profiles of cores from Holes M0063C and D, we obtain an expansion function that is used to adjust the depth of each core to conform to its known penetration. The variance in these profiles allows for quantification of uncertainty in the adjusted depth scale. Using a number of bulk 14C dates, we explore how the presence of multiple carbon source pathways leads to poorly constrained radiocarbon reservoir age variability that significantly affects age and sedimentation rate calculations.

Age, size, and position of H ii regions in the Galaxy. Expansion of ionized gas in turbulent molecular clouds

NASA Astrophysics Data System (ADS)

Tremblin, P.; Anderson, L. D.; Didelon, P.; Raga, A. C.; Minier, V.; Ntormousi, E.; Pettitt, A.; Pinto, C.; Samal, M. R.; Schneider, N.; Zavagno, A.

2014-08-01

Aims: This work aims to improve the current understanding of the interaction between H ii regions and turbulent molecular clouds. We propose a new method to determine the age of a large sample of OB associations by investigating the development of their associated H ii regions in the surrounding turbulent medium. Methods: Using analytical solutions, one-dimensional (1D), and three-dimensional (3D) simulations, we constrained the expansion of the ionized bubble depending on the turbulence level of the parent molecular cloud. A grid of 1D simulations was then computed in order to build isochrone curves for H ii regions in a pressure-size diagram. This grid of models allowed us to date a large sample of OB associations that we obtained from the H ii Region Discovery Survey (HRDS). Results: Analytical solutions and numerical simulations showed that the expansion of H ii regions is slowed down by the turbulence up to the point where the pressure of the ionized gas is in a quasi-equilibrium with the turbulent ram pressure. Based on this result, we built a grid of 1D models of the expansion of H ii regions in a profile based on Larson's laws. We take the 3D turbulence into account with an effective 1D temperature profile. The ages estimated by the isochrones of this grid agree well with literature values of well known regions such as Rosette, RCW 36, RCW 79, and M 16. We thus propose that this method can be used to find ages of young OB associations through the Galaxy and also in nearby extra-galactic sources.

Two-Body Orbit Expansion Due to Time-Dependent Relative Acceleration Rate of the Cosmological Scale Factor

NASA Astrophysics Data System (ADS)

Iorio, Lorenzo

2014-01-01

By phenomenologically assuming a slow temporal variation of the percent acceleration rate S̈S -1 of the cosmic scale factor S(t), it is shown that the orbit of a local binary undergoes a secular expansion. To first order in the power expansion of S̈S -1 around the present epoch t0, a non-vanishing shift per orbit (Δr) of the two-body relative distance r occurs for eccentric trajectories. A general relativistic expression, which turns out to be cubic in the Hubble parameter H0 at the present epoch, is explicitly calculated for it in the case of matter-dominated epochs with Dark Energy. For a highly eccentric Oort comet orbit with period Pb ≈ 31 Myr, the general relativistic distance shift per orbit turns out to be of the order of (Δr) ≈ 70 km. For the Large Magellanic Cloud, assumed on a bound elliptic orbit around the Milky Way, the shift per orbit is of the order of (Δr) ≈ 2-4 pc. Our result has a general validity since it holds in any cosmological model admitting the Hubble law and a slowly varying S̈S-1(t). More generally, it is valid for an arbitrary Hooke-like extra-acceleration whose "elastic" parameter κ is slowly time-dependent, irrespectively of the physical mechanism which may lead to it. The coefficient κ1 of the first-order term of the power expansion of κ(t) can be preliminarily constrained in a model-independent way down to a κ1 ≤ 2 x 10-13 year-3 level from latest Solar System's planetary observations. The radial velocities of the double lined spectroscopic binary ALPHA Cen AB yield κ1 ≤ 10-8 year-3.

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.

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.

Experimental constraints on the rheology and mechanical properties of lava erupted in the Holuhraun area during the 2014 rifting event at Bárðarbunga, Iceland

NASA Astrophysics Data System (ADS)

Lavallee, Yan; Kendrick, Jackie; Wall, Richard; von Aulock, Felix; Kennedy, Ben; Sigmundsson, Freysteinn

2015-04-01

A fissure eruption began at Holuhraun on 16 August 2014, following magma drainage from the Bárðarbunga volcanic system (Iceland). Extrusion initiated as fire fountaining along a segment of the fracture and rapidly localised to a series of small, aligned cones containing a lava lake that over spilled at both ends, feeding a large lava field. The lava composition and flow behaviour put some constraints on its rheology and mechanical properties. The lava erupted is a nearly aphyric basalt containing approximately 2-3% plagioclase with traces of olivine and pyroxene in a quenched groundmass composed of glass and 20-25% microlites. The transition from fire fountaining to lava flow leads to lava with variable vesicularities; pyroclasts expelled during fire fountaining reach up to 80% vesicles whilst the lava contain up to 45% vesicles. Textures in the lava vary from a'a to slabby pahoehoe, and flow thicknesses from several meters to few centimetres. Tension gashes, crease structures and shear zones in the upper lava carapace reveal the importance of both compressive and tensional stresses. In addition, occasional frictional marks at the base of the lava flow as well as bulldozing of sediments along the flow hint at the importance of frictional properties of the rocks during lava flow. Flow properties, textures and failure modes are strongly dependent on the material properties as well as the local conditions of stress and temperature. Here we expand our field observation with preliminary high-temperature experimental data on the rheological and mechanical properties of the erupted lava. Dilatometric measurements are used to constrain the thermal expansion coefficient of the lava important to constrain the dynamics of cooling of the flow. Micropenetration is further employed to determine the viscosity of the melt at super-liquidus temperature, which is compared to the temperature-dependence of viscosity as constrained by geochemistry. Lastly, uniaxial compression and tension tests are presented to constrain the mechanical properties (strength and Young's modulus) of the rocks, forming the cooler carapace of the flow. This high-temperature experimental dataset will be integrated to field observations to constrain lava flow emplacement.

General approach to polymer chains confined by interacting boundaries

NASA Astrophysics Data System (ADS)

Freed, Karl F.; Dudowicz, Jacek; Stukalin, Evgeny B.; Douglas, Jack F.

2010-09-01

Polymer chains, confined to cavities or polymer layers with dimensions less than the chain radius of gyration, appear in many phenomena, such as gel chromatography, rubber elasticity, viscolelasticity of high molar mass polymer melts, the translocation of polymers through nanopores and nanotubes, polymer adsorption, etc. Thus, the description of how the constraints alter polymer thermodynamic properties is a recurrent theoretical problem. A realistic treatment requires the incorporation of impenetrable interacting (attractive or repulsive) boundaries, a process that introduces significant mathematical complications. The standard approach involves developing the generalized diffusion equation description of the interaction of flexible polymers with impenetrable confining surfaces into a discrete eigenfunction expansion, where the solutions are normally truncated at the first mode (the "ground state dominance" approximation). This approximation is mathematically well justified under conditions of strong confinement, i.e., a confinement length scale much smaller than the chain radius of gyration, but becomes unreliable when the polymers are confined to dimensions comparable to their typically nanoscale size. We extend a general approach to describe polymers under conditions of weak to moderate confinement and apply this semianalytic method specifically to determine the thermodynamics and static structure factor for a flexible polymer confined between impenetrable interacting parallel plate boundaries. The method is first illustrated by analyzing chain partitioning between a pore and a large external reservoir, a model system with application to chromatography. Improved agreement is found for the partition coefficients of a polymer chain in the pore geometry. An expression is derived for the structure factor S(k ) in a slit geometry to assist in more accurately estimating chain dimensions from scattering measurements for thin polymer films.

Squirmers with swirl: a model for Volvox swimming.

PubMed

Pedley, T J; Brumley, D R; Goldstein, R E

2016-07-10

Colonies of the green alga Volvox are spheres that swim through the beating of pairs of flagella on their surface somatic cells. The somatic cells themselves are mounted rigidly in a polymeric extracellular matrix, fixing the orientation of the flagella so that they beat approximately in a meridional plane, with axis of symmetry in the swimming direction, but with a roughly [Formula: see text] azimuthal offset which results in the eponymous rotation of the colonies about a body-fixed axis. Experiments on colonies of Volvox carteri held stationary on a micropipette show that the beating pattern takes the form of a symplectic metachronal wave (Brumley  et al.   Phys. Rev. Lett. , vol. 109, 2012, 268102). Here we extend the Lighthill/Blake axisymmetric, Stokes-flow model of a free-swimming spherical squirmer (Lighthill  Commun. Pure Appl. Maths , vol. 5, 1952, pp. 109-118; Blake  J. Fluid Mech. , vol. 46, 1971 b , pp. 199-208) to include azimuthal swirl. The measured kinematics of the metachronal wave for 60 different colonies are used to calculate the coefficients in the eigenfunction expansions and hence predict the mean swimming speeds and rotation rates, proportional to the square of the beating amplitude, as functions of colony radius. As a test of the squirmer model, the results are compared with measurements (Drescher  et al.   Phys. Rev. Lett. , vol. 102, 2009, 168101) of the mean swimming speeds and angular velocities of a different set of 220 colonies, also given as functions of colony radius. The predicted variation with radius is qualitatively correct, but the model underestimates both the mean swimming speed and the mean angular velocity unless the amplitude of the flagellar beat is taken to be larger than previously thought. The reasons for this discrepancy are discussed.

Statistical dynamo theory: Mode excitation.

PubMed

Hoyng, P

2009-04-01

We compute statistical properties of the lowest-order multipole coefficients of the magnetic field generated by a dynamo of arbitrary shape. To this end we expand the field in a complete biorthogonal set of base functions, viz. B= summation operator_{k}a;{k}(t)b;{k}(r) . The properties of these biorthogonal function sets are treated in detail. We consider a linear problem and the statistical properties of the fluid flow are supposed to be given. The turbulent convection may have an arbitrary distribution of spatial scales. The time evolution of the expansion coefficients a;{k} is governed by a stochastic differential equation from which we infer their averages a;{k} , autocorrelation functions a;{k}(t)a;{k *}(t+tau) , and an equation for the cross correlations a;{k}a;{l *} . The eigenfunctions of the dynamo equation (with eigenvalues lambda_{k} ) turn out to be a preferred set in terms of which our results assume their simplest form. The magnetic field of the dynamo is shown to consist of transiently excited eigenmodes whose frequency and coherence time is given by Ilambda_{k} and -1/Rlambda_{k} , respectively. The relative rms excitation level of the eigenmodes, and hence the distribution of magnetic energy over spatial scales, is determined by linear theory. An expression is derived for |a;{k}|;{2}/|a;{0}|;{2} in case the fundamental mode b;{0} has a dominant amplitude, and we outline how this expression may be evaluated. It is estimated that |a;{k}|;{2}/|a;{0}|;{2} approximately 1/N , where N is the number of convective cells in the dynamo. We show that the old problem of a short correlation time (or first-order smoothing approximation) has been partially eliminated. Finally we prove that for a simple statistically steady dynamo with finite resistivity all eigenvalues obey Rlambda_{k}<0 .

Landau parameters for energy density functionals generated by local finite-range pseudopotentials

NASA Astrophysics Data System (ADS)

Idini, A.; Bennaceur, K.; Dobaczewski, J.

2017-06-01

In Landau theory of Fermi liquids, the particle-hole interaction near the Fermi energy in different spin-isospin channels is probed in terms of an expansion over the Legendre polynomials. This provides a useful and efficient way to constrain properties of nuclear energy density functionals in symmetric nuclear matter and finite nuclei. In this study, we present general expressions for Landau parameters corresponding to a two-body central local regularized pseudopotential. We also show results obtained for two recently adjusted NLO and N2LO parametrizations. Such pseudopotentials will be used to determine mean-field and beyond-mean-field properties of paired nuclei across the entire nuclear chart.

Modal identities for elastic bodies, with application to vehicle dynamics and control

NASA Technical Reports Server (NTRS)

Hughes, P. C.

1980-01-01

It is a standard procedure to analyze a flexible vehicle in terms of its vibration frequencies and mode shapes. However, the entire mode shape is not needed per se, but two integrals of the mode shape, pi and hi, which correspond to the momentum and angular momentum in Mode i. Together with the natural frequencies omega-i, these modal parameters satisfy several important identities, 25 of which are derived in this paper. Expansions in terms of both constrained and unconstrained modes are considered. A simple illustrative example is included. The paper concludes with some remarks on the theoretical and practical utility of these results, and several potential extensions to the theory are suggested.

2015 RAD-AID Conference on International Radiology for Developing Countries: The Evolving Global Radiology Landscape.

PubMed

Kesselman, Andrew; Soroosh, Garshasb; Mollura, Daniel J

2016-09-01

Radiology in low- and middle-income (developing) countries continues to make progress. Research and international outreach projects presented at the 2015 annual RAD-AID conference emphasize important global themes, including (1) recent slowing of emerging market growth that threatens to constrain the advance of radiology, (2) increasing global noncommunicable diseases (such as cancer and cardiovascular disease) needing radiology for detection and management, (3) strategic prioritization for pediatric radiology in global public health initiatives, (4) continuous expansion of global health curricula at radiology residencies and the RAD-AID Chapter Network's participating institutions, and (5) technologic innovation for recently accelerated implementation of PACS in low-resource countries. Published by Elsevier Inc.

Constraining the mass and radius of neutron star by future observations

NASA Astrophysics Data System (ADS)

Kwak, Kyujin; Lee, Chang-Hwan; Kim, Myungkuk; Kim, Young-Min

2018-04-01

The mass and radius of neutron star (NS) in the low mass X-ray binary (LMXB) can be measured simultaneously from the evolving spectra of the photospheric radius expansion (PRE) X-ray bursts (XRBs). Precise measurements require the distance to the target, information on the radiating surface, and the composition of accreted material. Future observations with large ground-based telescopes such as Giant Magellan Telescope (GMT) and Thirty Meter Telescope (TMT) may reduce the uncertainties in the estimation of the mass and radius of NS because they could provide information on the composition of accreted material by identifying the companion stars in LMXBs. We investigate these possibilities and present our results for selected targets.

USING ForeCAT DEFLECTIONS AND ROTATIONS TO CONSTRAIN THE EARLY EVOLUTION OF CMEs

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

Kay, C.; Opher, M.; Colaninno, R. C.

2016-08-10

To accurately predict the space weather effects of the impacts of coronal mass ejection (CME) at Earth one must know if and when a CME will impact Earth and the CME parameters upon impact. In 2015 Kay et al. presented Forecasting a CME’s Altered Trajectory (ForeCAT), a model for CME deflections based on the magnetic forces from the background solar magnetic field. Knowing the deflection and rotation of a CME enables prediction of Earth impacts and the orientation of the CME upon impact. We first reconstruct the positions of the 2010 April 8 and the 2012 July 12 CMEs frommore » the observations. The first of these CMEs exhibits significant deflection and rotation (34° deflection and 58° rotation), while the second shows almost no deflection or rotation (<3° each). Using ForeCAT, we explore a range of initial parameters, such as the CME’s location and size, and find parameters that can successfully reproduce the behavior for each CME. Additionally, since the deflection depends strongly on the behavior of a CME in the low corona, we are able to constrain the expansion and propagation of these CMEs in the low corona.« less

A constrained multinomial Probit route choice model in the metro network: Formulation, estimation and application

PubMed Central

Zhang, Yongsheng; Wei, Heng; Zheng, Kangning

2017-01-01

Considering that metro network expansion brings us with more alternative routes, it is attractive to integrate the impacts of routes set and the interdependency among alternative routes on route choice probability into route choice modeling. Therefore, the formulation, estimation and application of a constrained multinomial probit (CMNP) route choice model in the metro network are carried out in this paper. The utility function is formulated as three components: the compensatory component is a function of influencing factors; the non-compensatory component measures the impacts of routes set on utility; following a multivariate normal distribution, the covariance of error component is structured into three parts, representing the correlation among routes, the transfer variance of route, and the unobserved variance respectively. Considering multidimensional integrals of the multivariate normal probability density function, the CMNP model is rewritten as Hierarchical Bayes formula and M-H sampling algorithm based Monte Carlo Markov Chain approach is constructed to estimate all parameters. Based on Guangzhou Metro data, reliable estimation results are gained. Furthermore, the proposed CMNP model also shows a good forecasting performance for the route choice probabilities calculation and a good application performance for transfer flow volume prediction. PMID:28591188

Scientific Decision Making, Policy Decisions, and the Obesity Pandemic

PubMed Central

Hebert, James R.; Allison, David B.; Archer, Edward; Lavie, Carl J.; Blair, Steven N.

2013-01-01

Rising and epidemic rates of obesity in many parts of the world are leading to increased suffering and economic stress from diverting health care resources to treating a variety of serious, but preventable, chronic diseases etiologically linked to obesity, particularly type 2 diabetes mellitus and cardiovascular diseases. Despite decades of research into the causes of the obesity pandemic, we seem to be no nearer to a solution now than when the rise in body weights was first chronicled decades ago. The case is made that impediments to a clear understanding of the nature of the problem occur at many levels. These obstacles begin with defining obesity and include lax application of scientific standards of review, tenuous assumption making, flawed measurement and other methods, constrained discourse limiting examination of alternative explanations of cause, and policies that determine funding priorities. These issues constrain creativity and stifle expansive thinking that could otherwise advance the field in preventing and treating obesity and its complications. Suggestions are made to create a climate of open exchange of ideas and redirection of policies that can remove the barriers that prevent us from making material progress in solving a pressing major public health problem of the early 21st century. PMID:23726399

Constraining qqtt operators from four-top production: a case for enhanced EFT sensitivity

NASA Astrophysics Data System (ADS)

Zhang, Cen

2018-02-01

Recently, experimental collaborations have reported O(10) upper limits on the signal strength of four-top production at the LHC. Surprisingly, we find that the constraining power of four-top production on the qqtt type of operators is already competitive with the measurements of top-pair production, even though the precision level of the latter is more than two orders of magnitude better. This is explained by the enhanced sensitivity of the four-top cross section to qqtt operators, due to multiple insertion of operators in the squared amplitude, and to the large threshold energy of four-top production. We point out that even though the dominant contribution beyond the standard model comes from the O({C}4/{{{Λ }}}8) terms, the effective field theory expansion remains valid for a wide range of underlying theories. Considering the possible improvements of this measurement with higher integrated luminosity, we believe that this process will become even more crucial for probing and testing the standard model deviations in the top-quark sector, and will eventually provide valuable information about the top-quark properties, leading to significant improvements in precision top physics. Supported by the 100-talent project of Chinese Academy of Sciences

Instability of liquid crystal elastomers

NASA Astrophysics Data System (ADS)

An, Ning; Li, Meie; Zhou, Jinxiong

2016-01-01

Nematic liquid crystal elastomers (LCEs) contract in the director direction but expand in other directions, perpendicular to the director, when heated. If the expansion of an LCE is constrained, compressive stress builds up in the LCE, and it wrinkles or buckles to release the stored elastic energy. Although the instability of soft materials is ubiquitous, the mechanism and programmable modulation of LCE instability has not yet been fully explored. We describe a finite element method (FEM) scheme to model the inhomogeneous deformation and instability of LCEs. A constrained LCE beam working as a valve for microfluidic flow, and a piece of LCE laminated with a nanoscale poly(styrene) (PS) film are analyzed in detail. The former uses the buckling of the LCE beam to occlude the microfluidic channel, while the latter utilizes wrinkling or buckling to measure the mechanical properties of hard film or to realize self-folding. Through rigorous instability analysis, we predict the critical conditions for the onset of instability, the wavelength and amplitude evolution of instability, and the instability patterns. The FEM results are found to correlate well with analytical results and reported experiments. These efforts shed light on the understanding and exploitation of the instabilities of LCEs.

Niche Limits of Symbiotic Gut Microbiota Constrain the Salinity Tolerance of Brine Shrimp.

PubMed

Nougué, Odrade; Gallet, Romain; Chevin, Luis-Miguel; Lenormand, Thomas

2015-09-01

Symbiosis generally causes an expansion of the niche of each partner along the axis for which a service is mutually provided. However, for other axes, the niche can be restricted to the intersection of each partner's niche and can thus be constrained rather than expanded by mutualism. We explore this phenomenon using Artemia as a model system. This crustacean is able to survive at very high salinities but not at low salinities, although its hemolymph's salinity is close to freshwater. We hypothesized that this low-salinity paradox results from poor performance of its associated microbiota at low salinity. We showed that, in sterile conditions, Artemia had low survival at all salinities when algae were the only source of carbon. In contrast, survival was high at all salinities when fed with yeast. We also demonstrated that bacteria isolated from Artemia's gut reached higher densities at high salinities than at low salinities, including when grown on algae. Taken together, our results show that Artemia can survive at low salinities, but their gut microbiota, which are required for algae digestion, have reduced fitness. Widespread facultative symbiosis may thus be an important determinant of niche limits along axes not specific to the mutualistic interaction.

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.

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.

Water-Constrained Electric Sector Capacity Expansion Modeling Under Climate Change Scenarios

NASA Astrophysics Data System (ADS)

Cohen, S. M.; Macknick, J.; Miara, A.; Vorosmarty, C. J.; Averyt, K.; Meldrum, J.; Corsi, F.; Prousevitch, A.; Rangwala, I.

2015-12-01

Over 80% of U.S. electricity generation uses a thermoelectric process, which requires significant quantities of water for power plant cooling. This water requirement exposes the electric sector to vulnerabilities related to shifts in water availability driven by climate change as well as reductions in power plant efficiencies. Electricity demand is also sensitive to climate change, which in most of the United States leads to warming temperatures that increase total cooling-degree days. The resulting demand increase is typically greater for peak demand periods. This work examines the sensitivity of the development and operations of the U.S. electric sector to the impacts of climate change using an electric sector capacity expansion model that endogenously represents seasonal and local water resource availability as well as climate impacts on water availability, electricity demand, and electricity system performance. Capacity expansion portfolios and water resource implications from 2010 to 2050 are shown at high spatial resolution under a series of climate scenarios. Results demonstrate the importance of water availability for future electric sector capacity planning and operations, especially under more extreme hotter and drier climate scenarios. In addition, region-specific changes in electricity demand and water resources require region-specific responses that depend on local renewable resource availability and electricity market conditions. Climate change and the associated impacts on water availability and temperature can affect the types of power plants that are built, their location, and their impact on regional water resources.

Validity of the "Laplace Swindle" in Calculation of Giant-Planet Gravity Fields

NASA Astrophysics Data System (ADS)

Hubbard, William B.

2014-11-01

Jupiter and Saturn have large rotation-induced distortions, providing an opportunity to constrain interior structure via precise measurement of external gravity. Anticipated high-precision gravity measurements close to the surfaces of Jupiter (Juno spacecraft) and Saturn (Cassini spacecraft), possibly detecting zonal harmonics to J10 and beyond, will place unprecedented requirements on gravitational modeling via the theory of figures (TOF). It is not widely appreciated that the traditional TOF employs a formally nonconvergent expansion attributed to Laplace. This suspect expansion is intimately related to the standard zonal harmonic (J-coefficient) expansion of the external gravity potential. It can be shown (Hubbard, Schubert, Kong, and Zhang: Icarus, in press) that both Jupiter and Saturn are in the domain where Laplace's "swindle" works exactly, or at least as well as necessary. More highly-distorted objects such as rapidly spinning asteroids may not be in this domain, however. I present a numerical test for the validity and precision of TOF via polar "audit points". I extend the audit-point test to objects rotating differentially on cylinders, obtaining zonal harmonics to J20 and beyond. Models with only low-order differential rotation do not exhibit dramatic effects in the shape of the zonal harmonic spectrum. However, a model with Jupiter-like zonal winds exhibits a break in the zonal harmonic spectrum above about J10, and generally follows the more shallow Kaula power rule at higher orders. This confirms an earlier result obtained by a different method (Hubbard: Icarus 137, 357-359, 1999).

Resistance to radial expansion limits muscle strain and work

PubMed Central

Deslauriers, A. R.; Holt, N. C.; Eaton, C. E.

2018-01-01

The collagenous extracellular matrix (ECM) of skeletal muscle functions to transmit force, protect sensitive structures, and generate passive tension to resist stretch. The mechanical properties of the ECM change with age, atrophy, and neuromuscular pathologies, resulting in an increase in the relative amount of collagen and an increase in stiffness. Although numerous studies have focused on the effect of muscle fibrosis on passive muscle stiffness, few have examined how these structural changes may compromise contractile performance. Here we combine a mathematical model and experimental manipulations to examine how changes in the mechanical properties of the ECM constrain the ability of muscle fibers and fascicles to radially expand and how such a constraint may limit active muscle shortening. We model the mechanical interaction between a contracting muscle and the ECM using a constant volume, pressurized, fiber-wound cylinder. Our model shows that as the proportion of a muscle cross section made up of ECM increases, the muscle’s ability to expand radially is compromised, which in turn restricts muscle shortening. In our experiments, we use a physical constraint placed around the muscle to restrict radial expansion during a contraction. Our experimental results are consistent with model predictions and show that muscles restricted from radial expansion undergo less shortening and generate less mechanical work under identical loads and stimulation conditions. This work highlights the intimate mechanical interaction between contractile and connective tissue structures within skeletal muscle and shows how a deviation from a healthy, well-tuned relationship can compromise performance. PMID:28432448

Constraining the Dynamical Formation and the Size of the Primordial Building Blocks for Comet 67P/Churyumov-Gerasimenko Using the CONSERT Observations

NASA Astrophysics Data System (ADS)

Heggy, E.; Palmer, E. M.; Kofman, W. W.; Herique, A.; El Maarry, M. R.

2017-12-01

Rosetta's two-year orbital mission at comet 67P/Churyumov-Gerasimenko significantly improved our understanding of the Radar properties of cometary bodies and how they can be used to constrain the ambiguities associated to the dynamical formation of 67P by setting an upper limit on the size of the comet's initial building blocks using the CONSERT, VIRTIS and OSIRIS observations. We present here in an updated post-rendezvous three-dimensional dielectric, textural and structural model of the comet's surface and subsurface at VHF-, X- and S-band radar frequencies. We assess the radar properties of potential structural heterogeneities observed in the upper meters of the shallow subsurface as well as deeper structures across the comet head. We use CONSERT's bistatic radar sounding measurements of the nucleus `head' interior to constrain the dielectric properties and structure of the interior; VIRTIS' multi-spectral observations to constrain the surface mineralogy and the distribution of water-ice on the surface and the implications of the above on the spatial variability of the surface and shallow subsurface dielectric properties. Surface and shallow subsurface structural elements are derived from the OSIRIS' images of exposed outcrops and pit walls. Our dielectric analysis showing the lack of sufficient dielectric contrast correlated with the lack of signal broadening in the 90-MHz radar echoes observed by CONSERT suggests that the the apparent meter-sized inhomogeneities in the walls of deep pits originally interpreted as cometesimals forming the comet's primordial blocks, could be localized evolutionary features of high centered polygons caused by seasonal modifications to the near-subsurface ice formed through thermal expansion and contraction and may not be continuous through the head. Considering the three-dimensional dielectric variability of 67P as derived from CONSERT, VIRTIS, Arecibo observations and laboratory measurement we set an upper limit on the size of the comet's initial building blocks.

Tying the spectral ends of the M9.0 Tohoku-Oki earthquake sequence: High-frequency radiators and early quasi-static afterslip

NASA Astrophysics Data System (ADS)

Inbal, A.; Ampuero, J. P.; Avouac, J.; Lengliné, O.; Helmberger, D. V.

2012-12-01

The March 11, 2011 M9.0 Tohoku-Oki earthquake was recorded by dense seismological and geodetical networks deployed in Japan, as well as by a vast number of seismic stations worldwide. These observations allow us to study the properties of the subduction interface with unprecedented accuracy and resolution. Here we examine the spectral tails of the co- and post-seismic stages using local geodetic and seismological recordings. First, we study the details of high-frequency (HF) energy radiation during the rupture by using strong-motion recordings. Second, we jointly invert 1Hz GPS, ocean-bottom GPS and aftershock data for the spatio-temporal distribution of early afterslip. In order to constrain the spatial distribution of HF radiators we model waveform envelopes recorded by Kik-net borehole accelerometers located in northeastern Japan. We compute theoretical envelopes for waves traveling in a heterogeneous scattering medium, and invert for the location and amplitude of energy radiators for frequencies ranging from 1 to 16 Hz. Because the inversion is extremely sensitive to the response of individual sites, we adopt an empirical approach and iteratively separate the source and site terms from the stacked spectra of numerous events recorded by the network. The output response functions for each site are used to stabilize the inversion. Preliminary results are consistent with far-field observations and suggest that the HF energy emitted during the M9.0 event originated at the down-dip limit of the rupture zone. We apply waveform cross-correlation to identify repeating events within the aftershock sequence, and locate them by match-filtering their waveforms with known templates. Many of these events occur on seismic asperities loaded by the surrounding creep. We jointly invert the slip histories on these fault patches and the available GPS data for the spatio-temporal distribution of afterslip during the first few hours following the mainshock. We use the Principal Component Analysis Inversion Method to determine the time history of slip on the megathrust during seismic slip and aseismic afterslip. The eigenfunctions are constrained in an iterative process that incorporates the slip histories of seismic asperities. This approach allows documenting the seismic and aseismic phases in a self-consistent manner. The GPS-only inversion places most of the early afterslip east of the hypocenter up to the trench, an area that seemed to have undergone dynamic overshoot.

Assessment of the interactions between economic growth and industrial wastewater discharges using co-integration analysis: a case study for China's Hunan Province.

PubMed

Xiao, Qiang; Gao, Yang; Hu, Dan; Tan, Hong; Wang, Tianxiang

2011-07-01

We have investigated the interactions between economic growth and industrial wastewater discharge from 1978 to 2007 in China's Hunan Province using co-integration theory and an error-correction model. Two main economic growth indicators and four representative industrial wastewater pollutants were selected to demonstrate the interaction mechanism. We found a long-term equilibrium relationship between economic growth and the discharge of industrial pollutants in wastewater between 1978 and 2007 in Hunan Province. The error-correction mechanism prevented the variable expansion for long-term relationship at quantity and scale, and the size of the error-correction parameters reflected short-term adjustments that deviate from the long-term equilibrium. When economic growth changes within a short term, the discharge of pollutants will constrain growth because the values of the parameters in the short-term equation are smaller than those in the long-term co-integrated regression equation, indicating that a remarkable long-term influence of economic growth on the discharge of industrial wastewater pollutants and that increasing pollutant discharge constrained economic growth. Economic growth is the main driving factor that affects the discharge of industrial wastewater pollutants in Hunan Province. On the other hand, the discharge constrains economic growth by producing external pressure on growth, although this feedback mechanism has a lag effect. Economic growth plays an important role in explaining the predicted decomposition of the variance in the discharge of industrial wastewater pollutants, but this discharge contributes less to predictions of the variations in economic growth.

Mapping the rheology of the Central Chile subduction zone with aftershocks

NASA Astrophysics Data System (ADS)

Frank, William B.; Poli, Piero; Perfettini, Hugo

2017-06-01

The postseismic deformation following a large (Mw >7) earthquake is expressed both seismically and aseismically. Recent studies have appealed to a model that suggests that the aseismic slip on the plate interface following the mainshock can be the driving factor in aftershock sequences, reproducing both the geodetic (afterslip) and seismic (aftershocks) observables of postseismic deformation. Exploiting this model, we demonstrate how a dense catalog of aftershocks following the 2015 Mw 8.3 Illapel earthquake in Central Chile can constrain the frictional and rheological properties of the creeping regions of the subduction interface. We first expand the aftershock catalog via a 19 month continuous matched-filter search and highlight the log-time expansion of seismicity following the mainshock, suggestive of afterslip as the main driver of aftershock activity. We then show how the time history of aftershocks can constrain the temporal evolution of afterslip. Finally, we use our dense aftershock catalog to estimate the rate and state rheological parameter (a - b)σ as a function of depth and demonstrate that this low value is compatible either with a nearly velocity-neutral friction (a≈b) in the regions of the megathrust that host afterslip, or an elevated pore fluid pressure (low effective normal stress σ) along the plate interface. Our results present the first snapshot of rheology in depth together with the evolution of the tectonic stressing rate along a plate boundary. The framework described here can be generalized to any tectonic context and provides a novel way to constrain the frictional properties and loading conditions of active faults.

Assessment of the Interactions between Economic Growth and Industrial Wastewater Discharges Using Co-integration Analysis: A Case Study for China’s Hunan Province

PubMed Central

Xiao, Qiang; Gao, Yang; Hu, Dan; Tan, Hong; Wang, Tianxiang

2011-01-01

We have investigated the interactions between economic growth and industrial wastewater discharge from 1978 to 2007 in China’s Hunan Province using co-integration theory and an error-correction model. Two main economic growth indicators and four representative industrial wastewater pollutants were selected to demonstrate the interaction mechanism. We found a long-term equilibrium relationship between economic growth and the discharge of industrial pollutants in wastewater between 1978 and 2007 in Hunan Province. The error-correction mechanism prevented the variable expansion for long-term relationship at quantity and scale, and the size of the error-correction parameters reflected short-term adjustments that deviate from the long-term equilibrium. When economic growth changes within a short term, the discharge of pollutants will constrain growth because the values of the parameters in the short-term equation are smaller than those in the long-term co-integrated regression equation, indicating that a remarkable long-term influence of economic growth on the discharge of industrial wastewater pollutants and that increasing pollutant discharge constrained economic growth. Economic growth is the main driving factor that affects the discharge of industrial wastewater pollutants in Hunan Province. On the other hand, the discharge constrains economic growth by producing external pressure on growth, although this feedback mechanism has a lag effect. Economic growth plays an important role in explaining the predicted decomposition of the variance in the discharge of industrial wastewater pollutants, but this discharge contributes less to predictions of the variations in economic growth. PMID:21845167

Reconstructing spatial and temporal patterns of paleoglaciation across Central Asia

NASA Astrophysics Data System (ADS)

Stroeven, Arjen P.

2014-05-01

Understanding the behaviour of mountain glaciers and ice caps, the evolution of mountain landscapes, and testing global climate models all require well-constrained information on past spatial and temporal patterns of glacier change. Particularly important are transitional regions that have high spatial and temporal variation in glacier activity and that can provide a sensitive record of past climate change. Central Asia is an extreme continental location with glaciers that have responded sensitively to variations in major regional climate systems. As an international team, we are reconstructing glacial histories of several areas of the Tibetan Plateau as well as along the Tian Shan, Altai and Kunlun Mountains. Building on previous work, we are using remote sensing-based geomorphological mapping augmented with field observations to map out glacial landforms and the maximum distributions of erratics. We then use cosmogenic nuclide Be-10 and Al-26, optically stimulated luminescence, and electron spin resonance dating of moraines and other landforms to compare dating techniques and to constrain the ages of defined extents of paleo-glaciers and ice caps. Comparing consistently dated glacial histories across central Asia provides an opportunity to examine shifts in the dominance patterns of climate systems over time in the region. Results to date show significant variations in the timing and extent of glaciation, including areas in the southeast Tibetan Plateau and Tian Shan with extensive valley and small polythermal ice cap glaciation during the global last glacial maximum in contrast to areas in central and northeast Tibetan Plateau that had very limited valley glacier expansion then. Initial numerical modelling attempting to simulate mapped and dated paleoglacial extents indicates that relatively limited cooling is sufficient to produce observed past expansions of glaciers across the Tibetan Plateau, and predicts complex basal thermal regimes in some locations that match patterns of past glacial erosion inferred from landform patterns and ages. Future modelling will examine glacier behaviour along major mountain ranges across central Asia.

Is There a Need for a More Expansive Use of Ethics and Values in Reflecting on the Use of Animals in Scientific Research?

PubMed Central

Fisher, Mark W.

2014-01-01

Simple Summary Debates about animal research are often polarized. On one side, increased knowledge, medical treatments or enhanced animal production are seen to justify harms. On the other, animals have rights constraining their use. Both sides fail to provide adequate support for this contentious use of animals. Reflecting the richness of ethics, it is suggested that empathy and respect for the animal, and greater acknowledgement of the value of experiences and care could also be considered. Along with a more informed understanding of the benefits of research and of the aims of animal rights, a more sophisticated ethic may reflect the common ground between the poles of the debate. Abstract Although reflecting a long tradition of moral reflection that the use of animals is acceptable as long as it is humane, the tension between causing harm to animals in research and the benefits to humans can nevertheless be troubling. Utilitarian arguments that appeal to the value of those practices in sustaining and enhancing human lives, and rights-based arguments which seek to constrain them, can be inadequate. Reflecting a more engaging, inclusive and sophisticated understanding of human activity, justification for animal use could be expanded to reflect the fullness and richness of ethical thinking. This might see more explicit inclusion of perspectives borne of virtues, caring, experiences, and respect for the essence of the animal, and different ways of understanding and knowing animals, values drawn from the middle ground of commonly acceptable human-animal relationships. Such values, already clearly evident in research, could be more widely integrated into arguments justifying animal use. A more expansive approach would not only reflect reality and acknowledge that costs and benefits are shared more widely, but it might result in more equitable, effective and humane science. It might also serve to reduce some of the tension long evident in the relationship between humans and animals.

Applying time series Landsat data for vegetation change analysis in the Florida Everglades Water Conservation Area 2A during 1996-2016

NASA Astrophysics Data System (ADS)

Zhang, Caiyun; Smith, Molly; Lv, Jie; Fang, Chaoyang

2017-05-01

Mapping plant communities and documenting their changes is critical to the on-going Florida Everglades restoration project. In this study, a framework was designed to map dominant vegetation communities and inventory their changes in the Florida Everglades Water Conservation Area 2A (WCA-2A) using time series Landsat images spanning 1996-2016. The object-based change analysis technique was combined in the framework. A hybrid pixel/object-based change detection approach was developed to effectively collect training samples for historical images with sparse reference data. An object-based quantification approach was also developed to assess the expansion/reduction of a specific class such as cattail (an invasive species in the Everglades) from the object-based classifications of two dates of imagery. The study confirmed the results in the literature that cattail was largely expanded during 1996-2007. It also revealed that cattail expansion was constrained after 2007. Application of time series Landsat data is valuable to document vegetation changes for the WCA-2A impoundment. The digital techniques developed will benefit global wetland mapping and change analysis in general, and the Florida Everglades WCA-2A in particular.

The Cardassian expansion revisited: constraints from updated Hubble parameter measurements and type Ia supernova data

NASA Astrophysics Data System (ADS)

Magaña, Juan; Amante, Mario H.; Garcia-Aspeitia, Miguel A.; Motta, V.

2018-05-01

Motivated by an updated compilation of observational Hubble data (OHD) that consist of 51 points in the redshift range of 0.07 < z < 2.36, we study an interesting model known as Cardassian that drives the late cosmic acceleration without a dark energy component. Our compilation contains 31 data points measured with the differential age method by Jimenez & Loeb (2002), and 20 data points obtained from clustering of galaxies. We focus on two modified Friedmann equations: the original Cardassian (OC) expansion and the modified polytropic Cardassian (MPC). The dimensionless Hubble, E(z), and the deceleration parameter, q(z), are revisited in order to constrain the OC and MPC free parameters, first with the OHD and then contrasted with recent observations of type Ia supernova (SN Ia) using the compressed and full joint-light-analysis (JLA) samples (Betoule et al.). We also perform a joint analysis using the combination OHD plus compressed JLA. Our results show that the OC and MPC models are in agreement with the standard cosmology and naturally introduce a cosmological-constant-like extra term in the canonical Friedmann equation with the capability of accelerating the Universe without dark energy.

Resurgence and hydrodynamic attractors in Gauss-Bonnet holography

NASA Astrophysics Data System (ADS)

Casalderrey-Solana, Jorge; Gushterov, Nikola I.; Meiring, Ben

2018-04-01

We study the convergence of the hydrodynamic series in the gravity dual of Gauss-Bonnet gravity in five dimensions with negative cosmological constant via holography. By imposing boost invariance symmetry, we find a solution to the Gauss-Bonnet equation of motion in inverse powers of the proper time, from which we can extract high order corrections to Bjorken flow for different values of the Gauss-Bonnet parameter λGB. As in all other known examples the gradient expansion is, at most, an asymptotic series which can be understood through applying the techniques of Borel-Padé summation. As expected from the behaviour of the quasi-normal modes in the theory, we observe that the singularities in the Borel plane of this series show qualitative features that interpolate between the infinitely strong coupling limit of N=4 Super Yang Mills theory and the expectation from kinetic theory. We further perform the Borel resummation to constrain the behaviour of hydrodynamic attractors beyond leading order in the hydrodynamic expansion. We find that for all values of λGB considered, the convergence of different initial conditions to the resummation and its hydrodynamization occur at large and comparable values of the pressure anisotropy.

Ability of the oriental fruit moth Grapholita molesta (Lepidoptera: Tortricidae) to detoxify juglone, the main secondary metabolite of the non-host plant walnut.

PubMed

Piskorski, Rafal; Ineichen, Simon; Dorn, Silvia

2011-10-01

Many plant species produce toxic secondary metabolites that limit attacks by herbivorous insects, and may thereby constrain insect expansion to new hosts. Walnut is a host for the codling moth Cydia pomonella, which efficiently detoxifies the main walnut defensive compound juglone (5-hydroxy-1,4-naphthoquinone). The oriental fruit moth Grapholita molesta, which also belongs to the tribe Grapholitini, does not feed on walnut. We tested the performance of G. molesta, a highly invasive species, on artificial diets containing juglone at levels mimicking those found in walnut over the growing season. Juglone-fed G. molesta survived relatively well to adulthood, but larval and adult body weights were reduced, and larval developmental time was prolonged in a dose-dependent fashion. Chemical analysis of frass from larvae that had been fed a juglone-containing diet suggests that G. molesta reduces juglone to non-toxic 1,4,5-trihydroxynaphthalene in its gut. This unexpected tolerance of G. molesta to high levels of juglone may facilitate expansion of the host range beyond the current rosacean fruit trees used by this invasive pest.

The IR obstruction to UV completion for Dante’s Inferno model with higher-dimensional gauge theory origin

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

Furuuchi, Kazuyuki; Koyama, Yoji

We continue our investigation of large field inflation models obtained from higher-dimensional gauge theories, initiated in our previous study http://dx.doi.org/10.1088/1475-7516/2015/02/031. We focus on Dante’s Inferno model which was the most preferred model in our previous analysis. We point out the relevance of the IR obstruction to UV completion, which constrains the form of the potential of the massive vector field, under the current observational upper bound on the tensor to scalar ratio. We also show that in simple examples of the potential arising from DBI action of a D5-brane and that of an NS5-brane that the inflation takes place inmore » the field range which is within the convergence radius of the Taylor expansion. This is in contrast to the well known examples of axion monodromy inflation where inflaton takes place outside the convergence radius of the Taylor expansion. This difference arises from the very essence of Dante’s Inferno model that the effective inflaton potential is stretched in the inflaton field direction compared with the potential for the original field.« less

PLASMA TURBULENCE AND KINETIC INSTABILITIES AT ION SCALES IN THE EXPANDING SOLAR WIND

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

Hellinger, Petr; Trávnícek, Pavel M.; Matteini, Lorenzo

The relationship between a decaying strong turbulence and kinetic instabilities in a slowly expanding plasma is investigated using two-dimensional (2D) hybrid expanding box simulations. We impose an initial ambient magnetic field perpendicular to the simulation box, and we start with a spectrum of large-scale, linearly polarized, random-phase Alfvénic fluctuations that have energy equipartition between kinetic and magnetic fluctuations and vanishing correlation between the two fields. A turbulent cascade rapidly develops; magnetic field fluctuations exhibit a power-law spectrum at large scales and a steeper spectrum at ion scales. The turbulent cascade leads to an overall anisotropic proton heating, protons are heatedmore » in the perpendicular direction, and, initially, also in the parallel direction. The imposed expansion leads to generation of a large parallel proton temperature anisotropy which is at later stages partly reduced by turbulence. The turbulent heating is not sufficient to overcome the expansion-driven perpendicular cooling and the system eventually drives the oblique firehose instability in a form of localized nonlinear wave packets which efficiently reduce the parallel temperature anisotropy. This work demonstrates that kinetic instabilities may coexist with strong plasma turbulence even in a constrained 2D regime.« less

A common explosion mechanism for type Ia supernovae.

PubMed

Mazzali, Paolo A; Röpke, Friedrich K; Benetti, Stefano; Hillebrandt, Wolfgang

2007-02-09

Type Ia supernovae, the thermonuclear explosions of white dwarf stars composed of carbon and oxygen, were instrumental as distance indicators in establishing the acceleration of the universe's expansion. However, the physics of the explosion are debated. Here we report a systematic spectral analysis of a large sample of well-observed type Ia supernovae. Mapping the velocity distribution of the main products of nuclear burning, we constrain theoretical scenarios. We find that all supernovae have low-velocity cores of stable iron-group elements. Outside this core, nickel-56 dominates the supernova ejecta. The outer extent of the iron-group material depends on the amount of nickel-56 and coincides with the inner extent of silicon, the principal product of incomplete burning. The outer extent of the bulk of silicon is similar in all supernovae, having an expansion velocity of approximately 11,000 kilometers per second and corresponding to a mass of slightly over one solar mass. This indicates that all the supernovae considered here burned similar masses and suggests that their progenitors had the same mass. Synthetic light-curve parameters and three-dimensional explosion simulations support this interpretation. A single explosion scenario, possibly a delayed detonation, may thus explain most type Ia supernovae.

Λ(t) CDM and the present accelerating expansion of the universe from 5D scalar vacuum

NASA Astrophysics Data System (ADS)

Madriz Aguilar, José Edgar; Zamarripa, J.; Peraza, A.; Licea, J. A.

2017-12-01

In this letter we investigate some consequences of considering our 4D observable universe as locally and isometrically embedded in a 5D spacetime, where gravity is described by a Brans-Dicke theory in vacuum. Once we impose the embedding conditions we obtain that gravity on the 4D spacetime is governed by the Einstein field equations modified by an extra term that can play the role of a dynamical cosmological constant. Two examples were studied. In the first we derive a cosmological model of a universe filled only with a cosmological constant. In the second we obtain a cosmological solution describing a universe filled with matter, radiation and a dynamical cosmological constant. We constrain the model by using the current observational data combination Planck + WP + BAO + SN. The present acceleration in the expansion of the universe is explained by the geometrically induced dynamical cosmological constant avoiding the introduction of a dark energy component and without addressing the underlying cosmological constant problem. Moreover, all 4D matter sources are geometrically induced in the same manner as it is usually done in the Wesson's induced matter theory.

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.

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.

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.

Thermal Expansivity Between 150 and 800°C of Hydrothermally Altered Conduit Dyke Samples from USDP-4 Drill Core (Mt Unzen, Shimabara, Japan)

NASA Astrophysics Data System (ADS)

Yilmaz, T. I.; Hess, K. U.; Vasseur, J.; Wadsworth, F. B.; Gilg, H. A.; Nakada, S.; Dingwell, D. B.

2017-12-01

When hot magma intrudes the crust, the surrounding rocks expand. Similarly, the cooling magma contracts. The expansion and contraction of these multiphase materials is not simple and often requires empirical constraint. Therefore, we constrained the thermal expansivity of Unzen dome and conduit samples using a NETZSCH® DIL 402C. Following experiments, those samples were scanned using a Phoenix v|tome|x m to observe the cracks that may have developed during the heating and cooling. The dome samples do not show petrological or chemical signs of alteration. However, the alteration of the conduit dykes is represented by the occurrence of the main secondary phases such as chlorite, sulfides, carbonates, R1 (Reichweite parameter) illite-smectite, and kaolinite. These alteration products indicate an (I) early weak to moderate argillic magmatic alteration, and a (II) second stage weak to moderate propylitic hydrothermal alteration. The linear thermal expansion coefficient aL of the dome material is K-1 between 150° and 800°C and shows a sharp peak of up to K-1 around the alpha-beta-quartz-transition ( 573°C). In contrast, aL of the hydrothermally altered conduit samples starts to increase around 180° and reaches K-1 at 400°C. We interpret this effect as being due to the water content of the kaolinite and the R1 illite-smectite, which induces larger expansions per degree temperature change. Furthermore, the altered conduit samples show a more pronounced increases of aL between 500 and 650°C of up to peaks at K-1, which is generated by the breakdown of chlorite, iron-rich dolomite solid solutions, calcite, and pyrite. We use a 1D conductive model of heat transfer to explore how the country rock around the Unzen conduit zone would heat up after intrusion. In turn, we convert these temperature profiles to thermal stress profiles, assuming the edifice is largely undeformable. We show that these high linear thermal expansion coefficients of the hydrothermally altered conduit rocks may large induce thermal stresses in the surrounding host rock and therefore promotes cracking, which may in turn lead to edifice instability.

Irrigation as a determinant of the land use impacts of biofuels

NASA Astrophysics Data System (ADS)

Liu, J.; Hertel, T. W.; Taheripour, F.

2011-12-01

Previous research into the global land use impacts of biofuels has assumed that cropland area could expand in most regions of the world. Indeed, such expansion into more carbon-rich land cover such as grassland or forest is the focus of research into the contributions of indirect land use to the GHG impacts of biofuels. Several studies have examined the global land use consequences of biofuel production. However, all of these studies have effectively treated all cropland as being rainfed. The role of irrigation in biofuel-induced cropland expansion has been wholly ignored. Irrigated croplands typically have much higher yields than their rainfed counterparts. As a consequence, irrigated lands that represent 20% global cropland cover account for 42% of global crop production. Thus, the question of whether expansion of biofuel involves irrigated or rainfed lands makes a significant difference in terms of how much new land will be required to provide the additional production called for in the presence of biofuels. If the new lands are irrigated, and therefore have higher yields than rainfed lands in the same Agro Ecological Zone (AEZs), then less land conversion will be required. However, this land conversion saving may be impossible because expansion of irrigated area is often constrained, either by insufficient water, or insufficient capacity. In this paper we explore the impact on iLUC estimates if irrigated area cannot be expanded. Since earlier studies have assumed the opposite (no constraint whatsoever on expansion), this paper offers an upper bound on the change in land use patterns once one accounts for irrigation. Results show that the change in global cropland area is 15% larger when the irrigation constraint is imposed. This is a direct consequence of the lower yields in rainfed areas. The figure is larger in the US, where the elimination of potential for expanding irrigated areas results in 23% more cropland cover change. The results also show that the presence of potential irrigation constraints significantly alters the geographic pattern of land use change in the wake of the US ethanol expansion. Since rainfed agriculture is more likely than irrigated agriculture to compete with forest, the irrigation-enhanced model shows greater conversion of forest to cropland (up from 23% to 27% of total cropland conversion globally). As a consequence, the GHG emissions from this indirect land use change are significantly higher than the previous estimates - this stems both from greater cropland expansion overall, as well as from the tendency to convert more forest per hectare of cropland.

AGN feedback through UFO and galaxy-wide winds in the early Universe

NASA Astrophysics Data System (ADS)

Feruglio, C.; Piconcelli, E.; Bischetti, M.; Zappacosta, L.; Fiore, F.

2017-10-01

AGN feedback through massive molecular winds is today routinely observed in local AGN host galaxies, but not as such in the early universe. I will present the first evidence for a massive, AGN-driven molecular wind in the z 4 QSO APM08279, which also hosts the most well studied and persistent nuclear semi-raltivistic wind (UFO). This observation directly probes the expansion mechanism of a nuclear wind into the ISM on galaxy wide scales, that so far was constrained by a couple of other objects only (Feruglio et al. 2015, Tombesi et al. 2015). This result also opens the path toward the exploration of molecular AGN-driven winds at early epochs, close after the end of the Epoch of Reionisation (EoR).

Geomorphic Units on Titan: constraints on the origin of Undifferentiated Plains

NASA Astrophysics Data System (ADS)

Lopes, R. M. C.; Malaska, M. J.; Solomonidou, A.; LeGall, A.; Janssen, M. A.; Neish, C.; Turtle, E. P.; Birch, S. P. D.; Hayes, A. G.; Radebaugh, J.; Coustenis, A.

2015-10-01

We present the global distribution of the major classes of units and, where there are direct morphological contacts, describe how these classes of units relate to each other in terms of setting and emplacement history (Fig. 1). In particular, we focus on constraining the origin of the Undifferentiated Plains, which cover large expanses of Titan's surface (Fig. 2). We examined and evaluated different formation mechanisms, including (i) cryovolcanic origin, consisting of overlapping flows of low relief or (ii) sedimentary origins, resulting from fluvial/lacustrine or aeolian deposition, or accumulation of photolysis products created in the atmosphere. The results from our analysis suggest that a sedimentary origin is the most likely, with all the aforementioned processes possibly contributing.

The SkyMapper Transient Survey

NASA Astrophysics Data System (ADS)

Scalzo, R. A.; Yuan, F.; Childress, M. J.; Möller, A.; Schmidt, B. P.; Tucker, B. E.; Zhang, B. R.; Onken, C. A.; Wolf, C.; Astier, P.; Betoule, M.; Regnault, N.

2017-07-01

The SkyMapper 1.3 m telescope at Siding Spring Observatory has now begun regular operations. Alongside the Southern Sky Survey, a comprehensive digital survey of the entire southern sky, SkyMapper will carry out a search for supernovae and other transients. The search strategy, covering a total footprint area of 2 000 deg2 with a cadence of ⩽5 d, is optimised for discovery and follow-up of low-redshift type Ia supernovae to constrain cosmic expansion and peculiar velocities. We describe the search operations and infrastructure, including a parallelised software pipeline to discover variable objects in difference imaging; simulations of the performance of the survey over its lifetime; public access to discovered transients; and some first results from the Science Verification data.

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

Potential macro-detritivore range expansion into the subarctic stimulates litter decomposition: a new positive feedback mechanism to climate change?

PubMed

van Geffen, Koert G; Berg, Matty P; Aerts, Rien

2011-12-01

As a result of low decomposition rates, high-latitude ecosystems store large amounts of carbon. Litter decomposition in these ecosystems is constrained by harsh abiotic conditions, but also by the absence of macro-detritivores. We have studied the potential effects of their climate change-driven northward range expansion on the decomposition of two contrasting subarctic litter types. Litter of Alnus incana and Betula pubescens was incubated in microcosms together with monocultures and all possible combinations of three functionally different macro-detritivores (the earthworm Lumbricus rubellus, isopod Oniscus asellus, and millipede Julus scandinavius). Our results show that these macro-detritivores stimulated decomposition, especially of the high-quality A. incana litter and that the macro-detritivores tested differed in their decomposition-stimulating effects, with earthworms having the largest influence. Decomposition processes increased with increasing number of macro-detritivore species, and positive net diveristy effects occurred in several macro-detritivore treatments. However, after correction for macro-detritivore biomass, all interspecific differences in macro-detritivore effects, as well as the positive effects of species number on subarctic litter decomposition disappeared. The net diversity effects also appeared to be driven by variation in biomass, with a possible exception of net diversity effects in mass loss. Based on these results, we conclude that the expected climate change-induced range expansion of macro-detritivores into subarctic regions is likely to result in accelerated decomposition rates. Our results also indicate that the magnitude of macro-detritivore effects on subarctic decomposition will mainly depend on macro-detritivore biomass, rather than on macro-detritivore species number or identity.

Chemical kinetic model uncertainty minimization through laminar flame speed measurements

PubMed Central

Park, Okjoo; Veloo, Peter S.; Sheen, David A.; Tao, Yujie; Egolfopoulos, Fokion N.; Wang, Hai

2016-01-01

Laminar flame speed measurements were carried for mixture of air with eight C3-4 hydrocarbons (propene, propane, 1,3-butadiene, 1-butene, 2-butene, iso-butene, n-butane, and iso-butane) at the room temperature and ambient pressure. Along with C1-2 hydrocarbon data reported in a recent study, the entire dataset was used to demonstrate how laminar flame speed data can be utilized to explore and minimize the uncertainties in a reaction model for foundation fuels. The USC Mech II kinetic model was chosen as a case study. The method of uncertainty minimization using polynomial chaos expansions (MUM-PCE) (D.A. Sheen and H. Wang, Combust. Flame 2011, 158, 2358–2374) was employed to constrain the model uncertainty for laminar flame speed predictions. Results demonstrate that a reaction model constrained only by the laminar flame speed values of methane/air flames notably reduces the uncertainty in the predictions of the laminar flame speeds of C3 and C4 alkanes, because the key chemical pathways of all of these flames are similar to each other. The uncertainty in model predictions for flames of unsaturated C3-4 hydrocarbons remain significant without considering fuel specific laminar flames speeds in the constraining target data set, because the secondary rate controlling reaction steps are different from those in the saturated alkanes. It is shown that the constraints provided by the laminar flame speeds of the foundation fuels could reduce notably the uncertainties in the predictions of laminar flame speeds of C4 alcohol/air mixtures. Furthermore, it is demonstrated that an accurate prediction of the laminar flame speed of a particular C4 alcohol/air mixture is better achieved through measurements for key molecular intermediates formed during the pyrolysis and oxidation of the parent fuel. PMID:27890938

Chemical kinetic model uncertainty minimization through laminar flame speed measurements.

PubMed

Park, Okjoo; Veloo, Peter S; Sheen, David A; Tao, Yujie; Egolfopoulos, Fokion N; Wang, Hai

2016-10-01

Laminar flame speed measurements were carried for mixture of air with eight C 3-4 hydrocarbons (propene, propane, 1,3-butadiene, 1-butene, 2-butene, iso -butene, n -butane, and iso -butane) at the room temperature and ambient pressure. Along with C 1-2 hydrocarbon data reported in a recent study, the entire dataset was used to demonstrate how laminar flame speed data can be utilized to explore and minimize the uncertainties in a reaction model for foundation fuels. The USC Mech II kinetic model was chosen as a case study. The method of uncertainty minimization using polynomial chaos expansions (MUM-PCE) (D.A. Sheen and H. Wang, Combust. Flame 2011, 158, 2358-2374) was employed to constrain the model uncertainty for laminar flame speed predictions. Results demonstrate that a reaction model constrained only by the laminar flame speed values of methane/air flames notably reduces the uncertainty in the predictions of the laminar flame speeds of C 3 and C 4 alkanes, because the key chemical pathways of all of these flames are similar to each other. The uncertainty in model predictions for flames of unsaturated C 3-4 hydrocarbons remain significant without considering fuel specific laminar flames speeds in the constraining target data set, because the secondary rate controlling reaction steps are different from those in the saturated alkanes. It is shown that the constraints provided by the laminar flame speeds of the foundation fuels could reduce notably the uncertainties in the predictions of laminar flame speeds of C 4 alcohol/air mixtures. Furthermore, it is demonstrated that an accurate prediction of the laminar flame speed of a particular C 4 alcohol/air mixture is better achieved through measurements for key molecular intermediates formed during the pyrolysis and oxidation of the parent fuel.

PREDICTING CME EJECTA AND SHEATH FRONT ARRIVAL AT L1 WITH A DATA-CONSTRAINED PHYSICAL MODEL

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

Hess, Phillip; Zhang, Jie, E-mail: phess4@gmu.edu

2015-10-20

We present a method for predicting the arrival of a coronal mass ejection (CME) flux rope in situ, as well as the sheath of solar wind plasma accumulated ahead of the driver. For faster CMEs, the front of this sheath will be a shock. The method is based upon geometrical separate measurement of the CME ejecta and sheath. These measurements are used to constrain a drag-based model, improved by including both a height dependence and accurate de-projected velocities. We also constrain the geometry of the model to determine the error introduced as a function of the deviation of the CMEmore » nose from the Sun–Earth line. The CME standoff-distance in the heliosphere fit is also calculated, fit, and combined with the ejecta model to determine sheath arrival. Combining these factors allows us to create predictions for both fronts at the L1 point and compare them against observations. We demonstrate an ability to predict the sheath arrival with an average error of under 3.5 hr, with an rms error of about 1.58 hr. For the ejecta the error is less than 1.5 hr, with an rms error within 0.76 hr. We also discuss the physical implications of our model for CME expansion and density evolution. We show the power of our method with ideal data and demonstrate the practical implications of having a permanent L5 observer with space weather forecasting capabilities, while also discussing the limitations of the method that will have to be addressed in order to create a real-time forecasting tool.« less

HIFI observations of water in the atmosphere of comet C/2008 Q3 (Garradd)

NASA Astrophysics Data System (ADS)

Hartogh, P.; Crovisier, J.; de Val-Borro, M.; Bockelée-Morvan, D.; Biver, N.; Lis, D. C.; Moreno, R.; Jarchow, C.; Rengel, M.; Emprechtinger, M.; Szutowicz, S.; Banaszkiewicz, M.; Bensch, F.; Blecka, M. I.; Cavalié, T.; Encrenaz, T.; Jehin, E.; Küppers, M.; Lara, L.-M.; Lellouch, E.; Swinyard, B. M.; Vandenbussche, B.; Bergin, E. A.; Blake, G. A.; Blommaert, J. A. D. L.; Cernicharo, J.; Decin, L.; Encrenaz, P.; de Graauw, T.; Hutsemekers, D.; Kidger, M.; Manfroid, J.; Medvedev, A. S.; Naylor, D. A.; Schieder, R.; Thomas, N.; Waelkens, C.; Roelfsema, P. R.; Dieleman, P.; Güsten, R.; Klein, T.; Kasemann, C.; Caris, M.; Olberg, M.; Benz, A. O.

2010-07-01

High-resolution far-infrared and sub-millimetre spectroscopy of water lines is an important tool to understand the physical and chemical properties of cometary atmospheres. We present observations of several rotational ortho- and para-water transitions in comet C/2008 Q3 (Garradd) performed with HIFI on Herschel. These observations have provided the first detection of the 212-101 (1669 GHz) ortho and 111-000 (1113 GHz) para transitions of water in a cometary spectrum. In addition, the ground-state transition 110-101 at 557 GHz is detected and mapped. By detecting several water lines quasi-simultaneously and mapping their emission we can constrain the excitation parameters in the coma. Synthetic line profiles are computed using excitation models which include excitation by collisions, solar infrared radiation, and radiation trapping. We obtain the gas kinetic temperature, constrain the electron density profile, and estimate the coma expansion velocity by analyzing the map and line shapes. We derive water production rates of 1.7-2.8 × 1028 s-1 over the range rh = 1.83-1.85 AU. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.Figure 5 is only available in electronic form at http://www.aanda.org

What can the CMB tell about the microphysics of cosmic reheating?

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

Drewes, Marco, E-mail: marcodrewes@googlemail.com

In inflationary cosmology, cosmic reheating after inflation sets the initial conditions for the hot big bang. We investigate how CMB data can be used to study the effective potential and couplings of the inflaton during reheating to constrain the underlying microphysics. If there is a phase of preheating that is driven by a parametric resonance or other instability, then the thermal history and expansion history during the reheating era depend on a large number of microphysical parameters in a complicated way. In this case the connection between CMB observables and microphysical parameters can only established with intense numerical studies. Suchmore » studies can help to improve CMB constraints on the effective inflaton potential in specific models, but parameter degeneracies usually make it impossible to extract meaningful best-fit values for individual microphysical parameters. If, on the other hand, reheating is driven by perturbative processes, then it can be possible to constrain the inflaton couplings and the reheating temperature from CMB data. This provides an indirect probe of fundamental microphysical parameters that most likely can never be measured directly in the laboratory, but have an immense impact on the evolution of the cosmos by setting the stage for the hot big bang.« less

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.

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.

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.

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.

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)).

Application of the top-on-top model to 135Pr

NASA Astrophysics Data System (ADS)

Sugawara-Tanabe, Kazuko; Tanabe, Kosai

2017-09-01

It is proved that the Holstein-Primakoff (HP) boson expansion method is very effective for a case where both total and single-particle angular momenta have the diagonal representation along the same direction. The algebraic solution is described by two kinds of quantum numbers classifying the rotational band’s characteristic of the particle-rotor model. One is related with the wobbling motion of the rotor, and the other to the precession of the single-particle angular momentum. Employing angular-momentum dependent rigid (rig) moments of inertia (MoI), which simulate Coriolis anti-pairing effect based on the constrained self-consistent Hartree-Fock-Bogoliubov (HFB) equation, we obtain good fitting not only to the energy-level scheme, but also to the electromagnetic transition rates and the mixing ratio for 135Pr.

Arbitrary-order corrections for finite-time drift and diffusion coefficients

NASA Astrophysics Data System (ADS)

Anteneodo, C.; Riera, R.

2009-09-01

We address a standard class of diffusion processes with linear drift and quadratic diffusion coefficients. These contributions to dynamic equations can be directly drawn from data time series. However, real data are constrained to finite sampling rates and therefore it is crucial to establish a suitable mathematical description of the required finite-time corrections. Based on Itô-Taylor expansions, we present the exact corrections to the finite-time drift and diffusion coefficients. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments that furnish extra theoretical checks for this class of diffusion models. The analytical predictions are compared with the numerical outcomes of representative artificial time series.

ASTROPHYSICS. Atom-interferometry constraints on dark energy.

PubMed

Hamilton, P; Jaffe, M; Haslinger, P; Simmons, Q; Müller, H; Khoury, J

2015-08-21

If dark energy, which drives the accelerated expansion of the universe, consists of a light scalar field, it might be detectable as a "fifth force" between normal-matter objects, in potential conflict with precision tests of gravity. Chameleon fields and other theories with screening mechanisms, however, can evade these tests by suppressing the forces in regions of high density, such as the laboratory. Using a cesium matter-wave interferometer near a spherical mass in an ultrahigh-vacuum chamber, we reduced the screening mechanism by probing the field with individual atoms rather than with bulk matter. We thereby constrained a wide class of dark energy theories, including a range of chameleon and other theories that reproduce the observed cosmic acceleration. Copyright © 2015, American Association for the Advancement of Science.

Dark photon decay beyond the Euler-Heisenberg limit

NASA Astrophysics Data System (ADS)

McDermott, Samuel D.; Patel, Hiren H.; Ramani, Harikrishnan

2018-04-01

We calculate the exact width for a dark photon decaying to three photons at one-loop order for dark photon masses m' below the e+e- production threshold of 2 me. We find substantial deviations from previous results derived from the lowest order Euler-Heisenberg effective Lagrangian in the range me≲m'≤2 me, where higher order terms in the derivative expansion are non-negligible. This mass range is precisely where the three photon decay takes place on cosmologically relevant timescales. Our improved analysis reveals a window for dark photons in the range 850 KeV ≲m'≤2 me , 10-5≲ɛ ≲10-4 that is only constrained by possibly model-dependent bounds on the number of light degrees of freedom in the early Universe.

The evolution of Mercury's crust: a global perspective from MESSENGER.

PubMed

Denevi, Brett W; Robinson, Mark S; Solomon, Sean C; Murchie, Scott L; Blewett, David T; Domingue, Deborah L; McCoy, Timothy J; Ernst, Carolyn M; Head, James W; Watters, Thomas R; Chabot, Nancy L

2009-05-01

Mapping the distribution and extent of major terrain types on a planet's surface helps to constrain the origin and evolution of its crust. Together, MESSENGER and Mariner 10 observations of Mercury now provide a near-global look at the planet, revealing lateral and vertical heterogeneities in the color and thus composition of Mercury's crust. Smooth plains cover approximately 40% of the surface, and evidence for the volcanic origin of large expanses of plains suggests that a substantial portion of the crust originated volcanically. A low-reflectance, relatively blue component affects at least 15% of the surface and is concentrated in crater and basin ejecta. Its spectral characteristics and likely origin at depth are consistent with its apparent excavation from a lower crust or upper mantle enriched in iron- and titanium-bearing oxides.

Phenomenology of nonperturbative charm in the nucleon

DOE PAGES

Hobbs, T. J.; Londergan, J. T.; Melnitchouk, W.

2014-04-02

We perform a comprehensive analysis of the role of nonperturbative (or intrinsic) charm in the nucleon, generated through Fock state expansions of the nucleon wave function involving five-quark virtual states represented by charmed mesons and baryons. We consider contributions from a variety of charmed meson-baryon states and find surprisingly dominant effects from the D¯ *0 Λ c + configuration. We pay particular attention to the existence and persistence of high-x structure for intrinsic charm, and the x dependence of the c-c¯ asymmetry predicted in meson-baryon models. We discuss how studies of charmed baryons and mesons in hadronic reactions can bemore » used to constrain models, and outline future measurements that could further illuminate the intrinsic charm component of the nucleon.« less

Access to Schooling in a Post-Apartheid South Africa: Linking Concepts to Context

NASA Astrophysics Data System (ADS)

Fataar, Aslam

1997-07-01

This paper focuses on the policy issue of expanding schooling in a post-apartheid South Africa. The Project of placing about two million children of school-going age in school is viewed as central to the rebuilding of South Africa. The paper argues that this project should be located within the peculiar history of this country's educational underdevelopment. Challenging the constraining influence of the New Right context should be central in conceptualising the provision of expanded school access. Access policy should be based on a notion of educational development that is linked to the overall socioeconomic development of this society. The view is promoted in this paper that a policy of quantitative expansion of schooling should not ignore the quality of such schooling.

Constraining the interior density profile of a Jovian planet from precision gravity field data

NASA Astrophysics Data System (ADS)

Movshovitz, Naor; Fortney, Jonathan J.; Helled, Ravit; Hubbard, William B.; Thorngren, Daniel; Mankovich, Chris; Wahl, Sean; Militzer, Burkhard; Durante, Daniele

2017-10-01

The external gravity field of a planetary body is determined by the distribution of mass in its interior. Therefore, a measurement of the external field, properly interpreted, tells us about the interior density profile, ρ(r), which in turn can be used to constrain the composition in the interior and thereby learn about the formation mechanism of the planet. Planetary gravity fields are usually described by the coefficients in an expansion of the gravitational potential. Recently, high precision measurements of these coefficients for Jupiter and Saturn have been made by the radio science instruments on the Juno and Cassini spacecraft, respectively.The resulting coefficients come with an associated uncertainty. And while the task of matching a given density profile with a given set of gravity coefficients is relatively straightforward, the question of how best to account for the uncertainty is not. In essentially all prior work on matching models to gravity field data, inferences about planetary structure have rested on imperfect knowledge of the H/He equation of state and on the assumption of an adiabatic interior. Here we wish to vastly expand the phase space of such calculations. We present a framework for describing all the possible interior density structures of a Jovian planet, constrained only by a given set of gravity coefficients and their associated uncertainties. Our approach is statistical. We produce a random sample of ρ(a) curves drawn from the underlying (and unknown) probability distribution of all curves, where ρ is the density on an interior level surface with equatorial radius a. Since the resulting set of density curves is a random sample, that is, curves appear with frequency proportional to the likelihood of their being consistent with the measured gravity, we can compute probability distributions for any quantity that is a function of ρ, such as central pressure, oblateness, core mass and radius, etc. Our approach is also bayesian, in that it can utilize any prior assumptions about the planet's interior, as necessary, without being overly constrained by them.We demonstrate this approach with a sample of Jupiter interior models based on recent Juno data and discuss prospects for Saturn.

Effects of the f(R) and f(G) Gravities and the Exotic Particle on Primordial Nucleosynthesis

NASA Astrophysics Data System (ADS)

Kusakabe, Motohiko; Koh, Seoktae; Kim, K. S.; Cheoun, Myung-Ki; Kajino, Toshitaka; Mathews, Grant J.

A plateau Li/H abundance of metal-poor stars is smaller than those predicted in the standard big bang nucleosynthesis (BBN) model by a factor of ˜3, for the baryon density determined from Planck. This discrepancy may be caused by a non-standard cosmic thermal history or reactions of a hypothetical particle. We consider the BBN in specific modified gravity models characterized by f(R) and f(G) terms in the gravitational actions. These models have cosmic expansion rates different from that in the standard model, and abundances of all light elements are affected. The modified gravities are constrained mainly from observational deuterium abundances. No solution is found for the Li problem because a significant modification of the expansion rate results in a large change of D abundance. This result is quite a contrast to that of a BBN model including a long-lived negatively charged massive particle X-. The 7Be nuclide is destroyed via the recombination with an X- followed by the radiative proton capture. The X- particle selectively decreases the abundance of 7Be, and the primordial abundance of 7Li originating from the electron capture of 7Be is reduced. We have an important theoretical lesson: Some physical process must have operated preferentially on 7Be nuclei.

Aeroelastic Model Structure Computation for Envelope Expansion

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2007-01-01

Structure detection is a procedure for selecting a subset of candidate terms, from a full model description, that best describes the observed output. This is a necessary procedure to compute an efficient system description which may afford greater insight into the functionality of the system or a simpler controller design. Structure computation as a tool for black-box modelling may be of critical importance in the development of robust, parsimonious models for the flight-test community. Moreover, this approach may lead to efficient strategies for rapid envelope expansion which may save significant development time and costs. In this study, a least absolute shrinkage and selection operator (LASSO) technique is investigated for computing efficient model descriptions of nonlinear aeroelastic systems. The LASSO minimises the residual sum of squares by the addition of an l(sub 1) penalty term on the parameter vector of the traditional 2 minimisation problem. Its use for structure detection is a natural extension of this constrained minimisation approach to pseudolinear regression problems which produces some model parameters that are exactly zero and, therefore, yields a parsimonious system description. Applicability of this technique for model structure computation for the F/A-18 Active Aeroelastic Wing using flight test data is shown for several flight conditions (Mach numbers) by identifying a parsimonious system description with a high percent fit for cross-validated data.

Processes of inclusion and adverse incorporation: oil palm and agrarian change in Sumatra, Indonesia.

PubMed

McCarthy, John

2010-01-01

Changes in globalised agriculture raise critical questions as rapid agricultural development leads to widespread social and environmental transformation. With increased global demand for vegetable oils and biofuel, in Indonesia the area under oil palm has doubled over the last decade. This paper presents a case study of how micro-processes that are linked to wider dynamics shape oil palm related agrarian change in villages in Sumatra, Indonesia. It pursues related questions regarding the impact of agribusiness-driven agriculture, the fate of smallholders experiencing contemporary agrarian transition, and the impact of increased demand for vegetable oils and biofuels on agrarian structures in Sumatra. It argues that the paths of agrarian change are highly uneven and depend on how changing livelihood strategies are enabled or constrained by economic, social and political relations that vary over time and space. In contrast to simplifying narratives of inclusion/exclusion, it argues that outcomes depend on the terms under which smallholders engage with oil palm. Distinguishing between exogenous processes of agribusiness expansion and endogenous commodity market expansion, it finds each is associated with characteristic processes of change. It concludes that the way successive policy interventions have worked with the specific characteristics of oil palm have cumulatively shaped the space where agrarian change occurs in Sumatra.

Pigeonholing pyroclasts: Insights from the 19 March 2008 explosive eruption of Kīlauea volcano

USGS Publications Warehouse

Houghton, Bruce F.; Swanson, D.A.; Carey, R.J.; Rausch, J.; Sutton, A.J.

2011-01-01

We think, conventionally, of volcanic explosive eruptions as being triggered in one of two ways: by release and expansion of volatiles dissolved in the ejected magma (magmatic explosions) or by transfer of heat from magma into an external source of water (phreatic or phreatomagmatic explosions). We document here an event where neither magma nor an external water source was involved in explosive activity at K??lauea. Instead, the eruption was powered by the expansion of decoupled magmatic volatiles released from deeper magma, which was not ejected by the eruption, and the trigger was a collapse of near-surface wall rocks that then momentarily blocked that volatile flux. Mapping of the advected fall deposit a day after this eruption has highlighted the difficulty of constraining deposit edges from unobserved or prehistoric eruptions of all magnitudes. Our results suggest that the dispersal area of advected fall deposits could be miscalculated by up to 30% of the total, raising issues for accurate hazard zoning and assessment. Eruptions of this type challenge existing classification schemes for pyroclastic deposits and explosive eruptions and, in the past, have probably been interpreted as phreatic explosions, where the eruptive mechanism has been assumed to involve flashing of groundwater to steam. ?? 2011 Geological Society of America.

Theoretical Perspectives on the Statics and Dynamics of Species’ Borders in Patchy Environments

PubMed Central

Holt, Robert D.; Barfield, Michael

2016-01-01

Understanding range limits is a fundamental problem in ecology and evolutionary biology. In 1963, Mayr argued that “contaminating” gene flow from central populations constrained adaptation in marginal populations, preventing range expansion, while in 1984, Bradshaw suggested that absence of genetic variation prevented species from occurring everywhere. Understanding stability of range boundaries requires unraveling the interplay of demography, gene flow, and evolution of populations in concrete landscape settings. We walk through a set of interrelated spatial scenarios that illustrate interesting complexities of this interplay. To motivate our individual-based model results, we consider a hypothetical zooplankter in a landscape of discrete water bodies coupled by dispersal. We examine how patterns of dispersal influence adaptation in sink habitats where conditions are outside the species’ niche. The likelihood of observing niche evolution (and thus range expansion) over any given timescale depends on (1) the degree of initial maladaptation; (2) pattern (pulsed vs. continuous, uni- vs. bidirectional), timing (juvenile vs. adult), and rate of dispersal (and hence population size); (3) mutation rate; (4) sexuality; and (5) the degree of heterogeneity in the occupied range. We also show how the genetic architecture of polygenic adaptation is influenced by the interplay of selection and dispersal in heterogeneous landscapes. PMID:21956092

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

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.

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

Magmatic-vapor expansion and the formation of high-sulfidation gold deposits: Structural controls on hydrothermal alteration and ore mineralization

USGS Publications Warehouse

Berger, Byron R.; Henley, Richard W.

2011-01-01

High-sulfidation copper–gold lode deposits such as Chinkuashih, Taiwan, Lepanto, Philippines, and Goldfield, Nevada, formed within 1500 m of the paleosurface in volcanic terranes. All underwent an early stage of extensive advanced argillic silica–alunite alteration followed by an abrupt change to spatially much more restricted stages of fracture-controlled sulfide–sulfosalt mineral assemblages and gold–silver mineralization. The alteration as well as ore mineralization stages of these deposits were controlled by the dynamics and history of syn-hydrothermal faulting.At the Sulfate Stage, aggressive advanced argillic alteration and silicification were consequent on the in situ formation of acidic condensate from magmatic vapor as it expanded through secondary fracture networks alongside active faults. The reduction of permeability at this stage due to alteration decreased fluid flow to the surface, and progressively developed a barrier between magmatic-vapor expansion constrained by the active faults and peripheral hydrothermal activity dominated by hot-water flow. In conjunction with the increased rock strength resulting from alteration, subsequent fault-slip inversion in response to an increase in compressional stress generated new, highly permeable fractures localized by the embrittled, altered rock. The new fractures focused magmatic-vapor expansion with much lower heat loss so that condensation occurred. Sulfide Stage sulfosalt, sulfide, and gold–silver deposition then resulted from destabilization of vapor phase metal species due to vapor decompression through the new fracture array. The switch from sulfate to sulfide assemblages is, therefore, a logical consequence of changes in structural permeability due to the coupling of alteration and fracture dynamics rather than to changes in the chemistry of the fluid phase at its magmatic source.

Boundary-value problems in ODE

NASA Astrophysics Data System (ADS)

Tanriverdi, Tanfer

In this thesis we discuss two problems. The first problem is that of Fanno flow in a tube. In [10] the authors have discussed the mathematics of the Fanno model in much more detail than had been previously been done. The analysis in [10] indicates that the Fanno model becomes relevant, if t indicates the unscaled time and t=et , only when t is at least of order O(e- 1) . Indeed, two most important time scales are when t=O(e-1) and t=O(e- 2) . The authors, in the former case, set t=e- 1t1 (t1=t),x=e -11, and obtain the equation 62u6t 21- 62u 6x21=- 2u6 2u6t21 , ( 0.0.1) where u is the velocity of the gas, with p=1,6x1=0 (x1=0). One can follow the solution along the characteristic x1=t1 , and to match with the inviscid behaviour when t1-->0 , u=2+t1 (x1=t1). (0.0.2) In the region t=O(e2) , the authors set t=e2t2, x=e2x2,h= x2t2. For small e , the BC (0.0.02) now becomes u=t2 (x2=t 2), (0.0.3) so that (0.0.1) now has a similarity solution of the form u=t2g( h), u2=e- 1u, and (h2- 1)g'' +4hg'+2g=2g(g+hg' ),' =/ (0.0.4) with g(h)-->2 ash-->1- ,from(0.0.3) (0.0.5) g(h)-->∞ ash-->0- ,(fromthe pressure). ( 0.0.6) In a recent paper [11] the authors discuss the existence of a solution of (0.0.4)-(0.0.6) by using a two dimensional topological shooting method. We also discuss the existence of a solution of (0.0.4)-(0.0.6) by using a shooting method. We first turn the nonlinear ode (0.0.4) into an integral equation and then shoot from the singularity at ∞. The second problem arises when one considers eigenfunction expansions associated with second order ordinary differential equations, as Titchmarsh does in his book. One is concerned with the solutions of the equation - d2ydx2+ q(x)y=ly, (0.0.7) along with certain boundary conditions, where q(x)=-( n2- /)sech 2(x), n=n+/. The problem (0.0.7) has an application in the study of discrete reaction-diffusion equations. Our purpose in this problem is to look in some detail at the equation (0.0.7). We first use contour integrations to give an explicit solution. Secondly, we explore the eigenvalues and the eigenfunctions with the certain boundary conditions. We not only find the spectrum for n = 1, 2, 3, 4 but also explore the eigenvalues for general n where a=0,a=/ and BC is y(x)cosa +y'(x)sin a=0.

Cost-effectiveness of population-level expansion of highly active antiretroviral treatment for HIV in British Columbia, Canada: a modelling study.

PubMed

Nosyk, Bohdan; Min, Jeong E; Lima, Viviane D; Hogg, Robert S; Montaner, Julio S G

2015-09-01

Widespread HIV screening and access to highly active antiretroviral treatment (ART) were cost effective in mathematical models, but population-level implementation has led to questions about cost, value, and feasibility. In 1996, British Columbia, Canada, introduced universal coverage of drug and other health-care costs for people with HIV/AIDS and and began extensive scale-up in access to ART. We aimed to assess the cost-effectiveness of ART scale-up in British Columbia compared with hypothetical scenarios of constrained treatment access. Using comprehensive linked population-level data, we populated a dynamic, compartmental transmission model to simulate the HIV/AIDS epidemic in British Columbia from 1997 to 2010. We estimated HIV incidence, prevalence, mortality, costs (in 2010 CAN$), and quality-adjusted life-years (QALYs) for the study period, which was 1997-2010. We calculated incremental cost-effectiveness ratios from societal and third-party-payer perspectives to compare actual practice (true numbers of individuals accessing ART) to scenarios of constrained expansion (75% and 50% probability of accessing ART). We also investigated structural and parameter uncertainty. Actual practice resulted in 263 averted incident cases compared with 75% of observed access and 676 averted cases compared with 50% of observed access to ART. From a third-party-payer perspective, actual practice resulted in incremental cost-effectiveness ratios of $23 679 per QALY versus 75% access and $24 250 per QALY versus 50% access. From a societal perspective, actual practice was cost saving within the study period. When the model was extended to 2035, current observed access resulted in cumulative savings of $25·1 million compared with the 75% access scenario and $65·5 million compared with the 50% access scenario. ART scale-up in British Columbia has decreased HIV-related morbidity, mortality, and transmission. Resulting incremental cost-effectiveness ratios for actual practice, derived within a limited timeframe, were within established cost-effectiveness thresholds and were cost saving from a societal perspective. BC Ministry of Health, National Institute of Drug Abuse at the US National Institutes of Health. Copyright © 2015 Elsevier Ltd. All rights reserved.

Interval-parameter semi-infinite fuzzy-stochastic mixed-integer programming approach for environmental management under multiple uncertainties.

PubMed

Guo, P; Huang, G H

2010-03-01

In this study, an interval-parameter semi-infinite fuzzy-chance-constrained mixed-integer linear programming (ISIFCIP) approach is developed for supporting long-term planning of waste-management systems under multiple uncertainties in the City of Regina, Canada. The method improves upon the existing interval-parameter semi-infinite programming (ISIP) and fuzzy-chance-constrained programming (FCCP) by incorporating uncertainties expressed as dual uncertainties of functional intervals and multiple uncertainties of distributions with fuzzy-interval admissible probability of violating constraint within a general optimization framework. The binary-variable solutions represent the decisions of waste-management-facility expansion, and the continuous ones are related to decisions of waste-flow allocation. The interval solutions can help decision-makers to obtain multiple decision alternatives, as well as provide bases for further analyses of tradeoffs between waste-management cost and system-failure risk. In the application to the City of Regina, Canada, two scenarios are considered. In Scenario 1, the City's waste-management practices would be based on the existing policy over the next 25 years. The total diversion rate for the residential waste would be approximately 14%. Scenario 2 is associated with a policy for waste minimization and diversion, where 35% diversion of residential waste should be achieved within 15 years, and 50% diversion over 25 years. In this scenario, not only landfill would be expanded, but also CF and MRF would be expanded. Through the scenario analyses, useful decision support for the City's solid-waste managers and decision-makers has been generated. Three special characteristics of the proposed method make it unique compared with other optimization techniques that deal with uncertainties. Firstly, it is useful for tackling multiple uncertainties expressed as intervals, functional intervals, probability distributions, fuzzy sets, and their combinations; secondly, it has capability in addressing the temporal variations of the functional intervals; thirdly, it can facilitate dynamic analysis for decisions of facility-expansion planning and waste-flow allocation within a multi-facility, multi-period and multi-option context. Copyright 2009 Elsevier Ltd. All rights reserved.

Ca, Sr, Mo and U isotopes evidence ocean acidification and deoxygenation during the Late Permian mass extinction

NASA Astrophysics Data System (ADS)

Silva-Tamayo, Juan Carlos; Payne, Jon; Wignall, Paul; Newton, Rob; Eisenhauer, Anton; Weyer, Stenfan; Neubert, Nadja; Lau, Kim; Maher, Kate; Paytan, Adina; Lehrmann, Dan; Altiner, Demir; Yu, Meiyi

2014-05-01

The most catastrophic extinction event in the history of animal life occurred at the end of the Permian Period, ca. 252 Mya. Ocean acidification and global oceanic euxinia have each been proposed as causes of this biotic crisis, but the magnitude and timing of change in global ocean chemistry remains poorly constrained. Here we use multiple isotope systems - Ca, Sr, Mo and U - measured from well dated Upper Permian- Lower Triassic sedimentary sections to better constrain the magnitude and timing of change in ocean chemistry and the effects of ocean acidification and de-oxygenation through this interval. All the investigated carbonate successions (Turkey, Italy and China) exhibit decreasing δ44/40Ca compositions, from ~-1.4‰ to -2.0‰ in the interval preceding the main extinction. These values remain low during most of the Griesbachian, to finally return to -1.4‰ in the middle Dienerian. The limestone succession from southern Turkey also displays a major decrease in the δ88/86Sr values from 0.45‰ to 0.3‰ before the extinction. These values remain low during the Griesbachian and finally increase to 0.55‰ by the middle Dienerian. The paired negative anomalies on the carbonate δ44/40Ca and δ88/86Sr suggest a decrease in the carbonate precipitation and thus an episode of ocean acidification coincident with the major biotic crisis. The Mo and U isotope records also exhibit significant rapid negative anomalies at the onset of the main extinction interval, suggesting rapid expansion of anoxic and euxinic marine bottom waters during the extinction interval. The rapidity of the isotope excursions in Mo and U suggests substantially reduced residence times of these elements in seawater relative to the modern, consistent with expectations for a time of widespread anoxia. The large C-isotope variability within Lower Triassic rocks, which is similar to that of the Lower-Middle Cambrian, may reflect biologically controlled perturbations of the oceanic carbon cycle. These findings strengthen the evidence for a global ocean acidification event coupled with rapid expansion of anoxic zones as drivers of end-Permian extinction in the oceans.

Competition between reaction-induced expansion and creep compaction during gypsum formation: Experimental and numerical investigation

NASA Astrophysics Data System (ADS)

Skarbek, R. M.; Savage, H. M.; Spiegelman, M. W.; Kelemen, P. B.; Yancopoulos, D.

2017-12-01

Deformation and cracking caused by reaction-driven volume increase is an important process in many geological settings, however the conditions controlling these processes are poorly understood. The interaction of rocks with reactive fluids can change permeability and reactive surface area, leading to a large variety of feedbacks. Gypsum is an ideal material to study these processes. It forms rapidly at room temperature via bassanite hydration, and is commonly used as an analogue for rocks in high-temperature, high-pressure conditions. We conducted uniaxial strain experiments to study the effects of applied axial load on deformation and fluid flow during the formation of gypsum from bassanite. While hydration of bassanite to gypsum involves a solid volume increase, gypsum exhibits significant creep compaction when in contact with water. These two volume changing processes occur simultaneously during fluid flow through bassanite. We cold-pressed bassanite powder to form cylinders 2.5 cm in height and 1.2 cm in diameter. Samples were compressed with a static axial load of 0.01 to 4 MPa. Water infiltrated initially unsaturated samples through the bottom face and the height of the samples was recorded as a measure of the total volume change. We also performed experiments on pure gypsum samples to constrain the amount of creep observed in tests on bassanite hydration. At axial loads < 0.15 MPa, volume increase due to the reaction dominates and samples exhibit monotonic expansion. At loads > 1 MPa, creep in the gypsum dominates and samples exhibit monotonic compaction. At intermediate loads, samples exhibit alternating phases of compaction and expansion due to the interplay of the two volume changing processes. We observed a change from net compaction to net expansion at an axial load of 0.250 MPa. We explain this behavior with a simple model that predicts the strain evolution, but does not take fluid flow into account. We also implement a 1D poro-visco-elastic model of the imbibition process that includes the reaction and gypsum creep. We use the results of these models, with models of the creep rate in gypsum, to estimate the temperature dependence of the axial load where total strain transitions from compaction to expansion. Our results have implications for the depth dependence of reaction induced volume changes in the Earth.

A morpho-kinematic and spectroscopic study of the bipolar nebulae: M 2-9, Mz 3, and Hen 2-104

NASA Astrophysics Data System (ADS)

Clyne, N.; Akras, S.; Steffen, W.; Redman, M. P.; Gonçalves, D. R.; Harvey, E.

2015-10-01

Context. Complex bipolar shapes can be generated either as a planetary nebula or a symbiotic system. The origin of the material ionised by the white dwarf is very different in these two scenarios, and it complicates the understanding of the morphologies of planetary nebulae. Aims: The physical properties, structure, and dynamics of the bipolar nebulae, M 2-9, Mz 3, and Hen 2-104, are investigated in detail with the aim of understanding their nature, shaping mechanisms, and evolutionary history. Both a morpho-kinematic study and a spectroscopic analysis, can be used to more accurately determine the kinematics and nature of each nebula. Methods: Long-slit optical echelle spectra are used to investigate the morpho-kinematics of M 2-9, Mz 3, and Hen 2-104. The morpho-kinematic modelling software SHAPE is used to constrain both the morphology and kinematics of each nebula by means of detailed 3D models. Near-infrared (NIR) data, as well as optical, spectra are used to separate Galactic symbiotic-type nebulae from genuine planetary nebulae by means of a 2MASS J-H/H-Ks diagram and a λ4363/Hγ vs. λ5007/Hβ diagnostic diagram, respectively. Results: The best-fitted 3D models for M 2-9, Mz 3, and Hen 2-104 provide invaluable kinematical information on the expansion velocity of its nebular components by means of synthetic spectra. The observed spectra match up very well with the synthetic spectra for each model, thus showing that each model is tightly constrained both morphologically and kinematically. Kinematical ages of the different structures of M 2-9 and Mz 3 have also been determined. Both diagnostic diagrams show M 2-9 and Hen 2-104 to fall well within the category of having a symbiotic source, whereas Mz 3 borders the region of symbiotic and young planetary nebulae in the optical diagram but is located firmly in the symbiotic region of the NIR colour-colour diagram. The optical diagnostic diagram is shown to successfully separate the two types of nebulae, however, the NIR colour-colour diagram is not as accurate in separating these objects. Conclusions: The morphology, kinematics, and evolutionary history of M 2-9, Mz 3, and Hen 2-104 are better understood using the interactive 3D modelling tool shape. The expansion velocities of the components for each nebula are better constrained and fitted with a vector field to reveal their direction of motion. The optical and NIR diagnostic diagrams used are important techniques for separating Galactic symbiotic-type nebulae from genuine planetary nebulae.

Single-Photon Emission of a Hydrogenlike Atom

NASA Astrophysics Data System (ADS)

Skobelev, V. V.

2016-11-01

Implementing a previously obtained, original solution of the Dirac equation for an electron in the field of a nucleus ( Ze) expressed in terms of the wave function of the corresponding Schrödinger equation and its derivatives in spherical coordinates and the spin projection operator Σ3 associated with the eigenfunction, taking into account in each component of the spinor the leading term of the expansion in the small parameter ( Zα), α = e 2 / ħc ≈ 1 / 137, the partial probabilities W of emission of a photon ( Zα)* → ( Zα) + γ have been calculated. Here two orthogonal states of the linear polarization of the photon, and also the spin states of the electron, which previously had not been taken into consideration, have been taken into account in the transverse gauge. It turns out that the probabilities W of emission of a photon per unit time for any allowed transitions are proportional to (Zα)4, as was previously accepted, and the selection rules for the quantum number m have the usual form Δ m = 0,±1. It was found that a spin flip does not take place during emission. In contrast to the customary situation with the selection rules for the quantum number l being of the form Δ l = ±1, for Δ m = ±1 there also exist integrals over dcosθ which are not equal to zero for undetermined odd values of Δ l. In this, and also in a fundamentally different dependence of the amplitude on the quantum numbers consist the differences from the traditional approach to the problem. Necessary conditions are formulated, under the fulfillment of which the selection rules for l are not changed, having values Δ l = ±1 for arbitrary Δ m, but it was not possible, however, to give a complete proof of these rules.

Extinction models for cancer stem cell therapy

PubMed Central

Sehl, Mary; Zhou, Hua; Sinsheimer, Janet S.; Lange, Kenneth L.

2012-01-01

Cells with stem cell-like properties are now viewed as initiating and sustaining many cancers. This suggests that cancer can be cured by driving these cancer stem cells to extinction. The problem with this strategy is that ordinary stem cells are apt to be killed in the process. This paper sets bounds on the killing differential (difference between death rates of cancer stem cells and normal stem cells) that must exist for the survival of an adequate number of normal stem cells. Our main tools are birth–death Markov chains in continuous time. In this framework, we investigate the extinction times of cancer stem cells and normal stem cells. Application of extreme value theory from mathematical statistics yields an accurate asymptotic distribution and corresponding moments for both extinction times. We compare these distributions for the two cell populations as a function of the killing rates. Perhaps a more telling comparison involves the number of normal stem cells NH at the extinction time of the cancer stem cells. Conditioning on the asymptotic time to extinction of the cancer stem cells allows us to calculate the asymptotic mean and variance of NH. The full distribution of NH can be retrieved by the finite Fourier transform and, in some parameter regimes, by an eigenfunction expansion. Finally, we discuss the impact of quiescence (the resting state) on stem cell dynamics. Quiescence can act as a sanctuary for cancer stem cells and imperils the proposed therapy. We approach the complication of quiescence via multitype branching process models and stochastic simulation. Improvements to the τ-leaping method of stochastic simulation make it a versatile tool in this context. We conclude that the proposed therapy must target quiescent cancer stem cells as well as actively dividing cancer stem cells. The current cancer models demonstrate the virtue of attacking the same quantitative questions from a variety of modeling, mathematical, and computational perspectives. PMID:22001354

Extinction models for cancer stem cell therapy.

PubMed

Sehl, Mary; Zhou, Hua; Sinsheimer, Janet S; Lange, Kenneth L

2011-12-01

Cells with stem cell-like properties are now viewed as initiating and sustaining many cancers. This suggests that cancer can be cured by driving these cancer stem cells to extinction. The problem with this strategy is that ordinary stem cells are apt to be killed in the process. This paper sets bounds on the killing differential (difference between death rates of cancer stem cells and normal stem cells) that must exist for the survival of an adequate number of normal stem cells. Our main tools are birth-death Markov chains in continuous time. In this framework, we investigate the extinction times of cancer stem cells and normal stem cells. Application of extreme value theory from mathematical statistics yields an accurate asymptotic distribution and corresponding moments for both extinction times. We compare these distributions for the two cell populations as a function of the killing rates. Perhaps a more telling comparison involves the number of normal stem cells NH at the extinction time of the cancer stem cells. Conditioning on the asymptotic time to extinction of the cancer stem cells allows us to calculate the asymptotic mean and variance of NH. The full distribution of NH can be retrieved by the finite Fourier transform and, in some parameter regimes, by an eigenfunction expansion. Finally, we discuss the impact of quiescence (the resting state) on stem cell dynamics. Quiescence can act as a sanctuary for cancer stem cells and imperils the proposed therapy. We approach the complication of quiescence via multitype branching process models and stochastic simulation. Improvements to the τ-leaping method of stochastic simulation make it a versatile tool in this context. We conclude that the proposed therapy must target quiescent cancer stem cells as well as actively dividing cancer stem cells. The current cancer models demonstrate the virtue of attacking the same quantitative questions from a variety of modeling, mathematical, and computational perspectives. Copyright © 2011 Elsevier Inc. All rights reserved.

The two-electron atomic systems. S-states

NASA Astrophysics Data System (ADS)

Liverts, Evgeny Z.; Barnea, Nir

2010-01-01

A simple Mathematica program for computing the S-state energies and wave functions of two-electron (helium-like) atoms (ions) is presented. The well-known method of projecting the Schrödinger equation onto the finite subspace of basis functions was applied. The basis functions are composed of the exponentials combined with integer powers of the simplest perimetric coordinates. No special subroutines were used, only built-in objects supported by Mathematica. The accuracy of results and computation time depend on the basis size. The precise energy values of 7-8 significant figures along with the corresponding wave functions can be computed on a single processor within a few minutes. The resultant wave functions have a simple analytical form consisting of elementary functions, that enables one to calculate the expectation values of arbitrary physical operators without any difficulties. Program summaryProgram title: TwoElAtom-S Catalogue identifier: AEFK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 10 185 No. of bytes in distributed program, including test data, etc.: 495 164 Distribution format: tar.gz Programming language: Mathematica 6.0; 7.0 Computer: Any PC Operating system: Any which supports Mathematica; tested under Microsoft Windows XP and Linux SUSE 11.0 RAM:⩾10 bytes Classification: 2.1, 2.2, 2.7, 2.9 Nature of problem: The Schrödinger equation for atoms (ions) with more than one electron has not been solved analytically. Approximate methods must be applied in order to obtain the wave functions or other physical attributes from quantum mechanical calculations. Solution method: The S-wave function is expanded into a triple basis set in three perimetric coordinates. Method of projecting the two-electron Schrödinger equation (for atoms/ions) onto a subspace of the basis functions enables one to obtain the set of homogeneous linear equations F.C=0 for the coefficients C of the above expansion. The roots of equation det(F)=0 yield the bound energies. Restrictions: First, the too large length of expansion (basis size) takes the too large computation time giving no perceptible improvement in accuracy. Second, the order of polynomial Ω (input parameter) in the wave function expansion enables one to calculate the excited nS-states up to n=Ω+1 inclusive. Additional comments: The CPC Program Library includes "A program to calculate the eigenfunctions of the random phase approximation for two electron systems" (AAJD). It should be emphasized that this fortran code realizes a very rough approximation describing only the averaged electron density of the two electron systems. It does not characterize the properties of the individual electrons and has a number of input parameters including the Roothaan orbitals. Running time: ˜10 minutes (depends on basis size and computer speed)

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.

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.