Numerical and theoretical evaluations of AC losses for single and infinite numbers of superconductor strips with direct and alternating transport currents in external AC magnetic field

NASA Astrophysics Data System (ADS)

Kajikawa, K.; Funaki, K.; Shikimachi, K.; Hirano, N.; Nagaya, S.

2010-11-01

AC losses in a superconductor strip are numerically evaluated by means of a finite element method formulated with a current vector potential. The expressions of AC losses in an infinite slab that corresponds to a simple model of infinitely stacked strips are also derived theoretically. It is assumed that the voltage-current characteristics of the superconductors are represented by Bean's critical state model. The typical operation pattern of a Superconducting Magnetic Energy Storage (SMES) coil with direct and alternating transport currents in an external AC magnetic field is taken into account as the electromagnetic environment for both the single strip and the infinite slab. By using the obtained results of AC losses, the influences of the transport currents on the total losses are discussed quantitatively.

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.

2.5D Finite/infinite Element Approach for Simulating Train-Induced Ground Vibrations

NASA Astrophysics Data System (ADS)

Yang, Y. B.; Hung, H. H.; Kao, J. C.

2010-05-01

The 2.5D finite/infinite element approach for simulating the ground vibrations by surface or underground moving trains will be briefly summarized in this paper. By assuming the soils to be uniform along the direction of the railway, only a two-dimensional profile of the soil perpendicular to the railway need be considered in the modeling. Besides the two in-plane degrees of freedom (DOFs) per node conventionally used for plane strain elements, an extra DOF is introduced to account for the out-of-plane wave transmission. The profile of the half-space is divided into a near field and a semi-infinite far field. The near field containing the train loads and irregular structures is simulated by the finite elements, while the far field covering the soils with infinite boundary by the infinite elements, by which due account is taken of the radiation effects for the moving loads. Enhanced by the automated mesh expansion procedure proposed previously by the writers, the far field impedances for all the lower frequencies are generated repetitively from the mesh created for the highest frequency considered. Finally, incorporated with a proposed load generation mechanism that takes the rail irregularity and dynamic properties of trains into account, an illustrative case study was performed. This paper investigates the vibration isolation effect of the elastic foundation that separates the concrete slab track from the underlying soil or tunnel structure. In addition, the advantage of the 2.5D approach was clearly demonstrated in that the three-dimensional wave propagation effect can be virtually captured using a two-dimensional finite/infinite element mesh. Compared with the conventional 3D approach, the present approach appears to be simple, efficient and generally accurate.

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.

Boundary effect on the elastic field of a semi-infinite solid containing inhomogeneities

PubMed Central

Liu, Y. J.; Song, G.; Yin, H. M.

2015-01-01

The boundary effect of one inhomogeneity embedded in a semi-infinite solid at different depths has firstly been investigated using the fundamental solution for Mindlin's problem. Expanding the eigenstrain in a polynomial form and using the Eshelby's equivalent inclusion method, one can calculate the eigenstrain and thus obtain the elastic field. When the inhomogeneity is far from the boundary, the solution recovers Eshelby's solution. The method has been extended to a many-particle system in a semi-infinite solid, which is first demonstrated by the cases of two spheres. The comparison of the asymptotic form solution with the finite-element results shows the accuracy and capability of this method. The solution has been used to illustrate the boundary effects on its effective material behaviour of a semi-infinite simple cubic lattice particulate composite. The local field of a semi-infinite composite has been calculated at different volume fractions. A representative unit cell has been taken with different depths to the surface. The average stress and strain of the unit cell have been calculated under uniform loading conditions of normal or shear force on the surface, respectively. The effective elastic moduli of the unit cell not only depend on the material proportion, but also on its distance to the surface. The present model can be extended to other types of particle distribution and ellipsoidal particles. PMID:26345084

Boundary effect on the elastic field of a semi-infinite solid containing inhomogeneities.

PubMed

Liu, Y J; Song, G; Yin, H M

2015-07-08

The boundary effect of one inhomogeneity embedded in a semi-infinite solid at different depths has firstly been investigated using the fundamental solution for Mindlin's problem. Expanding the eigenstrain in a polynomial form and using the Eshelby's equivalent inclusion method, one can calculate the eigenstrain and thus obtain the elastic field. When the inhomogeneity is far from the boundary, the solution recovers Eshelby's solution. The method has been extended to a many-particle system in a semi-infinite solid, which is first demonstrated by the cases of two spheres. The comparison of the asymptotic form solution with the finite-element results shows the accuracy and capability of this method. The solution has been used to illustrate the boundary effects on its effective material behaviour of a semi-infinite simple cubic lattice particulate composite. The local field of a semi-infinite composite has been calculated at different volume fractions. A representative unit cell has been taken with different depths to the surface. The average stress and strain of the unit cell have been calculated under uniform loading conditions of normal or shear force on the surface, respectively. The effective elastic moduli of the unit cell not only depend on the material proportion, but also on its distance to the surface. The present model can be extended to other types of particle distribution and ellipsoidal particles.

Receive Mode Analysis and Design of Microstrip Reflectarrays

NASA Technical Reports Server (NTRS)

Rengarajan, Sembiam

2011-01-01

Traditionally microstrip or printed reflectarrays are designed using the transmit mode technique. In this method, the size of each printed element is chosen so as to provide the required value of the reflection phase such that a collimated beam results along a given direction. The reflection phase of each printed element is approximated using an infinite array model. The infinite array model is an excellent engineering approximation for a large microstrip array since the size or orientation of elements exhibits a slow spatial variation. In this model, the reflection phase from a given printed element is approximated by that of an infinite array of elements of the same size and orientation when illuminated by a local plane wave. Thus the reflection phase is a function of the size (or orientation) of the element, the elevation and azimuth angles of incidence of a local plane wave, and polarization. Typically, one computes the reflection phase of the infinite array as a function of several parameters such as size/orientation, elevation and azimuth angles of incidence, and in some cases for vertical and horizontal polarization. The design requires the selection of the size/orientation of the printed element to realize the required phase by interpolating or curve fitting all the computed data. This is a substantially complicated problem, especially in applications requiring a computationally intensive commercial code to determine the reflection phase. In dual polarization applications requiring rectangular patches, one needs to determine the reflection phase as a function of five parameters (dimensions of the rectangular patch, elevation and azimuth angles of incidence, and polarization). This is an extremely complex problem. The new method employs the reciprocity principle and reaction concept, two well-known concepts in electromagnetics to derive the receive mode analysis and design techniques. In the "receive mode design" technique, the reflection phase is computed for a plane wave incident on the reflectarray from the direction of the beam peak. In antenna applications with a single collimated beam, this method is extremely simple since all printed elements see the same angles of incidence. Thus the number of parameters is reduced by two when compared to the transmit mode design. The reflection phase computation as a function of five parameters in the rectangular patch array discussed previously is reduced to a computational problem with three parameters in the receive mode. Furthermore, if the beam peak is in the broadside direction, the receive mode design is polarization independent and the reflection phase computation is a function of two parameters only. For a square patch array, it is a function of the size, one parameter only, thus making it extremely simple.

Scan blindness in infinite phased arrays of printed dipoles

NASA Technical Reports Server (NTRS)

Pozar, D. M.; Schaubert, D. H.

1984-01-01

A comprehensive study of infinite phased arrays of printed dipole antennas is presented, with emphasis on the scan blindness phenomenon. A rigorous and efficient moment method procedure is used to calculate the array impedance versus scan angle. Data are presented for the input reflection coefficient for various element spacings and substrate parameters. A simple theory, based on coupling from Floquet modes to surface wave modes on the substrate, is shown to predict the occurrence of scan blindness. Measurements from a waveguide simulator of a blindness condition confirm the theory.

A boundary element alternating method for two-dimensional mixed-mode fracture problems

NASA Technical Reports Server (NTRS)

Raju, I. S.; Krishnamurthy, T.

1992-01-01

A boundary element alternating method, denoted herein as BEAM, is presented for two dimensional fracture problems. This is an iterative method which alternates between two solutions. An analytical solution for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate is used as the fundamental solution in the alternating method. A boundary element method for an uncracked finite plate is the second solution. For problems of edge cracks a technique of utilizing finite elements with BEAM is presented to overcome the inherent singularity in boundary element stress calculation near the boundaries. Several computational aspects that make the algorithm efficient are presented. Finally, the BEAM is applied to a variety of two dimensional crack problems with different configurations and loadings to assess the validity of the method. The method gives accurate stress intensity factors with minimal computing effort.

Automated Structural Optimization System (ASTROS) Damage Tolerance Module. Volume 1 - Final Report

DTIC Science & Technology

1999-02-01

cracks in the infinite do- main subjected to the unknown crack surface loading T. The second one, denoted as PFEM [shown in Fig. 2.13(b)], has the...same finite geometry as in the original problem except that the cracks are ignored. The boundary Tu of PFEM has the prescribed displacement u, while...Because of the absence of the cracks, the problem PFEM can be solved much easier by the finite element method (or the boundary element method). To

Analysis of microstrip dipoles and slots transversely coupled to a microstrip line using the FDTD method

NASA Technical Reports Server (NTRS)

Tulintseff, A. N.

1993-01-01

Printed dipole elements and their complement, linear slots, are elementary radiators that have found use in low-profile antenna arrays. Low-profile antenna arrays, in addition to their small size and low weight characteristics, offer the potential advantage of low-cost, high-volume production with easy integration with active integrated circuit components. The design of such arrays requires that the radiation and impedance characteristics of the radiating elements be known. The FDTD (Finite-Difference Time-Domain) method is a general, straight-forward implementation of Maxwell's equations and offers a relatively simple way of analyzing both printed dipole and slot elements. Investigated in this work is the application of the FDTD method to the analysis of printed dipole and slot elements transversely coupled to an infinite transmission line in a multilayered configuration. Such dipole and slot elements may be used in dipole and slot series-fed-type linear arrays, where element offsets and interelement line lengths are used to obtain the desired amplitude distribution and beam direction, respectively. The design of such arrays is achieved using transmission line theory with equivalent circuit models for the radiating elements. In an equivalent circuit model, the dipole represents a shunt impedance to the transmission line, where the impedance is a function of dipole offset, length, and width. Similarly, the slot represents a series impedance to the transmission line. The FDTD method is applied to single dipole and slot elements transversely coupled to an infinite microstrip line using a fixed rectangular grid with Mur's second order absorbing boundary conditions. Frequency-dependent circuit and scattering parameters are obtained by saving desired time-domain quantities and using the Fourier transform. A Gaussian pulse excitation is applied to the microstrip transmission line, where the resulting reflected signal due to the presence of the radiating element is used to determine the equivalent element impedance.

Convergence rates for finite element problems with singularities. Part 1: Antiplane shear. [crack

NASA Technical Reports Server (NTRS)

Plunkett, R.

1980-01-01

The problem of a finite crack in an infinite medium under antiplane shear load is considered. It is shown that the nodal forces at the tip of the crack accurately gives the order of singularity, that n energy release methods can give the strength to better than 1 percent with element size 1/10 the crack length, and that nodal forces give a much better estimate of the stress field than do the elements themselves. The finite element formulation and the factoring of tridiagonal matrices are discussed.

On Arithmetic-Geometric-Mean Polynomials

ERIC Educational Resources Information Center

Griffiths, Martin; MacHale, Des

2017-01-01

We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…

Finite-element analysis of dynamic fracture

NASA Technical Reports Server (NTRS)

Aberson, J. A.; Anderson, J. M.; King, W. W.

1976-01-01

Applications of the finite element method to the two dimensional elastodynamics of cracked structures are presented. Stress intensity factors are computed for two problems involving stationary cracks. The first serves as a vehicle for discussing lumped-mass and consistent-mass characterizations of inertia. In the second problem, the behavior of a photoelastic dynamic tear test specimen is determined for the time prior to crack propagation. Some results of a finite element simulation of rapid crack propagation in an infinite body are discussed.

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Analytical and numerical methods evaluating the stress-intensity factors for three-dimensional cracks in solids are presented, with reference to fatigue failure in aerospace structures. The exact solutions for embedded elliptical and circular cracks in infinite solids, and the approximate methods, including the finite-element, the boundary-integral equation, the line-spring models, and the mixed methods are discussed. Among the mixed methods, the superposition of analytical and finite element methods, the stress-difference, the discretization-error, the alternating, and the finite element-alternating methods are reviewed. Comparison of the stress-intensity factor solutions for some three-dimensional crack configurations showed good agreement. Thus, the choice of a particular method in evaluating the stress-intensity factor is limited only to the availability of resources and computer programs.

Extension of the frequency-domain pFFT method for wave structure interaction in finite depth

NASA Astrophysics Data System (ADS)

Teng, Bin; Song, Zhi-jie

2017-06-01

To analyze wave interaction with a large scale body in the frequency domain, a precorrected Fast Fourier Transform (pFFT) method has been proposed for infinite depth problems with the deep water Green function, as it can form a matrix with Toeplitz and Hankel properties. In this paper, a method is proposed to decompose the finite depth Green function into two terms, which can form matrices with the Toeplitz and a Hankel properties respectively. Then, a pFFT method for finite depth problems is developed. Based on the pFFT method, a numerical code pFFT-HOBEM is developed with the discretization of high order elements. The model is validated, and examinations on the computing efficiency and memory requirement of the new method have also been carried out. It shows that the new method has the same advantages as that for infinite depth.

Multiresolution Analysis by Infinitely Differentiable Compactly Supported Functions

DTIC Science & Technology

1992-09-01

Math. Surveys 45:1 (1990), 87-120. [I] (;. Strang and G. Fix, A Fourier analysis of the finite element variational method. C.I.M.F. I 1 Ciclo 1971, in Constructi’c Aspects of Functional Analyszs ed. G. Geymonat 1973, 793-840. 10

Two-Dimensional Diffusion Theory Analysis of Reactivity Effects of a Fuel-Plate-Removal Experiment

NASA Technical Reports Server (NTRS)

Gotsky, Edward R.; Cusick, James P.; Bogart, Donald

1959-01-01

Two-dimensional two-group diffusion calculations were performed on the NASA reactor simulator in order to evaluate the reactivity effects of fuel plates removed successively from the center experimental fuel element of a seven- by three-element core loading at the Oak Ridge Bulk Shielding Facility. The reactivity calculations were performed by two methods: In the first, the slowing-down properties of the experimental fuel element were represented by its infinite media parameters; and, in the second, the finite size of the experimental fuel element was recognized, and the slowing-down properties of the surrounding core were attributed to this small region. The latter calculation method agreed very well with the experimented reactivity effects; the former method underestimated the experimental reactivity effects.

On the dynamics of approximating schemes for dissipative nonlinear equations

NASA Technical Reports Server (NTRS)

Jones, Donald A.

1993-01-01

Since one can rarely write down the analytical solutions to nonlinear dissipative partial differential equations (PDE's), it is important to understand whether, and in what sense, the behavior of approximating schemes to these equations reflects the true dynamics of the original equations. Further, because standard error estimates between approximations of the true solutions coming from spectral methods - finite difference or finite element schemes, for example - and the exact solutions grow exponentially in time, this analysis provides little value in understanding the infinite time behavior of a given approximating scheme. The notion of the global attractor has been useful in quantifying the infinite time behavior of dissipative PDEs, such as the Navier-Stokes equations. Loosely speaking, the global attractor is all that remains of a sufficiently large bounded set in phase space mapped infinitely forward in time under the evolution of the PDE. Though the attractor has been shown to have some nice properties - it is compact, connected, and finite dimensional, for example - it is in general quite complicated. Nevertheless, the global attractor gives a way to understand how the infinite time behavior of approximating schemes such as the ones coming from a finite difference, finite element, or spectral method relates to that of the original PDE. Indeed, one can often show that such approximations also have a global attractor. We therefore only need to understand how the structure of the attractor for the PDE behaves under approximation. This is by no means a trivial task. Several interesting results have been obtained in this direction. However, we will not go into the details. We mention here that approximations generally lose information about the system no matter how accurate they are. There are examples that show certain parts of the attractor may be lost by arbitrary small perturbations of the original equations.

Krogh-cylinder and infinite-domain models for washout of an inert diffusible solute from tissue.

PubMed

Secomb, Timothy W

2015-01-01

Models based on the Krogh-cylinder concept are developed to analyze the washout from tissue by blood flow of an inert diffusible solute that permeates blood vessel walls. During the late phase of washout, the outflowing solute concentration decays exponentially with time. This washout decay rate is predicted for a range of conditions. A single capillary is assumed to lie on the axis of a cylindrical tissue region. In the classic "Krogh-cylinder" approach, a no-flux boundary condition is applied on the outside of the cylinder. An alternative "infinite-domain" approach is proposed that allows for solute exchange across the boundary, but with zero net exchange. Both models are analyzed, using finite-element and analytical methods. The washout decay rate depends on blood flow rate, tissue diffusivity and vessel permeability of solute, and assumed boundary conditions. At low blood flow rates, the washout rate can exceed the value for a single well-mixed compartment. The infinite-domain approach predicts slower washout decay rates than the Krogh-cylinder approach. The infinite-domain approach overcomes a significant limitation of the Krogh-cylinder approach, while retaining its simplicity. It provides a basis for developing methods to deduce transport properties of inert solutes from observations of washout decay rates. © 2014 John Wiley & Sons Ltd.

Stresses and strains in thick perforated orthotropic plates

Treesearch

A. Alshaya; John Hunt; R. Rowlands

2016-01-01

Stress and strain concentrations and in-plane and out-of-plane stress constraint factors associated with a circular hole in thick, loaded orthotropic composite plates are determined by three-dimensional finite element method. The plate has essentially infinite in-plane geometry but finite thickness. Results for Sitka Spruce wood are emphasized, although some for carbon...

Analysis and synthesis of (SAR) waveguide phased array antennas

NASA Astrophysics Data System (ADS)

Visser, H. J.

1994-02-01

This report describes work performed due to ESA contract No. 101 34/93/NL/PB. Started is with a literature study on dual polarized waveguide radiators, resulting in the choice for the open ended square waveguide. After a thorough description of the mode matching infinite waveguide array analysis method - including finiteness effects - that forms the basis for all further described analysis and synthesis methods, the accuracy of the analysis software is validated by comparison with measurements on two realized antennas. These antennas have centered irises in the waveguide apertures and a dielectric wide angle impedance matching sheet in front of the antenna. A synthesis method, using simulated annealing and downhill simplex, is described next and different antenna designs, based on the analysis of a single element in an infinite array environment, are presented. Next, designs of subarrays are presented. Shown is the paramount importance of including the array environment in the design of a subarray. A microstrip patch waveguide exciter and subarray feeding network are discussed and the depth of the waveguide radiator is estimated. Chosen is a rectangular grid array with waveguides of 2.5 cm depth without irises and without dielectric sheet, grouped in linear 8 elements subarrays.

Improvement of finite element meshes - Heat transfer in an infinite cylinder

NASA Technical Reports Server (NTRS)

Kittur, Madan G.; Huston, Ronald L.; Oswald, Fred B.

1989-01-01

An extension of a structural finite element mesh improvement technique to heat conduction analysis is presented. The mesh improvement concept was originally presented by Prager in studying tapered, axially loaded bars. It was further shown that an improved mesh can be obtained by minimizing the trace of the stiffnes matrix. These procedures are extended and applied to the analysis of heat conduction in an infinitely long hollow circular cylinder.

Improvement in finite element meshes: Heat transfer in an infinite cylinder

NASA Technical Reports Server (NTRS)

Kittur, Madan G.; Huston, Ronald L.; Oswald, Fred B.

1988-01-01

An extension of a structural finite element mesh improvement technique to heat conduction analysis is presented. The mesh improvement concept was originally presented by Prager in studying tapered, axially loaded bars. It was further shown that an improved mesh can be obtained by minimizing the trace of the stiffness matrix. These procedures are extended and applied to the analysis of heat conduction in an infinitely long hollow circular cylinder.

Finite element modeling of diffusion and partitioning in biological systems: the infinite composite medium problem.

PubMed

Missel, P J

2000-01-01

Four methods are proposed for modeling diffusion in heterogeneous media where diffusion and partition coefficients take on differing values in each subregion. The exercise was conducted to validate finite element modeling (FEM) procedures in anticipation of modeling drug diffusion with regional partitioning into ocular tissue, though the approach can be useful for other organs, or for modeling diffusion in laminate devices. Partitioning creates a discontinuous value in the dependent variable (concentration) at an intertissue boundary that is not easily handled by available general-purpose FEM codes, which allow for only one value at each node. The discontinuity is handled using a transformation on the dependent variable based upon the region-specific partition coefficient. Methods were evaluated by their ability to reproduce a known exact result, for the problem of the infinite composite medium (Crank, J. The Mathematics of Diffusion, 2nd ed. New York: Oxford University Press, 1975, pp. 38-39.). The most physically intuitive method is based upon the concept of chemical potential, which is continuous across an interphase boundary (method III). This method makes the equation of the dependent variable highly nonlinear. This can be linearized easily by a change of variables (method IV). Results are also given for a one-dimensional problem simulating bolus injection into the vitreous, predicting time disposition of drug in vitreous and retina.

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.

B and F Projection Methods for Nearly Incompressible Linear and Nonlinear Elasticity and Plasticity using Higher-order NURBS Elements

DTIC Science & Technology

2007-08-01

Infinite plate with a hole: sequence of meshes produced by h-refinement. The geometry of the coarsest mesh...recalled with an emphasis on k -refinement. In Section 3, the use of high-order NURBS within a projection technique is studied in the geometri - cally linear...case with a B̄ method to investigate the choice of approximation and projection spaces with NURBS.

Comment on 'Phase transition-like behavior in a low-pass filter'.

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

Uretsky, J. L.; High Energy Physics

2003-12-01

This is a reminder that an infinite series can be defined other than as the limit of a sequence of finite series. An example is provided in which a circuit element comprised of an infinite series of resistors has negative resistance.

The forced vibration of one-dimensional multi-coupled periodic structures: An application to finite element analysis

NASA Astrophysics Data System (ADS)

Mead, Denys J.

2009-01-01

A general theory for the forced vibration of multi-coupled one-dimensional periodic structures is presented as a sequel to a much earlier general theory for free vibration. Starting from the dynamic stiffness matrix of a single multi-coupled periodic element, it derives matrix equations for the magnitudes of the characteristic free waves excited in the whole structure by prescribed harmonic forces and/or displacements acting at a single periodic junction. The semi-infinite periodic system excited at its end is first analysed to provide the basis for analysing doubly infinite and finite periodic systems. In each case, total responses are found by considering just one periodic element. An already-known method of reducing the size of the computational problem is reexamined, expanded and extended in detail, involving reduction of the dynamic stiffness matrix of the periodic element through a wave-coordinate transformation. Use of the theory is illustrated in a combined periodic structure+finite element analysis of the forced harmonic in-plane motion of a uniform flat plate. Excellent agreement between the computed low-frequency responses and those predicted by simple engineering theories validates the detailed formulations of the paper. The primary purpose of the paper is not towards a specific application but to present a systematic and coherent forced vibration theory, carefully linked with the existing free-wave theory.

Stabilization of time domain acoustic boundary element method for the interior problem with impedance boundary conditions.

PubMed

Jang, Hae-Won; Ih, Jeong-Guon

2012-04-01

The time domain boundary element method (BEM) is associated with numerical instability that typically stems from the time marching scheme. In this work, a formulation of time domain BEM is derived to deal with all types of boundary conditions adopting a multi-input, multi-output, infinite impulse response structure. The fitted frequency domain impedance data are converted into a time domain expression as a form of an infinite impulse response filter, which can also invoke a modeling error. In the calculation, the response at each time step is projected onto the wave vector space of natural radiation modes, which can be obtained from the eigensolutions of the single iterative matrix. To stabilize the computation, unstable oscillatory modes are nullified, and the same decay rate is used for two nonoscillatory modes. As a test example, a transient sound field within a partially lined, parallelepiped box is used, within which a point source is excited by an octave band impulse. In comparison with the results of the inverse Fourier transform of a frequency domain BEM, the average of relative difference norm in the stabilized time response is found to be 4.4%.

Design of Particulate-Reinforced Composite Materials

PubMed Central

Muc, Aleksander; Barski, Marek

2018-01-01

A microstructure-based model is developed to study the effective anisotropic properties (magnetic, dielectric or thermal) of two-phase particle-filled composites. The Green’s function technique and the effective field method are used to theoretically derive the homogenized (averaged) properties for a representative volume element containing isolated inclusion and infinite, chain-structured particles. Those results are compared with the finite element approximations conducted for the assumed representative volume element. In addition, the Maxwell–Garnett model is retrieved as a special case when particle interactions are not considered. We also give some information on the optimal design of the effective anisotropic properties taking into account the shape of magnetic particles. PMID:29401678

Mean Green operators of deformable fiber networks embedded in a compliant matrix and property estimates

NASA Astrophysics Data System (ADS)

Franciosi, Patrick; Spagnuolo, Mario; Salman, Oguz Umut

2018-04-01

Composites comprising included phases in a continuous matrix constitute a huge class of meta-materials, whose effective properties, whether they be mechanical, physical or coupled, can be selectively optimized by using appropriate phase arrangements and architectures. An important subclass is represented by "network-reinforced matrices," say those materials in which one or more of the embedded phases are co-continuous with the matrix in one or more directions. In this article, we present a method to study effective properties of simple such structures from which more complex ones can be accessible. Effective properties are shown, in the framework of linear elasticity, estimable by using the global mean Green operator for the entire embedded fiber network which is by definition through sample spanning. This network operator is obtained from one of infinite planar alignments of infinite fibers, which the network can be seen as an interpenetrated set of, with the fiber interactions being fully accounted for in the alignments. The mean operator of such alignments is given in exact closed form for isotropic elastic-like or dielectric-like matrices. We first exemplify how these operators relevantly provide, from classic homogenization frameworks, effective properties in the case of 1D fiber bundles embedded in an isotropic elastic-like medium. It is also shown that using infinite patterns with fully interacting elements over their whole influence range at any element concentration suppresses the dilute approximation limit of these frameworks. We finally present a construction method for a global operator of fiber networks described as interpenetrated such bundles.

Hybrid transfer-matrix FDTD method for layered periodic structures.

PubMed

Deinega, Alexei; Belousov, Sergei; Valuev, Ilya

2009-03-15

A hybrid transfer-matrix finite-difference time-domain (FDTD) method is proposed for modeling the optical properties of finite-width planar periodic structures. This method can also be applied for calculation of the photonic bands in infinite photonic crystals. We describe the procedure of evaluating the transfer-matrix elements by a special numerical FDTD simulation. The accuracy of the new method is tested by comparing computed transmission spectra of a 32-layered photonic crystal composed of spherical or ellipsoidal scatterers with the results of direct FDTD and layer-multiple-scattering calculations.

Absolutely and uniformly convergent iterative approach to inverse scattering with an infinite radius of convergence

DOEpatents

Kouri, Donald J [Houston, TX; Vijay, Amrendra [Houston, TX; Zhang, Haiyan [Houston, TX; Zhang, Jingfeng [Houston, TX; Hoffman, David K [Ames, IA

2007-05-01

A method and system for solving the inverse acoustic scattering problem using an iterative approach with consideration of half-off-shell transition matrix elements (near-field) information, where the Volterra inverse series correctly predicts the first two moments of the interaction, while the Fredholm inverse series is correct only for the first moment and that the Volterra approach provides a method for exactly obtaining interactions which can be written as a sum of delta functions.

Comparison of finite element and transfer matrix methods for numerical investigation of surface plasmon waveguides

NASA Astrophysics Data System (ADS)

Haddouche, Issam; Cherbi, Lynda

2017-01-01

In this paper, we investigate Surface Plasmon Polaritons (SPPs) in the visible regime at a metal/dielectric interface within two different waveguide structures, the first is a Photonic Crystal Fiber where the Full Vector Finite Element Method (FVFEM) is used and the second is a slab waveguide where the transfer matrix method (TMM) is used. Knowing the diversities between the two methods in terms of speed, simplicity, and scope of application, computation is implemented with respect to wavelength and metal layer thickness in order to analyze and compare the performances of the two methods. Simulation results show that the TMM can be a good approximation for the FVFEM and that SPPs behave more like modes propagating in a semi infinite metal/dielectric structure as metal thickness increases from about 150 nm.

Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method.

PubMed

Reck, Kasper; Thomsen, Erik V; Hansen, Ole

2011-01-31

The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution.

Solving three-body-breakup problems with outgoing-flux asymptotic conditions

NASA Astrophysics Data System (ADS)

Randazzo, J. M.; Buezas, F.; Frapiccini, A. L.; Colavecchia, F. D.; Gasaneo, G.

2011-11-01

An analytically solvable three-body collision system (s wave) model is used to test two different theoretical methods. The first one is a configuration interaction expansion of the scattering wave function using a basis set of Generalized Sturmian Functions (GSF) with purely outgoing flux (CISF), introduced recently in A. L. Frapicinni, J. M. Randazzo, G. Gasaneo, and F. D. Colavecchia [J. Phys. B: At. Mol. Opt. Phys.JPAPEH0953-407510.1088/0953-4075/43/10/101001 43, 101001 (2010)]. The second one is a finite element method (FEM) calculation performed with a commercial code. Both methods are employed to analyze different ways of modeling the asymptotic behavior of the wave function in finite computational domains. The asymptotes can be simulated very accurately by choosing hyperspherical or rectangular contours with the FEM software. In contrast, the CISF method can be defined both in an infinite domain or within a confined region in space. We found that the hyperspherical (rectangular) FEM calculation and the infinite domain (confined) CISF evaluation are equivalent. Finally, we apply these models to the Temkin-Poet approach of hydrogen ionization.

Contact interaction of thin-walled elements with an elastic layer and an infinite circular cylinder under torsion

NASA Astrophysics Data System (ADS)

Kanetsyan, E. G.; Mkrtchyan, M. S.; Mkhitaryan, S. M.

2018-04-01

We consider a class of contact torsion problems on interaction of thin-walled elements shaped as an elastic thin washer – a flat circular plate of small height – with an elastic layer, in particular, with a half-space, and on interaction of thin cylindrical shells with a solid elastic cylinder, infinite in both directions. The governing equations of the physical models of elastic thin washers and thin circular cylindrical shells under torsion are derived from the exact equations of mathematical theory of elasticity using the Hankel and Fourier transforms. Within the framework of the accepted physical models, the solution of the contact problem between an elastic washer and an elastic layer is reduced to solving the Fredholm integral equation of the first kind with a kernel representable as a sum of the Weber–Sonin integral and some integral regular kernel, while solving the contact problem between a cylindrical shell and solid cylinder is reduced to a singular integral equation (SIE). An effective method for solving the governing integral equations of these problems are specified.

Coupled Finite Element and Cellular Automata Methods for Analysis of Composite Structures in an Acoustic Domain

DTIC Science & Technology

2012-09-01

the geometry and constraints of the structure with the material properties of its components to generate a response (e.g., displacement, stress, and...phenomena with relative simplicity. Generally, both space and time are treated discretely and the value of the quantity in question is limited to a ...Feit [45] was used. Consider a semi- infinite fluid-filled space with a given uniform

Semismooth Newton method for gradient constrained minimization problem

NASA Astrophysics Data System (ADS)

Anyyeva, Serbiniyaz; Kunisch, Karl

2012-08-01

In this paper we treat a gradient constrained minimization problem, particular case of which is the elasto-plastic torsion problem. In order to get the numerical approximation to the solution we have developed an algorithm in an infinite dimensional space framework using the concept of the generalized (Newton) differentiation. Regularization was done in order to approximate the problem with the unconstrained minimization problem and to make the pointwise maximum function Newton differentiable. Using semismooth Newton method, continuation method was developed in function space. For the numerical implementation the variational equations at Newton steps are discretized using finite elements method.

Device for adapting continuously variable transmissions to infinitely variable transmissions with forward-neutral-reverse capabilities

DOEpatents

Wilkes, Donald F.; Purvis, James W.; Miller, A. Keith

1997-01-01

An infinitely variable transmission is capable of operating between a maximum speed in one direction and a minimum speed in an opposite direction, including a zero output angular velocity, while being supplied with energy at a constant angular velocity. Input energy is divided between a first power path carrying an orbital set of elements and a second path that includes a variable speed adjustment mechanism. The second power path also connects with the orbital set of elements in such a way as to vary the rate of angular rotation thereof. The combined effects of power from the first and second power paths are combined and delivered to an output element by the orbital element set. The transmission can be designed to operate over a preselected ratio of forward to reverse output speeds.

Modeling and control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Mingori, D. L.

1988-01-01

This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.

Radiation Characteristics of Cavity Backed Aperture Antennas in Finite Ground Plane Using the Hybrid FEM/MoM Technique and Geometrical Theory of Diffraction

NASA Technical Reports Server (NTRS)

Reddy, C. J.; Deshpande, M. D.; Cockrell, C. R.; Beck, F. B.

1996-01-01

A technique using hybrid Finite Element Method (FEM)/Method of Moments (MoM), and Geometrical Theory of Diffraction (GTD) is presented to analyze the radiation characteristics of cavity fed aperture antennas in a finite ground plane. The cavity which excites the aperture is assumed to be fed by a cylindrical transmission line. The electromagnetic (EM) fields inside the cavity are obtained using FEM. The EM fields and their normal derivatives required for FEM solution are obtained using (1) the modal expansion in the feed region and (2) the MoM for the radiating aperture region(assuming an infinite ground plane). The finiteness of the ground plane is taken into account using GTD. The input admittance of open ended circular, rectangular, and coaxial line radiating into free space through an infinite ground plane are computed and compared with earlier published results. Radiation characteristics of a coaxial cavity fed circular aperture in a finite rectangular ground plane are verified with experimental results.

A finite element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.

1990-01-01

A numerical technique is proposed for the electromagnetic characterization of the scattering by a three-dimensional cavity-backed aperture in an infinite ground plane. The technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity. Specifically, the finite element method is employed to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane. Unlike traditional approaches, the proposed technique does not require knowledge of the cavity's Green's function and is, therefore, applicable to arbitrary shape depressions and material fillings. Furthermore, the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms.

Relativistic, model-independent, multichannel 2 → 2 transition amplitudes in a finite volume

DOE PAGES

Briceno, Raul A.; Hansen, Maxwell T.

2016-07-13

We derive formalism for determining 2 + J → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of themore » $$\\rho$$-meson form factor, in which the unstable nature of the $$\\rho$$ is rigorously accommodated. In conclusion, we also discuss how this work will impact future extractions of nuclear parity and hadronic long-range matrix elements from lattice QCD.« less

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Strip Yield Model Numerical Application to Different Geometries and Loading Conditions

NASA Technical Reports Server (NTRS)

Hatamleh, Omar; Forman, Royce; Shivakumar, Venkataraman; Lyons, Jed

2006-01-01

A new numerical method based on the strip-yield analysis approach was developed for calculating the Crack Tip Opening Displacement (CTOD). This approach can be applied for different crack configurations having infinite and finite geometries, and arbitrary applied loading conditions. The new technique adapts the boundary element / dislocation density method to obtain crack-face opening displacements at any point on a crack, and succeeds by obtaining requisite values as a series of definite integrals, the functional parts of each being evaluated exactly in a closed form.

Predicting the Rotor-Stator Interaction Acoustics of a Ducted Fan Engine

NASA Technical Reports Server (NTRS)

Biedron, Robert T.; Rumsey, Christopher L.; Podboy, Gary G.; Dunn, M. H.

2001-01-01

A Navier-Stokes computation is performed for a ducted-fan configuration with the goal of predicting rotor-stator noise generation without having to resort to heuristic modeling. The calculated pressure field in the inlet region is decomposed into classical infinite-duct modes, which are then used in either a hybrid finite-element/Kirchhoff surface method or boundary integral equation method to calculate the far field noise. Comparisons with experimental data are presented, including rotor wake surveys and far field sound pressure levels for two blade passage frequency (BPF) tones.

Unified control/structure design and modeling research

NASA Technical Reports Server (NTRS)

Mingori, D. L.; Gibson, J. S.; Blelloch, P. A.; Adamian, A.

1986-01-01

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.

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.

Temperature field determination in slabs, circular plates and spheres with saw tooth heat generating sources

NASA Astrophysics Data System (ADS)

Diestra Cruz, Heberth Alexander

The Green's functions integral technique is used to determine the conduction heat transfer temperature field in flat plates, circular plates, and solid spheres with saw tooth heat generating sources. In all cases the boundary temperature is specified (Dirichlet's condition) and the thermal conductivity is constant. The method of images is used to find the Green's function in infinite solids, semi-infinite solids, infinite quadrants, circular plates, and solid spheres. The saw tooth heat generation source has been modeled using Dirac delta function and Heaviside step function. The use of Green's functions allows obtain the temperature distribution in the form of an integral that avoids the convergence problems of infinite series. For the infinite solid and the sphere, the temperature distribution is three-dimensional and in the cases of semi-infinite solid, infinite quadrant and circular plate the distribution is two-dimensional. The method used in this work is superior to other methods because it obtains elegant analytical or quasi-analytical solutions to complex heat conduction problems with less computational effort and more accuracy than the use of fully numerical methods.

Prediction and Measurement of the Vibration and Acoustic Radiation of Panels Subjected to Acoustic Loading

NASA Technical Reports Server (NTRS)

Turner, Travis L.; Rizzi, Stephen A.

1995-01-01

Interior noise and sonic fatigue are important issues in the development and design of advanced subsonic and supersonic aircraft. Conventional aircraft typically employ passive treatments, such as constrained layer damping and acoustic absorption materials, to reduce the structural response and resulting acoustic levels in the aircraft interior. These techniques require significant addition of mass and only attenuate relatively high frequency noise transmitted through the fuselage. Although structural acoustic coupling is in general very important in the study of aircraft fuselage interior noise, analysis of noise transmission through a panel supported in an infinite rigid baffle (separating two semi-infinite acoustic domains) can be useful in evaluating the effects of active/adaptive materials, complex loading, etc. Recent work has been aimed at developing adaptive and/or active methods of controlling the structural acoustic response of panels to reduce the transmitted noise1. A finite element formulation was recently developed to study the dynamic response of shape memory alloy (SMA) hybrid composite panels (conventional composite panel with embedded SMA fibers) subject to combined acoustic and thermal loads2. Further analysis has been performed to predict the far-field acoustic radiation using the finite element dynamic panel response prediction3. The purpose of the present work is to validate the panel vibration and acoustic radiation prediction methods with baseline experimental results obtained from an isotropic panel, without the effect of SMA.

Performance of Infinitely Wide Parabolic and Inclined Slider Bearings Lubricated with Couple Stress or Magnetic Fluids

NASA Astrophysics Data System (ADS)

Oladeinde, Mobolaji Humphrey; Akpobi, John Ajokpaoghene

2011-10-01

The hydrodynamic and magnetohydrodynamic (MHD) lubrication problem of infinitely wide inclined and parabolic slider bearings is solved numerically using the finite element method. The bearing configurations are discretized into three-node isoparametric quadratic elements. Stiffness integrals obtained from the weak form of the governing equations are solved using Gauss quadrature to obtain a finite number of stiffness matrices. The global system of equations obtained from enforcing nodal continuity of pressure for the bearings are solved using the Gauss-Seidel iterative scheme with a convergence criterion of 10-10. Numerical computations reveal that, when compared for similar profile and couple stress parameters, greater pressure builds up in a parabolic slider compared to an inclined slider, indicating a greater wedge effect in the parabolic slider. The parabolic slider bearing is also shown to develop a greater load capacity when lubricated with magnetic fluids. The superior performance of parabolic slider bearing is more pronounced at greater Hartmann numbers for identical bearing structural parameters. It is also shown that when load carrying capacity is the yardstick for comparison, the parabolic slider bearings are superior to the inclined bearings when lubricated with couple stress or magnetic lubricants.

A combined dislocation fan-finite element (DF-FE) method for stress field simulation of dislocations emerging at the free surfaces of 3D elastically anisotropic crystals

NASA Astrophysics Data System (ADS)

Balusu, K.; Huang, H.

2017-04-01

A combined dislocation fan-finite element (DF-FE) method is presented for efficient and accurate simulation of dislocation nodal forces in 3D elastically anisotropic crystals with dislocations intersecting the free surfaces. The finite domain problem is decomposed into half-spaces with singular traction stresses, an infinite domain, and a finite domain with non-singular traction stresses. As such, the singular and non-singular parts of the traction stresses are addressed separately; the dislocation fan (DF) method is introduced to balance the singular traction stresses in the half-spaces while the finite element method (FEM) is employed to enforce the non-singular boundary conditions. The accuracy and efficiency of the DF method is demonstrated using a simple isotropic test case, by comparing it with the analytical solution as well as the FEM solution. The DF-FE method is subsequently used for calculating the dislocation nodal forces in a finite elastically anisotropic crystal, which produces dislocation nodal forces that converge rapidly with increasing mesh resolutions. In comparison, the FEM solution fails to converge, especially for nodes closer to the surfaces.

A Control Concept for Large Flexible Spacecraft Using Order Reduction Techniques

NASA Technical Reports Server (NTRS)

Thieme, G.; Roth, H.

1985-01-01

Results found during the investigation of control problems of large flexible spacecraft are given. A triple plate configuration of such a spacecraft is defined and studied. The model is defined by modal data derived from infinite element modeling. The order reduction method applied is briefly described. An attitude control concept with low and high authority control has been developed to design an attitude controller for the reduced model. The stability and response of the original system together with the reduced controller is analyzed.

Analytical solutions for determining residual stresses in two-dimensional domains using the contour method

PubMed Central

Kartal, Mehmet E.

2013-01-01

The contour method is one of the most prevalent destructive techniques for residual stress measurement. Up to now, the method has involved the use of the finite-element (FE) method to determine the residual stresses from the experimental measurements. This paper presents analytical solutions, obtained for a semi-infinite strip and a finite rectangle, which can be used to calculate the residual stresses directly from the measured data; thereby, eliminating the need for an FE approach. The technique is then used to determine the residual stresses in a variable-polarity plasma-arc welded plate and the results show good agreement with independent neutron diffraction measurements. PMID:24204187

Implementation of the infinite-range exterior complex scaling to the time-dependent complete-active-space self-consistent-field method

NASA Astrophysics Data System (ADS)

Orimo, Yuki; Sato, Takeshi; Scrinzi, Armin; Ishikawa, Kenichi L.

2018-02-01

We present a numerical implementation of the infinite-range exterior complex scaling [Scrinzi, Phys. Rev. A 81, 053845 (2010), 10.1103/PhysRevA.81.053845] as an efficient absorbing boundary to the time-dependent complete-active-space self-consistent field method [Sato, Ishikawa, Březinová, Lackner, Nagele, and Burgdörfer, Phys. Rev. A 94, 023405 (2016), 10.1103/PhysRevA.94.023405] for multielectron atoms subject to an intense laser pulse. We introduce Gauss-Laguerre-Radau quadrature points to construct discrete variable representation basis functions in the last radial finite element extending to infinity. This implementation is applied to strong-field ionization and high-harmonic generation in He, Be, and Ne atoms. It efficiently prevents unphysical reflection of photoelectron wave packets at the simulation boundary, enabling accurate simulations with substantially reduced computational cost, even under significant (≈50 % ) double ionization. For the case of a simulation of high-harmonic generation from Ne, for example, 80% cost reduction is achieved, compared to a mask-function absorption boundary.

The direct field boundary impedance of two-dimensional periodic structures with application to high frequency vibration prediction.

PubMed

Langley, Robin S; Cotoni, Vincent

2010-04-01

Large sections of many types of engineering construction can be considered to constitute a two-dimensional periodic structure, with examples ranging from an orthogonally stiffened shell to a honeycomb sandwich panel. In this paper, a method is presented for computing the boundary (or edge) impedance of a semi-infinite two-dimensional periodic structure, a quantity which is referred to as the direct field boundary impedance matrix. This terminology arises from the fact that none of the waves generated at the boundary (the direct field) are reflected back to the boundary in a semi-infinite system. The direct field impedance matrix can be used to calculate elastic wave transmission coefficients, and also to calculate the coupling loss factors (CLFs), which are required by the statistical energy analysis (SEA) approach to predicting high frequency vibration levels in built-up systems. The calculation of the relevant CLFs enables a two-dimensional periodic region of a structure to be modeled very efficiently as a single subsystem within SEA, and also within related methods, such as a recently developed hybrid approach, which couples the finite element method with SEA. The analysis is illustrated by various numerical examples involving stiffened plate structures.

Hilbert's Hotel in polarization singularities.

PubMed

Wang, Yangyundou; Gbur, Greg

2017-12-15

We demonstrate theoretically how the creation of polarization singularities by the evolution of a fractional nonuniform polarization optical element involves the peculiar mathematics of countably infinite sets in the form of "Hilbert's Hotel." Two distinct topological processes can be observed, depending on the structure of the fractional optical element.

Net Force of an Ideal Conductor on an Element of a Line of Charge Moving With Extreme Relativistic Speed

ERIC Educational Resources Information Center

Cawley, Robert

1978-01-01

Considers the problem of determining the force on an element of a finite length line of charge moving horizontally with extreme relativistic speed through an evacuated space above an infinite plane ideal conducting surface. (SL)

Thermal form-factor approach to dynamical correlation functions of integrable lattice models

NASA Astrophysics Data System (ADS)

Göhmann, Frank; Karbach, Michael; Klümper, Andreas; Kozlowski, Karol K.; Suzuki, Junji

2017-11-01

We propose a method for calculating dynamical correlation functions at finite temperature in integrable lattice models of Yang-Baxter type. The method is based on an expansion of the correlation functions as a series over matrix elements of a time-dependent quantum transfer matrix rather than the Hamiltonian. In the infinite Trotter-number limit the matrix elements become time independent and turn into the thermal form factors studied previously in the context of static correlation functions. We make this explicit with the example of the XXZ model. We show how the form factors can be summed utilizing certain auxiliary functions solving finite sets of nonlinear integral equations. The case of the XX model is worked out in more detail leading to a novel form-factor series representation of the dynamical transverse two-point function.

Magnetic fields end-face effect investigation of HTS bulk over PMG with 3D-modeling numerical method

NASA Astrophysics Data System (ADS)

Qin, Yujie; Lu, Yiyun

2015-09-01

In this paper, the magnetic fields end-face effect of high temperature superconducting (HTS) bulk over a permanent magnetic guideway (PMG) is researched with 3D-modeling numerical method. The electromagnetic behavior of the bulk is simulated using finite element method (FEM). The framework is formulated by the magnetic field vector method (H-method). A superconducting levitation system composed of one rectangular HTS bulk and one infinite long PMG is successfully investigated using the proposed method. The simulation results show that for finite geometrical HTS bulk, even the applied magnetic field is only distributed in x-y plane, the magnetic field component Hz which is along the z-axis can be observed interior the HTS bulk.

A coupled modal-finite element method for the wave propagation modeling in irregular open waveguides.

PubMed

Pelat, Adrien; Felix, Simon; Pagneux, Vincent

2011-03-01

In modeling the wave propagation within a street canyon, particular attention must be paid to the description of both the multiple reflections of the wave on the building facades and the radiation in the free space above the street. The street canyon being considered as an open waveguide with a discontinuously varying cross-section, a coupled modal-finite element formulation is proposed to solve the three-dimensional wave equation within. The originally open configuration-the street canyon open in the sky above-is artificially turned into a close waveguiding structure by using perfectly matched layers that truncate the infinite sky without introducing numerical reflection. Then the eigenmodes of the resulting waveguide are determined by a finite element method computation in the cross-section. The eigensolutions can finally be used in a multimodal formulation of the wave propagation along the canyon, given its geometry and the end conditions at its extremities: initial field condition at the entrance and radiation condition at the output. © 2011 Acoustical Society of America

Simulation of ultrasonic wave propagation in anisotropic poroelastic bone plate using hybrid spectral/finite element method.

PubMed

Nguyen, Vu-Hieu; Naili, Salah

2012-08-01

This paper deals with the modeling of guided waves propagation in in vivo cortical long bone, which is known to be anisotropic medium with functionally graded porosity. The bone is modeled as an anisotropic poroelastic material by using Biot's theory formulated in high frequency domain. A hybrid spectral/finite element formulation has been developed to find the time-domain solution of ultrasonic waves propagating in a poroelastic plate immersed in two fluid halfspaces. The numerical technique is based on a combined Laplace-Fourier transform, which allows to obtain a reduced dimension problem in the frequency-wavenumber domain. In the spectral domain, as radiation conditions representing infinite fluid halfspaces may be exactly introduced, only the heterogeneous solid layer needs to be analyzed by using finite element method. Several numerical tests are presented showing very good performance of the proposed procedure. A preliminary study on the first arrived signal velocities computed by using equivalent elastic and poroelastic models will be presented. Copyright © 2012 John Wiley & Sons, Ltd.

Recent Advances in Laplace Transform Analytic Element Method (LT-AEM) Theory and Application to Transient Groundwater Flow

NASA Astrophysics Data System (ADS)

Kuhlman, K. L.; Neuman, S. P.

2006-12-01

Furman and Neuman (2003) proposed a Laplace Transform Analytic Element Method (LT-AEM) for transient groundwater flow. LT-AEM applies the traditionally steady-state AEM to the Laplace transformed groundwater flow equation, and back-transforms the resulting solution to the time domain using a Fourier Series numerical inverse Laplace transform method (de Hoog, et.al., 1982). We have extended the method so it can compute hydraulic head and flow velocity distributions due to any two-dimensional combination and arrangement of point, line, circular and elliptical area sinks and sources, nested circular or elliptical regions having different hydraulic properties, and areas of specified head, flux or initial condition. The strengths of all sinks and sources, and the specified head and flux values, can all vary in both space and time in an independent and arbitrary fashion. Initial conditions may vary from one area element to another. A solution is obtained by matching heads and normal fluxes along the boundary of each element. The effect which each element has on the total flow is expressed in terms of generalized Fourier series which converge rapidly (<20 terms) in most cases. As there are more matching points than unknown Fourier terms, the matching is accomplished in Laplace space using least-squares. The method is illustrated by calculating the resulting transient head and flow velocities due to an arrangement of elements in both finite and infinite domains. The 2D LT-AEM elements already developed and implemented are currently being extended to solve the 3D groundwater flow equation.

Calculation of Heat-Bearing Agent’s Steady Flow in Fuel Bundle

NASA Astrophysics Data System (ADS)

Amosova, E. V.; Guba, G. G.

2017-11-01

This paper introduces the result of studying the heat exchange in the fuel bundle of the nuclear reactor’s fuel magazine. The article considers the fuel bundle of the infinite number of fuel elements, fuel elements are considered in the checkerboard fashion (at the tops of a regular triangle a fuel element is a plain round rod. The inhomogeneity of volume energy release in the rod forms the inhomogeneity of temperature and velocity fields, and pressure. Computational methods for studying hydrodynamics in magazines and cores with rod-shape fuel elements are based on a significant simplification of the problem: using basic (averaged) equations, isobaric section hypothesis, porous body model, etc. This could be explained by the complexity of math description of the three-dimensional fluid flow in the multi-connected area with the transfer coefficient anisotropy, curved boundaries and technical computation difficulties. Thus, calculative studying suggests itself as promising and important. There was developed a method for calculating the heat-mass exchange processes of inter-channel fuel element motions, which allows considering the contribution of natural convection to the heat-mass exchange based on the Navier-Stokes equations and Boussinesq approximation.

Nanoengineering Testbed for Nanosolar Cell and Piezoelectric Compounds

DTIC Science & Technology

2012-02-29

element mesh. The third model was a 3D finite element mesh that included complete geometric representation of Berkovich tip. This model allows for a...height of the specimen. These simulations suggest the proper specimen size to approximate a body of semi-infinite extent for a given indentation depth...tip nanoindentation model was the third and final finite element mesh created for analysis and comparison. The material model and the finite element

A Curved, Elastostatic Boundary Element for Plane Anisotropic Structures

NASA Technical Reports Server (NTRS)

Smeltzer, Stanley S.; Klang, Eric C.

2001-01-01

The plane-stress equations of linear elasticity are used in conjunction with those of the boundary element method to develop a novel curved, quadratic boundary element applicable to structures composed of anisotropic materials in a state of plane stress or plane strain. The curved boundary element is developed to solve two-dimensional, elastostatic problems of arbitrary shape, connectivity, and material type. As a result of the anisotropy, complex variables are employed in the fundamental solution derivations for a concentrated unit-magnitude force in an infinite elastic anisotropic medium. Once known, the fundamental solutions are evaluated numerically by using the known displacement and traction boundary values in an integral formulation with Gaussian quadrature. All the integral equations of the boundary element method are evaluated using one of two methods: either regular Gaussian quadrature or a combination of regular and logarithmic Gaussian quadrature. The regular Gaussian quadrature is used to evaluate most of the integrals along the boundary, and the combined scheme is employed for integrals that are singular. Individual element contributions are assembled into the global matrices of the standard boundary element method, manipulated to form a system of linear equations, and the resulting system is solved. The interior displacements and stresses are found through a separate set of auxiliary equations that are derived using an Airy-type stress function in terms of complex variables. The capabilities and accuracy of this method are demonstrated for a laminated-composite plate with a central, elliptical cutout that is subjected to uniform tension along one of the straight edges of the plate. Comparison of the boundary element results for this problem with corresponding results from an analytical model show a difference of less than 1%.

Infinite Multiplets

DOE R&D Accomplishments Database

Nambu, Y.

1967-01-01

The main ingredients of the method of infinite multiplets consist of: 1) the use of wave functions with an infinite number of components for describing an infinite tower of discrete states of an isolated system (such as an atom, a nucleus, or a hadron), 2) the use of group theory, instead of dynamical considerations, in determining the properties of the wave functions.

Metriplectic integrators for the Landau collision operator

DOE PAGES

Kraus, Michael; Hirvijoki, Eero

2017-10-02

Here, we present a novel framework for addressing the nonlinear Landau collision integral in terms of finite element and other subspace projection methods. We employ the underlying metriplectic structure of the Landau collision integral and, using a Galerkin discretization for the velocity space, we transform the infinite-dimensional system into a finite-dimensional, time-continuous metriplectic system. Temporal discretization is accomplished using the concept of discrete gradients. The conservation of energy, momentum, and particle densities, as well as the production of entropy is demonstrated algebraically for the fully discrete system. Due to the generality of our approach, the conservation properties and the monotonicmore » behavior of entropy are guaranteed for finite element discretizations, in general, independently of the mesh configuration.« less

Errors due to the truncation of the computational domain in static three-dimensional electrical impedance tomography.

PubMed

Vauhkonen, P J; Vauhkonen, M; Kaipio, J P

2000-02-01

In electrical impedance tomography (EIT), an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the body. The currents spread out in three dimensions and therefore off-plane structures have a significant effect on the reconstructed images. A question arises: how far from the current carrying electrodes should the discretized model of the object be extended? If the model is truncated too near the electrodes, errors are produced in the reconstructed images. On the other hand if the model is extended very far from the electrodes the computational time may become too long in practice. In this paper the model truncation problem is studied with the extended finite element method. Forward solutions obtained using so-called infinite elements, long finite elements and separable long finite elements are compared to the correct solution. The effects of the truncation of the computational domain on the reconstructed images are also discussed and results from the three-dimensional (3D) sensitivity analysis are given. We show that if the finite element method with ordinary elements is used in static 3D EIT, the dimension of the problem can become fairly large if the errors associated with the domain truncation are to be avoided.

An infinitely-stiff elastic system via a tuned negative-stiffness component stabilized by rotation-produced gyroscopic forces

NASA Astrophysics Data System (ADS)

Kochmann, D. M.; Drugan, W. J.

2016-06-01

An elastic system containing a negative-stiffness element tuned to produce positive-infinite system stiffness, although statically unstable as is any such elastic system if unconstrained, is proved to be stabilized by rotation-produced gyroscopic forces at sufficiently high rotation rates. This is accomplished in possibly the simplest model of a composite structure (or solid) containing a negative-stiffness component that exhibits all these features, facilitating a conceptually and mathematically transparent, completely closed-form analysis.

Seismic damage analysis of the outlet piers of arch dams using the finite element sub-model method

NASA Astrophysics Data System (ADS)

Song, Liangfeng; Wu, Mingxin; Wang, Jinting; Xu, Yanjie

2016-09-01

This study aims to analyze seismic damage of reinforced outlet piers of arch dams by the nonlinear finite element (FE) sub-model method. First, the dam-foundation system is modeled and analyzed, in which the effects of infinite foundation, contraction joints, and nonlinear concrete are taken into account. The detailed structures of the outlet pier are then simulated with a refined FE model in the sub-model analysis. In this way the damage mechanism of the plain (unreinforced) outlet pier is analyzed, and the effects of two reinforcement measures (i.e., post-tensioned anchor cables and reinforcing bar) on the dynamic damage to the outlet pier are investigated comprehensively. Results show that the plain pier is damaged severely by strong earthquakes while implementation of post-tensioned anchor cables strengthens the pier effectively. In addition, radiation damping strongly alleviates seismic damage to the piers.

A new method for constructing analytic elements for groundwater flow.

NASA Astrophysics Data System (ADS)

Strack, O. D.

2007-12-01

The analytic element method is based upon the superposition of analytic functions that are defined throughout the infinite domain, and can be used to meet a variety of boundary conditions. Analytic elements have been use successfully for a number of problems, mainly dealing with the Poisson equation (see, e.g., Theory and Applications of the Analytic Element Method, Reviews of Geophysics, 41,2/1005 2003 by O.D.L. Strack). The majority of these analytic elements consists of functions that exhibit jumps along lines or curves. Such linear analytic elements have been developed also for other partial differential equations, e.g., the modified Helmholz equation and the heat equation, and were constructed by integrating elementary solutions, the point sink and the point doublet, along a line. This approach is limiting for two reasons. First, the existence is required of the elementary solutions, and, second, the integration tends to limit the range of solutions that can be obtained. We present a procedure for generating analytic elements that requires merely the existence of a harmonic function with the desired properties; such functions exist in abundance. The procedure to be presented is used to generalize this harmonic function in such a way that the resulting expression satisfies the applicable differential equation. The approach will be applied, along with numerical examples, for the modified Helmholz equation and for the heat equation, while it is noted that the method is in no way restricted to these equations. The procedure is carried out entirely in terms of complex variables, using Wirtinger calculus.

Numerical scheme approximating solution and parameters in a beam equation

NASA Astrophysics Data System (ADS)

Ferdinand, Robert R.

2003-12-01

We present a mathematical model which describes vibration in a metallic beam about its equilibrium position. This model takes the form of a nonlinear second-order (in time) and fourth-order (in space) partial differential equation with boundary and initial conditions. A finite-element Galerkin approximation scheme is used to estimate model solution. Infinite-dimensional model parameters are then estimated numerically using an inverse method procedure which involves the minimization of a least-squares cost functional. Numerical results are presented and future work to be done is discussed.

Analysis of the sound field in finite length infinite baffled cylindrical ducts with vibrating walls of finite impedance.

PubMed

Shao, Wei; Mechefske, Chris K

2005-04-01

This paper describes an analytical model of finite cylindrical ducts with infinite flanges. This model is used to investigate the sound radiation characteristics of the gradient coil system of a magnetic resonance imaging (MRI) scanner. The sound field in the duct satisfies both the boundary conditions at the wall and at the open ends. The vibrating cylindrical wall of the duct is assumed to be the only sound source. Different acoustic conditions for the wall (rigid and absorptive) are used in the simulations. The wave reflection phenomenon at the open ends of the finite duct is described by general radiation impedance. The analytical model is validated by the comparison with its counterpart in a commercial code based on the boundary element method (BEM). The analytical model shows significant advantages over the BEM model with better numerical efficiency and a direct relation between the design parameters and the sound field inside the duct.

Estimating the vibration level of an L-shaped beam using power flow techniques

NASA Technical Reports Server (NTRS)

Cuschieri, J. M.; Mccollum, M.; Rassineux, J. L.; Gilbert, T.

1986-01-01

The response of one component of an L-shaped beam, with point force excitation on the other component, is estimated using the power flow method. The transmitted power from the source component to the receiver component is expressed in terms of the transfer and input mobilities at the excitation point and the joint. The response is estimated both in narrow frequency bands, using the exact geometry of the beams, and as a frequency averaged response using infinite beam models. The results using this power flow technique are compared to the results obtained using finite element analysis (FEA) of the L-shaped beam for the low frequency response and to results obtained using statistical energy analysis (SEA) for the high frequencies. The agreement between the FEA results and the power flow method results at low frequencies is very good. SEA results are in terms of frequency averaged levels and these are in perfect agreement with the results obtained using the infinite beam models in the power flow method. The narrow frequency band results from the power flow method also converge to the SEA results at high frequencies. The advantage of the power flow method is that detail of the response can be retained while reducing computation time, which will allow the narrow frequency band analysis of the response to be extended to higher frequencies.

Texture zeros and hierarchical masses from flavour (mis)alignment

NASA Astrophysics Data System (ADS)

Hollik, W. G.; Saldana-Salazar, U. J.

2018-03-01

We introduce an unconventional interpretation of the fermion mass matrix elements. As the full rotational freedom of the gauge-kinetic terms renders a set of infinite bases called weak bases, basis-dependent structures as mass matrices are unphysical. Matrix invariants, on the other hand, provide a set of basis-independent objects which are of more relevance. We employ one of these invariants to give a new parametrisation of the mass matrices. By virtue of it, one gains control over its implicit implications on several mass matrix structures. The key element is the trace invariant which resembles the equation of a hypersphere with a radius equal to the Frobenius norm of the mass matrix. With the concepts of alignment or misalignment we can identify texture zeros with certain alignments whereas Froggatt-Nielsen structures in the matrix elements are governed by misalignment. This method allows further insights of traditional approaches to the underlying flavour geometry.

Equations of motion for a spectrum-generating algebra: Lipkin Meshkov Glick model

NASA Astrophysics Data System (ADS)

Rosensteel, G.; Rowe, D. J.; Ho, S. Y.

2008-01-01

For a spectrum-generating Lie algebra, a generalized equations-of-motion scheme determines numerical values of excitation energies and algebra matrix elements. In the approach to the infinite particle number limit or, more generally, whenever the dimension of the quantum state space is very large, the equations-of-motion method may achieve results that are impractical to obtain by diagonalization of the Hamiltonian matrix. To test the method's effectiveness, we apply it to the well-known Lipkin-Meshkov-Glick (LMG) model to find its low-energy spectrum and associated generator matrix elements in the eigenenergy basis. When the dimension of the LMG representation space is 106, computation time on a notebook computer is a few minutes. For a large particle number in the LMG model, the low-energy spectrum makes a quantum phase transition from a nondegenerate harmonic vibrator to a twofold degenerate harmonic oscillator. The equations-of-motion method computes critical exponents at the transition point.

Turbofan Acoustic Propagation and Radiation

NASA Technical Reports Server (NTRS)

Eversman, Walter

2000-01-01

This document describes progress in the development of finite element codes for the prediction of near and far field acoustic radiation from the inlet and aft fan ducts of turbofan engines. The report consists of nine papers which have appeared in archival journals and conference proceedings, or are presently in review for publication. Topics included are: 1. Aft Fan Duct Acoustic Radiation; 2. Mapped Infinite Wave Envelope Elements for Acoustic Radiation in a Uniformly Moving Medium; 3. A Reflection Free Boundary Condition for Propagation in Uniform Flow Using Mapped Infinite Wave Envelope Elements; 4. A Numerical Comparison Between Multiple-Scales and FEM Solution for Sound Propagation in Lined Flow Ducts; 5. Acoustic Propagation at High Frequencies in Ducts; 6. The Boundary Condition at an Impedance Wall in a Nonuniform Duct with Potential Flow; 7. A Reverse Flow Theorem and Acoustic Reciprocity in Compressible Potential Flows; 8. Reciprocity and Acoustics Power in One Dimensional Compressible Potential Flows; and 9. Numerical Experiments on Acoustic Reciprocity in Compressible Potential Flows.

Application of AWE Along with a Combined FEM/MoM Technique to Compute RCS of a Cavity-Backed Aperture in an Infinite Ground Plane Over a Frequency Range

NASA Technical Reports Server (NTRS)

Reddy, C.J.; Deshpande, M.D.

1997-01-01

A hybrid Finite Element Method (FEM)/Method of Moments (MoM) technique in conjunction with the Asymptotic Waveform Evaluation (AWE) technique is applied to obtain radar cross section (RCS) of a cavity-backed aperture in an infinite ground plane over a frequency range. The hybrid FEM/MoM technique when applied to the cavity-backed aperture results in an integro-differential equation with electric field as the unknown variable, the electric field obtained from the solution of the integro-differential equation is expanded in Taylor series. The coefficients of the Taylor series are obtained using the frequency derivatives of the integro-differential equation formed by the hybrid FEM/MoM technique. The series is then matched via the Pade approximation to a rational polynomial, which can be used to extrapolate the electric field over a frequency range. The RCS of the cavity-backed aperture is calculated using the electric field at different frequencies. Numerical results for a rectangular cavity, a circular cavity, and a material filled cavity are presented over a frequency range. Good agreement between AWE and the exact solution over the frequency range is obtained.

Source-Device-Independent Ultrafast Quantum Random Number Generation.

PubMed

Marangon, Davide G; Vallone, Giuseppe; Villoresi, Paolo

2017-02-10

Secure random numbers are a fundamental element of many applications in science, statistics, cryptography and more in general in security protocols. We present a method that enables the generation of high-speed unpredictable random numbers from the quadratures of an electromagnetic field without any assumption on the input state. The method allows us to eliminate the numbers that can be predicted due to the presence of classical and quantum side information. In particular, we introduce a procedure to estimate a bound on the conditional min-entropy based on the entropic uncertainty principle for position and momentum observables of infinite dimensional quantum systems. By the above method, we experimentally demonstrated the generation of secure true random bits at a rate greater than 1.7 Gbit/s.

A microstructural lattice model for strain oriented problems: A combined Monte Carlo finite element technique

NASA Technical Reports Server (NTRS)

Gayda, J.; Srolovitz, D. J.

1987-01-01

A specialized, microstructural lattice model, termed MCFET for combined Monte Carlo Finite Element Technique, was developed which simulates microstructural evolution in material systems where modulated phases occur and the directionality of the modulation is influenced by internal and external stresses. In this approach, the microstructure is discretized onto a fine lattice. Each element in the lattice is labelled in accordance with its microstructural identity. Diffusion of material at elevated temperatures is simulated by allowing exchanges of neighboring elements if the exchange lowers the total energy of the system. A Monte Carlo approach is used to select the exchange site while the change in energy associated with stress fields is computed using a finite element technique. The MCFET analysis was validated by comparing this approach with a closed form, analytical method for stress assisted, shape changes of a single particle in an infinite matrix. Sample MCFET analytical for multiparticle problems were also run and in general the resulting microstructural changes associated with the application of an external stress are similar to that observed in Ni-Al-Cr alloys at elevated temperature.

Work distributions for random sudden quantum quenches

NASA Astrophysics Data System (ADS)

Łobejko, Marcin; Łuczka, Jerzy; Talkner, Peter

2017-05-01

The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary ensemble (GUE) consisting of Hermitian matrices with identically, Gaussian distributed matrix elements. A probability density function (pdf) of work in terms of initial and final energy distributions is derived and evaluated for a two-level system. Explicit results are obtained for quenches with a sharply given initial Hamiltonian, while the work pdfs for quenches between Hamiltonians from two independent GUEs can only be determined in explicit form in the limits of zero and infinite temperature. The same work distribution as for a sudden random quench is obtained for an adiabatic, i.e., infinitely slow, protocol connecting the same initial and final Hamiltonians.

Mechanical behaviour of synthetic surgical meshes: finite element simulation of the herniated abdominal wall.

PubMed

Hernández-Gascón, B; Peña, E; Melero, H; Pascual, G; Doblaré, M; Ginebra, M P; Bellón, J M; Calvo, B

2011-11-01

The material properties of meshes used in hernia surgery contribute to the overall mechanical behaviour of the repaired abdominal wall. The mechanical response of a surgical mesh has to be defined since the haphazard orientation of an anisotropic mesh can lead to inconsistent surgical outcomes. This study was designed to characterize the mechanical behaviour of three surgical meshes (Surgipro®, Optilene® and Infinit®) and to describe a mechanical constitutive law that accurately reproduces the experimental results. Finally, through finite element simulation, the behaviour of the abdominal wall was modelled before and after surgical mesh implant. Uniaxial loading of mesh samples in two perpendicular directions revealed the isotropic response of Surgipro® and the anisotropic behaviour of Optilene® and Infinit®. A phenomenological constitutive law was used to reproduce the measured experimental curves. To analyze the mechanical effect of the meshes once implanted in the abdomen, finite element simulation of the healthy and partially herniated repaired rabbit abdominal wall served to reproduce wall behaviour before and after mesh implant. In all cases, maximal displacements were lower and maximal principal stresses higher in the implanted abdomen than the intact wall model. Despite the fact that no mesh showed a behaviour that perfectly matched that of abdominal muscle, the Infinit® mesh was able to best comply with the biomechanics of the abdominal wall. Copyright © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Multi-Region Boundary Element Analysis for Coupled Thermal-Fracturing Processes in Geomaterials

NASA Astrophysics Data System (ADS)

Shen, Baotang; Kim, Hyung-Mok; Park, Eui-Seob; Kim, Taek-Kon; Wuttke, Manfred W.; Rinne, Mikael; Backers, Tobias; Stephansson, Ove

2013-01-01

This paper describes a boundary element code development on coupled thermal-mechanical processes of rock fracture propagation. The code development was based on the fracture mechanics code FRACOD that has previously been developed by Shen and Stephansson (Int J Eng Fracture Mech 47:177-189, 1993) and FRACOM (A fracture propagation code—FRACOD, User's manual. FRACOM Ltd. 2002) and simulates complex fracture propagation in rocks governed by both tensile and shear mechanisms. For the coupled thermal-fracturing analysis, an indirect boundary element method, namely the fictitious heat source method, was implemented in FRACOD to simulate the temperature change and thermal stresses in rocks. This indirect method is particularly suitable for the thermal-fracturing coupling in FRACOD where the displacement discontinuity method is used for mechanical simulation. The coupled code was also extended to simulate multiple region problems in which rock mass, concrete linings and insulation layers with different thermal and mechanical properties were present. Both verification and application cases were presented where a point heat source in a 2D infinite medium and a pilot LNG underground cavern were solved and studied using the coupled code. Good agreement was observed between the simulation results, analytical solutions and in situ measurements which validates an applicability of the developed coupled code.

What's Cooler Than Being Cool? Ice-Sheet Models Using a Fluidity-Based FOSLS Approach to Nonlinear-Stokes Flow

NASA Astrophysics Data System (ADS)

Allen, Jeffery M.

This research involves a few First-Order System Least Squares (FOSLS) formulations of a nonlinear-Stokes flow model for ice sheets. In Glen's flow law, a commonly used constitutive equation for ice rheology, the viscosity becomes infinite as the velocity gradients approach zero. This typically occurs near the ice surface or where there is basal sliding. The computational difficulties associated with the infinite viscosity are often overcome by an arbitrary modification of Glen's law that bounds the maximum viscosity. The FOSLS formulations developed in this thesis are designed to overcome this difficulty. The first FOSLS formulation is just the first-order representation of the standard nonlinear, full-Stokes and is known as the viscosity formulation and suffers from the problem above. To overcome the problem of infinite viscosity, two new formulation exploit the fact that the deviatoric stress, the product of viscosity and strain-rate, approaches zero as the viscosity goes to infinity. Using the deviatoric stress as the basis for a first-order system results in the the basic fluidity system. Augmenting the basic fluidity system with a curl-type equation results in the augmented fluidity system, which is more amenable to the iterative solver, Algebraic MultiGrid (AMG). A Nested Iteration (NI) Newton-FOSLS-AMG approach is used to solve the nonlinear-Stokes problems. Several test problems from the ISMIP set of benchmarks is examined to test the effectiveness of the various formulations. These test show that the viscosity based method is more expensive and less accurate. The basic fluidity system shows optimal finite-element convergence. However, there is not yet an efficient iterative solver for this type of system and this is the topic of future research. Alternatively, AMG performs better on the augmented fluidity system when using specific scaling. Unfortunately, this scaling results in reduced finite-element convergence.

A two-field modified Lagrangian formulation for robust simulations of extrinsic cohesive zone models

NASA Astrophysics Data System (ADS)

Cazes, F.; Coret, M.; Combescure, A.

2013-06-01

This paper presents the robust implementation of a cohesive zone model based on extrinsic cohesive laws (i.e. laws involving an infinite initial stiffness). To this end, a two-field Lagrangian weak formulation in which cohesive tractions are chosen as the field variables along the crack's path is presented. Unfortunately, this formulation cannot model the infinite compliance of the broken elements accurately, and no simple criterion can be defined to determine the loading-unloading change of state at the integration points of the cohesive elements. Therefore, a modified Lagrangian formulation using a fictitious cohesive traction instead of the classical cohesive traction as the field variable is proposed. Thanks to this change of variable, the cohesive law becomes an increasing function of the equivalent displacement jump, which eliminates the problems mentioned previously. The ability of the proposed formulations to simulate fracture accurately and without field oscillations is investigated through three numerical test examples.

Propagation of SH waves in an infinite/semi-infinite piezoelectric/piezomagnetic periodically layered structure.

PubMed

Pang, Yu; Liu, Yu-Shan; Liu, Jin-Xi; Feng, Wen-Jie

2016-04-01

In this paper, SH bulk/surface waves propagating in the corresponding infinite/semi-infinite piezoelectric (PE)/piezomagnetic (PM) and PM/PE periodically layered composites are investigated by two methods, the stiffness matrix method and the transfer matrix method. For a semi-infinite PE/PM or PM/PE medium, the free surface is parallel to the layer interface. Both PE and PM materials are assumed to be transversely isotropic solids. Dispersion equations are derived by the stiffness/transfer matrix methods, respectively. The effects of electric-magnetic (ME) boundary conditions at the free surface and the layer thickness ratios on dispersion curves are considered in detail. Numerical examples show that the results calculated by the two methods are the same. The dispersion curves of SH surface waves are below the bulk bands or inside the frequency gaps. The ratio of the layer thickness has an important effect not only on the bulk bands but also on the dispersion curves of SH surface waves. Electric and magnetic boundary conditions, respectively, determine the dispersion curves of SH surface waves for the PE/PM and PM/PE semi-infinite structures. The band structures of SH bulk waves are consistent for the PE/PM and PM/PE structures, however, the dispersive behaviors of SH surface waves are indeed different for the two composites. The realization of the above-mentioned characteristics of SH waves will make it possible to design PE/PM acoustic wave devices with periodical structures and achieve the better performance. Copyright © 2016 Elsevier B.V. All rights reserved.

Calculation of catalyst crust thickness from full elemental laser-induced breakdown spectroscopy images

NASA Astrophysics Data System (ADS)

Sorbier, L.; Trichard, F.; Moncayo, S.; Lienemann, C. P.; Motto-Ros, V.

2018-01-01

We propose a methodology to compute the crust thickness of an element in an egg-shell catalyst from a two-dimensional elemental map. The methodology handles two important catalyst shapes: infinite extrudates of arbitrary section and spheres. The methodology is validated with synthetic analytical profiles on simple shapes (cylinder and sphere). Its relative accuracy is shown close to few percent with a decrease inversely proportional to the square root of the number of sampled pixels. The crust thickness obtained by this method from quantitative Pd maps acquired by laser-induced breakdown spectroscopy are comparable with values obtained from electron-probe microanalysis profiles. Some discrepancies are found and are explained by the heterogeneity of the crust thickness within a grain. As a full map is more representative than a single profile, fast mapping and the methodology exposed in this paper are expected to become valuable tools for the development of new generations of egg-shell deposited catalysts.

Linear theory of boundary effects in open wind tunnels with finite jet lengths

NASA Technical Reports Server (NTRS)

Katzoff, S; Gardner, Clifford S; Diesendruck, Leo; Eisenstadt, Bertram J

1950-01-01

In the first part, the boundary conditions for an open wind tunnel (incompressible flow) are examined with special reference to the effects of the closed entrance and exit sections. Basic conditions are that the velocity must be continuous at the entrance lip and that the velocities in the upstream and downstream closed portions must be equal. In the second part, solutions are derived for four types of two-dimensional open tunnels, including one in which the pressures on the two free surfaces are not equal. Numerical results are given for every case. In general, if the lifting element is more than half the tunnel height from the inlet, the boundary effect at the lifting element is the same as for an infinitely long open tunnel. In the third part, a general method is given for calculating the boundary effect in an open circular wind tunnel of finite jet length. Numerical results are given for a lifting element concentrate at a point on the axis.

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

Analytical and numerical analyses for a penny-shaped crack embedded in an infinite transversely isotropic multi-ferroic composite medium: semi-permeable electro-magnetic boundary condition

NASA Astrophysics Data System (ADS)

Zheng, R.-F.; Wu, T.-H.; Li, X.-Y.; Chen, W.-Q.

2018-06-01

The problem of a penny-shaped crack embedded in an infinite space of transversely isotropic multi-ferroic composite medium is investigated. The crack is assumed to be subjected to uniformly distributed mechanical, electric and magnetic loads applied symmetrically on the upper and lower crack surfaces. The semi-permeable (limited-permeable) electro-magnetic boundary condition is adopted. By virtue of the generalized method of potential theory and the general solutions, the boundary integro-differential equations governing the mode I crack problem, which are of nonlinear nature, are established and solved analytically. Exact and complete coupling magneto-electro-elastic field is obtained in terms of elementary functions. Important parameters in fracture mechanics on the crack plane, e.g., the generalized crack surface displacements, the distributions of generalized stresses at the crack tip, the generalized stress intensity factors and the energy release rate, are explicitly presented. To validate the present solutions, a numerical code by virtue of finite element method is established for 3D crack problems in the framework of magneto-electro-elasticity. To evaluate conveniently the effect of the medium inside the crack, several empirical formulae are developed, based on the numerical results.

``Dressing'' lines and vertices in calculations of matrix elements with the coupled-cluster method and determination of Cs atomic properties

NASA Astrophysics Data System (ADS)

Derevianko, Andrei; Porsev, Sergey G.

2005-03-01

We consider evaluation of matrix elements with the coupled-cluster method. Such calculations formally involve infinite number of terms and we devise a method of partial summation (dressing) of the resulting series. Our formalism is built upon an expansion of the product C†C of cluster amplitudes C into a sum of n -body insertions. We consider two types of insertions: particle (hole) line insertion and two-particle (two-hole) random-phase-approximation-like insertion. We demonstrate how to “dress” these insertions and formulate iterative equations. We illustrate the dressing equations in the case when the cluster operator is truncated at single and double excitations. Using univalent systems as an example, we upgrade coupled-cluster diagrams for matrix elements with the dressed insertions and highlight a relation to pertinent fourth-order diagrams. We illustrate our formalism with relativistic calculations of the hyperfine constant A(6s) and the 6s1/2-6p1/2 electric-dipole transition amplitude for the Cs atom. Finally, we augment the truncated coupled-cluster calculations with otherwise omitted fourth order diagrams. The resulting analysis for Cs is complete through the fourth order of many-body perturbation theory and reveals an important role of triple and disconnected quadruple excitations.

On the geometry dependence of differential pathlength factor for near-infrared spectroscopy. I. Steady-state with homogeneous medium

PubMed Central

Piao, Daqing; Barbour, Randall L.; Graber, Harry L.; Lee, Daniel C.

2015-01-01

Abstract. This work analytically examines some dependences of the differential pathlength factor (DPF) for steady-state photon diffusion in a homogeneous medium on the shape, dimension, and absorption and reduced scattering coefficients of the medium. The medium geometries considered include a semi-infinite geometry, an infinite-length cylinder evaluated along the azimuthal direction, and a sphere. Steady-state photon fluence rate in the cylinder and sphere geometries is represented by a form involving the physical source, its image with respect to the associated extrapolated half-plane, and a radius-dependent term, leading to simplified formula for estimating the DPFs. With the source-detector distance and medium optical properties held fixed across all three geometries, and equal radii for the cylinder and sphere, the DPF is the greatest in the semi-infinite and the smallest in the sphere geometry. When compared to the results from finite-element method, the DPFs analytically estimated for 10 to 25 mm source–detector separations on a sphere of 50 mm radius with μa=0.01  mm−1 and μs′=1.0  mm−1 are on average less than 5% different. The approximation for sphere, generally valid for a diameter ≥20 times of the effective attenuation pathlength, may be useful for rapid estimation of DPFs in near-infrared spectroscopy of an infant head and for short source–detector separation. PMID:26465613

A novel phase assignment protocol and driving system for a high-density focused ultrasound array.

PubMed

Caulfield, R Erich; Yin, Xiangtao; Juste, Jose; Hynynen, Kullervo

2007-04-01

Currently, most phased-array systems intended for therapy are one-dimensional (1-D) and use between 5 and 200 elements, with a few two-dimensional (2-D) systems using several hundred elements. The move toward lambda/2 interelement spacing, which provides complete 3-D beam steering, would require a large number of closely spaced elements (0.15 mm to 3 mm). A solution to the resulting problem of cost and cable assembly size, which this study examines, is to quantize the phases available at the array input. By connecting elements with similar phases to a single wire, a significant reduction in the number of incoming lines can be achieved while maintaining focusing and beam steering capability. This study has explored the feasibility of such an approach using computer simulations and experiments with a test circuit driving a 100-element linear array. Simulation results demonstrated that adequate focusing can be obtained with only four phase signals without large increases in the grating lobes or the dimensions of the focus. Experiments showed that the method can be implemented in practice, and adequate focusing can be achieved with four phase signals with a reduction of 20% in the peak pressure amplitude squared when compared with the infinite-phase resolution case. Results indicate that the use of this technique would make it possible to drive more than 10,000 elements with 33 input lines. The implementation of this method could have a large impact on ultrasound therapy and diagnostic devices.

Design and Fabrication of Orthotropic Deck Details

DOT National Transportation Integrated Search

2016-02-01

The objectives of the research were to verify the design and fabrication of the orthotropic deck details proposed for the lift bridge, for infinite fatigue life. Multi-level 3D finite element analyses (FEA) of the proposed deck were performed to dete...

An analytic solution for numerical modeling validation in electromagnetics: the resistive sphere

NASA Astrophysics Data System (ADS)

Swidinsky, Andrei; Liu, Lifei

2017-11-01

We derive the electromagnetic response of a resistive sphere to an electric dipole source buried in a conductive whole space. The solution consists of an infinite series of spherical Bessel functions and associated Legendre polynomials, and follows the well-studied problem of a conductive sphere buried in a resistive whole space in the presence of a magnetic dipole. Our result is particularly useful for controlled-source electromagnetic problems using a grounded electric dipole transmitter and can be used to check numerical methods of calculating the response of resistive targets (such as finite difference, finite volume, finite element and integral equation). While we elect to focus on the resistive sphere in our examples, the expressions in this paper are completely general and allow for arbitrary source frequency, sphere radius, transmitter position, receiver position and sphere/host conductivity contrast so that conductive target responses can also be checked. Commonly used mesh validation techniques consist of comparisons against other numerical codes, but such solutions may not always be reliable or readily available. Alternatively, the response of simple 1-D models can be tested against well-known whole space, half-space and layered earth solutions, but such an approach is inadequate for validating models with curved surfaces. We demonstrate that our theoretical results can be used as a complementary validation tool by comparing analytic electric fields to those calculated through a finite-element analysis; the software implementation of this infinite series solution is made available for direct and immediate application.

Stress-intensity factor calculations using the boundary force method

NASA Technical Reports Server (NTRS)

Tan, P. W.; Raju, I. S.; Newman, J. C., Jr.

1987-01-01

The Boundary Force Method (BFM) was formulated for the three fundamental problems of elasticity: the stress boundary value problem, the displacement boundary value problem, and the mixed boundary value problem. Because the BFM is a form of an indirect boundary element method, only the boundaries of the region of interest are modeled. The elasticity solution for the stress distribution due to concentrated forces and a moment applied at an arbitrary point in a cracked infinite plate is used as the fundamental solution. Thus, unlike other boundary element methods, here the crack face need not be modeled as part of the boundary. The formulation of the BFM is described and the accuracy of the method is established by analyzing a center-cracked specimen subjected to mixed boundary conditions and a three-hole cracked configuration subjected to traction boundary conditions. The results obtained are in good agreement with accepted numerical solutions. The method is then used to generate stress-intensity solutions for two common cracked configurations: an edge crack emanating from a semi-elliptical notch, and an edge crack emanating from a V-notch. The BFM is a versatile technique that can be used to obtain very accurate stress intensity factors for complex crack configurations subjected to stress, displacement, or mixed boundary conditions. The method requires a minimal amount of modeling effort.

Infrared thermography applied to the study of heated and solar pavement: from numerical modeling to small scale laboratory experiments

NASA Astrophysics Data System (ADS)

Le Touz, N.; Toullier, T.; Dumoulin, J.

2017-05-01

The present study addresses the thermal behaviour of a modified pavement structure to prevent icing at its surface in adverse winter time conditions or overheating in hot summer conditions. First a multi-physic model based on infinite elements method was built to predict the evolution of the surface temperature. In a second time, laboratory experiments on small specimen were carried out and the surface temperature was monitored by infrared thermography. Results obtained are analyzed and performances of the numerical model for real scale outdoor application are discussed. Finally conclusion and perspectives are proposed.

Thermoelastic damping in bilayered microbar resonators with circular cross-section

NASA Astrophysics Data System (ADS)

Liang, Xiaoyao; Li, Pu

2017-11-01

It is always a challenge to determine the Thermoelastic damping (TED) in bilayered microbars precisely. In this paper, a model for TED in the bilayered and cantilevered microbar was proposed, in which the total damping was derived by calculating the energy evanished in each layer. The distribution of temperature in the bilayered microbar with a thermodynamically ideal boundary receiving a time-harmonic force is obtained. An infinite summation for the computing of TED in the bilayered slender microbars under axial loading is presented, and the convergence rate of it is discussed. There are little differences between the results computed by our model and that by finite element method (FEM).

Viscous dissipation impact on MHD free convection radiating fluid flow past a vertical porous plate

NASA Astrophysics Data System (ADS)

Raju, R. Srinivasa; Reddy, G. Jithender; Kumar, M. Anil

2018-05-01

An attempt has been made to study the radiation effects on unsteady MHD free convective flow of an incompressible fluid past an infinite vertical porous plate in the presence of viscous dissipation. The governing partial differential equations are solved numerically by using Galerkin finite element method. Computations were performed for a wide range of governing flow parameters viz., Magnetic Parameter, Schmidt number, Thermal radiation, Prandtl number, Eckert number and Permeability parameter. The effects of these flow parameters on velocity, temperature are shown graphically. In addition the local values of the Skin friction coefficient are shown in tabular form.

Design-Parameters Setup for Power-Split Dual-Regime IVT

NASA Astrophysics Data System (ADS)

Preda, Ion; Ciolan, Gheorghe; Covaciu, Dinu

2017-10-01

To analyze the working possibilities of power-split infinitely variable transmissions (IVTs) it is necessary to follow a systematic approach. The method proposed in this paper consists of generating a block diagram of the transmission and then, based on this diagram, to derive the kinematics and dynamics equations of the transmission. For an actual numerical case, the derived equations are used to find characteristic values of the transmission components (gear and chain drives, planetary units) necessary to calculate the speed ratios, the speeds, torques and powers acting on the shafts and coupling (control) elements, and even to estimate the overall efficiency of the transmission.

Dry granular avalanche impact force on a rigid wall of semi-infinite height

NASA Astrophysics Data System (ADS)

Albaba, Adel; Lambert, Stéphane; Faug, Thierry

2017-06-01

The present paper tackles the problem of the impact of a dry granular avalanche-flow on a rigid wall of semi-infinite height. An analytic force model based on depth-averaged shock theory is proposed to describe the flow-wall interaction and the resulting impact force on the wall. Provided that the analytic force model is fed with the incoming flow conditions regarding thickness, velocity and density, all averaged over a certain distance downstream of the undisturbed incoming flow, it reproduces very well the time history of the impact force actually measured by detailed discrete element simulations, for a wide range of slope angles.

Finding Limit Cycles in self-excited oscillators with infinite-series damping functions

NASA Astrophysics Data System (ADS)

Das, Debapriya; Banerjee, Dhruba; Bhattacharjee, Jayanta K.

2015-03-01

In this paper we present a simple method for finding the location of limit cycles of self excited oscillators whose damping functions can be represented by some infinite convergent series. We have used standard results of first-order perturbation theory to arrive at amplitude equations. The approach has been kept pedagogic by first working out the cases of finite polynomials using elementary algebra. Then the method has been extended to various infinite polynomials, where the fixed points of the corresponding amplitude equations cannot be found out. Hopf bifurcations for systems with nonlinear powers in velocities have also been discussed.

A new leakage measurement method for damaged seal material

NASA Astrophysics Data System (ADS)

Wang, Shen; Yao, Xue Feng; Yang, Heng; Yuan, Li; Dong, Yi Feng

2018-07-01

In this paper, a new leakage measurement method based on the temperature field and temperature gradient field is proposed for detecting the leakage location and measuring the leakage rate in damaged seal material. First, a heat transfer leakage model is established, which can calculate the leakage rate based on the temperature gradient field near the damaged zone. Second, a finite element model of an infinite plate with a damaged zone is built to calculate the leakage rate, which fits the simulated leakage rate well. Finally, specimens in a tubular rubber seal with different damage shapes are used to conduct the leakage experiment, validating the correctness of this new measurement principle for the leakage rate and the leakage position. The results indicate the feasibility of the leakage measurement method for damaged seal material based on the temperature gradient field from infrared thermography.

Effect of periodic fluctuation of soil particle rotation resistance on interface shear behaviour

NASA Astrophysics Data System (ADS)

Ebrahimian, Babak; Noorzad, Asadollah

2010-06-01

The interface behaviour between infinite extended narrow granular layer and bounding structure is numerically investigated using finite element method. The micro-polar (Cosserat) continuum approach within the framework of elasto-plasticity is employed to remove the numerical difficulties caused by strain-softening of materials in classical continuum mechanics. Mechanical properties of cohesionless granular soil are described with Lade's model enhanced with polar terms including Cosserat rotations, curvatures and couple stresses via mean grain diameter as the internal length. The main attention of paper is laid on the influence of spatial periodic fluctuation of rotation resistance of soil particles interlocked with the surface of bounding structure on evolution and location of shear band developed inside granular body. The finite element results demonstrate that the location and evolution of shear localization in granular body is strongly affected by prescribed non-uniform micro-polar kinematic boundary conditions along the interface.

Ultrasonic wave propagation in viscoelastic cortical bone plate coupled with fluids: a spectral finite element study.

PubMed

Nguyen, Vu-Hieu; Naili, Salah

2013-01-01

This work deals with the ultrasonic wave propagation in the cortical layer of long bones which is known as being a functionally graded anisotropic material coupled with fluids. The viscous effects are taken into account. The geometrical configuration mimics the one of axial transmission technique used for evaluating the bone quality. We present a numerical procedure adapted for this purpose which is based on the spectral finite element method (FEM). By using a combined Laplace-Fourier transform, the vibroacoustic problem may be transformed into the frequency-wavenumber domain in which, as radiation conditions may be exactly introduced in the infinite fluid halfspaces, only the heterogeneous solid layer needs to be analysed using FEM. Several numerical tests are presented showing very good performance of the proposed approach. We present some results to study the influence of the frequency on the first arriving signal velocity in (visco)elastic bone plate.

Markov chains of infinite order and asymptotic satisfaction of balance: application to the adaptive integration method.

PubMed

Earl, David J; Deem, Michael W

2005-04-14

Adaptive Monte Carlo methods can be viewed as implementations of Markov chains with infinite memory. We derive a general condition for the convergence of a Monte Carlo method whose history dependence is contained within the simulated density distribution. In convergent cases, our result implies that the balance condition need only be satisfied asymptotically. As an example, we show that the adaptive integration method converges.

The Transition from Optional to Required Subjects.

ERIC Educational Resources Information Center

O'Grady, William; And Others

1989-01-01

Proposes that the optional subject phenomenon in early child language arises because children have not yet acquired the morphological elements (primarily modal and tense) necessary to distinguish subject-taking verbs (e.g., finite verbs) from their non-subject-taking counterparts (e.g., infinitives). (Author/CB)

Mathematical Techniques for Nonlinear System Theory.

DTIC Science & Technology

1981-09-01

This report deals with research results obtained in the following areas: (1) Finite-dimensional linear system theory by algebraic methods--linear...Infinite-dimensional linear systems--realization theory of infinite-dimensional linear systems; (3) Nonlinear system theory --basic properties of

The finite scaling for S = 1 XXZ chains with uniaxial single-ion-type anisotropy

NASA Astrophysics Data System (ADS)

Wang, Honglei; Xiong, Xingliang

2014-03-01

The scaling behavior of criticality for spin-1 XXZ chains with uniaxial single-ion-type anisotropy is investigated by employing the infinite matrix product state representation with the infinite time evolving block decimation method. At criticality, the accuracy of the ground state of a system is limited by the truncation dimension χ of the local Hilbert space. We present four evidences for the scaling of the entanglement entropy, the largest eigenvalue of the Schmidt decomposition, the correlation length, and the connection between the actual correlation length ξ and the energy. The result shows that the finite scalings are governed by the central charge of the critical system. Also, it demonstrates that the infinite time evolving block decimation algorithm by the infinite matrix product state representation can be a quite accurate method to simulate the critical properties at criticality.

Infinite product expansion of the Fokker-Planck equation with steady-state solution.

PubMed

Martin, R J; Craster, R V; Kearney, M J

2015-07-08

We present an analytical technique for solving Fokker-Planck equations that have a steady-state solution by representing the solution as an infinite product rather than, as usual, an infinite sum. This method has many advantages: automatically ensuring positivity of the resulting approximation, and by design exactly matching both the short- and long-term behaviour. The efficacy of the technique is demonstrated via comparisons with computations of typical examples.

Infinite product expansion of the Fokker–Planck equation with steady-state solution

PubMed Central

Martin, R. J.; Craster, R. V.; Kearney, M. J.

2015-01-01

We present an analytical technique for solving Fokker–Planck equations that have a steady-state solution by representing the solution as an infinite product rather than, as usual, an infinite sum. This method has many advantages: automatically ensuring positivity of the resulting approximation, and by design exactly matching both the short- and long-term behaviour. The efficacy of the technique is demonstrated via comparisons with computations of typical examples. PMID:26346100

Calculations of axisymmetric vortex sheet roll-up using a panel and a filament model

NASA Technical Reports Server (NTRS)

Kantelis, J. P.; Widnall, S. E.

1986-01-01

A method for calculating the self-induced motion of a vortex sheet using discrete vortex elements is presented. Vortex panels and vortex filaments are used to simulate two-dimensional and axisymmetric vortex sheet roll-up. A straight forward application using vortex elements to simulate the motion of a disk of vorticity with an elliptic circulation distribution yields unsatisfactroy results where the vortex elements move in a chaotic manner. The difficulty is assumed to be due to the inability of a finite number of discrete vortex elements to model the singularity at the sheet edge and due to large velocity calculation errors which result from uneven sheet stretching. A model of the inner portion of the spiral is introduced to eliminate the difficulty with the sheet edge singularity. The model replaces the outermost portion of the sheet with a single vortex of equivalent circulation and a number of higher order terms which account for the asymmetry of the spiral. The resulting discrete vortex model is applied to both two-dimensional and axisymmetric sheets. The two-dimensional roll-up is compared to the solution for a semi-infinite sheet with good results.

Properties of one-dimensional anharmonic lattice solitons

NASA Astrophysics Data System (ADS)

Szeftel, Jacob; Laurent-Gengoux, Pascal; Ilisca, Ernest; Hebbache, Mohamed

2000-12-01

The existence of bell- and kink-shaped solitons moving at constant velocity while keeping a permanent profile is studied in infinite periodic monoatomic chains of arbitrary anharmonicity by taking advantage of the equation of motion being integrable with respect to solitons. A second-order, non-linear differential equation involving advanced and retarded terms must be solved, which is done by implementing a scheme based on the finite element and Newton's methods. If the potential has a harmonic limit, the asymptotic time-decay behaves exponentially and there is a dispersion relation between propagation velocity and decay time. Inversely if the potential has no harmonic limit, the asymptotic regime shows up either as a power-law or faster than exponential. Excellent agreement is achieved with Toda's model. Illustrative examples are also given for the Fermi-Pasta-Ulam and sine-Gordon potentials. Owing to integrability an effective one-body potential is worked out in each case. Lattice and continuum solitons differ markedly from one another as regards the amplitude versus propagation velocity relationship and the asymptotic time behavior. The relevance of the linear stability analysis when applied to solitons propagating in an infinite crystal is questioned. The reasons preventing solitons from arising in a diatomic lattice are discussed.

Measurement of the Infinite Multiplication Constant of Natural Uranium--Graphite Lattices in the RB-1 Critical Assembly by Means of the Zero Reactivity Method. MISURA DELLA COSTANTE DI MOLTIPLICAZIONE INFINITA DI RETICOLI A URANIO NATURALE E GRAFITE NELL'INSIEME CRITICO RB-1 CON IL METODO DELLA REATTIVITA' NULLA (in Italian)

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

Ghillardotti, G.

1966-07-01

To reduce uncertainties to the minimum, measurements in the RB-1 were conducted on the same materials and with the same instrumentation as those used previously in MARIUS. The values measured in the RB-1, compared with the already known substitution data, are as follows: (a) the difference between the multiplication and the absorption intensity; (b) the fine structure of the flux in the cell; (c) the Pu/U index. The infinite mutiplication factor K{sub infinity} is obtained by combining measurements (a) and (b). The results of this research can be summed up as follows: 1. A consistent and complete experimental procedure hasmore » been devised for measuring the K{sub infinity} of natural uranium/graphite lattices by means of the zero reactivity method. The same applies to the procedure for analysis of the experimental data. 2. The error in (K{sub infinity} -- 1) inherent in the measurement can in our opinion be reduced to 2%. This limit was reached in the last experiment on lattices consisting of tubular elements. 3. Agreement proved to be good with the results obtained by the CEA in the critical assembly MARIUS. (auth)« less

The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil

NASA Technical Reports Server (NTRS)

Meade, Andrew J., Jr.

1992-01-01

A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.

A Reduced Basis Method with Exact-Solution Certificates for Symmetric Coercive Equations

DTIC Science & Technology

2013-11-06

the energy associated with the infinite - dimensional weak solution of parametrized symmetric coercive partial differential equations with piecewise...builds bounds with respect to the infinite - dimensional weak solution, aims to entirely remove the issue of the “truth” within the certified reduced basis...framework. We in particular introduce a reduced basis method that provides rigorous upper and lower bounds

A General No-Cloning Theorem for an infinite Multiverse

NASA Astrophysics Data System (ADS)

Gauthier, Yvon

2013-10-01

In this paper, I formulate a general no-cloning theorem which covers the quantum-mechanical and the theoretical quantum information cases as well as the cosmological multiverse theory. However, the main argument is topological and does not involve the peculiar copier devices of the quantum-mechanical and information-theoretic approaches to the no-cloning thesis. It is shown that a combinatorial set-theoretic treatment of the mathematical and physical spacetime continuum in cosmological or quantum-mechanical terms forbids an infinite (countable or uncountable) number of exact copies of finite elements (states) in the uncountable multiverse cosmology. The historical background draws on ideas from Weyl to Conway and Kochen on the free will theorem in quantum mechanics.

Semi-discrete Galerkin solution of the compressible boundary-layer equations with viscous-inviscid interaction

NASA Technical Reports Server (NTRS)

Day, Brad A.; Meade, Andrew J., Jr.

1993-01-01

A semi-discrete Galerkin (SDG) method is under development to model attached, turbulent, and compressible boundary layers for transonic airfoil analysis problems. For the boundary-layer formulation the method models the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby providing high resolution near the wall and permitting the use of a uniform finite element grid which automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past RAE 2822 and NACA 0012 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack.

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.

Probabilistic Graphical Models for the Analysis and Synthesis of Musical Audio

DTIC Science & Technology

2010-11-01

Abbreviation for the names Griffiths, Engen , and McCloskey. Often used to de- note the stick-breaking distribution over infinite vectors whose elements...of state calculations by fast computing machines. Journal of Chemical Physics, 21:1087–1092, 1953. [65] R. Miotto, L. Barrington, and G. Lanckriet

Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory

NASA Technical Reports Server (NTRS)

Tsang, Leung; Chan, Chi Hou; Kong, Jin AU; Joseph, James

1992-01-01

Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.

The Kirillov picture for the Wigner particle

NASA Astrophysics Data System (ADS)

Gracia-Bondía, J. M.; Lizzi, F.; Várilly, J. C.; Vitale, P.

2018-06-01

We discuss the Kirillov method for massless Wigner particles, usually (mis)named ‘continuous spin’ or ‘infinite spin’ particles. These appear in Wigner’s classification of the unitary representations of the Poincaré group, labelled by elements of the enveloping algebra of the Poincaré Lie algebra. Now, the coadjoint orbit procedure introduced by Kirillov is a prelude to quantization. Here we exhibit for those particles the classical Casimir functions on phase space, in parallel to quantum representation theory. A good set of position coordinates are identified on the coadjoint orbits of the Wigner particles; the stabilizer subgroups and the symplectic structures of these orbits are also described. In memory of E C G Sudarshan.

A Monte Carlo-finite element model for strain energy controlled microstructural evolution - 'Rafting' in superalloys

NASA Technical Reports Server (NTRS)

Gayda, J.; Srolovitz, D. J.

1989-01-01

This paper presents a specialized microstructural lattice model, MCFET (Monte Carlo finite element technique), which simulates microstructural evolution in materials in which strain energy has an important role in determining morphology. The model is capable of accounting for externally applied stress, surface tension, misfit, elastic inhomogeneity, elastic anisotropy, and arbitrary temperatures. The MCFET analysis was found to compare well with the results of analytical calculations of the equilibrium morphologies of isolated particles in an infinite matrix.

Multi-Dimensional Shallow Landslide Stability Analysis Suitable for Application at the Watershed Scale

NASA Astrophysics Data System (ADS)

Milledge, D.; Bellugi, D.; McKean, J. A.; Dietrich, W.

2012-12-01

The infinite slope model is the basis for almost all watershed scale slope stability models. However, it assumes that a potential landslide is infinitely long and wide. As a result, it cannot represent resistance at the margins of a potential landslide (e.g. from lateral roots), and is unable to predict the size of a potential landslide. Existing three-dimensional models generally require computationally expensive numerical solutions and have previously been applied only at the hillslope scale. Here we derive an alternative analytical treatment that accounts for lateral resistance by representing the forces acting on each margin of an unstable block. We apply 'at rest' earth pressure on the lateral sides, and 'active' and 'passive' pressure using a log-spiral method on the upslope and downslope margins. We represent root reinforcement on each margin assuming that root cohesion is an exponential function of soil depth. We benchmark this treatment against other more complete approaches (Finite Element (FE) and closed form solutions) and find that our model: 1) converges on the infinite slope predictions as length / depth and width / depth ratios become large; 2) agrees with the predictions from state-of-the-art FE models to within +/- 30% error, for the specific cases in which these can be applied. We then test our model's ability to predict failure of an actual (mapped) landslide where the relevant parameters are relatively well constrained. We find that our model predicts failure at the observed location with a nearly identical shape and predicts that larger or smaller shapes conformal to the observed shape are indeed more stable. Finally, we perform a sensitivity analysis using our model to show that lateral reinforcement sets a minimum landslide size, while the additional strength at the downslope boundary means that the optimum shape for a given size is longer in a downslope direction. However, reinforcement effects cannot fully explain the size or shape distributions of observed landslides, highlighting the importance of spatial patterns of key parameters (e.g. pore water pressure) and motivating the model's watershed scale application. This watershed scale application requires an efficient method to find the least stable shapes among an almost infinite set. However, when applied in this context, it allows a more complete examination of the controls on landslide size, shape and location.

A high frequency analysis of electromagnetic plane wave scattering by perfectly-conducting semi-infinite parallel plate and rectangular waveguides with absorber coated inner walls

NASA Technical Reports Server (NTRS)

Noh, H. M.; Pathak, P. H.

1986-01-01

An approximate but sufficiently accurate high frequency solution which combines the uniform geometrical theory of diffraction (UTD) and the aperture integration (AI) method is developed for analyzing the problem of electromagnetic (EM) plane wave scattering by an open-ended, perfectly-conducting, semi-infinite hollow rectangular waveguide (or duct) with a thin, uniform layer of lossy or absorbing material on its inner wall, and with a planar termination inside. In addition, a high frequency solution for the EM scattering by a two dimensional (2-D), semi-infinite parallel plate waveguide with a absorber coating on the inner walls is also developed as a first step before analyzing the open-ended semi-infinite three dimensional (3-D) rectangular waveguide geometry. The total field scattered by the semi-infinite waveguide consists firstly of the fields scattered from the edges of the aperture at the open-end, and secondly of the fields which are coupled into the waveguide from the open-end and then reflected back from the interior termination to radiate out of the open-end. The first contribution to the scattered field can be found directly via the UTD ray method. The second contribution is found via the AI method which employs rays to describe the fields in the aperture that arrive there after reflecting from the interior termination. It is assumed that the direction of the incident plane wave and the direction of observation lie well inside the forward half space tht exists outside the half space containing the semi-infinite waveguide geometry. Also, the medium exterior to the waveguide is assumed to be free space.

Three-Dimensional Dynamic Analyses of Track-Embankment-Ground System Subjected to High Speed Train Loads

PubMed Central

2014-01-01

A three-dimensional finite element model was developed to investigate dynamic response of track-embankment-ground system subjected to moving loads caused by high speed trains. The track-embankment-ground systems such as the sleepers, the ballast, the embankment, and the ground are represented by 8-noded solid elements. The infinite elements are used to represent the infinite boundary condition to absorb vibration waves induced by the passing of train load at the boundary. The loads were applied on the rails directly to simulate the real moving loads of trains. The effects of train speed on dynamic response of the system are considered. The effect of material parameters, especially the modulus changes of ballast and embankment, is taken into account to demonstrate the effectiveness of strengthening the ballast, embankment, and ground for mitigating system vibration in detail. The numerical results show that the model is reliable for predicting the amplitude of vibrations produced in the track-embankment-ground system by high-speed trains. Stiffening of fill under the embankment can reduce the vibration level, on the other hand, it can be realized by installing a concrete slab under the embankment. The influence of axle load on the vibration of the system is obviously lower than that of train speed. PMID:24723838

Three-dimensional dynamic analyses of track-embankment-ground system subjected to high speed train loads.

PubMed

Fu, Qiang; Zheng, Changjie

2014-01-01

A three-dimensional finite element model was developed to investigate dynamic response of track-embankment-ground system subjected to moving loads caused by high speed trains. The track-embankment-ground systems such as the sleepers, the ballast, the embankment, and the ground are represented by 8-noded solid elements. The infinite elements are used to represent the infinite boundary condition to absorb vibration waves induced by the passing of train load at the boundary. The loads were applied on the rails directly to simulate the real moving loads of trains. The effects of train speed on dynamic response of the system are considered. The effect of material parameters, especially the modulus changes of ballast and embankment, is taken into account to demonstrate the effectiveness of strengthening the ballast, embankment, and ground for mitigating system vibration in detail. The numerical results show that the model is reliable for predicting the amplitude of vibrations produced in the track-embankment-ground system by high-speed trains. Stiffening of fill under the embankment can reduce the vibration level, on the other hand, it can be realized by installing a concrete slab under the embankment. The influence of axle load on the vibration of the system is obviously lower than that of train speed.

Infinite projected entangled-pair state algorithm for ruby and triangle-honeycomb lattices

NASA Astrophysics Data System (ADS)

Jahromi, Saeed S.; Orús, Román; Kargarian, Mehdi; Langari, Abdollah

2018-03-01

The infinite projected entangled-pair state (iPEPS) algorithm is one of the most efficient techniques for studying the ground-state properties of two-dimensional quantum lattice Hamiltonians in the thermodynamic limit. Here, we show how the algorithm can be adapted to explore nearest-neighbor local Hamiltonians on the ruby and triangle-honeycomb lattices, using the corner transfer matrix (CTM) renormalization group for 2D tensor network contraction. Additionally, we show how the CTM method can be used to calculate the ground-state fidelity per lattice site and the boundary density operator and entanglement entropy (EE) on an infinite cylinder. As a benchmark, we apply the iPEPS method to the ruby model with anisotropic interactions and explore the ground-state properties of the system. We further extract the phase diagram of the model in different regimes of the couplings by measuring two-point correlators, ground-state fidelity, and EE on an infinite cylinder. Our phase diagram is in agreement with previous studies of the model by exact diagonalization.

Infinitely dilute partial molar properties of proteins from computer simulation.

PubMed

Ploetz, Elizabeth A; Smith, Paul E

2014-11-13

A detailed understanding of temperature and pressure effects on an infinitely dilute protein's conformational equilibrium requires knowledge of the corresponding infinitely dilute partial molar properties. Established molecular dynamics methodologies generally have not provided a way to calculate these properties without either a loss of thermodynamic rigor, the introduction of nonunique parameters, or a loss of information about which solute conformations specifically contributed to the output values. Here we implement a simple method that is thermodynamically rigorous and possesses none of the above disadvantages, and we report on the method's feasibility and computational demands. We calculate infinitely dilute partial molar properties for two proteins and attempt to distinguish the thermodynamic differences between a native and a denatured conformation of a designed miniprotein. We conclude that simple ensemble average properties can be calculated with very reasonable amounts of computational power. In contrast, properties corresponding to fluctuating quantities are computationally demanding to calculate precisely, although they can be obtained more easily by following the temperature and/or pressure dependence of the corresponding ensemble averages.

Electromagnetic pulse excitation of finite- and infinitely-long lossy conductors over a lossy ground plane

DOE PAGES

Campione, Salvatore; Warne, Larry K.; Basilio, Lorena I.; ...

2017-01-13

This study details a model for the response of a finite- or an infinite-length wire interacting with a conducting ground to an electromagnetic pulse excitation. We develop a frequency–domain method based on transmission line theory that we name ATLOG – Analytic Transmission Line Over Ground. This method is developed as an alternative to full-wave methods, as it delivers a fast and reliable solution. It allows for the treatment of finite or infinite lossy, coated wires, and lossy grounds. The cases of wire above ground, as well as resting on the ground and buried beneath the ground are treated. The reportedmore » method is general and the time response of the induced current is obtained using an inverse Fourier transform of the current in the frequency domain. The focus is on the characteristics and propagation of the transmission line mode. Comparisons with full-wave simulations strengthen the validity of the proposed method.« less

Electromagnetic pulse excitation of finite- and infinitely-long lossy conductors over a lossy ground plane

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

Campione, Salvatore; Warne, Larry K.; Basilio, Lorena I.

This study details a model for the response of a finite- or an infinite-length wire interacting with a conducting ground to an electromagnetic pulse excitation. We develop a frequency–domain method based on transmission line theory that we name ATLOG – Analytic Transmission Line Over Ground. This method is developed as an alternative to full-wave methods, as it delivers a fast and reliable solution. It allows for the treatment of finite or infinite lossy, coated wires, and lossy grounds. The cases of wire above ground, as well as resting on the ground and buried beneath the ground are treated. The reportedmore » method is general and the time response of the induced current is obtained using an inverse Fourier transform of the current in the frequency domain. The focus is on the characteristics and propagation of the transmission line mode. Comparisons with full-wave simulations strengthen the validity of the proposed method.« less

Multirate sampled-data yaw-damper and modal suppression system design

NASA Technical Reports Server (NTRS)

Berg, Martin C.; Mason, Gregory S.

1990-01-01

A multirate control law synthesized algorithm based on an infinite-time quadratic cost function, was developed along with a method for analyzing the robustness of multirate systems. A generalized multirate sampled-data control law structure (GMCLS) was introduced. A new infinite-time-based parameter optimization multirate sampled-data control law synthesis method and solution algorithm were developed. A singular-value-based method for determining gain and phase margins for multirate systems was also developed. The finite-time-based parameter optimization multirate sampled-data control law synthesis algorithm originally intended to be applied to the aircraft problem was instead demonstrated by application to a simpler problem involving the control of the tip position of a two-link robot arm. The GMCLS, the infinite-time-based parameter optimization multirate control law synthesis method and solution algorithm, and the singular-value based method for determining gain and phase margins were all demonstrated by application to the aircraft control problem originally proposed for this project.

Ice Engineering - study of Related Properties of Floating Sea-Ice Sheets and Summary of Elastic and Viscoelastic Analyses

DTIC Science & Technology

1977-12-01

Ice Plate Example. To demonstrate the capability of the visco- elastic finite-element computer code (5), the structural response of an infinite ... sea -ice plate on a fluid foundation is investigated for a simulated aircraft loading condition and, using relaxation functions, is determined

Diversity of Poissonian populations.

PubMed

Eliazar, Iddo I; Sokolov, Igor M

2010-01-01

Populations represented by collections of points scattered randomly on the real line are ubiquitous in science and engineering. The statistical modeling of such populations leads naturally to Poissonian populations-Poisson processes on the real line with a distinguished maximal point. Poissonian populations are infinite objects underlying key issues in statistical physics, probability theory, and random fractals. Due to their infiniteness, measuring the diversity of Poissonian populations depends on the lower-bound cut-off applied. This research characterizes the classes of Poissonian populations whose diversities are invariant with respect to the cut-off level applied and establishes an elemental connection between these classes and extreme-value theory. The measures of diversity considered are variance and dispersion, Simpson's index and inverse participation ratio, Shannon's entropy and Rényi's entropy, and Gini's index.

A Novel Coordination Polymer Based on Trinuclear Cobalt Building Blocks Cluster: Synthesis, Crystal Structure, and Properties

NASA Astrophysics Data System (ADS)

Lu, J. F.; Tang, Z. H.; Shi, J.; Ge, H. G.; Jiang, M.; Song, J.; Jin, L. X.

2017-12-01

The title compound {[Co3(μ3-OH)(μ2-H2O)2(H2O)5(BTC)2] · 6H2O} n (H3BTC is a 1,3,5-benzenetricarboxylic acid) was prepared and characterized by single crystal and powder X-ray diffraction, Fourier transform infrared spectroscopy, thermogravimetric and elemental analyses. The single crystal X-ray diffraction reveals that the title compound consists of 1D infinite zigzag chains which were constructed by trinuclear cobalt cluster and BTC3- ligand. Neighbouring above-mentioned 1D infinite zigzag chains are further linked by intermolecular hydrogen bonding to form a 3D supermolecular structure. In addition, the luminescent properties of the title compound were investigated.

A boundary element model of the transport of a semi-infinite bubble through a microvessel bifurcation

NASA Astrophysics Data System (ADS)

Calderon, Andres J.; Eshpuniyani, Brijesh; Fowlkes, J. Brian; Bull, Joseph L.

2010-06-01

Motivated by a developmental gas embolotherapy technique for selective occlusion of blood flow to tumors, we examined the transport of a pressure-driven semi-infinite bubble through a liquid-filled bifurcating channel. Homogeneity of bubble splitting as the bubble passes through a vessel bifurcation affects the degree to which the vascular network near the tumor can be uniformly occluded. The homogeneity of bubble splitting was found to increase with bubble driving pressure and to decrease with increased bifurcation angle. Viscous losses at the bifurcation were observed to affect the bubble speed significantly. The potential for oscillating bubble interfaces to induce flow recirculation and impart high stresses on the vessel endothelium was also observed.

Fourier/Chebyshev methods for the incompressible Navier-Stokes equations in finite domains

NASA Technical Reports Server (NTRS)

Corral, Roque; Jimenez, Javier

1992-01-01

A fully spectral numerical scheme for the incompressible Navier-Stokes equations in domains which are infinite or semi-infinite in one dimension. The domain is not mapped, and standard Fourier or Chebyshev expansions can be used. The handling of the infinite domain does not introduce any significant overhead. The scheme assumes that the vorticity in the flow is essentially concentrated in a finite region, which is represented numerically by standard spectral collocation methods. To accomodate the slow exponential decay of the velocities at infinity, extra expansion functions are introduced, which are handled analytically. A detailed error analysis is presented, and two applications to Direct Numerical Simulation of turbulent flows are discussed in relation with the numerical performance of the scheme.

Three-dimensional piezoelectric boundary elements

NASA Astrophysics Data System (ADS)

Hill, Lisa Renee

The strong coupling between mechanical and electrical fields in piezoelectric ceramics makes them appropriate for use as actuation devices; as a result, they are an important part of the emerging technologies of smart materials and structures. These piezoceramics are very brittle and susceptible to fracture, especially under the severe loading conditions which may occur in service. A significant portion of the applications under investigation involve dynamic loading conditions. Once a crack is initiated in the piezoelectric medium, the mechanical and electrical fields can act to drive the crack growth. Failure of the actuator can result from a catastrophic fracture event or from the cumulative effects of cyclic fatigue. The presence of these cracks, or other types of material defects, alter the mechanical and electrical fields inside the body. Specifically, concentrations of stress and electric field are present near a flaw and can lead to material yielding or localized depoling, which in turn can affect the sensor/actuator performance or cause failure. Understanding these effects is critical to the success of these smart structures. The complex coupling behavior and the anisotropy of the material makes the use of numerical methods necessary for all but the simplest problems. To this end, a three-dimensional boundary element method program is developed to evaluate the effect of flaws on these piezoelectric materials. The program is based on the linear governing equations of piezoelectricity and relies on a numerically evaluated Green's function for solution. The boundary element method was selected as the evaluation tool due to its ability to model the interior domain exactly. Thus, for piezoelectric materials the coupling between mechanical and electrical fields is not approximated inside the body. Holes in infinite and finite piezoceramics are investigated, with the localized stresses and electric fields clearly developed. The accuracy of the piezoelectric boundary element method is demonstrated with two problems: a two-dimensional circular void and a three-dimensional spherical cavity, both inside infinite solids. Application of the program to a finite body with a centered, spherical void illustrates the complex nature of the mechanical and electrical coupling. Mode I fracture is also examined, combining the linear boundary element solution with the modified crack closure integral to determine strain energy release rates. Experimental research has shown that the strain, rather than the total, energy release rate is a better predictor of crack growth in piezoelectric materials. Solutions for a two-dimensional slit-like crack and for three-dimensional penny and elliptical cracks are presented. These solutions are developed using the insulated crack face electrical boundary condition. Although this boundary condition is used by most researchers, recent discussion indicates that it may not be an accurate model for the slender crack geometry. The boundary element method is used with the penny crack problem to investigate the effect of different electrical boundary conditions on the strain energy release rate. Use of a conductive crack face boundary condition, rather than an insulated one, acts to increase the strain energy release rate for the penny crack. These conductive strain energies are closer to the values determined using a permeable electrical boundary condition than to the original conductive boundary condition ones. It is shown that conclusions about structural integrity are strongly dependent on the choice of boundary conditions.

THE SEMIGROUP OF METRIC MEASURE SPACES AND ITS INFINITELY DIVISIBLE PROBABILITY MEASURES

PubMed Central

EVANS, STEVEN N.; MOLCHANOV, ILYA

2015-01-01

A metric measure space is a complete, separable metric space equipped with a probability measure that has full support. Two such spaces are equivalent if they are isometric as metric spaces via an isometry that maps the probability measure on the first space to the probability measure on the second. The resulting set of equivalence classes can be metrized with the Gromov–Prohorov metric of Greven, Pfaffelhuber and Winter. We consider the natural binary operation ⊞ on this space that takes two metric measure spaces and forms their Cartesian product equipped with the sum of the two metrics and the product of the two probability measures. We show that the metric measure spaces equipped with this operation form a cancellative, commutative, Polish semigroup with a translation invariant metric. There is an explicit family of continuous semicharacters that is extremely useful for, inter alia, establishing that there are no infinitely divisible elements and that each element has a unique factorization into prime elements. We investigate the interaction between the semigroup structure and the natural action of the positive real numbers on this space that arises from scaling the metric. For example, we show that for any given positive real numbers a, b, c the trivial space is the only space that satisfies a ⊞ b = c . We establish that there is no analogue of the law of large numbers: if X1, X2, … is an identically distributed independent sequence of random spaces, then no subsequence of 1n⊞k=1nXk converges in distribution unless each Xk is almost surely equal to the trivial space. We characterize the infinitely divisible probability measures and the Lévy processes on this semigroup, characterize the stable probability measures and establish a counterpart of the LePage representation for the latter class. PMID:28065980

High-order dynamic modeling and parameter identification of structural discontinuities in Timoshenko beams by using reflection coefficients

NASA Astrophysics Data System (ADS)

Fan, Qiang; Huang, Zhenyu; Zhang, Bing; Chen, Dayue

2013-02-01

Properties of discontinuities, such as bolt joints and cracks in the waveguide structures, are difficult to evaluate by either analytical or numerical methods due to the complexity and uncertainty of the discontinuities. In this paper, the discontinuity in a Timoshenko beam is modeled with high-order parameters and then these parameters are identified by using reflection coefficients at the discontinuity. The high-order model is composed of several one-order sub-models in series and each sub-model consists of inertia, stiffness and damping components in parallel. The order of the discontinuity model is determined based on the characteristics of the reflection coefficient curve and the accuracy requirement of the dynamic modeling. The model parameters are identified through the least-square fitting iteration method, of which the undetermined model parameters are updated in iteration to fit the dynamic reflection coefficient curve with the wave-based one. By using the spectral super-element method (SSEM), simulation cases, including one-order discontinuities on infinite- and finite-beams and a two-order discontinuity on an infinite beam, were employed to evaluate both the accuracy of the discontinuity model and the effectiveness of the identification method. For practical considerations, effects of measurement noise on the discontinuity parameter identification are investigated by adding different levels of noise to the simulated data. The simulation results were then validated by the corresponding experiments. Both the simulation and experimental results show that (1) the one-order discontinuities can be identified accurately with the maximum errors of 6.8% and 8.7%, respectively; (2) and the high-order discontinuities can be identified with the maximum errors of 15.8% and 16.2%, respectively; and (3) the high-order model can predict the complex discontinuity much more accurately than the one-order discontinuity model.

Modal density of rectangular structures in a wide frequency range

NASA Astrophysics Data System (ADS)

Parrinello, A.; Ghiringhelli, G. L.

2018-04-01

A novel approach to investigate the modal density of a rectangular structure in a wide frequency range is presented. First, the modal density is derived, in the whole frequency range of interest, on the basis of sound transmission through the infinite counterpart of the structure; then, it is corrected by means of the low-frequency modal behavior of the structure, taking into account actual size and boundary conditions. A statistical analysis reveals the connection between the modal density of the structure and the transmission of sound through its thickness. A transfer matrix approach is used to compute the required acoustic parameters, making it possible to deal with structures having arbitrary stratifications of different layers. A finite element method is applied on coarse grids to derive the first few eigenfrequencies required to correct the modal density. Both the transfer matrix approach and the coarse grids involved in the finite element analysis grant high efficiency. Comparison with alternative formulations demonstrates the effectiveness of the proposed methodology.

Theory and experimental verifications of the resonator Q and equivalent electrical parameters due to viscoelastic and mounting supports losses.

PubMed

Yong, Yook-Kong; Patel, Mihir S; Tanaka, Masako

2010-08-01

A novel analytical/numerical method for calculating the resonator Q and its equivalent electrical parameters due to viscoelastic, conductivity, and mounting supports losses is presented. The method presented will be quite useful for designing new resonators and reducing the time and costs of prototyping. There was also a necessity for better and more realistic modeling of the resonators because of miniaturization and the rapid advances in the frequency ranges of telecommunication. We present new 3-D finite elements models of quartz resonators with viscoelasticity, conductivity, and mounting support losses. The losses at the mounting supports were modeled by perfectly matched layers (PMLs). A previously published theory for dissipative anisotropic piezoelectric solids was formulated in a weak form for finite element (FE) applications. PMLs were placed at the base of the mounting supports to simulate the energy losses to a semi-infinite base substrate. FE simulations were carried out for free vibrations and forced vibrations of quartz tuning fork and AT-cut resonators. Results for quartz tuning fork and thickness shear AT-cut resonators were presented and compared with experimental data. Results for the resonator Q and the equivalent electrical parameters were compared with their measured values. Good equivalences were found. Results for both low- and high-Q AT-cut quartz resonators compared well with their experimental values. A method for estimating the Q directly from the frequency spectrum obtained for free vibrations was also presented. An important determinant of the quality factor Q of a quartz resonator is the loss of energy from the electrode area to the base via the mountings. The acoustical characteristics of the plate resonator are changed when the plate is mounted onto a base substrate. The base affects the frequency spectra of the plate resonator. A resonator with a high Q may not have a similarly high Q when mounted on a base. Hence, the base is an energy sink and the Q will be affected by the shape and size of this base. A lower-bound Q will be obtained if the base is a semi-infinite base because it will absorb all acoustical energies radiated from the resonator.

The Effect of Finite Thickness Extent on Estimating Depth to Basement from Aeromagnetic Data

NASA Astrophysics Data System (ADS)

Blakely, R. J.; Salem, A.; Green, C. M.; Fairhead, D.; Ravat, D.

2014-12-01

Depth to basement estimation methods using various components of the spectral content of magnetic anomalies are in common use by geophysicists. Examples of these are the Tilt-Depth and SPI methods. These methods use simple models having the base of the magnetic body at infinity. Recent publications have shown that this 'infinite depth' assumption causes underestimation of the depth to the top of sources, especially in areas where the bottom of the magnetic layer is shallow, as would occur in high heat-flow regions. This error has been demonstrated in both model studies and using real data with seismic or well control. To overcome the limitation of infinite depth this contribution presents the mathematics for a finite depth contact body in the Tilt depth and SPI methods and applies it to the central Red Sea where the Curie isotherm and Moho are shallow. The difference in the depth estimation between the infinite and finite contacts is such a case is significant and can exceed 200%.

Thermal diffusion effect on MHD mixed convective flow along a vertically inclined plate: A casson fluid flow

NASA Astrophysics Data System (ADS)

Prasad, D. V. V. Krishna; Chaitanya, G. S. Krishna; Raju, R. Srinivasa

2018-05-01

The nature of Casson fluid on MHD free convective flow of over an impulsively started infinite vertically inclined plate in presence of thermal diffusion (Soret), thermal radiation, heat and mass transfer effects is studied. The basic governing nonlinear coupled partial differential equations are solved numerically using finite element method. The relevant physical parameters appearing in velocity, temperature and concentration profiles are analyzed and discussed through graphs. Finally, the results for velocity profiles and the reduced Nusselt and Sherwood numbers are obtained and compared with previous results in the literature and are found to be in excellent agreement. Applications of the present study would be useful in magnetic material processing and chemical engineering systems.

Approximate analytic solutions to 3D unconfined groundwater flow within regional 2D models

NASA Astrophysics Data System (ADS)

Luther, K.; Haitjema, H. M.

2000-04-01

We present methods for finding approximate analytic solutions to three-dimensional (3D) unconfined steady state groundwater flow near partially penetrating and horizontal wells, and for combining those solutions with regional two-dimensional (2D) models. The 3D solutions use distributed singularities (analytic elements) to enforce boundary conditions on the phreatic surface and seepage faces at vertical wells, and to maintain fixed-head boundary conditions, obtained from the 2D model, at the perimeter of the 3D model. The approximate 3D solutions are analytic (continuous and differentiable) everywhere, including on the phreatic surface itself. While continuity of flow is satisfied exactly in the infinite 3D flow domain, water balance errors can occur across the phreatic surface.

Evaluation of the operatorial Q-system for non-compact super spin chains

NASA Astrophysics Data System (ADS)

Frassek, Rouven; Marboe, Christian; Meidinger, David

2017-09-01

We present an approach to evaluate the full operatorial Q-system of all u(p,q\\Big|r+s) -invariant spin chains with representations of Jordan-Schwinger type. In particular, this includes the super spin chain of planar N=4 super Yang-Mills theory at one loop in the presence of a diagonal twist. Our method is based on the oscillator construction of Q-operators. The Q-operators are built as traces over Lax operators which are degenerate solutions of the Yang-Baxter equation. For non-compact representations these Lax operators may contain multiple infinite sums that conceal the form of the resulting functions. We determine these infinite sums and calculate the matrix elements of the lowest level Q-operators. Transforming the Lax operators corresponding to the Q-operators into a representation involving only finite sums allows us to take the supertrace and to obtain the explicit form of the Q-operators in terms of finite matrices for a given magnon sector. Imposing the functional relations, we then bootstrap the other Q-operators from those of the lowest level. We exemplify this approach for non-compact spin - s spin chains and apply it to N=4 at the one-loop level using the BMN vacuum as an example.

An Infinite Game in a Finite Setting: Visualizing Foreign Language Teaching and Learning in America.

ERIC Educational Resources Information Center

Mantero, Miguel

According to contemporary thought and foundational research, this paper presents various elements of the foreign language teaching profession and language learning environment in the United States as either product-driven or process-based. It is argued that a process-based approach to language teaching and learning benefits not only second…

Revealing plant cryptotypes: defining meaningful phenotypes among infinite traits.

PubMed

Chitwood, Daniel H; Topp, Christopher N

2015-04-01

The plant phenotype is infinite. Plants vary morphologically and molecularly over developmental time, in response to the environment, and genetically. Exhaustive phenotyping remains not only out of reach, but is also the limiting factor to interpreting the wealth of genetic information currently available. Although phenotyping methods are always improving, an impasse remains: even if we could measure the entirety of phenotype, how would we interpret it? We propose the concept of cryptotype to describe latent, multivariate phenotypes that maximize the separation of a priori classes. Whether the infinite points comprising a leaf outline or shape descriptors defining root architecture, statistical methods to discern the quantitative essence of an organism will be required as we approach measuring the totality of phenotype. Copyright © 2015 Elsevier Ltd. All rights reserved.

On an adaptive preconditioned Crank-Nicolson MCMC algorithm for infinite dimensional Bayesian inference

NASA Astrophysics Data System (ADS)

Hu, Zixi; Yao, Zhewei; Li, Jinglai

2017-03-01

Many scientific and engineering problems require to perform Bayesian inference for unknowns of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary slow under the mesh refinement, which is referred to as being dimension dependent. To this end, a family of dimensional independent MCMC algorithms, known as the preconditioned Crank-Nicolson (pCN) methods, were proposed to sample the infinite dimensional parameters. In this work we develop an adaptive version of the pCN algorithm, where the covariance operator of the proposal distribution is adjusted based on sampling history to improve the simulation efficiency. We show that the proposed algorithm satisfies an important ergodicity condition under some mild assumptions. Finally we provide numerical examples to demonstrate the performance of the proposed method.

Verifying the Simulation Hypothesis via Infinite Nested Universe Simulacrum Loops

NASA Astrophysics Data System (ADS)

Sharma, Vikrant

2017-01-01

The simulation hypothesis proposes that local reality exists as a simulacrum within a hypothetical computer's dimension. More specifically, Bostrom's trilemma proposes that the number of simulations an advanced 'posthuman' civilization could produce makes the proposition very likely. In this paper a hypothetical method to verify the simulation hypothesis is discussed using infinite regression applied to a new type of infinite loop. Assign dimension n to any computer in our present reality, where dimension signifies the hierarchical level in nested simulations our reality exists in. A computer simulating known reality would be dimension (n-1), and likewise a computer simulating an artificial reality, such as a video game, would be dimension (n +1). In this method, among others, four key assumptions are made about the nature of the original computer dimension n. Summations show that regressing such a reality infinitely will create convergence, implying that the verification of whether local reality is a grand simulation is feasible to detect with adequate compute capability. The action of reaching said convergence point halts the simulation of local reality. Sensitivities to the four assumptions and implications are discussed.

On beam shaping of the field radiated by a line source coupled to finite or infinite photonic crystals.

PubMed

Ceccuzzi, Silvio; Jandieri, Vakhtang; Baccarelli, Paolo; Ponti, Cristina; Schettini, Giuseppe

2016-04-01

Comparison of the beam-shaping effect of a field radiated by a line source, when an ideal infinite structure constituted by two photonic crystals and an actual finite one are considered, has been carried out by means of two different methods. The lattice sums technique combined with the generalized reflection matrix method is used to rigorously investigate the radiation from the infinite photonic crystals, whereas radiation from crystals composed of a finite number of rods along the layers is analyzed using the cylindrical-wave approach. A directive radiation is observed with the line source embedded in the structure. With an increased separation distance between the crystals, a significant edge diffraction appears that provides the main radiation mechanism in the finite layout. Suitable absorbers are implemented to reduce the above-mentioned diffraction and the reflections at the boundaries, thus obtaining good agreement between radiation patterns of a localized line source coupled to finite and infinite photonic crystals, when the number of periods of the finite structure is properly chosen.

Computation of type curves for flow to partially penetrating wells in water-table aquifers

USGS Publications Warehouse

Moench, Allen F.

1993-01-01

Evaluation of Neuman's analytical solution for flow to a well in a homogeneous, anisotropic, water-table aquifer commonly requires large amounts of computation time and can produce inaccurate results for selected combinations of parameters. Large computation times occur because the integrand of a semi-infinite integral involves the summation of an infinite series. Each term of the series requires evaluation of the roots of equations, and the series itself is sometimes slowly convergent. Inaccuracies can result from lack of computer precision or from the use of improper methods of numerical integration. In this paper it is proposed to use a method of numerical inversion of the Laplace transform solution, provided by Neuman, to overcome these difficulties. The solution in Laplace space is simpler in form than the real-time solution; that is, the integrand of the semi-infinite integral does not involve an infinite series or the need to evaluate roots of equations. Because the integrand is evaluated rapidly, advanced methods of numerical integration can be used to improve accuracy with an overall reduction in computation time. The proposed method of computing type curves, for which a partially documented computer program (WTAQ1) was written, was found to reduce computation time by factors of 2 to 20 over the time needed to evaluate the closed-form, real-time solution.

A hybrid finite element-transfer matrix model for vibroacoustic systems with flat and homogeneous acoustic treatments.

PubMed

Alimonti, Luca; Atalla, Noureddine; Berry, Alain; Sgard, Franck

2015-02-01

Practical vibroacoustic systems involve passive acoustic treatments consisting of highly dissipative media such as poroelastic materials. The numerical modeling of such systems at low to mid frequencies typically relies on substructuring methodologies based on finite element models. Namely, the master subsystems (i.e., structural and acoustic domains) are described by a finite set of uncoupled modes, whereas condensation procedures are typically preferred for the acoustic treatments. However, although accurate, such methodology is computationally expensive when real life applications are considered. A potential reduction of the computational burden could be obtained by approximating the effect of the acoustic treatment on the master subsystems without introducing physical degrees of freedom. To do that, the treatment has to be assumed homogeneous, flat, and of infinite lateral extent. Under these hypotheses, simple analytical tools like the transfer matrix method can be employed. In this paper, a hybrid finite element-transfer matrix methodology is proposed. The impact of the limiting assumptions inherent within the analytical framework are assessed for the case of plate-cavity systems involving flat and homogeneous acoustic treatments. The results prove that the hybrid model can capture the qualitative behavior of the vibroacoustic system while reducing the computational effort.

A real time, FEM based optimal control algorithm and its implementation using parallel processing hardware (transistors) in a microprocessor environment

NASA Technical Reports Server (NTRS)

Patten, William Neff

1989-01-01

There is an evident need to discover a means of establishing reliable, implementable controls for systems that are plagued by nonlinear and, or uncertain, model dynamics. The development of a generic controller design tool for tough-to-control systems is reported. The method utilizes a moving grid, time infinite element based solution of the necessary conditions that describe an optimal controller for a system. The technique produces a discrete feedback controller. Real time laboratory experiments are now being conducted to demonstrate the viability of the method. The algorithm that results is being implemented in a microprocessor environment. Critical computational tasks are accomplished using a low cost, on-board, multiprocessor (INMOS T800 Transputers) and parallel processing. Progress to date validates the methodology presented. Applications of the technique to the control of highly flexible robotic appendages are suggested.

A Combined FEM/MoM/GTD Technique To Analyze Elliptically Polarized Cavity-Backed Antennas With Finite Ground Plane

NASA Technical Reports Server (NTRS)

Reddy, C. J.; Deshpande, M. D.; Fralick, D. T.; Cockrell, C. R.; Beck, F. B.

1996-01-01

Radiation pattern prediction analysis of elliptically polarized cavity-backed aperture antennas in a finite ground plane is performed using a combined Finite Element Method/Method of Moments/Geometrical Theory of Diffraction (FEM/MoM/GTD) technique. The magnetic current on the cavity-backed aperture in an infinite ground plane is calculated using the combined FEM/MoM analysis. GTD, including the slope diffraction contribution, is used to calculate the diffracted fields caused by both soft and hard polarizations at the edges of the finite ground plane. Explicit expressions for regular diffraction coefficients and slope diffraction coefficients are presented. The slope of the incident magnetic field at the diffraction points is derived and analytical expressions are presented. Numerical results for the radiation patterns of a cavity-backed circular spiral microstrip patch antenna excited by a coaxial probe in a finite rectangular ground plane are computed and compared with experimental results.

On the contact interaction of two identical stringers with an elastic semi-infinite continuous or vertically cracked plate

NASA Astrophysics Data System (ADS)

Grigoryan, M. S.

2018-04-01

This paper considers two connected contact problems on the interaction of stringers with an elastic semi-infinite plate. In the first problem, an elastic half-infinite continuous plate is reinforced on its boundary by two identical stringers exposed to a tensile external force. In the second problem, in the presence of the same stringers, the plate contains a collinear system of cracks on its vertical axis. The solution of both problems is reduced to the solution of singular integral equations (SIE) that are solved by a known numerical-analytical method.

Stable Direct Adaptive Control of Linear Infinite-dimensional Systems Using a Command Generator Tracker Approach

NASA Technical Reports Server (NTRS)

Balas, M. J.; Kaufman, H.; Wen, J.

1985-01-01

A command generator tracker approach to model following contol of linear distributed parameter systems (DPS) whose dynamics are described on infinite dimensional Hilbert spaces is presented. This method generates finite dimensional controllers capable of exponentially stable tracking of the reference trajectories when certain ideal trajectories are known to exist for the open loop DPS; we present conditions for the existence of these ideal trajectories. An adaptive version of this type of controller is also presented and shown to achieve (in some cases, asymptotically) stable finite dimensional control of the infinite dimensional DPS.

The effects of magnetohydrodynamic and radiation on flow of second grade fluid past an infinite inclined plate in porous medium

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

Ismail, Zulkhibri; Khan, Ilyas; Nasir, Nadirah Mohd

2015-02-03

An analysis of the exact solutions of second grade fluid problem for unsteady magnetohydrodynamic (MHD) flows past an infinite inclined plate in a porous medium is presented. It is assumed that the bounding infinite inclined plate has a constant temperature with radiation effects. Based on Boussinesq approximation the expressions for dimensionless velocity, temperature and concentration are obtained by using Laplace transform method. The derived solutions satisfying the involved differential equations, and all the boundary and initial conditions. The influence of various parameters on the velocity has been illustrated graphically and analyzed.

Geometric MCMC for infinite-dimensional inverse problems

NASA Astrophysics Data System (ADS)

Beskos, Alexandros; Girolami, Mark; Lan, Shiwei; Farrell, Patrick E.; Stuart, Andrew M.

2017-04-01

Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and thus are expensive as a function of dimension. Recently, a new class of MCMC methods with mesh-independent convergence times has emerged. However, few of them take into account the geometry of the posterior informed by the data. At the same time, recently developed geometric MCMC algorithms have been found to be powerful in exploring complicated distributions that deviate significantly from elliptic Gaussian laws, but are in general computationally intractable for models defined in infinite dimensions. In this work, we combine geometric methods on a finite-dimensional subspace with mesh-independent infinite-dimensional approaches. Our objective is to speed up MCMC mixing times, without significantly increasing the computational cost per step (for instance, in comparison with the vanilla preconditioned Crank-Nicolson (pCN) method). This is achieved by using ideas from geometric MCMC to probe the complex structure of an intrinsic finite-dimensional subspace where most data information concentrates, while retaining robust mixing times as the dimension grows by using pCN-like methods in the complementary subspace. The resulting algorithms are demonstrated in the context of three challenging inverse problems arising in subsurface flow, heat conduction and incompressible flow control. The algorithms exhibit up to two orders of magnitude improvement in sampling efficiency when compared with the pCN method.

An efficient numerical method for the solution of the problem of elasticity for 3D-homogeneous elastic medium with cracks and inclusions

NASA Astrophysics Data System (ADS)

Kanaun, S.; Markov, A.

2017-06-01

An efficient numerical method for solution of static problems of elasticity for an infinite homogeneous medium containing inhomogeneities (cracks and inclusions) is developed. Finite number of heterogeneous inclusions and planar parallel cracks of arbitrary shapes is considered. The problem is reduced to a system of surface integral equations for crack opening vectors and volume integral equations for stress tensors inside the inclusions. For the numerical solution of these equations, a class of Gaussian approximating functions is used. The method based on these functions is mesh free. For such functions, the elements of the matrix of the discretized system are combinations of explicit analytical functions and five standard 1D-integrals that can be tabulated. Thus, the numerical integration is excluded from the construction of the matrix of the discretized problem. For regular node grids, the matrix of the discretized system has Toeplitz's properties, and Fast Fourier Transform technique can be used for calculation matrix-vector products of such matrices.

Finding Sums for an Infinite Class of Alternating Series

ERIC Educational Resources Information Center

Chen, Zhibo; Wei, Sheng; Xiao, Xuerong

2012-01-01

Calculus II students know that many alternating series are convergent by the Alternating Series Test. However, they know few alternating series (except geometric series and some trivial ones) for which they can find the sum. In this article, we present a method that enables the students to find sums for infinitely many alternating series in the…

Prediction of the interaction between a simple moving vehicle and an infinite periodically supported rail - Green's functions approach

NASA Astrophysics Data System (ADS)

Mazilu, Traian

2010-09-01

This paper herein describes the interaction between a simple moving vehicle and an infinite periodically supported rail, in order to signalise the basic features of the vehicle/track vibration behaviour in general, and wheel/rail vibration, in particular. The rail is modelled as an infinite Timoshenko beam resting on semi-sleepers via three-directional rail pads and ballast. The time-domain analysis was performed applying Green's matrix of the track method. This method allows taking into account the nonlinearities of the wheel/rail contact and the Doppler effect. The numerical analysis is dedicated to the wheel/rail response due to two types of excitation: the steady-state interaction and rail irregularities. The study points out to certain aspects regarding the parametric resonance, the amplitude-modulated vibration due to corrugation and the Doppler effect.

Multilayer solar cell waveguide structures containing metamaterials

NASA Astrophysics Data System (ADS)

Hamouche, Houria.; Shabat, Mohammed. M.; Schaadt, Daniel M.

2017-01-01

Multilayer antireflection coating structures made from silicon and metamaterials are designed and investigated using the Transfer Matrix Method (TMM). The Transfer Matrix Method is a very useful algorithm for the analysis of periodic structures. We investigate in this paper two anti-reflection coating structures for silicon solar cells with a metamaterial film layer. In the first structure, the metamaterial film layer is sandwiched between a semi-infinite glass cover layer and a semi-infinite silicon substrate layer. The second structure consists of a four layers, a pair of metamaterial-dielectric layer with opposite real part of refractive indices, is placed between the two semi-infinite cover and substrate. We have simulated the absorptivity property of the structures for adjustable thicknesses by using MAPLE software. The absorptivity of the structures achieves greater than 80% for incident electromagnetic wave of transverse magnetic (TM) polarization.

The surface-induced spatial-temporal structures in confined binary alloys

NASA Astrophysics Data System (ADS)

Krasnyuk, Igor B.; Taranets, Roman M.; Chugunova, Marina

2014-12-01

This paper examines surface-induced ordering in confined binary alloys. The hyperbolic initial boundary value problem (IBVP) is used to describe a scenario of spatiotemporal ordering in a disordered phase for concentration of one component of binary alloy and order parameter with non-linear dynamic boundary conditions. This hyperbolic model consists of two coupled second order differential equations for order parameter and concentration. It also takes into account effects of the “memory” on the ordering of atoms and their densities in the alloy. The boundary conditions characterize surface velocities of order parameter and concentration changing which is due to surface (super)cooling on walls confining the binary alloy. It is shown that for large times there are three classes of dynamic non-linear boundary conditions which lead to three different types of attractor’s elements for the IBVP. Namely, the elements of attractor are the limit periodic simple shock waves with fronts of “discontinuities” Γ. If Γ is finite, then the attractor contains spatiotemporal functions of relaxation type. If Γ is infinite and countable then we observe the functions of pre-turbulent type. If Γ is infinite and uncountable then we obtain the functions of turbulent type.

Single-scatter vector-wave scattering from surfaces with infinite slopes using the Kirchhoff approximation.

PubMed

Bruce, Neil C

2008-08-01

This paper presents a new formulation of the 3D Kirchhoff approximation that allows calculation of the scattering of vector waves from 2D rough surfaces containing structures with infinite slopes. This type of surface has applications, for example, in remote sensing and in testing or imaging of printed circuits. Some preliminary calculations for rectangular-shaped grooves in a plane are presented for the 2D surface method and are compared with the equivalent 1D surface calculations for the Kirchhoff and integral equation methods. Good agreement is found between the methods.

Tensor network simulation of QED on infinite lattices: Learning from (1 +1 ) d , and prospects for (2 +1 ) d

NASA Astrophysics Data System (ADS)

Zapp, Kai; Orús, Román

2017-06-01

The simulation of lattice gauge theories with tensor network (TN) methods is becoming increasingly fruitful. The vision is that such methods will, eventually, be used to simulate theories in (3 +1 ) dimensions in regimes difficult for other methods. So far, however, TN methods have mostly simulated lattice gauge theories in (1 +1 ) dimensions. The aim of this paper is to explore the simulation of quantum electrodynamics (QED) on infinite lattices with TNs, i.e., fermionic matter fields coupled to a U (1 ) gauge field, directly in the thermodynamic limit. With this idea in mind we first consider a gauge-invariant infinite density matrix renormalization group simulation of the Schwinger model—i.e., QED in (1 +1 ) d . After giving a precise description of the numerical method, we benchmark our simulations by computing the subtracted chiral condensate in the continuum, in good agreement with other approaches. Our simulations of the Schwinger model allow us to build intuition about how a simulation should proceed in (2 +1 ) dimensions. Based on this, we propose a variational ansatz using infinite projected entangled pair states (PEPS) to describe the ground state of (2 +1 ) d QED. The ansatz includes U (1 ) gauge symmetry at the level of the tensors, as well as fermionic (matter) and bosonic (gauge) degrees of freedom both at the physical and virtual levels. We argue that all the necessary ingredients for the simulation of (2 +1 ) d QED are, a priori, already in place, paving the way for future upcoming results.

Jeffrey fluid effect on free convective over a vertically inclined plate with magnetic field: A numerical approach

NASA Astrophysics Data System (ADS)

Rao, J. Anand; Raju, R. Srinivasa; Bucchaiah, C. D.

2018-05-01

In this work, the effect of magnetohydrodynamic natural or free convective of an incompressible, viscous and electrically conducting non-newtonian Jeffrey fluid over a semi-infinite vertically inclined permeable moving plate embedded in a porous medium in the presence of heat absorption, heat and mass transfer. By using non-dimensional quantities, the fundamental governing non-linear partial differential equations are transformed into linear partial differential equations and these equations together with associated boundary conditions are solved numerically by using versatile, extensively validated, variational finite element method. The sway of important key parameters on hydrodynamic, thermal and concentration boundary layers are examined in detail and the results are shown graphically. Finally the results are compared with the works published previously and found to be excellent agreement.

One-loop β-function for an infinite-parameter family of gauge theories

NASA Astrophysics Data System (ADS)

Krasnov, Kirill

2015-03-01

We continue to study an infinite-parametric family of gauge theories with an arbitrary function of the self-dual part of the field strength as the Lagrangian. The arising one-loop divergences are computed using the background field method. We show that they can all be absorbed by a local redefinition of the gauge field, as well as multiplicative renormalisations of the couplings. Thus, this family of theories is one-loop renormalisable. The infinite set of β-functions for the couplings is compactly stored in a renormalisation group flow for a single function of the curvature. The flow is obtained explicitly.

Quasi-periodic continuation along a continuous symmetry

NASA Astrophysics Data System (ADS)

Salomone, Matthew David

Given a system of differential equations which admits a continuous group of symmetries and possesses a periodic solution, we show that under certain nondegeneracy assumptions there always exists a continuous family containing infinitely many periodic and quasi-periodic trajectories. This generalizes the continuation method of Poincaré to orbits which are not necessarily periodic. We apply these results in the setting of the Lagrangian N -body problem of homogeneous potential to characterize an infinite family of rotating nonplanar "hip-hop" orbits in the four-body problem of equal masses, and show how some other trajectories in the N -body theory may be extended to infinite families of periodic and quasi-periodic trajectories.

Recursive boson system in the Cuntz algebra O{sub {infinity}}

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

Kawamura, Katsunori

2007-09-15

Bosons and fermions are often written by elements of other algebras. Abe (private communication) gave a realization of bosons by formal infinite sums of the canonical generators of the Cuntz algebra O{sub {infinity}}. We show that such formal infinite sum always makes sense on a certain dense subspace of any permutative representation of O{sub {infinity}}. In this meaning, we can regard as if the algebra B of bosons was a unital *-subalgebra of O{sub {infinity}} on a given permutative representation. According to this relation, we compute branching laws arising from restrictions of representations of O{sub {infinity}} on B. For example,more » it is shown that the Fock representation of B is given as the restriction of the standard representation of O{sub {infinity}} on B.« less

Electronic transport close to semi-infinite 2D systems and their interfaces

NASA Astrophysics Data System (ADS)

Xia, Fanbing; Wang, Jian; Jian Wang's research Group Team

Transport properties of 2D materials especially close to their boundary has received much attention after the successful fabrication of Graphene. While most previous work is devoted to the conventional lead-device-lead setup with a finite size center area, this project investigates real space transport properties of infinite and semi-infinite 2D systems under the framework of Non-equilibrium Green's function. The commonly used method of calculating Green's function by inverting matrices in the real space can be unstable in dealing with large systems as sometimes it gives non-converging result. By transforming from the real space to momentum space, the author managed to replace the matrix inverting process by Brillouin Zone integral which can be greatly simplified by the application of contour integral. Combining this methodology with Dyson equations, we are able to calculate transport properties of semi-infinite graphene close to its zigzag boundary and its combination with other material including s-wave superconductor. Interference pattern of transmitted and reflected electrons, Graphene lensing effects and difference between Specular Andreev reflection and normal Andreev reflection are verified. We also generalize how to apply this method to a broad range of 2D materials. The University of Hong Kong.

Arrowheaded enhanced multivariance products representation for matrices (AEMPRM): Specifically focusing on infinite matrices and converting arrowheadedness to tridiagonality

NASA Astrophysics Data System (ADS)

Özdemir, Gizem; Demiralp, Metin

2015-12-01

In this work, Enhanced Multivariance Products Representation (EMPR) approach which is a Demiralp-and-his- group extension to the Sobol's High Dimensional Model Representation (HDMR) has been used as the basic tool. Their discrete form have also been developed and used in practice by Demiralp and his group in addition to some other authors for the decomposition of the arrays like vectors, matrices, or multiway arrays. This work specifically focuses on the decomposition of infinite matrices involving denumerable infinitely many rows and columns. To this end the target matrix is first decomposed to the sum of certain outer products and then each outer product is treated by Tridiagonal Matrix Enhanced Multivariance Products Representation (TMEMPR) which has been developed by Demiralp and his group. The result is a three-matrix- factor-product whose kernel (the middle factor) is an arrowheaded matrix while the pre and post factors are invertable matrices decomposed of the support vectors of TMEMPR. This new method is called as Arrowheaded Enhanced Multivariance Products Representation for Matrices. The general purpose is approximation of denumerably infinite matrices with the new method.

Determination of diffusion coefficients of various livestock antibiotics in water at infinite dilution

NASA Astrophysics Data System (ADS)

Soriano, Allan N.; Adamos, Kristoni G.; Bonifacio, Pauline B.; Adornado, Adonis P.; Bungay, Vergel C.; Vairavan, Rajendaran

2017-11-01

The fate of antibiotics entering the environment raised concerns on the possible effect of antimicrobial resistance bacteria. Prediction of the fate and transport of these particles are needed to be determined, significantly the diffusion coefficient of antibiotic in water at infinite dilution. A systematic determination of diffusion coefficient of antibiotic in water at infinite dilution of five different kinds of livestock antibiotics namely: Amtyl, Ciprotyl, Doxylak Forte, Trisullak, and Vetracin Gold in the 293.15 to 313.15 K temperature range are reported through the use of the method involving the electrolytic conductivity measurements. A continuous stirred tank reactor is utilized to measure the electrolytic conductivities of the considered systems. These conductivities are correlated by using the Nernst-Haskell equation to determine the infinite dilution diffusion coefficient. Determined diffusion coefficients are based on the assumption that in dilute solution, these antibiotics behave as strong electrolyte from which H+ cation dissociate from the antibiotic's anion.

Accuracy of the Generalized Self-Consistent Method in Modelling the Elastic Behaviour of Periodic Composites

NASA Technical Reports Server (NTRS)

Walker, Kevin P.; Freed, Alan D.; Jordan, Eric H.

1993-01-01

Local stress and strain fields in the unit cell of an infinite, two-dimensional, periodic fibrous lattice have been determined by an integral equation approach. The effect of the fibres is assimilated to an infinite two-dimensional array of fictitious body forces in the matrix constituent phase of the unit cell. By subtracting a volume averaged strain polarization term from the integral equation we effectively embed a finite number of unit cells in a homogenized medium in which the overall stress and strain correspond to the volume averaged stress and strain of the constrained unit cell. This paper demonstrates that the zeroth term in the governing integral equation expansion, which embeds one unit cell in the homogenized medium, corresponds to the generalized self-consistent approximation. By comparing the zeroth term approximation with higher order approximations to the integral equation summation, both the accuracy of the generalized self-consistent composite model and the rate of convergence of the integral summation can be assessed. Two example composites are studied. For a tungsten/copper elastic fibrous composite the generalized self-consistent model is shown to provide accurate, effective, elastic moduli and local field representations. The local elastic transverse stress field within the representative volume element of the generalized self-consistent method is shown to be in error by much larger amounts for a composite with periodically distributed voids, but homogenization leads to a cancelling of errors, and the effective transverse Young's modulus of the voided composite is shown to be in error by only 23% at a void volume fraction of 75%.

Dispersion analysis of leaky guided waves in fluid-loaded waveguides of generic shape.

PubMed

Mazzotti, M; Marzani, A; Bartoli, I

2014-01-01

A fully coupled 2.5D formulation is proposed to compute the dispersive parameters of waveguides with arbitrary cross-section immersed in infinite inviscid fluids. The discretization of the waveguide is performed by means of a Semi-Analytical Finite Element (SAFE) approach, whereas a 2.5D BEM formulation is used to model the impedance of the surrounding infinite fluid. The kernels of the boundary integrals contain the fundamental solutions of the space Fourier-transformed Helmholtz equation, which governs the wave propagation process in the fluid domain. Numerical difficulties related to the evaluation of singular integrals are avoided by using a regularization procedure. To improve the numerical stability of the discretized boundary integral equations for the external Helmholtz problem, the so called CHIEF method is used. The discrete wave equation results in a nonlinear eigenvalue problem in the complex axial wavenumbers that is solved at the frequencies of interest by means of a contour integral algorithm. In order to separate physical from non-physical solutions and to fulfill the requirement of holomorphicity of the dynamic stiffness matrix inside the complex wavenumber contour, the phase of the radial bulk wavenumber is uniquely defined by enforcing the Snell-Descartes law at the fluid-waveguide interface. Three numerical applications are presented. The computed dispersion curves for a circular bar immersed in oil are in agreement with those extracted using the Global Matrix Method. Novel results are presented for viscoelastic steel bars of square and L-shaped cross-section immersed in water. Copyright © 2013 Elsevier B.V. All rights reserved.

The Geometry of Quadratic Polynomial Differential Systems with a Finite and an Infinite Saddle-Node (C)

NASA Astrophysics Data System (ADS)

Artés, Joan C.; Rezende, Alex C.; Oliveira, Regilene D. S.

Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular, Hilbert's 16th problem [Hilbert, 1900, 1902], are still open for this family. Our goal is to make a global study of the family QsnSN of all real quadratic polynomial differential systems which have a finite semi-elemental saddle-node and an infinite saddle-node formed by the collision of two infinite singular points. This family can be divided into three different subfamilies, all of them with the finite saddle-node in the origin of the plane with the eigenvectors on the axes and with the eigenvector associated with the zero eigenvalue on the horizontal axis and (A) with the infinite saddle-node in the horizontal axis, (B) with the infinite saddle-node in the vertical axis and (C) with the infinite saddle-node in the bisector of the first and third quadrants. These three subfamilies modulo the action of the affine group and time homotheties are three-dimensional and we give the bifurcation diagram of their closure with respect to specific normal forms, in the three-dimensional real projective space. The subfamilies (A) and (B) have already been studied [Artés et al., 2013b] and in this paper we provide the complete study of the geometry of the last family (C). The bifurcation diagram for the subfamily (C) yields 371 topologically distinct phase portraits with and without limit cycles for systems in the closure /line{QsnSN(C)} within the representatives of QsnSN(C) given by a chosen normal form. Algebraic invariants are used to construct the bifurcation set. The phase portraits are represented on the Poincaré disk. The bifurcation set of /line{QsnSN(C)} is not only algebraic due to the presence of some surfaces found numerically. All points in these surfaces correspond to either connections of separatrices, or the presence of a double limit cycle.

Application of 'steady' state finite element and transient finite difference theory to sound propagation in a variable duct - A comparison with experiment

NASA Technical Reports Server (NTRS)

Baumeister, K. J.; Eversman, W.; Astley, R. J.; White, J. W.

1981-01-01

Experimental data are presented for sound propagation in a simulated infinite hard wall duct with a large change in duct cross sectional area. The data are conveniently tabulated for further use. The 'steady' state finite element theory of Astley and Eversman (1981) and the transient finite difference theory of White (1981) are in good agreement with the data for both the axial and transverse pressure profiles and the axial phase angle. Therefore, numerical finite difference and finite element theories appear to be ideally suited for handling duct propagation problems which encounter large axial gradients in acoustic parameters. The measured energy reflection coefficient agrees with the values from the Astley-Eversman modal coupling model.

A correlation method to predict the surface pressure distribution on an infinite plate from which a jet is issuing. [effects of a lifting jet

NASA Technical Reports Server (NTRS)

Perkins, S. C., Jr.; Menhall, M. R.

1978-01-01

A correlation method to predict pressures induced on an infinite plate by a jet issuing from the plate into a subsonic free stream was developed. The complete method consists of an analytical method which models the blockage and entrainment properties of the jet and a correlation which accounts for the effects of separation. The method was developed for jet velocity ratios up to ten and for radial distances up to five diameters from the jet. Correlation curves and data comparisons are presented for jets issuing normally from a flat plate with velocity ratios one to twelve. Also, a list of references which deal with jets in a crossflow is presented.

Application of the discrete generalized multigroup method to ultra-fine energy mesh in infinite medium calculations

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

Gibson, N. A.; Forget, B.

2012-07-01

The Discrete Generalized Multigroup (DGM) method uses discrete Legendre orthogonal polynomials to expand the energy dependence of the multigroup neutron transport equation. This allows a solution on a fine energy mesh to be approximated for a cost comparable to a solution on a coarse energy mesh. The DGM method is applied to an ultra-fine energy mesh (14,767 groups) to avoid using self-shielding methodologies without introducing the cost usually associated with such energy discretization. Results show DGM to converge to the reference ultra-fine solution after a small number of recondensation steps for multiple infinite medium compositions. (authors)

A non-stochastic iterative computational method to model light propagation in turbid media

NASA Astrophysics Data System (ADS)

McIntyre, Thomas J.; Zemp, Roger J.

2015-03-01

Monte Carlo models are widely used to model light transport in turbid media, however their results implicitly contain stochastic variations. These fluctuations are not ideal, especially for inverse problems where Jacobian matrix errors can lead to large uncertainties upon matrix inversion. Yet Monte Carlo approaches are more computationally favorable than solving the full Radiative Transport Equation. Here, a non-stochastic computational method of estimating fluence distributions in turbid media is proposed, which is called the Non-Stochastic Propagation by Iterative Radiance Evaluation method (NSPIRE). Rather than using stochastic means to determine a random walk for each photon packet, the propagation of light from any element to all other elements in a grid is modelled simultaneously. For locally homogeneous anisotropic turbid media, the matrices used to represent scattering and projection are shown to be block Toeplitz, which leads to computational simplifications via convolution operators. To evaluate the accuracy of the algorithm, 2D simulations were done and compared against Monte Carlo models for the cases of an isotropic point source and a pencil beam incident on a semi-infinite turbid medium. The model was shown to have a mean percent error less than 2%. The algorithm represents a new paradigm in radiative transport modelling and may offer a non-stochastic alternative to modeling light transport in anisotropic scattering media for applications where the diffusion approximation is insufficient.

Stability analysis and backward whirl investigation of cracked rotors with time-varying stiffness

NASA Astrophysics Data System (ADS)

AL-Shudeifat, Mohammad A.

2015-07-01

The dynamic stability of dynamical systems with time-periodic stiffness is addressed here. Cracked rotor systems with time-periodic stiffness are well-known examples of such systems. Time-varying area moments of inertia at the cracked element cross-section of a cracked rotor have been used to formulate the time-periodic finite element stiffness matrix. The semi-infinite coefficient matrix obtained by applying the harmonic balance (HB) solution to the finite element (FE) equations of motion is employed here to study the dynamic stability of the system. Consequently, the sign of the determinant of a scaled version of a sub-matrix of this semi-infinite coefficient matrix at a finite number of harmonics in the HB solution is found to be sufficient for identifying the major unstable zones of the system in the parameter plane. Specifically, it is found that the negative determinant always corresponds to unstable zones in all of the systems considered. This approach is applied to a parametrically excited Mathieu's equation, a two degree-of-freedom linear time-periodic dynamical system, a cracked Jeffcott rotor and a finite element model of the cracked rotor system. Compared to the corresponding results obtained by Floquet's theory, the sign of the determinant of the scaled sub-matrix is found to be an efficient tool for identifying the major unstable zones of the linear time-periodic parametrically excited systems, especially large-scale FE systems. Moreover, it is found that the unstable zones for a FE cracked rotor with an open transverse crack model only appear at the backward whirl. The theoretical and experimental results have been found to agree well for verifying that the open crack model excites the backward whirl amplitudes at the critical backward whirling rotational speeds.

The dynamics of maternal-effect selfish genetic elements.

PubMed

Smith, N G

1998-03-21

Maternal-effect selfish genes such as Medea or Scat act to kill progeny that do not bear a copy of the selfish gene present in the mother. Previous models of this system allowed for two types of allele, the selfish (killer) type and the sensitive (susceptible) wild-type. These models predict that the invasion conditions of the selfish allele are quite broad and that if invasion is possible a high frequency equilibrium is to be expected. The selfish element is therefore predicted to persist. Here a hypothetical third allele that neither kills nor is killed (i.e. insensitive) is considered. Such an allele could enter a population by recombination, mutation or migration. The incorporation of this third allele profoundly affects the dynamics of the system and, under some parameter values, it is possible for the spread of the insensitive allele to lead, eventually, to the fixation of the wild-type allele (reversible evolution). This is most likely if the death of progeny provides no direct benefit to the surviving sibs (i.e. in the absence of fitness compensation), as in insects without gregarious broods. Under these circumstances the selfish element cannot spread when infinitely rare, only after having risen to some finite frequency. A fitness cost to bearing the killer allele then causes its loss. However, if fitness compensation is found (e.g. in placental mammals) the invasion of the selfish element from an infinitely low level is possible for a wide range of costs and both stable coexistences of all three alleles and limit cycles of all three are then found. It is therefore to be expected that in mammals selfish maternal-effect genes are more likely both to spread and to persist than in insects, due to their different levels of fitness compensation.

Free Convection from a Semi-Infinite Vertical Plate with Discontinuous Blowing or Suction.

DTIC Science & Technology

1981-03-01

SCHIESSR UNCLASSIFIED; EhEllllEllEE EE[E]hEEEIllIEllhlEEIl EEEEEIIIEEEEI EEEIIIIIIIIII EIIIEIIEEEEII EEEIIIIIIIIIIE LVEL NAVAL POSTGRADUATE SCHOOL Monterey...the unsteady free convective flow past a simi-infinite porous plate with constant suction were studied through mathematical analysis by Soundalgekar...boundary-layers and; therefore, will often indicate a preferred method of analytical solution. Although there are several possible mathematical techniques

Experimental evaluation of effective atomic number of composite materials using back-scattering of gamma photons

NASA Astrophysics Data System (ADS)

Singh, Inderjeet; Singh, Bhajan; Sandhu, B. S.; Sabharwal, Arvind D.

2017-04-01

A method has been presented for calculation of effective atomic number (Zeff) of composite materials, by using back-scattering of 662 keV gamma photons obtained from a 137Cs mono-energetic radioactive source. The present technique is a non-destructive approach, and is employed to evaluate Zeff of different composite materials, by interacting gamma photons with semi-infinite material in a back-scattering geometry, using a 3″ × 3″ NaI(Tl) scintillation detector. The present work is undertaken to study the effect of target thickness on intensity distribution of gamma photons which are multiply back-scattered from targets (pure elements) and composites (mixtures of different elements). The intensity of multiply back-scattered events increases with increasing target thickness and finally saturates. The saturation thickness for multiply back-scattered events is used to assign a number (Zeff) for multi-element materials. Response function of the 3″ × 3″ NaI(Tl) scintillation detector is applied on observed pulse-height distribution to include the contribution of partially absorbed photons. The reduced value of signal-to-noise ratio interprets the increase in multiply back-scattered data of a response corrected spectrum. Data obtained from Monte Carlo simulations and literature also support the present experimental results.

Matrix Transformations between Certain Sequence Spaces over the Non-Newtonian Complex Field

PubMed Central

Efe, Hakan

2014-01-01

In some cases, the most general linear operator between two sequence spaces is given by an infinite matrix. So the theory of matrix transformations has always been of great interest in the study of sequence spaces. In the present paper, we introduce the matrix transformations in sequence spaces over the field ℂ* and characterize some classes of infinite matrices with respect to the non-Newtonian calculus. Also we give the necessary and sufficient conditions on an infinite matrix transforming one of the classical sets over ℂ* to another one. Furthermore, the concept for sequence-to-sequence and series-to-series methods of summability is given with some illustrated examples. PMID:25110740

On improvement of the series convergence in the problem of the vibrations of orhotropic rectangular prism

NASA Astrophysics Data System (ADS)

Lyashko, A. D.

2017-11-01

A new analytical presentation of the solution for steady-state oscillations of orthotopic rectangular prism is found. The corresponding infinite system of linear algebraic equations has been deduced by the superposition method. A countable set of precise eigenfrequencies and elementary eigenforms is found. The identities are found which make it possible to improve the convergence of all the infinite series in the solution of the problem. All the infinite series in presentation of solution are analytically summed up. Numerical calculations of stresses in the rectangular orthotropic prism with a uniform along the border and harmonic in time load on two opposite faces have been performed.

Least-squares Legendre spectral element solutions to sound propagation problems.

PubMed

Lin, W H

2001-02-01

This paper presents a novel algorithm and numerical results of sound wave propagation. The method is based on a least-squares Legendre spectral element approach for spatial discretization and the Crank-Nicolson [Proc. Cambridge Philos. Soc. 43, 50-67 (1947)] and Adams-Bashforth [D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications (CBMS-NSF Monograph, Siam 1977)] schemes for temporal discretization to solve the linearized acoustic field equations for sound propagation. Two types of NASA Computational Aeroacoustics (CAA) Workshop benchmark problems [ICASE/LaRC Workshop on Benchmark Problems in Computational Aeroacoustics, edited by J. C. Hardin, J. R. Ristorcelli, and C. K. W. Tam, NASA Conference Publication 3300, 1995a] are considered: a narrow Gaussian sound wave propagating in a one-dimensional space without flows, and the reflection of a two-dimensional acoustic pulse off a rigid wall in the presence of a uniform flow of Mach 0.5 in a semi-infinite space. The first problem was used to examine the numerical dispersion and dissipation characteristics of the proposed algorithm. The second problem was to demonstrate the capability of the algorithm in treating sound propagation in a flow. Comparisons were made of the computed results with analytical results and results obtained by other methods. It is shown that all results computed by the present method are in good agreement with the analytical solutions and results of the first problem agree very well with those predicted by other schemes.

Suppression of sound radiation to far field of near-field acoustic communication system using evanescent sound field

NASA Astrophysics Data System (ADS)

Fujii, Ayaka; Wakatsuki, Naoto; Mizutani, Koichi

2016-01-01

A method of suppressing sound radiation to the far field of a near-field acoustic communication system using an evanescent sound field is proposed. The amplitude of the evanescent sound field generated from an infinite vibrating plate attenuates exponentially with increasing a distance from the surface of the vibrating plate. However, a discontinuity of the sound field exists at the edge of the finite vibrating plate in practice, which broadens the wavenumber spectrum. A sound wave radiates over the evanescent sound field because of broadening of the wavenumber spectrum. Therefore, we calculated the optimum distribution of the particle velocity on the vibrating plate to reduce the broadening of the wavenumber spectrum. We focused on a window function that is utilized in the field of signal analysis for reducing the broadening of the frequency spectrum. The optimization calculation is necessary for the design of window function suitable for suppressing sound radiation and securing a spatial area for data communication. In addition, a wide frequency bandwidth is required to increase the data transmission speed. Therefore, we investigated a suitable method for calculating the sound pressure level at the far field to confirm the variation of the distribution of sound pressure level determined on the basis of the window shape and frequency. The distribution of the sound pressure level at a finite distance was in good agreement with that obtained at an infinite far field under the condition generating the evanescent sound field. Consequently, the window function was optimized by the method used to calculate the distribution of the sound pressure level at an infinite far field using the wavenumber spectrum on the vibrating plate. According to the result of comparing the distributions of the sound pressure level in the cases with and without the window function, it was confirmed that the area whose sound pressure level was reduced from the maximum level to -50 dB was extended. Additionally, we designed a sound insulator so as to realize a similar distribution of the particle velocity to that obtained using the optimized window function. Sound radiation was suppressed using a sound insulator put above the vibrating surface in the simulation using the three-dimensional finite element method. On the basis of this finding, it was suggested that near-field acoustic communication which suppressed sound radiation can be realized by applying the optimized window function to the particle velocity field.

Haag duality for Kitaev’s quantum double model for abelian groups

NASA Astrophysics Data System (ADS)

Fiedler, Leander; Naaijkens, Pieter

2015-11-01

We prove Haag duality for cone-like regions in the ground state representation corresponding to the translational invariant ground state of Kitaev’s quantum double model for finite abelian groups. This property says that if an observable commutes with all observables localized outside the cone region, it actually is an element of the von Neumann algebra generated by the local observables inside the cone. This strengthens locality, which says that observables localized in disjoint regions commute. As an application, we consider the superselection structure of the quantum double model for abelian groups on an infinite lattice in the spirit of the Doplicher-Haag-Roberts program in algebraic quantum field theory. We find that, as is the case for the toric code model on an infinite lattice, the superselection structure is given by the category of irreducible representations of the quantum double.

Conceptual structure modulates structural priming in the production of complex sentences

PubMed Central

Griffin, Zenzi M.; Weinstein-Tull, Justin

2016-01-01

Speakers tend to reproduce syntactic structures that they have recently comprehended or produced. This structural or syntactic priming occurs despite differences in the particular conceptual or event roles expressed in prime and target sentences (Bock & Loebell, 1990). In two sentence recall studies, we used the tendency of speakers to paraphrase the finite complements of object-raising verbs as infinitive complements (e.g., “John believed that Mary was nice” as “John believed Mary to be nice”) to test whether an additional conceptual role would affect priming. Prime constructions with identical constituent orders as object-raising infinitives but an additional conceptual role (“John persuaded Mary to be nice”) resulted in fewer paraphrases. Contrasts with other constructions suggest that the critical difference between primes was this extra conceptual role. Thus, subtle differences in conceptual structures can affect how speakers grammatically encode message elements. PMID:28066128

Electromagnetic propagation in PEC and absorbing curved S-ducts

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.

1988-01-01

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

Greek Cosmology and Cosmogony

NASA Astrophysics Data System (ADS)

Jones, Alexander

The structure, composition, and long-term history of the cosmos were prominent topics in many ancient Greek philosophical systems. Philosophers and philosophically informed astronomers differed over whether the cosmos was finite or infinite, eternal or transient, and composed of discrete particles or continuous, homogeneous elements. The Aristotelian cosmology preferred by astronomers following Ptolemy assumed a finite, spherical shell of eternally unalterable matter enclosing a terrestrial globe composed of earth, water, air, and fire.

Relativistic density functional theory with picture-change corrected electron density based on infinite-order Douglas-Kroll-Hess method

NASA Astrophysics Data System (ADS)

Oyama, Takuro; Ikabata, Yasuhiro; Seino, Junji; Nakai, Hiromi

2017-07-01

This Letter proposes a density functional treatment based on the two-component relativistic scheme at the infinite-order Douglas-Kroll-Hess (IODKH) level. The exchange-correlation energy and potential are calculated using the electron density based on the picture-change corrected density operator transformed by the IODKH method. Numerical assessments indicated that the picture-change uncorrected density functional terms generate significant errors, on the order of hartree for heavy atoms. The present scheme was found to reproduce the energetics in the four-component treatment with high accuracy.

The transmission or scattering of elastic waves by an inhomogeneity of simple geometry: A comparison of theories

NASA Technical Reports Server (NTRS)

Sheu, Y. C.; Fu, L. S.

1983-01-01

The extended method of equivalent inclusions is applied to study the specific wave problems: (1) the transmission of elastic waves in an infinite medium containing a layer of inhomogeneity, and (2) the scattering of elastic waves in an infinite medium containing a perfect spherical inhomogeneity. Eigenstrains are expanded as a geometric series and a method of integration based on the inhomogeneous Helmholtz operator is adopted. This study compares results, obtained by using limited number of terms in the eigenstrain expansion, with exact solutions for the layer problem and that for a perfect sphere.

Vibrationally-resolved Charge Transfer of O^3+ Ions with Molecular Hydrogen

NASA Astrophysics Data System (ADS)

Wang, J. G.; Stancil, P. C.; Turner, A. R.; Cooper, D. L.

2003-05-01

Charge transfer processes due to collisions of ground state O^3+ ions with H2 are investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) method. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond approach. Vibrationally-resolved cross sections for energies between 0.1 eV/u and 2 keV/u using the infinite order sudden approximation (IOSA), vibrational sudden approximation (VSA), and electronic approximation (EA), but including Frank-Condon factors (the centroid approximation) will be presented. Comparison with existing experimental data for total cross sections shows best agreement with IOSA and discrepancies for VSA and EA. Triplet-singlet cross section ratios obtained with IOSA are found generally to be in harmony with experiment. JGW and PCS acknowledge support from NASA grant 11453.

A FORTRAN program for calculating nonlinear seismic ground response

USGS Publications Warehouse

Joyner, William B.

1977-01-01

The program described here was designed for calculating the nonlinear seismic response of a system of horizontal soil layers underlain by a semi-infinite elastic medium representing bedrock. Excitation is a vertically incident shear wave in the underlying medium. The nonlinear hysteretic behavior of the soil is represented by a model consisting of simple linear springs and Coulomb friction elements arranged as shown. A boundary condition is used which takes account of finite rigidity in the elastic substratum. The computations are performed by an explicit finite-difference scheme that proceeds step by step in space and time. A brief program description is provided here with instructions for preparing the input and a source listing. A more detailed discussion of the method is presented elsewhere as is the description of a different program employing implicit integration.

Semi-Infinite Geology Modeling Algorithm (SIGMA): a Modular Approach to 3D Gravity

NASA Astrophysics Data System (ADS)

Chang, J. C.; Crain, K.

2015-12-01

Conventional 3D gravity computations can take up to days, weeks, and even months, depending on the size and resolution of the data being modeled. Additional modeling runs, due to technical malfunctions or additional data modifications, only compound computation times even further. We propose a new modeling algorithm that utilizes vertical line elements to approximate mass, and non-gridded (point) gravity observations. This algorithm is (1) magnitudes faster than conventional methods, (2) accurate to less than 0.1% error, and (3) modular. The modularity of this methodology means that researchers can modify their geology/terrain or gravity data, and only the modified component needs to be re-run. Additionally, land-, sea-, and air-based platforms can be modeled at their observation point, without having to filter data into a synthesized grid.

Deformed coset models from gauged WZW actions

NASA Astrophysics Data System (ADS)

Park, Q.-Han

1994-06-01

A general Lagrangian formulation of integrably deformed G/H-coset models is given. We consider the G/H-coset model in terms of the gauged Wess-Zumino-Witten action and obtain an integrable deformation by adding a potential energy term Tr(gTg -1overlineT) , where algebra elements T, overlineT belong to the center of the algebra h associated with the subgroup H. We show that the classical equation of motion of the deformed coset model can be identified with the integrability condition of certain linear equations which makes the use of the inverse scattering method possible. Using the linear equation, we give a systematic way to construct infinitely many conserved currents as well as soliton solutions. In the case of the parafermionic SU(2)/U(1)-coset model, we derive n-solitons and conserved currents explicitly.

Efficient Transition Probability Computation for Continuous-Time Branching Processes via Compressed Sensing.

PubMed

Xu, Jason; Minin, Vladimir N

2015-07-01

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, and sampling-based alternatives are computationally intensive, requiring integration over all possible hidden events. Recent work has successfully applied generating function techniques to computing transition probabilities for linear multi-type branching processes. While these techniques often require significantly fewer computations than matrix exponentiation, they also become prohibitive in applications with large populations. We propose a compressed sensing framework that significantly accelerates the generating function method, decreasing computational cost up to a logarithmic factor by only assuming the probability mass of transitions is sparse. We demonstrate accurate and efficient transition probability computations in branching process models for blood cell formation and evolution of self-replicating transposable elements in bacterial genomes.

Stress state reassessment of Romanian offshore structures taking into account corrosion influence

NASA Astrophysics Data System (ADS)

Joavină, R.; Zăgan, S.; Zăgan, R.; Popa, M.

2017-08-01

Progressive degradation analysis for extraction or exploration offshore structure, with appraisal of failure potential and the causes that can be correlated with the service age, depends on the various sources of uncertainty that require particular attention in design, construction and exploitation phases. Romanian self erecting platforms are spatial lattice structures consist of tubular steel joints, forming a continuous system with an infinite number of dynamic degrees of freedom. Reassessment of a structure at fixed intervals of time, recorrelation of initial design elements with the actual situation encountered in location and with structural behaviour represents a major asset in lowering vulnerabilities of offshore structure. This paper proposes a comparative reassessment of the stress state for an offshore structure Gloria type, when leaving the shipyard and at the end of that interval corresponding to capital revision, taking into account sectional changes due to marine environment corrosion. The calculation was done using Newmark integration method on a 3D model, asses of the dynamic loads was made through probabilistic spectral method.

Efficient Transition Probability Computation for Continuous-Time Branching Processes via Compressed Sensing

PubMed Central

Xu, Jason; Minin, Vladimir N.

2016-01-01

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, and sampling-based alternatives are computationally intensive, requiring integration over all possible hidden events. Recent work has successfully applied generating function techniques to computing transition probabilities for linear multi-type branching processes. While these techniques often require significantly fewer computations than matrix exponentiation, they also become prohibitive in applications with large populations. We propose a compressed sensing framework that significantly accelerates the generating function method, decreasing computational cost up to a logarithmic factor by only assuming the probability mass of transitions is sparse. We demonstrate accurate and efficient transition probability computations in branching process models for blood cell formation and evolution of self-replicating transposable elements in bacterial genomes. PMID:26949377

Numerical algorithms for computations of feedback laws arising in control of flexible systems

NASA Technical Reports Server (NTRS)

Lasiecka, Irena

1989-01-01

Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.

Data eye monitor method and apparatus

DOEpatents

Gara, Alan G [Mount Kisco, NY; Marcella, James A [Rochester, MN; Ohmacht, Martin [Yorktown Heights, NY

2012-01-31

An apparatus and method for providing a data eye monitor. The data eye monitor apparatus utilizes an inverter/latch string circuit and a set of latches to save the data eye for providing an infinite persistent data eye. In operation, incoming read data signals are adjusted in the first stage individually and latched to provide the read data to the requesting unit. The data is also simultaneously fed into a balanced XOR tree to combine the transitions of all incoming read data signals into a single signal. This signal is passed along a delay chain and tapped at constant intervals. The tap points are fed into latches, capturing the transitions at a delay element interval resolution. Using XORs, differences between adjacent taps and therefore transitions are detected. The eye is defined by segments that show no transitions over a series of samples. The eye size and position can be used to readjust the delay of incoming signals and/or to control environment parameters like voltage, clock speed and temperature.

Bifurcating fronts for the Taylor-Couette problem in infinite cylinders

NASA Astrophysics Data System (ADS)

Hărăguş-Courcelle, M.; Schneider, G.

We show the existence of bifurcating fronts for the weakly unstable Taylor-Couette problem in an infinite cylinder. These fronts connect a stationary bifurcating pattern, here the Taylor vortices, with the trivial ground state, here the Couette flow. In order to show the existence result we improve a method which was already used in establishing the existence of bifurcating fronts for the Swift-Hohenberg equation by Collet and Eckmann, 1986, and by Eckmann and Wayne, 1991. The existence proof is based on spatial dynamics and center manifold theory. One of the difficulties in applying center manifold theory comes from an infinite number of eigenvalues on the imaginary axis for vanishing bifurcation parameter. But nevertheless, a finite dimensional reduction is possible, since the eigenvalues leave the imaginary axis with different velocities, if the bifurcation parameter is increased. In contrast to previous work we have to use normalform methods and a non-standard cut-off function to obtain a center manifold which is large enough to contain the bifurcating fronts.

The Green's matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs.

PubMed

Sorokin, Sergey V

2011-03-01

Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis. © 2011 Acoustical Society of America

Higher Order Lagrange Finite Elements In M3D

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

J. Chen; H.R. Strauss; S.C. Jardin

The M3D code has been using linear finite elements to represent multilevel MHD on 2-D poloidal planes. Triangular higher order elements, up to third order, are constructed here in order to provide M3D the capability to solve highly anisotropic transport problems. It is found that higher order elements are essential to resolve the thin transition layer characteristic of the anisotropic transport equation, particularly when the strong anisotropic direction is not aligned with one of the Cartesian coordinates. The transition layer is measured by the profile width, which is zero for infinite anisotropy. It is shown that only higher order schemesmore » have the ability to make this layer converge towards zero when the anisotropy gets stronger and stronger. Two cases are considered. One has the strong transport direction partially aligned with one of the element edges, the other doesn't have any alignment. Both cases have the strong transport direction misaligned with the grid line by some angles.« less

Direct numerical simulation of instabilities in parallel flow with spherical roughness elements

NASA Technical Reports Server (NTRS)

Deanna, R. G.

1992-01-01

Results from a direct numerical simulation of laminar flow over a flat surface with spherical roughness elements using a spectral-element method are given. The numerical simulation approximates roughness as a cellular pattern of identical spheres protruding from a smooth wall. Periodic boundary conditions on the domain's horizontal faces simulate an infinite array of roughness elements extending in the streamwise and spanwise directions, which implies the parallel-flow assumption, and results in a closed domain. A body force, designed to yield the horizontal Blasius velocity in the absence of roughness, sustains the flow. Instabilities above a critical Reynolds number reveal negligible oscillations in the recirculation regions behind each sphere and in the free stream, high-amplitude oscillations in the layer directly above the spheres, and a mean profile with an inflection point near the sphere's crest. The inflection point yields an unstable layer above the roughness (where U''(y) is less than 0) and a stable region within the roughness (where U''(y) is greater than 0). Evidently, the instability begins when the low-momentum or wake region behind an element, being the region most affected by disturbances (purely numerical in this case), goes unstable and moves. In compressible flow with periodic boundaries, this motion sends disturbances to all regions of the domain. In the unstable layer just above the inflection point, the disturbances grow while being carried downstream with a propagation speed equal to the local mean velocity; they do not grow amid the low energy region near the roughness patch. The most amplified disturbance eventually arrives at the next roughness element downstream, perturbing its wake and inducing a global response at a frequency governed by the streamwise spacing between spheres and the mean velocity of the most amplified layer.

A flexible and accurate quantification algorithm for electron probe X-ray microanalysis based on thin-film element yields

NASA Astrophysics Data System (ADS)

Schalm, O.; Janssens, K.

2003-04-01

Quantitative analysis by means of electron probe X-ray microanalysis (EPXMA) of low Z materials such as silicate glasses can be hampered by the fact that ice or other contaminants build up on the Si(Li) detector beryllium window or (in the case of a windowless detector) on the Si(Li) crystal itself. These layers act as an additional absorber in front of the detector crystal, decreasing the detection efficiency at low energies (<5 keV). Since the layer thickness gradually changes with time, also the detector efficiency in the low energy region is not constant. Using the normal ZAF approach to quantification of EPXMA data is cumbersome in these conditions, because spectra from reference materials and from unknown samples must be acquired within a fairly short period of time in order to avoid the effect of the change in efficiency. To avoid this problem, an alternative approach to quantification of EPXMA data is proposed, following a philosophy often employed in quantitative analysis of X-ray fluorescence (XRF) and proton-induced X-ray emission (PIXE) data. This approach is based on the (experimental) determination of thin-film element yields, rather than starting from infinitely thick and single element calibration standards. These thin-film sensitivity coefficients can also be interpolated to allow quantification of elements for which no suitable standards are available. The change in detector efficiency can be monitored by collecting an X-ray spectrum of one multi-element glass standard. This information is used to adapt the previously determined thin-film sensitivity coefficients to the actual detector efficiency conditions valid on the day that the experiments were carried out. The main advantage of this method is that spectra collected from the standards and from the unknown samples should not be acquired within a short period of time. This new approach is evaluated for glass and metal matrices and is compared with a standard ZAF method.

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

Liemert, André, E-mail: andre.liemert@ilm.uni-ulm.de; Kienle, Alwin

Purpose: Explicit solutions of the monoenergetic radiative transport equation in the P{sub 3} approximation have been derived which can be evaluated with nearly the same computational effort as needed for solving the standard diffusion equation (DE). In detail, the authors considered the important case of a semi-infinite medium which is illuminated by a collimated beam of light. Methods: A combination of the classic spherical harmonics method and the recently developed method of rotated reference frames is used for solving the P{sub 3} equations in closed form. Results: The derived solutions are illustrated and compared to exact solutions of the radiativemore » transport equation obtained via the Monte Carlo (MC) method as well as with other approximated analytical solutions. It is shown that for the considered cases which are relevant for biomedical optics applications, the P{sub 3} approximation is close to the exact solution of the radiative transport equation. Conclusions: The authors derived exact analytical solutions of the P{sub 3} equations under consideration of boundary conditions for defining a semi-infinite medium. The good agreement to Monte Carlo simulations in the investigated domains, for example, in the steady-state and time domains, as well as the short evaluation time needed suggests that the derived equations can replace the often applied solutions of the diffusion equation for the homogeneous semi-infinite medium.« less

An improved technique for determining reflection from semi-infinite atmospheres with linearly anisotropic phase functions. [radiative transfer

NASA Technical Reports Server (NTRS)

Fricke, C. L.

1975-01-01

A solution to the problem of reflection from a semi-infinite atmosphere is presented, based upon Chandrasekhar's H-function method for linearly anisotropic phase functions. A modification to the Gauss quadrature formula which gives about the same accuracy with 10 points as the conventional Gauss quadrature does with 100 points was developed. A computer program achieving this solution is described and results are presented for several illustrative cases.

Quantum networks in divergence-free circuit QED

NASA Astrophysics Data System (ADS)

Parra-Rodriguez, A.; Rico, E.; Solano, E.; Egusquiza, I. L.

2018-04-01

Superconducting circuits are one of the leading quantum platforms for quantum technologies. With growing system complexity, it is of crucial importance to develop scalable circuit models that contain the minimum information required to predict the behaviour of the physical system. Based on microwave engineering methods, divergent and non-divergent Hamiltonian models in circuit quantum electrodynamics have been proposed to explain the dynamics of superconducting quantum networks coupled to infinite-dimensional systems, such as transmission lines and general impedance environments. Here, we study systematically common linear coupling configurations between networks and infinite-dimensional systems. The main result is that the simple Lagrangian models for these configurations present an intrinsic natural length that provides a natural ultraviolet cutoff. This length is due to the unavoidable dressing of the environment modes by the network. In this manner, the coupling parameters between their components correctly manifest their natural decoupling at high frequencies. Furthermore, we show the requirements to correctly separate infinite-dimensional coupled systems in local bases. We also compare our analytical results with other analytical and approximate methods available in the literature. Finally, we propose several applications of these general methods to analogue quantum simulation of multi-spin-boson models in non-perturbative coupling regimes.

Interaction between moving tandem wheels and an infinite rail with periodic supports - Green's matrices of the track method in stationary reference frame

NASA Astrophysics Data System (ADS)

Mazilu, Traian

2017-08-01

This paper approaches the issue of the interaction between moving tandem wheels and an infinite periodically supported rail and points out at the basic characteristics in the steady-state interaction behaviour and in the interaction in the presence of the rail random irregularity. The rail is modelled as an infinite Timoshenko beam resting on supports which are discretely modelling the inertia of the sleepers and ballast and also the viscoelastic features of the rail pads, the ballast and the subgrade. Green‧s matrices of the track method in stationary reference frame were applied so as to conduct the time-domain analysis. This method allows to consider the nonlinearities of the wheel/rail contact and the Doppler effect. The study highlights certain aspects regarding the influence of the wheel base on the wheels/rail contact forces, particularly at the parametric resonance, due to the coincidence between the wheel/rail natural frequency and the passing frequency and also when the rail surface exhibits random irregularity. It has been shown that the wheel/rail dynamic behaviour is less intense when the wheel base equals integer multiple of the sleeper bay.

Deciding Full Branching Time Logic by Program Transformation

NASA Astrophysics Data System (ADS)

Pettorossi, Alberto; Proietti, Maurizio; Senni, Valerio

We present a method based on logic program transformation, for verifying Computation Tree Logic (CTL*) properties of finite state reactive systems. The finite state systems and the CTL* properties we want to verify, are encoded as logic programs on infinite lists. Our verification method consists of two steps. In the first step we transform the logic program that encodes the given system and the given property, into a monadic ω -program, that is, a stratified program defining nullary or unary predicates on infinite lists. This transformation is performed by applying unfold/fold rules that preserve the perfect model of the initial program. In the second step we verify the property of interest by using a proof method for monadic ω-programs.

On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scales

NASA Astrophysics Data System (ADS)

Sergeyev, Yaroslav D.; Kvasov, Dmitri E.; Mukhametzhanov, Marat S.

2018-06-01

The necessity to find the global optimum of multiextremal functions arises in many applied problems where finding local solutions is insufficient. One of the desirable properties of global optimization methods is strong homogeneity meaning that a method produces the same sequences of points where the objective function is evaluated independently both of multiplication of the function by a scaling constant and of adding a shifting constant. In this paper, several aspects of global optimization using strongly homogeneous methods are considered. First, it is shown that even if a method possesses this property theoretically, numerically very small and large scaling constants can lead to ill-conditioning of the scaled problem. Second, a new class of global optimization problems where the objective function can have not only finite but also infinite or infinitesimal Lipschitz constants is introduced. Third, the strong homogeneity of several Lipschitz global optimization algorithms is studied in the framework of the Infinity Computing paradigm allowing one to work numerically with a variety of infinities and infinitesimals. Fourth, it is proved that a class of efficient univariate methods enjoys this property for finite, infinite and infinitesimal scaling and shifting constants. Finally, it is shown that in certain cases the usage of numerical infinities and infinitesimals can avoid ill-conditioning produced by scaling. Numerical experiments illustrating theoretical results are described.

A Numerical Method for Obtaining Monoenergetic Neutron Flux Distributions and Transmissions in Multiple-Region Slabs

NASA Technical Reports Server (NTRS)

Schneider, Harold

1959-01-01

This method is investigated for semi-infinite multiple-slab configurations of arbitrary width, composition, and source distribution. Isotropic scattering in the laboratory system is assumed. Isotropic scattering implies that the fraction of neutrons scattered in the i(sup th) volume element or subregion that will make their next collision in the j(sup th) volume element or subregion is the same for all collisions. These so-called "transfer probabilities" between subregions are calculated and used to obtain successive-collision densities from which the flux and transmission probabilities directly follow. For a thick slab with little or no absorption, a successive-collisions technique proves impractical because an unreasonably large number of collisions must be followed in order to obtain the flux. Here the appropriate integral equation is converted into a set of linear simultaneous algebraic equations that are solved for the average total flux in each subregion. When ordinary diffusion theory applies with satisfactory precision in a portion of the multiple-slab configuration, the problem is solved by ordinary diffusion theory, but the flux is plotted only in the region of validity. The angular distribution of neutrons entering the remaining portion is determined from the known diffusion flux and the remaining region is solved by higher order theory. Several procedures for applying the numerical method are presented and discussed. To illustrate the calculational procedure, a symmetrical slab ia vacuum is worked by the numerical, Monte Carlo, and P(sub 3) spherical harmonics methods. In addition, an unsymmetrical double-slab problem is solved by the numerical and Monte Carlo methods. The numerical approach proved faster and more accurate in these examples. Adaptation of the method to anisotropic scattering in slabs is indicated, although no example is included in this paper.

Space structure vibration modes: How many exist? Which ones are important?

NASA Technical Reports Server (NTRS)

Hughes, P. C.

1984-01-01

This report attempts to shed some light on the two issues raised in the title, namely, how many vibration modes does a real structure have, and which of these modes are important? The surprise-free answers to these two questions are, respectively, an infinite number and the first several modes. The author argues that the absurd subspace (all but the first billion modes) is not a strength of continuum modeling, but, in fact, a weakness. Partial differential equations are not real structures, only mathematical models. This note also explains (1) that the PDE model and the finite element model are, in fact, the same model, the latter being a numerical method for dealing with the former, (2) that modes may be selected on dynamical grounds other than frequency alone, and (3) that long slender rods are useful as primitive cases but dangerous to extrapolate from.

Narrow sidebranch arrays for low frequency duct noise control.

PubMed

Tang, S K

2012-11-01

The present study investigates the sound transmission loss across a section of an infinitely long duct where one or more narrow sidebranch tubes are installed flushed with the duct wall. The finite-element method is used to compute the wave propagation characteristics, and a simplified theoretical analysis is carried out at the same time to explain the wave mechanism at frequencies of high sound reduction. Results show that the high sound transmission loss at a particular frequency is due to the concerted actions of three consecutive sidebranch tubes with the most upstream one in the resonant state. The expansion chamber effect of the setup also plays a role in enhancing sound attenuation at non-resonance frequencies. Broadband performance of the device can be greatly enhanced by appropriate arrangements of tube lengths and/or by coupling arrays on the two sides of the duct.

Constraining the braneworld with gravitational wave observations.

PubMed

McWilliams, Sean T

2010-04-09

Some braneworld models may have observable consequences that, if detected, would validate a requisite element of string theory. In the infinite Randall-Sundrum model (RS2), the AdS radius of curvature, l, of the extra dimension supports a single bound state of the massless graviton on the brane, thereby reproducing Newtonian gravity in the weak-field limit. However, using the AdS/CFT correspondence, it has been suggested that one possible consequence of RS2 is an enormous increase in Hawking radiation emitted by black holes. We utilize this possibility to derive two novel methods for constraining l via gravitational wave measurements. We show that the EMRI event rate detected by LISA can constrain l at the approximately 1 microm level for optimal cases, while the observation of a single galactic black hole binary with LISA results in an optimal constraint of l < or = 5 microm.

Constraining the Braneworld with Gravitational Wave Observations

NASA Technical Reports Server (NTRS)

McWilliams, Sean T.

2011-01-01

Some braneworld models may have observable consequences that, if detected, would validate a requisite element of string theory. In the infinite Randall-Sundrum model (RS2), the AdS radius of curvature, L, of the extra dimension supports a single bound state of the massless graviton on the brane, thereby reproducing Newtonian gravity in the weak-field limit. However, using the AdS/CFT correspondence, it has been suggested that one possible consequence of RS2 is an enormous increase in Hawking radiation emitted by black holes. We utilize this possibility to derive two novel methods for constraining L via gravitational wave measurements. We show that the EMRI event rate detected by LISA can constrain L at the approximately 1 micron level for optimal cases, while the observation of a single galactic black hole binary with LISA results in an optimal constraint of L less than or equal to 5 microns.

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

Itagaki, Masafumi; Miyoshi, Yoshinori; Hirose, Hideyuki

A procedure is presented for the determination of geometric buckling for regular polygons. A new computation technique, the multiple reciprocity boundary element method (MRBEM), has been applied to solve the one-group neutron diffusion equation. The main difficulty in applying the ordinary boundary element method (BEM) to neutron diffusion problems has been the need to compute a domain integral, resulting from the fission source. The MRBEM has been developed for transforming this type of domain integral into an equivalent boundary integral. The basic idea of the MRBEM is to apply repeatedly the reciprocity theorem (Green's second formula) using a sequence ofmore » higher order fundamental solutions. The MRBEM requires discretization of the boundary only rather than of the domain. This advantage is useful for extensive survey analyses of buckling for complex geometries. The results of survey analyses have indicated that the general form of geometric buckling is B[sub g][sup 2] = (a[sub n]/R[sub c])[sup 2], where R[sub c] represents the radius of the circumscribed circle of the regular polygon under consideration. The geometric constant A[sub n] depends on the type of regular polygon and takes the value of [pi] for a square and 2.405 for a circle, an extreme case that has an infinite number of sides. Values of a[sub n] for a triangle, pentagon, hexagon, and octagon have been calculated as 4.190, 2.281, 2.675, and 2.547, respectively.« less

Fuzzy parametric uncertainty analysis of linear dynamical systems: A surrogate modeling approach

NASA Astrophysics Data System (ADS)

Chowdhury, R.; Adhikari, S.

2012-10-01

Uncertainty propagation engineering systems possess significant computational challenges. This paper explores the possibility of using correlated function expansion based metamodelling approach when uncertain system parameters are modeled using Fuzzy variables. In particular, the application of High-Dimensional Model Representation (HDMR) is proposed for fuzzy finite element analysis of dynamical systems. The HDMR expansion is a set of quantitative model assessment and analysis tools for capturing high-dimensional input-output system behavior based on a hierarchy of functions of increasing dimensions. The input variables may be either finite-dimensional (i.e., a vector of parameters chosen from the Euclidean space RM) or may be infinite-dimensional as in the function space CM[0,1]. The computational effort to determine the expansion functions using the alpha cut method scales polynomially with the number of variables rather than exponentially. This logic is based on the fundamental assumption underlying the HDMR representation that only low-order correlations among the input variables are likely to have significant impacts upon the outputs for most high-dimensional complex systems. The proposed method is integrated with a commercial Finite Element software. Modal analysis of a simplified aircraft wing with Fuzzy parameters has been used to illustrate the generality of the proposed approach. In the numerical examples, triangular membership functions have been used and the results have been validated against direct Monte Carlo simulations.

Backscatter RCS for TE and TM excitations of dielectric-filled cavity-backed apertures in two-dimensional bodies

NASA Technical Reports Server (NTRS)

Goggans, Paul M.; Shumpert, Thomas H.

1991-01-01

Transverse electric (TE) and transverse magnetic (TM) scattering from dielectric-filled, cavity-backed apertures in two-dimensional bodies are treated using the method of moments technique to solve a set of combined-field integral equations for the equivalent induced electric and magnetic currents on the exterior of the scattering body and on the associated aperture. Results are presented for the backscatter radar cross section (RCS) versus the electrical size of the scatterer for two different dielectric-filled cavity-backed geometries. The first geometry is a circular cylinder of infinite length which has an infinite length slot aperture along one side. The cavity inside the cylinder is dielectric filled and is also of circular cross section. The two cylinders (external and internal) are of different radii and their respective longitudinal axes are parallel but not collocated. The second is a square cylinder of infinite length which has an infinite length slot aperture along one side. The cavity inside the square cylinder is dielectric-filled and is also of square cross section.

Infinitely Dilute Partial Molar Properties of Proteins from Computer Simulation

PubMed Central

2015-01-01

A detailed understanding of temperature and pressure effects on an infinitely dilute protein’s conformational equilibrium requires knowledge of the corresponding infinitely dilute partial molar properties. Established molecular dynamics methodologies generally have not provided a way to calculate these properties without either a loss of thermodynamic rigor, the introduction of nonunique parameters, or a loss of information about which solute conformations specifically contributed to the output values. Here we implement a simple method that is thermodynamically rigorous and possesses none of the above disadvantages, and we report on the method’s feasibility and computational demands. We calculate infinitely dilute partial molar properties for two proteins and attempt to distinguish the thermodynamic differences between a native and a denatured conformation of a designed miniprotein. We conclude that simple ensemble average properties can be calculated with very reasonable amounts of computational power. In contrast, properties corresponding to fluctuating quantities are computationally demanding to calculate precisely, although they can be obtained more easily by following the temperature and/or pressure dependence of the corresponding ensemble averages. PMID:25325571

Application of shifted Jacobi pseudospectral method for solving (in)finite-horizon min-max optimal control problems with uncertainty

NASA Astrophysics Data System (ADS)

Nikooeinejad, Z.; Delavarkhalafi, A.; Heydari, M.

2018-03-01

The difficulty of solving the min-max optimal control problems (M-MOCPs) with uncertainty using generalised Euler-Lagrange equations is caused by the combination of split boundary conditions, nonlinear differential equations and the manner in which the final time is treated. In this investigation, the shifted Jacobi pseudospectral method (SJPM) as a numerical technique for solving two-point boundary value problems (TPBVPs) in M-MOCPs for several boundary states is proposed. At first, a novel framework of approximate solutions which satisfied the split boundary conditions automatically for various boundary states is presented. Then, by applying the generalised Euler-Lagrange equations and expanding the required approximate solutions as elements of shifted Jacobi polynomials, finding a solution of TPBVPs in nonlinear M-MOCPs with uncertainty is reduced to the solution of a system of algebraic equations. Moreover, the Jacobi polynomials are particularly useful for boundary value problems in unbounded domain, which allow us to solve infinite- as well as finite and free final time problems by domain truncation method. Some numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. A comparative study between the proposed method and other existing methods shows that the SJPM is simple and accurate.

Uncovering low dimensional macroscopic chaotic dynamics of large finite size complex systems

NASA Astrophysics Data System (ADS)

Skardal, Per Sebastian; Restrepo, Juan G.; Ott, Edward

2017-08-01

In the last decade, it has been shown that a large class of phase oscillator models admit low dimensional descriptions for the macroscopic system dynamics in the limit of an infinite number N of oscillators. The question of whether the macroscopic dynamics of other similar systems also have a low dimensional description in the infinite N limit has, however, remained elusive. In this paper, we show how techniques originally designed to analyze noisy experimental chaotic time series can be used to identify effective low dimensional macroscopic descriptions from simulations with a finite number of elements. We illustrate and verify the effectiveness of our approach by applying it to the dynamics of an ensemble of globally coupled Landau-Stuart oscillators for which we demonstrate low dimensional macroscopic chaotic behavior with an effective 4-dimensional description. By using this description, we show that one can calculate dynamical invariants such as Lyapunov exponents and attractor dimensions. One could also use the reconstruction to generate short-term predictions of the macroscopic dynamics.

Recursion-transform method and potential formulae of the m × n cobweb and fan networks

NASA Astrophysics Data System (ADS)

Tan, Zhi-Zhong

2017-08-01

In this paper, we made a new breakthrough, which proposes a new Recursion-Transform (RT) method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m× n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms. Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20161278).

The study of the behaviour of a disturbed semi-infinite liquid jet using a spatial instability method

NASA Astrophysics Data System (ADS)

Basu (‧nee De), Shukla

2001-11-01

A study has been made of the behaviour of a disturbed semi-infinite liquid jet using a spatial instability method. A sinusoidal disturbance in the axial component of jet velocity at the nozzle is considered which resulted in an elliptic free surface boundary value problem with two non-linear boundary conditions. The system is linearised using perturbation techniques and the first order solution resulted in the dispersion relation. The jet stability is found to depend explicitly on the frequency of the disturbance and the Weber number. The second and third order solutions have been derived analytically which are used to predict on jet break-up and satellite formation.

Existence of Hartree-Fock excited states for atoms and molecules

NASA Astrophysics Data System (ADS)

Lewin, Mathieu

2018-04-01

For neutral and positively charged atoms and molecules, we prove the existence of infinitely many Hartree-Fock critical points below the first energy threshold (that is, the lowest energy of the same system with one electron removed). This is the equivalent, in Hartree-Fock theory, of the famous Zhislin-Sigalov theorem which states the existence of infinitely many eigenvalues below the bottom of the essential spectrum of the N-particle linear Schrödinger operator. Our result improves a theorem of Lions in 1987 who already constructed infinitely many Hartree-Fock critical points, but with much higher energy. Our main contribution is the proof that the Hartree-Fock functional satisfies the Palais-Smale property below the first energy threshold. We then use minimax methods in the N-particle space, instead of working in the one-particle space.

A new scheme of the time-domain fluorescence tomography for a semi-infinite turbid medium

NASA Astrophysics Data System (ADS)

Prieto, Kernel; Nishimura, Goro

2017-04-01

A new scheme for reconstruction of a fluorophore target embedded in a semi-infinite medium was proposed and evaluated. In this scheme, we neglected the presence of the fluorophore target for the excitation light and used an analytical solution of the time-dependent radiative transfer equation (RTE) for the excitation light in a homogeneous semi-infinite media instead of solving the RTE numerically in the forward calculation. The inverse problem for imaging the fluorophore target was solved using the Landweber-Kaczmarz method with the concept of the adjoint fields. Numerical experiments show that the proposed scheme provides acceptable results of the reconstructed shape and location of the target. The computation times of the solution of the forward problem and the whole reconstruction process were reduced by about 40 and 15%, respectively.

A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics

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

Brunovsky, Pavol, E-mail: brunovsky@fmph.uniba.sk; Cerny, Ales, E-mail: ales.cerny.1@city.ac.uk; Winkler, Michael, E-mail: michael.winkler@uni-due.de

2013-10-15

We consider the ordinary differential equation x{sup 2} u'' = axu'+bu-c(u'-1){sup 2}, x Element-Of (0,x{sub 0}), with a Element-Of R, b Element-Of R , c>0 and the singular initial condition u(0)=0, which in financial economics describes optimal disposal of an asset in a market with liquidity effects. It is shown in the paper that if a+b<0 then no continuous solutions exist, whereas if a+b>0 then there are infinitely many continuous solutions with indistinguishable asymptotics near 0. Moreover, it is proved that in the latter case there is precisely one solution u corresponding to the choice x{sub 0}={infinity} which is suchmore » that 0{<=}u(x){<=}x for all x>0, and that this solution is strictly increasing and concave.« less

Load concentration due to missing members in planar faces of a large space truss

NASA Technical Reports Server (NTRS)

Waltz, J. E.

1979-01-01

A large space structure with members missing was investigated using a finite element analysis. The particular structural configuration was the tetrahedral truss, with attention restricted to one of its planar faces. Initially the finite element model of a complete face was verified by comparing it with known results for some basic loadings. Then an analysis was made of the structure with members near the center removed. Some calculations were made on the influence of the mesh size of a structure containing a hexagonal hole, and an analysis was also made of a structure with a rigid hexagonal insert. In general, load concentration effects in these trusses were significantly lower than classical stress concentration effects in an infinitely wide isotropic plate with a circular rigid inclusion, although larger effects were obtained when a hole extended over several rings of elements.

Scalable Computing of the Mesh Size Effect on Modeling Damage Mechanics in Woven Armor Composites

DTIC Science & Technology

2008-12-01

manner of a user defined material subroutine to provide overall stress increments to, the parallel LS-DYNA3D a Lagrangian explicit code used in...finite element code, as a user defined material subroutine . The ability of this subroutine to model the effect of the progressions of a select number...is added as a user defined material subroutine to parallel LS-DYNA3D. The computations of the global mesh are handled by LS-DYNA3D and are spread

Coupling coefficients for tensor product representations of quantum SU(2)

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

Groenevelt, Wolter, E-mail: w.g.m.groenevelt@tudelft.nl

2014-10-15

We study tensor products of infinite dimensional irreducible {sup *}-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometricmore » orthogonal polynomials and q-Bessel-type functions.« less

Temperature field for radiative tomato peeling

NASA Astrophysics Data System (ADS)

Cuccurullo, G.; Giordano, L.

2017-01-01

Nowadays peeling of tomatoes is performed by using steam or lye, which are expensive and polluting techniques, thus sustainable alternatives are searched for dry peeling and, among that, radiative heating seems to be a fairly promising method. This paper aims to speed up the prediction of surface temperatures useful for realizing dry-peeling, thus a 1D-analytical model for the unsteady temperature field in a rotating tomato exposed to a radiative heating source is presented. Since only short times are of interest for the problem at hand, the model involves a semi-infinite slab cooled by convective heat transfer while heated by a pulsating heat source. The model being linear, the solution is derived following the Laplace Transform method. A 3D finite element model of the rotating tomato is introduced as well in order to validate the analytical solution. A satisfactory agreement is attained. Therefore, two different ways to predict the onset of the peeling conditions are available which can be of help for proper design of peeling plants. Particular attention is paid to study surface temperature uniformity, that being a critical parameter for realizing an easy tomato peeling.

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.

Existence and Non-uniqueness of Global Weak Solutions to Inviscid Primitive and Boussinesq Equations

NASA Astrophysics Data System (ADS)

Chiodaroli, Elisabetta; Michálek, Martin

2017-08-01

We consider the initial value problem for the inviscid Primitive and Boussinesq equations in three spatial dimensions. We recast both systems as an abstract Euler-type system and apply the methods of convex integration of De Lellis and Székelyhidi to show the existence of infinitely many global weak solutions of the studied equations for general initial data. We also introduce an appropriate notion of dissipative solutions and show the existence of suitable initial data which generate infinitely many dissipative solutions.

A Large Deviations Analysis of Certain Qualitative Properties of Parallel Tempering and Infinite Swapping Algorithms

DOE PAGES

Doll, J.; Dupuis, P.; Nyquist, P.

2017-02-08

Parallel tempering, or replica exchange, is a popular method for simulating complex systems. The idea is to run parallel simulations at different temperatures, and at a given swap rate exchange configurations between the parallel simulations. From the perspective of large deviations it is optimal to let the swap rate tend to infinity and it is possible to construct a corresponding simulation scheme, known as infinite swapping. In this paper we propose a novel use of large deviations for empirical measures for a more detailed analysis of the infinite swapping limit in the setting of continuous time jump Markov processes. Usingmore » the large deviations rate function and associated stochastic control problems we consider a diagnostic based on temperature assignments, which can be easily computed during a simulation. We show that the convergence of this diagnostic to its a priori known limit is a necessary condition for the convergence of infinite swapping. The rate function is also used to investigate the impact of asymmetries in the underlying potential landscape, and where in the state space poor sampling is most likely to occur.« less

Rewriting Modulo SMT

NASA Technical Reports Server (NTRS)

Rocha, Camilo; Meseguer, Jose; Munoz, Cesar A.

2013-01-01

Combining symbolic techniques such as: (i) SMT solving, (ii) rewriting modulo theories, and (iii) model checking can enable the analysis of infinite-state systems outside the scope of each such technique. This paper proposes rewriting modulo SMT as a new technique combining the powers of (i)-(iii) and ideally suited to model and analyze infinite-state open systems; that is, systems that interact with a non-deterministic environment. Such systems exhibit both internal non-determinism due to the system, and external non-determinism due to the environment. They are not amenable to finite-state model checking analysis because they typically are infinite-state. By being reducible to standard rewriting using reflective techniques, rewriting modulo SMT can both naturally model and analyze open systems without requiring any changes to rewriting-based reachability analysis techniques for closed systems. This is illustrated by the analysis of a real-time system beyond the scope of timed automata methods.

Generalized symmetries of an 𝓝 = 1 supersymmetric Boiti-Leon-Manna-Pempinelli system

NASA Astrophysics Data System (ADS)

Wang, Jian-Yong; Tang, Xiao-Yan; Liang, Zu-Feng; Lou, Sen-Yue

2015-05-01

The formal series symmetry approach (FSSA), a quite powerful and straightforward method to establish infinitely many generalized symmetries of classical integrable systems, has been successfully extended in the supersymmetric framework to explore series of infinitely many generalized symmetries for supersymmetric systems. Taking the 𝒩 = 1 supersymmetric Boiti-Leon-Manna-Pempinelli system as a concrete example, it is shown that the application of the extended FSSA to this supersymmetric system leads to a set of infinitely many generalized symmetries with an arbitrary function f (t). Some interesting special cases of symmetry algebras are presented, including a limit case f (t) = 1 related to the commutativity of higher order generalized symmetries. Project supported by the National Natural Science Foundation of China (Grant Nos. 11275123, 11175092, 11475052, and 11435005), the Shanghai Knowledge Service Platform for Trustworthy Internet of Things, China (Grant No. ZF1213), and the Talent Fund and K CWong Magna Fund in Ningbo University, China.

The converse approach to NMR chemical shifts from first-principles: application to finite and infinite aromatic compounds

NASA Astrophysics Data System (ADS)

Thonhauser, T.; Ceresoli, D.; Marzari, N.

2009-03-01

We present first-principles, density-functional theory calculations of the NMR chemical shifts for polycyclic aromatic hydrocarbons, starting with benzene and increasing sizes up to the one- and two-dimensional infinite limits of graphene ribbons and sheets. Our calculations are performed using a combination of the recently developed theory of orbital magnetization in solids, and a novel approach to NMR calculations where chemical shifts are obtained from the derivative of the orbital magnetization with respect to a microscopic, localized magnetic dipole. Using these methods we study on equal footing the ^1H and ^13C shifts in benzene, pyrene, coronene, in naphthalene, anthracene, naphthacene, and pentacene, and finally in graphene, graphite, and an infinite graphene ribbon. Our results show very good agreement with experiments and allow us to characterize the trends for the chemical shifts as a function of system size.

On optimal infinite impulse response edge detection filters

NASA Technical Reports Server (NTRS)

Sarkar, Sudeep; Boyer, Kim L.

1991-01-01

The authors outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter. The optimal filter is computed based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise. An expression for the width of the filter, which is appropriate for infinite-length filters, is incorporated directly in the expression for spurious responses. The three criteria are maximized using the variational method and nonlinear constrained optimization. The optimal filter parameters are tabulated for various values of the filter performance criteria. A complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented. The approximating recursive digital filter is separable into two linear filters operating in two orthogonal directions. The implementation is very simple and computationally efficient, has a constant time of execution for different sizes of the operator, and is readily amenable to real-time hardware implementation.

Elastic strain relaxation in interfacial dislocation patterns: I. A parametric energy-based framework

NASA Astrophysics Data System (ADS)

Vattré, A.

2017-08-01

A parametric energy-based framework is developed to describe the elastic strain relaxation of interface dislocations. By means of the Stroh sextic formalism with a Fourier series technique, the proposed approach couples the classical anisotropic elasticity theory with surface/interface stress and elasticity properties in heterogeneous interface-dominated materials. For any semicoherent interface of interest, the strain energy landscape is computed using the persistent elastic fields produced by infinitely periodic hexagonal-shaped dislocation configurations with planar three-fold nodes. A finite element based procedure combined with the conjugate gradient and nudged elastic band methods is applied to determine the minimum-energy paths for which the pre-computed energy landscapes yield to elastically favorable dislocation reactions. Several applications on the Au/Cu heterosystems are given. The simple and limiting case of a single set of infinitely periodic dislocations is introduced to determine exact closed-form expressions for stresses. The second limiting case of the pure (010) Au/Cu heterophase interfaces containing two crossing sets of straight dislocations investigates the effects due to the non-classical boundary conditions on the stress distributions, including separate and appropriate constitutive relations at semicoherent interfaces and free surfaces. Using the quantized Frank-Bilby equation, it is shown that the elastic strain landscape exhibits intrinsic dislocation configurations for which the junction formation is energetically unfavorable. On the other hand, the mismatched (111) Au/Cu system gives rise to the existence of a minimum-energy path where the fully strain-relaxed equilibrium and non-regular intrinsic hexagonal-shaped dislocation rearrangement is accompanied by a significant removal of the short-range elastic energy.

On physical property tensors invariant under line groups.

PubMed

Litvin, Daniel B

2014-03-01

The form of physical property tensors of a quasi-one-dimensional material such as a nanotube or a polymer can be determined from the point group of its symmetry group, one of an infinite number of line groups. Such forms are calculated using a method based on the use of trigonometric summations. With this method, it is shown that materials invariant under infinite subsets of line groups have physical property tensors of the same form. For line group types of a family of line groups characterized by an index n and a physical property tensor of rank m, the form of the tensor for all line group types indexed with n > m is the same, leaving only a finite number of tensor forms to be determined.

Broadband computation of the scattering coefficients of infinite arbitrary cylinders.

PubMed

Blanchard, Cédric; Guizal, Brahim; Felbacq, Didier

2012-07-01

We employ a time-domain method to compute the near field on a contour enclosing infinitely long cylinders of arbitrary cross section and constitution. We therefore recover the cylindrical Hankel coefficients of the expansion of the field outside the circumscribed circle of the structure. The recovered coefficients enable the wideband analysis of complex systems, e.g., the determination of the radar cross section becomes straightforward. The prescription for constructing such a numerical tool is provided in great detail. The method is validated by computing the scattering coefficients for a homogeneous circular cylinder illuminated by a plane wave, a problem for which an analytical solution exists. Finally, some radiation properties of an optical antenna are examined by employing the proposed technique.

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Adamian, A.

1988-01-01

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

Gini estimation under infinite variance

NASA Astrophysics Data System (ADS)

Fontanari, Andrea; Taleb, Nassim Nicholas; Cirillo, Pasquale

2018-07-01

We study the problems related to the estimation of the Gini index in presence of a fat-tailed data generating process, i.e. one in the stable distribution class with finite mean but infinite variance (i.e. with tail index α ∈(1 , 2)). We show that, in such a case, the Gini coefficient cannot be reliably estimated using conventional nonparametric methods, because of a downward bias that emerges under fat tails. This has important implications for the ongoing discussion about economic inequality. We start by discussing how the nonparametric estimator of the Gini index undergoes a phase transition in the symmetry structure of its asymptotic distribution, as the data distribution shifts from the domain of attraction of a light-tailed distribution to that of a fat-tailed one, especially in the case of infinite variance. We also show how the nonparametric Gini bias increases with lower values of α. We then prove that maximum likelihood estimation outperforms nonparametric methods, requiring a much smaller sample size to reach efficiency. Finally, for fat-tailed data, we provide a simple correction mechanism to the small sample bias of the nonparametric estimator based on the distance between the mode and the mean of its asymptotic distribution.

On the Invariant Cantor Sets of Period Doubling Type of Infinitely Renormalizable Area-Preserving Maps

NASA Astrophysics Data System (ADS)

Lilja, Dan

2018-03-01

Since its inception in the 1970s at the hands of Feigenbaum and, independently, Coullet and Tresser the study of renormalization operators in dynamics has been very successful at explaining universality phenomena observed in certain families of dynamical systems. The first proof of existence of a hyperbolic fixed point for renormalization of area-preserving maps was given by Eckmann et al. (Mem Am Math Soc 47(289):vi+122, 1984). However, there are still many things that are unknown in this setting, in particular regarding the invariant Cantor sets of infinitely renormalizable maps. In this paper we show that the invariant Cantor set of period doubling type of any infinitely renormalizable area-preserving map in the universality class of the Eckmann-Koch-Wittwer renormalization fixed point is always contained in a Lipschitz curve but never contained in a smooth curve. This extends previous results by de Carvalho, Lyubich and Martens about strongly dissipative maps of the plane close to unimodal maps to the area-preserving setting. The method used for constructing the Lipschitz curve is very similar to the method used in the dissipative case but proving the nonexistence of smooth curves requires new techniques.

Analytical energy gradient based on spin-free infinite-order Douglas-Kroll-Hess method with local unitary transformation

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

Nakajima, Yuya; Seino, Junji; Nakai, Hiromi, E-mail: nakai@waseda.jp

In this study, the analytical energy gradient for the spin-free infinite-order Douglas-Kroll-Hess (IODKH) method at the levels of the Hartree-Fock (HF), density functional theory (DFT), and second-order Møller-Plesset perturbation theory (MP2) is developed. Furthermore, adopting the local unitary transformation (LUT) scheme for the IODKH method improves the efficiency in computation of the analytical energy gradient. Numerical assessments of the present gradient method are performed at the HF, DFT, and MP2 levels for the IODKH with and without the LUT scheme. The accuracies are examined for diatomic molecules such as hydrogen halides, halogen dimers, coinage metal (Cu, Ag, and Au) halides,more » and coinage metal dimers, and 20 metal complexes, including the fourth–sixth row transition metals. In addition, the efficiencies are investigated for one-, two-, and three-dimensional silver clusters. The numerical results confirm the accuracy and efficiency of the present method.« less

Symplectic analysis of vertical random vibration for coupled vehicle track systems

NASA Astrophysics Data System (ADS)

Lu, F.; Kennedy, D.; Williams, F. W.; Lin, J. H.

2008-10-01

A computational model for random vibration analysis of vehicle-track systems is proposed and solutions use the pseudo excitation method (PEM) and the symplectic method. The vehicle is modelled as a mass, spring and damping system with 10 degrees of freedom (dofs) which consist of vertical and pitching motion for the vehicle body and its two bogies and vertical motion for the four wheelsets. The track is treated as an infinite Bernoulli-Euler beam connected to sleepers and hence to ballast and is regarded as a periodic structure. Linear springs couple the vehicle and the track. Hence, the coupled vehicle-track system has only 26 dofs. A fixed excitation model is used, i.e. the vehicle does not move along the track but instead the track irregularity profile moves backwards at the vehicle velocity. This irregularity is assumed to be a stationary random process. Random vibration theory is used to obtain the response power spectral densities (PSDs), by using PEM to transform this random multiexcitation problem into a deterministic harmonic excitation one and then applying symplectic solution methodology. Numerical results for an example include verification of the proposed method by comparing with finite element method (FEM) results; comparison between the present model and the traditional rigid track model and; discussion of the influences of track damping and vehicle velocity.

Accurate traveltime computation in complex anisotropic media with discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Le Bouteiller, P.; Benjemaa, M.; Métivier, L.; Virieux, J.

2017-12-01

Travel time computation is of major interest for a large range of geophysical applications, among which source localization and characterization, phase identification, data windowing and tomography, from decametric scale up to global Earth scale.Ray-tracing tools, being essentially 1D Lagrangian integration along a path, have been used for their efficiency but present some drawbacks, such as a rather difficult control of the medium sampling. Moreover, they do not provide answers in shadow zones. Eikonal solvers, based on an Eulerian approach, have attracted attention in seismology with the pioneering work of Vidale (1988), while such approach has been proposed earlier by Riznichenko (1946). They have been used now for first-arrival travel-time tomography at various scales (Podvin & Lecomte (1991). The framework for solving this non-linear partial differential equation is now well understood and various finite-difference approaches have been proposed, essentially for smooth media. We propose a novel finite element approach which builds a precise solution for strongly heterogeneous anisotropic medium (still in the limit of Eikonal validity). The discontinuous Galerkin method we have developed allows local refinement of the mesh and local high orders of interpolation inside elements. High precision of the travel times and its spatial derivatives is obtained through this formulation. This finite element method also honors boundary conditions, such as complex topographies and absorbing boundaries for mimicking an infinite medium. Applications from travel-time tomography, slope tomography are expected, but also for migration and take-off angles estimation, thanks to the accuracy obtained when computing first-arrival times.References:Podvin, P. and Lecomte, I., 1991. Finite difference computation of traveltimes in very contrasted velocity model: a massively parallel approach and its associated tools, Geophys. J. Int., 105, 271-284.Riznichenko, Y., 1946. Geometrical seismics of layered media, Trudy Inst. Theor. Geophysics, Vol II, Moscow (in Russian).Vidale, J., 1988. Finite-difference calculation of travel times, Bull. seism. Soc. Am., 78, 2062-2076.

Seismic loading due to mining: Wave amplification and vibration of structures

NASA Astrophysics Data System (ADS)

Lokmane, N.; Semblat, J.-F.; Bonnet, G.; Driad, L.; Duval, A.-M.

2003-04-01

A vibration induced by the ground motion, whatever its source is, can in certain cases damage surface structures. The scientific works allowing the analysis of this phenomenon are numerous and well established. However, they generally concern dynamic motion from real earthquakes. The goal of this work is to analyse the impact of shaking induced by mining on the structures located on the surface. The methods allowing to assess the consequences of earthquakes of strong amplitude are well established, when the methodology to estimate the consequences of moderate but frequent dynamic loadings is not well defined. The mining such as the "Houillères de Bassin du Centre et du Midi" (HBCM) involves vibrations which are regularly felt on the surface. An extracting work of coal generates shaking similar to those caused by earthquakes (standard waves and laws of propagation) but of rather low magnitude. On the other hand, their recurrent feature makes the vibrations more harmful. A three-dimensional modeling of standard structure of the site was carried out. The first results show that the fundamental frequencies of this structure are compatible with the amplification measurements carried out on site. The motion amplification in the surface soil layers is then analyzed. The modeling works are performed on the surface soil layers of Gardanne (Provence), where measurements of microtremors were performed. The analysis of H/V spectral ratio (horizontal on vertical component) indeed makes it possible to characterize the fundamental frequencies of the surface soil layers. This experiment also allows to characterize local evolution of amplification induced by the topmost soil layers. The numerical methods we consider to model seismic wave propagation and amplification in the site, is the Boundary Element Methode (BEM) The main advantage of the boundary element method is to get rid of artificial truncations of the mesh (as in Finite Element Method) in the case of infinite medium. For dynamic problems, these truncations lead to spurious wave reflections giving a numerical error in the solution. The experimental and numerical (BEM) results on surface motion amplification are then compared in terms of both amplitude and frequency range.

On the convergence of an iterative formulation of the electromagnetic scattering from an infinite grating of thin wires

NASA Technical Reports Server (NTRS)

Brand, J. C.

1985-01-01

Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or k-space) formulation is presented with an emphasis on application to periodic surfaces. The mathematical background for formulating an iterative equation is covered using straightforward single variable examples including an extension to vector spaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.

Markov chain sampling of the O(n) loop models on the infinite plane

NASA Astrophysics Data System (ADS)

Herdeiro, Victor

2017-07-01

A numerical method was recently proposed in Herdeiro and Doyon [Phys. Rev. E 94, 043322 (2016), 10.1103/PhysRevE.94.043322] showing a precise sampling of the infinite plane two-dimensional critical Ising model for finite lattice subsections. The present note extends the method to a larger class of models, namely the O(n) loop gas models for n ∈(1 ,2 ] . We argue that even though the Gibbs measure is nonlocal, it is factorizable on finite subsections when sufficient information on the loops touching the boundaries is stored. Our results attempt to show that provided an efficient Markov chain mixing algorithm and an improved discrete lattice dilation procedure the planar limit of the O(n) models can be numerically studied with efficiency similar to the Ising case. This confirms that scale invariance is the only requirement for the present numerical method to work.

Combined effects on MHD flow of Newtonian fluid past infinite vertical porous plate

NASA Astrophysics Data System (ADS)

Subbanna, K.; Mohiddin, S. Gouse; Vijaya, R. Bhuvana

2018-05-01

In this paper, we discussed free convective flow of a viscous fluid past an infinite vertical porous plate under the influence of uniform transverse magnetic field. Time dependent permeability and oscillatory suction is considered. The equations of the flow field are solved by a routine perturbation method for small amplitude of the permeability. The solutions for the velocity, temperature and concentration have been derived analytically and also its behavior is computationally discussed with the help of profiles. The shear stress, the Nusselt number and Sherwood number are also obtained and their behavior discussed computationally

Behavior of a semi-infinite ice cover under periodic dynamic impact

NASA Astrophysics Data System (ADS)

Tkacheva, L. A.

2017-07-01

Oscillations of a semi-infinite ice cover in an ideal incompressible liquid of finite depth under local time-periodic axisymmetric load are considered. The ice cover is simulated by a thin elastic plate of constant thickness. An analytical solution of the problem is obtained using the Wiener-Hopf method. The asymptotic behavior of the amplitudes of oscillations of the plate and the liquid in the far field is studied. It is shown that the propagation of waves in the far field is uneven: in some directions, the waves propagate with a significantly greater amplitude.

Density matrix renormalization group for a highly degenerate quantum system: Sliding environment block approach

NASA Astrophysics Data System (ADS)

Schmitteckert, Peter

2018-04-01

We present an infinite lattice density matrix renormalization group sweeping procedure which can be used as a replacement for the standard infinite lattice blocking schemes. Although the scheme is generally applicable to any system, its main advantages are the correct representation of commensurability issues and the treatment of degenerate systems. As an example we apply the method to a spin chain featuring a highly degenerate ground-state space where the new sweeping scheme provides an increase in performance as well as accuracy by many orders of magnitude compared to a recently published work.

Structural control by the use of piezoelectric active members

NASA Technical Reports Server (NTRS)

Fanson, J. L.; Chen, J.-C.

1987-01-01

Large Space Structures (LSS) exhibit characteristics which make the LSS control problem different form other control problems. LSS will most likely exhibit low frequency, densely spaced and lightly damped modes. In theory, the number of these modes is infinite. Because these structures are flexible, Vibration Suppression (VS) is an important aspect of LSS operation. In terms of VS, the control actuators should be as low mass as possible, have infinite bandwidth, and be electrically powered. It is proposed that actuators be built into the structure as dual purpose structural elements. A piezoelectric active member is proposed for the control of LSS. Such a device would consist of a piezoelectric actuator and sensor for measuring strain, and screwjack actuator in series for use in quasi-static shape control. An experiment simulates an active member using piezoelectric ceramic thin sheet material on a thin, uniform cantilever beam. The feasibility of using the piezoelectric materials for VS on LSS was demonstrated. Positive positive feedback as a VS control strategy was implemented. Multi-mode VS was achieved with dramatic reduction in dynamic response.

PML solution of longitudinal wave propagation in heterogeneous media

NASA Astrophysics Data System (ADS)

Farzanian, M.; Arbabi, Freydoon; Pak, Ronald

2016-06-01

This paper describes the development of a model for unbounded heterogeneous domains with radiation damping produced by an unphysical wave absorbing layer. The Perfectly Matched Layer (PML) approach is used along with a displacement-based finite element. The heterogeneous model is validated using the closed-form solution of a benchmark problem: a free rod with two-part modulus subjected to a specified time history. Both elastically supported and unsupported semi-infinite rods with different degrees of inhomogeneity and loading are considered. Numerical results illustrate the effects of inhomogeneity on the response and are compared with those for equivalent homogeneous domains. The effects of characteristic features of the inhomogeneous problem, presence of local maxima and cut-off frequency are determined. A degenerate case of a homogeneous semi-infinite rod on elastic foundations is produced by tending the magnitude of the foundation stiffness to zero. The response of the latter is compared with that of a free rod. The importance of proper selection of the PML parameters to highly accurate and efficient results is demonstrated by example problems.

Penetration of rod projectiles in semi-infinite targets : a validation test for Eulerian X-FEM in ALEGRA.

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

Park, Byoung Yoon; Leavy, Richard Brian; Niederhaus, John Henry J.

2013-03-01

The finite-element shock hydrodynamics code ALEGRA has recently been upgraded to include an X-FEM implementation in 2D for simulating impact, sliding, and release between materials in the Eulerian frame. For validation testing purposes, the problem of long-rod penetration in semi-infinite targets is considered in this report, at velocities of 500 to 3000 m/s. We describe testing simulations done using ALEGRA with and without the X-FEM capability, in order to verify its adequacy by showing X-FEM recovers the good results found with the standard ALEGRA formulation. The X-FEM results for depth of penetration differ from previously measured experimental data by lessmore » than 2%, and from the standard formulation results by less than 1%. They converge monotonically under mesh refinement at first order. Sensitivities to domain size and rear boundary condition are investigated and shown to be small. Aside from some simulation stability issues, X-FEM is found to produce good results for this classical impact and penetration problem.« less

Infinite occupation number basis of bosons: Solving a numerical challenge

NASA Astrophysics Data System (ADS)

Geißler, Andreas; Hofstetter, Walter

2017-06-01

In any bosonic lattice system, which is not dominated by local interactions and thus "frozen" in a Mott-type state, numerical methods have to cope with the infinite size of the corresponding Hilbert space even for finite lattice sizes. While it is common practice to restrict the local occupation number basis to Nc lowest occupied states, the presence of a finite condensate fraction requires the complete number basis for an exact representation of the many-body ground state. In this work we present a truncation scheme to account for contributions from higher number states. By simply adding a single coherent-tail state to this common truncation, we demonstrate increased numerical accuracy and the possible increase in numerical efficiency of this method for the Gutzwiller variational wave function and within dynamical mean-field theory.

Comparison principle for impulsive functional differential equations with infinite delays and applications

NASA Astrophysics Data System (ADS)

Li, Xiaodi; Shen, Jianhua; Akca, Haydar; Rakkiyappan, R.

2018-04-01

We introduce the Razumikhin technique to comparison principle and establish some comparison results for impulsive functional differential equations (IFDEs) with infinite delays, where the infinite delays may be infinite time-varying delays or infinite distributed delays. The idea is, under the help of Razumikhin technique, to reduce the study of IFDEs with infinite delays to the study of scalar impulsive differential equations (IDEs) in which the solutions are easy to deal with. Based on the comparison principle, we study the qualitative properties of IFDEs with infinite delays , which include stability, asymptotic stability, exponential stability, practical stability, boundedness, etc. It should be mentioned that the developed results in this paper can be applied to IFDEs with not only infinite delays but also persistent impulsive perturbations. Moreover, even for the special cases of non-impulsive effects or/and finite delays, the criteria prove to be simpler and less conservative than some existing results. Finally, two examples are given to illustrate the effectiveness and advantages of the proposed results.

Finite-dimensional compensators for infinite-dimensional systems via Galerkin-type approximation

NASA Technical Reports Server (NTRS)

Ito, Kazufumi

1990-01-01

In this paper existence and construction of stabilizing compensators for linear time-invariant systems defined on Hilbert spaces are discussed. An existence result is established using Galkerin-type approximations in which independent basis elements are used instead of the complete set of eigenvectors. A design procedure based on approximate solutions of the optimal regulator and optimal observer via Galerkin-type approximation is given and the Schumacher approach is used to reduce the dimension of compensators. A detailed discussion for parabolic and hereditary differential systems is included.

Creation of the universe

NASA Astrophysics Data System (ADS)

Fang, Li Zhi; Li, Shu Xian

Philosophical aspects of current cosmological theories are explored in an introduction for general readers. Chapters are devoted to the physical implications of an ancient Chinese story, expansion without a center, the age of the universe, the finiteness or infiniteness of space, visible and invisible matter, the birth of order from chaos, and the thermal history of the universe. Consideration is given to the synthesis of elements, the origin of asymmetry, the inflation of vacuum, the physics of the first move, and the anthropic principle and physical constants. Diagrams and drawings are provided.

Numerical investigation of diffraction of acoustic waves by phononic crystals

NASA Astrophysics Data System (ADS)

Moiseyenko, Rayisa P.; Declercq, Nico F.; Laude, Vincent

2012-05-01

Diffraction as well as transmission of acoustic waves by two-dimensional phononic crystals (PCs) composed of steel rods in water are investigated in this paper. The finite element simulations were performed in order to compute pressure fields generated by a line source that are incident on a finite size PC. Such field maps are analyzed based on the complex band structure for the infinite periodic PC. Finite size computations indicate that the exponential decrease of the transmission at deaf frequencies is much stronger than that in Bragg band gaps.

Multigrid one shot methods for optimal control problems: Infinite dimensional control

NASA Technical Reports Server (NTRS)

Arian, Eyal; Taasan, Shlomo

1994-01-01

The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.

A correlation method to predict the surface pressure distribution of an infinite plate or a body of revolution from which a jet is issuing

NASA Technical Reports Server (NTRS)

Perkins, S. C., Jr.; Mendenhall, M. R.

1980-01-01

A correlation method to predict pressures induced on an infinite plate by a jet exhausting normal to the plate into a subsonic free stream was extended to jets exhausting at angles to the plate and to jets exhausting normal to the surface of a body revolution. The complete method consisted of an analytical method which models the blockage and entrainment properties of the jet and an empirical correlation which accounts for viscous effects. For the flat plate case, the method was applicable to jet velocity ratios up to ten, jet inclination angles up to 45 deg from the normal, and radial distances up to five diameters from the jet. For the body of revolution case, the method was applicable to a body at zero degrees angle of attack, jet velocity ratios 1.96 and 3.43, circumferential angles around the body up to 25 deg from the jet, axial distances up to seven diameters from the jet, and jet-to-body diameter ratios less than 0.1.

Numerical Solution of the Flow of a Perfect Gas Over A Circular Cylinder at Infinite Mach Number

NASA Technical Reports Server (NTRS)

Hamaker, Frank M.

1959-01-01

A solution for the two-dimensional flow of an inviscid perfect gas over a circular cylinder at infinite Mach number is obtained by numerical methods of analysis. Nonisentropic conditions of curved shock waves and vorticity are included in the solution. The analysis is divided into two distinct regions, the subsonic region which is analyzed by the relaxation method of Southwell and the supersonic region which was treated by the method of characteristics. Both these methods of analysis are inapplicable on the sonic line which is therefore considered separately. The shapes of the sonic line and the shock wave are obtained by iteration techniques. The striking result of the solution is the strong curvature of the sonic line and of the other lines of constant Mach number. Because of this the influence of the supersonic flow on the sonic line is negligible. On comparison with Newtonian flow methods, it is found that the approximate methods show a larger variation of surface pressure than is given by the present solution.

On Kronecker-Capelli type theorems for infinite systems

NASA Astrophysics Data System (ADS)

Fedorov, Foma M.; Potapova, Sargylana V.

2017-11-01

On the basis of the new concept of the decrement of an infinite matrices and determinants, we studied the inconsistency of a general infinite systems of linear algebraic equations. We proved the theorem on inconsistency of a infinite system when the decrement of its matrix is nonzero.

Assembly of a new inorganic-organic frameworks based on [Sb4Mo12(OH)6O48]10- polyanion

NASA Astrophysics Data System (ADS)

Thabet, Safa; Ayed, Meriem; Ayed, Brahim; Haddad, Amor

2014-10-01

A new organic-inorganic hybrid material, (C4N2H7)8[K(H2O)]2[Sb4Mo12(OH)6O48]ṡ16H2O (1) has been isolated by the conventional solution method and characterized by elemental analysis, single-crystal X-ray diffraction, infrared spectroscopy, UV-visible spectroscopies, cyclic voltammetry and TG-DTA analysis. The compound crystallizes in the triclinic space group P - 1 with a = 13.407(6) Å, b = 13.906(2) Å, c = 14.657(7) Å, α = 77.216(9)°, β = 71.284(6)°, γ = 71.312(3)° and Z = 1. The crystal structure exhibits an infinite 1D inorganic structure built from [Sb4Mo12(OH)6O48]10- clusters and potassium cations; adjacent chains are further joined up hydrogen bonding interactions between protonated 2-methylimidazolim cations, water molecules and polyoxoanions to form a 3D supramolecular architecture.

Watershed-based survey designs

USGS Publications Warehouse

Detenbeck, N.E.; Cincotta, D.; Denver, J.M.; Greenlee, S.K.; Olsen, A.R.; Pitchford, A.M.

2005-01-01

Watershed-based sampling design and assessment tools help serve the multiple goals for water quality monitoring required under the Clean Water Act, including assessment of regional conditions to meet Section 305(b), identification of impaired water bodies or watersheds to meet Section 303(d), and development of empirical relationships between causes or sources of impairment and biological responses. Creation of GIS databases for hydrography, hydrologically corrected digital elevation models, and hydrologic derivatives such as watershed boundaries and upstream–downstream topology of subcatchments would provide a consistent seamless nationwide framework for these designs. The elements of a watershed-based sample framework can be represented either as a continuous infinite set defined by points along a linear stream network, or as a discrete set of watershed polygons. Watershed-based designs can be developed with existing probabilistic survey methods, including the use of unequal probability weighting, stratification, and two-stage frames for sampling. Case studies for monitoring of Atlantic Coastal Plain streams, West Virginia wadeable streams, and coastal Oregon streams illustrate three different approaches for selecting sites for watershed-based survey designs.

Non-idealities in the 3ω method for thermal characterization in the low- and high-frequency regimes

NASA Astrophysics Data System (ADS)

Jaber, Wassim; Chapuis, Pierre-Olivier

2018-04-01

This work is devoted to analytical and numerical studies of diffusive heat conduction in configurations considered in 3ω experiments, which aim at measuring thermal conductivity of materials. The widespread 2D analytical model considers infinite media and translational invariance, a situation which cannot be met in practice in numerous cases due to the constraints in low-dimensional materials and systems. We investigate how thermal boundary resistance between heating wire and sample, native oxide and heating wire shape affect the temperature fields. 3D finite element modelling is also performed to account for the effect of the bonding pads and the 3D heat spreading down to a typical package. Emphasis is given on the low-frequency regime, which is less known than the so-called slope regime. These results will serve as guides for the design of ideal experiments where the 2D model can be applied and for the analyses of non-ideal ones.

Finite dimensional approximation of a class of constrained nonlinear optimal control problems

NASA Technical Reports Server (NTRS)

Gunzburger, Max D.; Hou, L. S.

1994-01-01

An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

Solvothermal synthesis and structure of 3D frameworks of Nd(III) and Y(III) with thiophene-2,5-dicarboxylate and N,N‧-diethylformamide

NASA Astrophysics Data System (ADS)

Sharma, Swati; Yawer, Mohd; Kariem, Mukaddus; Sheikh, Haq Nawaz

2016-08-01

Two new 3D MOFs [Nd2(TDA)3(DEF)2(H2O)]n (1) and [Y4(TDA)6(DEF)4]n (2) [Thiophene-2,5-dicarboxylic acid (H2TDA) and N,N‧-diethylformamide (DEF)] were synthesized by solvothermal method. They were characterized by elemental analyses, infrared spectroscopy and single crystal X-ray diffraction studies. The two MOFs (1) and (2) belong to the monoclinic system with space group P21/n and C 2 respectively. Structural characterizations by single-crystal X-ray crystallography reveal that 1 and 2 adopt three-dimensional frameworks constructed by cross-linking of rod shaped infinite chain secondary building unit (SBU) by thiophene-2,5-dicarboxylates as linker. These frameworks feature rhomboidal channels, inside which coordinated DEF/H2O solvent molecules are located. DEF plays pivotal role in reaction and design of MOFs. Thermogravimetric analysis shows that both MOFs are thermally robust.

Series of Reciprocal Triangular Numbers

ERIC Educational Resources Information Center

Bruckman, Paul; Dence, Joseph B.; Dence, Thomas P.; Young, Justin

2013-01-01

Reciprocal triangular numbers have appeared in series since the very first infinite series were summed. Here we attack a number of subseries of the reciprocal triangular numbers by methodically expressing them as integrals.

Matrix elements of Δ B =0 operators in heavy hadron chiral perturbation theory

NASA Astrophysics Data System (ADS)

Lee, Jong-Wan

2015-05-01

We study the light-quark mass and spatial volume dependence of the matrix elements of Δ B =0 four-quark operators relevant for the determination of Vu b and the lifetime ratios of single-b hadrons. To this end, one-loop diagrams are computed in the framework of heavy hadron chiral perturbation theory with partially quenched formalism for three light-quark flavors in the isospin limit; flavor-connected and -disconnected diagrams are carefully analyzed. These calculations include the leading light-quark flavor and heavy-quark spin symmetry breaking effects in the heavy hadron spectrum. Our results can be used in the chiral extrapolation of lattice calculations of the matrix elements to the physical light-quark masses and to infinite volume. To provide insight on such chiral extrapolation, we evaluate the one-loop contributions to the matrix elements containing external Bd, Bs mesons and Λb baryon in the QCD limit, where sea and valence quark masses become equal. In particular, we find that the matrix elements of the λ3 flavor-octet operators with an external Bd meson receive the contributions solely from connected diagrams in which current lattice techniques are capable of precise determination of the matrix elements. Finite volume effects are at most a few percent for typical lattice sizes and pion masses.

Acoustic propagation in curved ducts with extended reacting wall treatment

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.

1989-01-01

A finite-element Galerkin formulation was employed to study the attenuation of acoustic waves propagating in two-dimensional S-curved ducts with absorbing walls without a mean flow. The reflection and transmission at the entrance and the exit of a curved duct were determined by coupling the finite-element solutions in the curved duct to the eigenfunctions of an infinite, uniform, hard wall duct. In the frequency range where the duct height and acoustic wave length are nearly equal, the effects of duct length, curvature (duct offset) and absorber thickness were examined. For a given offset in the curved duct, the length of the S-duct was found to significantly affect both the absorptive and reflective characteristics of the duct. A means of reducing the number of elements in the absorber region was also presented. In addition, for a curved duct, power attenuation contours were examined to determine conditions for maximum acoustic power absorption. Again, wall curvature was found to significantly effect the optimization process.

Dipole excitation of surface plasmon on a conducting sheet: Finite element approximation and validation

NASA Astrophysics Data System (ADS)

Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell

2017-06-01

We formulate and validate a finite element approach to the propagation of a slowly decaying electromagnetic wave, called surface plasmon-polariton, excited along a conducting sheet, e.g., a single-layer graphene sheet, by an electric Hertzian dipole. By using a suitably rescaled form of time-harmonic Maxwell's equations, we derive a variational formulation that enables a direct numerical treatment of the associated class of boundary value problems by appropriate curl-conforming finite elements. The conducting sheet is modeled as an idealized hypersurface with an effective electric conductivity. The requisite weak discontinuity for the tangential magnetic field across the hypersurface can be incorporated naturally into the variational formulation. We carry out numerical simulations for an infinite sheet with constant isotropic conductivity embedded in two spatial dimensions; and validate our numerics against the closed-form exact solution obtained by the Fourier transform in the tangential coordinate. Numerical aspects of our treatment such as an absorbing perfectly matched layer, as well as local refinement and a posteriori error control are discussed.

Modeling of heat flow and effective thermal conductivity of fractured media: Analytical and numerical methods

NASA Astrophysics Data System (ADS)

Nguyen, S. T.; Vu, M.-H.; Vu, M. N.; Tang, A. M.

2017-05-01

The present work aims to modeling the thermal conductivity of fractured materials using homogenization-based analytical and pattern-based numerical methods. These materials are considered as a network of cracks distributed inside a solid matrix. Heat flow through such media is perturbed by the crack system. The problem of heat flow across a single crack is firstly investigated. The classical Eshelby's solution, extended to the thermal conduction problem of an ellipsoidal inclusion embedding in an infinite homogeneous matrix, gives an analytical solution of temperature discontinuity across a non-conducting penny-shaped crack. This solution is then validated by the numerical simulation based on the finite elements method. The numerical simulation allows analyzing the effect of crack conductivity. The problem of a single crack is then extended to a medium containing multiple cracks. Analytical estimations for effective thermal conductivity, that take into account the interaction between cracks and their spatial distribution, are developed for the case of non-conducting cracks. Pattern-based numerical method is then employed for both cases non-conducting and conducting cracks. In the case of non-conducting cracks, numerical and analytical methods, both account for the spatial distribution of the cracks, fit perfectly. In the case of conducting cracks, the numerical analyzing of crack conductivity effect shows that highly conducting cracks weakly affect heat flow and the effective thermal conductivity of fractured media.

Option pricing for stochastic volatility model with infinite activity Lévy jumps

NASA Astrophysics Data System (ADS)

Gong, Xiaoli; Zhuang, Xintian

2016-08-01

The purpose of this paper is to apply the stochastic volatility model driven by infinite activity Lévy processes to option pricing which displays infinite activity jumps behaviors and time varying volatility that is consistent with the phenomenon observed in underlying asset dynamics. We specially pay attention to three typical Lévy processes that replace the compound Poisson jumps in Bates model, aiming to capture the leptokurtic feature in asset returns and volatility clustering effect in returns variance. By utilizing the analytical characteristic function and fast Fourier transform technique, the closed form formula of option pricing can be derived. The intelligent global optimization search algorithm called Differential Evolution is introduced into the above highly dimensional models for parameters calibration so as to improve the calibration quality of fitted option models. Finally, we perform empirical researches using both time series data and options data on financial markets to illustrate the effectiveness and superiority of the proposed method.

Further summation formulae related to generalized harmonic numbers

NASA Astrophysics Data System (ADS)

Zheng, De-Yin

2007-11-01

By employing the univariate series expansion of classical hypergeometric series formulae, Shen [L.-C. Shen, Remarks on some integrals and series involving the Stirling numbers and [zeta](n), Trans. Amer. Math. Soc. 347 (1995) 1391-1399] and Choi and Srivastava [J. Choi, H.M. Srivastava, Certain classes of infinite series, Monatsh. Math. 127 (1999) 15-25; J. Choi, H.M. Srivastava, Explicit evaluation of Euler and related sums, Ramanujan J. 10 (2005) 51-70] investigated the evaluation of infinite series related to generalized harmonic numbers. More summation formulae have systematically been derived by Chu [W. Chu, Hypergeometric series and the Riemann Zeta function, Acta Arith. 82 (1997) 103-118], who developed fully this approach to the multivariate case. The present paper will explore the hypergeometric series method further and establish numerous summation formulae expressing infinite series related to generalized harmonic numbers in terms of the Riemann Zeta function [zeta](m) with m=5,6,7, including several known ones as examples.

Compactified cosmological simulations of the infinite universe

NASA Astrophysics Data System (ADS)

Rácz, Gábor; Szapudi, István; Csabai, István; Dobos, László

2018-06-01

We present a novel N-body simulation method that compactifies the infinite spatial extent of the Universe into a finite sphere with isotropic boundary conditions to follow the evolution of the large-scale structure. Our approach eliminates the need for periodic boundary conditions, a mere numerical convenience which is not supported by observation and which modifies the law of force on large scales in an unrealistic fashion. We demonstrate that our method outclasses standard simulations executed on workstation-scale hardware in dynamic range, it is balanced in following a comparable number of high and low k modes and, its fundamental geometry and topology match observations. Our approach is also capable of simulating an expanding, infinite universe in static coordinates with Newtonian dynamics. The price of these achievements is that most of the simulated volume has smoothly varying mass and spatial resolution, an approximation that carries different systematics than periodic simulations. Our initial implementation of the method is called StePS which stands for Stereographically projected cosmological simulations. It uses stereographic projection for space compactification and naive O(N^2) force calculation which is nevertheless faster to arrive at a correlation function of the same quality than any standard (tree or P3M) algorithm with similar spatial and mass resolution. The N2 force calculation is easy to adapt to modern graphics cards, hence our code can function as a high-speed prediction tool for modern large-scale surveys. To learn about the limits of the respective methods, we compare StePS with GADGET-2 running matching initial conditions.

Modality, Infinitives, and Finite Bare Verbs in Dutch and English Child Language

ERIC Educational Resources Information Center

Blom, Elma

2007-01-01

This article focuses on the meaning of nonfinite clauses ("root infinitives") in Dutch and English child language. I present experimental and naturalistic data confirming the claim that Dutch root infinitives are more often modal than English root infinitives. This cross-linguistic difference is significantly smaller than previously assumed,…

Measuring acoustic impedances using a semi-infinite waveguide reference: Applications to wind instruments and vocal tracts

NASA Astrophysics Data System (ADS)

Wolfe, Joe; Smith, John; Tann, John; France, Ryan

2002-11-01

Acoustic pressures may generally be measured with much greater sensitivity, dynamic range, and frequency response than acoustic currents. Consequently, most measurements of acoustic impedance consist of comparison with standard impedances. The method reported here uses a semi-infinite waveguide as the reference because its impedance is purely resistive, frequency independent and accurately known, independent of theories of the boundary layer. Waveguides are effectively infinite for pulses shorter than the echo return time, or if the attenuation due to wall losses (typically 80 dB) exceeds the dynamic range of the experiment. The measurement signal from a high output impedance source is calibrated to have Fourier components proportional to fn, where n may be 1 for convenience or chosen to improve the signal:noise ratio. The method has been used on diverse systems over the range 50 Hz to 13 kHz. When applied to systems with simple geometries, the technique yields results with a little higher wall losses than those expected from the calculations of Rayleigh and Benade. Discontinuities introduce further losses as well as the expected departures from simple one-dimensional models. Measurements on musical wind instruments and on the human vocal tract are reported. [Work supported by the Australian Research Council.

Scalable L-infinite coding of meshes.

PubMed

Munteanu, Adrian; Cernea, Dan C; Alecu, Alin; Cornelis, Jan; Schelkens, Peter

2010-01-01

The paper investigates the novel concept of local-error control in mesh geometry encoding. In contrast to traditional mesh-coding systems that use the mean-square error as target distortion metric, this paper proposes a new L-infinite mesh-coding approach, for which the target distortion metric is the L-infinite distortion. In this context, a novel wavelet-based L-infinite-constrained coding approach for meshes is proposed, which ensures that the maximum error between the vertex positions in the original and decoded meshes is lower than a given upper bound. Furthermore, the proposed system achieves scalability in L-infinite sense, that is, any decoding of the input stream will correspond to a perfectly predictable L-infinite distortion upper bound. An instantiation of the proposed L-infinite-coding approach is demonstrated for MESHGRID, which is a scalable 3D object encoding system, part of MPEG-4 AFX. In this context, the advantages of scalable L-infinite coding over L-2-oriented coding are experimentally demonstrated. One concludes that the proposed L-infinite mesh-coding approach guarantees an upper bound on the local error in the decoded mesh, it enables a fast real-time implementation of the rate allocation, and it preserves all the scalability features and animation capabilities of the employed scalable mesh codec.

An examination of the concept of driving point receptance

NASA Astrophysics Data System (ADS)

Sheng, X.; He, Y.; Zhong, T.

2018-04-01

In the field of vibration, driving point receptance is a well-established and widely applied concept. However, as demonstrated in this paper, when a driving point receptance is calculated using the finite element (FE) method with solid elements, it does not converge as the FE mesh becomes finer, suggesting that there is a singularity. Hence, the concept of driving point receptance deserves a rigorous examination. In this paper, it is firstly shown that, for a point harmonic force applied on the surface of an elastic half-space, the Boussinesq formula can be applied to calculate the displacement amplitude of the surface if the response point is sufficiently close to the load. Secondly, by applying the Betti reciprocal theorem, it is shown that the displacement of an elastic body near a point harmonic force can be decomposed into two parts, with the first one being the displacement of an elastic half-space. This decomposition is useful, since it provides a solid basis for the introduction of a contact spring between a wheel and a rail in interaction. However, according to the Boussinesq formula, this decomposition also leads to the conclusion that a driving point receptance is infinite (singular), and would be undefinable. Nevertheless, driving point receptances have been calculated using different methods. Since the singularity identified in this paper was not appreciated, no account was given to the singularity in these calculations. Thus, the validity of these calculation methods must be examined. This constructs the third part of the paper. As the final development of the paper, the above decomposition is utilised to define and determine driving point receptances required for dealing with wheel/rail interactions.

Free Oscillations of a Fluid-filled Cavity in an Infinite Elastic Medium

NASA Astrophysics Data System (ADS)

Sakuraba, A.

2016-12-01

Volcanic low-frequency earthquakes and tremor have been widely recognized as a good indicator of hidden activities of volcanoes. It is likely that existence or movement of underground magma and geothermal fluids play a crucial role in their generation mechanisms, but there are still many unknowns. This presentation aims to give a fundamental contribution to understanding and interpreting volcanic low-frequency seismic events. The problem we consider is to compute eigen modes of free oscillations of a fluid-filled cavity surrounded by an infinite linearly elastic medium. A standard boundary element method is used to solve fluid and elastic motion around a cavity of arbitrary shape. Nonlinear advection term is neglected, but viscosity is generally considered in a fluid medium. Of a great importance is to find not only characteristic frequencies but attenuation properties of the oscillations, the latter being determined by both viscous dissipation in the fluid cavity and elastic wave radiation to infinity. One of the simplest cases may be resonance of a fluid-filled crack, which has been studied numerically (Chouet, JGR 1986; Yamamoto and Kawakatsu, GJI 2008) and analytically (Maeda and Kumagai, GRL 2013). In the present study, we generally consider a three-dimensional cavity with emphasis on treating the crack model and other simplest models such as spherical and cylindrical resonators as the extreme cases. In order to reduce computational costs, we assume symmetries about three orthogonal planes and calculate the eigen modes separately for each symmetry. The current status of this project is that the computational code has been checked through comparison to eigen modes of a spherical inviscid cavity (Sakuraba et al., EPS 2002), and another comparison to resonance of a fluid-filled crack is undertook.

Improved phase shift approach to the energy correction of the infinite order sudden approximation

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

Chang, B.; Eno, L.; Rabitz, H.

1980-07-15

A new method is presented for obtaining energy corrections to the infinite order sudden (IOS) approximation by incorporating the effect of the internal molecular Hamiltonian into the IOS wave function. This is done by utilizing the JWKB approximation to transform the Schroedinger equation into a differential equation for the phase. It is found that the internal Hamiltonian generates an effective potential from which a new improved phase shift is obtained. This phase shift is then used in place of the IOS phase shift to generate new transition probabilities. As an illustration the resulting improved phase shift (IPS) method is appliedmore » to the Secrest--Johnson model for the collinear collision of an atom and diatom. In the vicinity of the sudden limit, the IPS method gives results for transition probabilities, P/sub n/..-->..n+..delta..n, in significantly better agreement with the 'exact' close coupling calculations than the IOS method, particularly for large ..delta..n. However, when the IOS results are not even qualitatively correct, the IPS method is unable to satisfactorily provide improvements.« less

Sinc-Galerkin estimation of diffusivity in parabolic problems

NASA Technical Reports Server (NTRS)

Smith, Ralph C.; Bowers, Kenneth L.

1991-01-01

A fully Sinc-Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newton/trust region algorithm. The L-curve technique for determining an approximate value of the regularization parameter is briefly discussed, and numerical examples are given which show the applicability of the method both for problems with noise-free data as well as for those whose data contains white noise.

Note on the eigensolution of a homogeneous equation with semi-infinite domain

NASA Technical Reports Server (NTRS)

Wadia, A. R.

1980-01-01

The 'variation-iteration' method using Green's functions to find the eigenvalues and the corresponding eigenfunctions of a homogeneous Fredholm integral equation is employed for the stability analysis of fluid hydromechanics problems with a semiinfinite (infinite) domain of application. The objective of the study is to develop a suitable numerical approach to the solution of such equations in order to better understand the full set of equations for 'real-world' flow models. The study involves a search for a suitable value of the length of the domain which is a fair finite approximation to infinity, which makes the eigensolution an approximation dependent on the length of the interval chosen. In the examples investigated y = 1 = a seems to be the best approximation of infinity; for y greater than unity this method fails due to the polynomial nature of Green's functions.

The transmission or scattering of elastic waves by an inhomogeneity of simple geometry: A comparison of theories

NASA Technical Reports Server (NTRS)

Sheu, Y. C.; Fu, L. S.

1982-01-01

The extended method of equivalent inclusion developed is applied to study the specific wave problems of the transmission of elastic waves in an infinite medium containing a layer of inhomogeneity, and of the scattering of elastic waves in an infinite medium containing a perfect spherical inhomogeneity. The eigenstrains are expanded as a geometric series and the method of integration for the inhomogeneous Helmholtz operator given by Fu and Mura is adopted. The results obtained by using a limited number of terms in the eigenstrain expansion are compared with exact solutions for the layer problem and for a perfect sphere. Two parameters are singled out for this comparison: the ratio of elastic moduli, and the ratio of the mass densities. General trends for three different situations are shown.

Boundary Conditions for Infinite Conservation Laws

NASA Astrophysics Data System (ADS)

Rosenhaus, V.; Bruzón, M. S.; Gandarias, M. L.

2016-12-01

Regular soliton equations (KdV, sine-Gordon, NLS) are known to possess infinite sets of local conservation laws. Some other classes of nonlinear PDE possess infinite-dimensional symmetries parametrized by arbitrary functions of independent or dependent variables; among them are Zabolotskaya-Khokhlov, Kadomtsev-Petviashvili, Davey-Stewartson equations and Born-Infeld equation. Boundary conditions were shown to play an important role for the existence of local conservation laws associated with infinite-dimensional symmetries. In this paper, we analyze boundary conditions for the infinite conserved densities of regular soliton equations: KdV, potential KdV, Sine-Gordon equation, and nonlinear Schrödinger equation, and compare them with boundary conditions for the conserved densities obtained from infinite-dimensional symmetries with arbitrary functions of independent and dependent variables.

An analytic model for acoustic scattering from an impedance cylinder placed normal to an impedance plane

NASA Astrophysics Data System (ADS)

Swearingen, Michelle E.

2004-04-01

An analytic model, developed in cylindrical coordinates, is described for the scattering of a spherical wave off a semi-infinite reight cylinder placed normal to a ground surface. The motivation for the research is to have a model with which one can simulate scattering from a single tree and which can be used as a fundamental element in a model for estimating the attenuation in a forest comprised of multiple tree trunks. Comparisons are made to the plane wave case, the transparent cylinder case, and the rigid and soft ground cases as a method of theoretically verifying the model for the contemplated range of model parameters. Agreement is regarded as excellent for these benchmark cases. Model sensitivity to five parameters is also explored. An experiment was performed to study the scattering from a cylinder normal to a ground surface. The data from the experiment is analyzed with a transfer function method to yield frequency and impulse responses, and calculations based on the analytic model are compared to the experimental data. Thesis advisor: David C. Swanson Copies of this thesis written in English can be obtained from

Radiation and scattering from cylindrically conformal printed antennas. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.

1994-01-01

Microstrip patch antennas offer considerable advantages in terms of weight, aerodynamic drag, cost, flexibility, and observables over more conventional protruding antennas. These flat patch antennas were first proposed over thirty years ago by Deschamps in the United States and Gutton and Baisinot in France. Such antennas have been analyzed and developed for planar as well as curved platforms. However, the methods used in these designs employ gross approximations, suffer from extreme computational burden, or require expensive physical experiments. The goal of this thesis is to develop accurate and efficient numerical modeling techniques which represent actual antenna structures mounted on curved surfaces with a high degree of fidelity. In this thesis, the finite element method is extended to cavity-backed conformal antenna arrays embedded in a circular, metallic, infinite cylinder. Both the boundary integral and absorbing boundary mesh closure conditions will be used for terminating the mesh. These two approaches will be contrasted and used to study the scattering and radiation behavior of several useful antenna configurations. An important feature of this study will be to examine the effect of curvature and cavity size on the scattering and radiation properties of wraparound conformal antenna arrays.

Investigation of the complex electroviscous effects on electrolyte (single and multiphase) flow in porous medi.

NASA Astrophysics Data System (ADS)

Bolet, A. J. S.; Linga, G.; Mathiesen, J.

2017-12-01

Surface charge is an important control parameter for wall-bounded flow of electrolyte solution. The electroviscous effect has been studied theoretically in model geometries such as infinite capillaries. However, in more complex geometries a quantification of the electroviscous effect is a non-trival task due to strong non-linarites of the underlying equations. In general, one has to rely on numerical methods. Here we present numerical studies of the full three-dimensional steady state Stokes-Poisson-Nernst-Planck problem in order to model electrolyte transport in artificial porous samples. The simulations are performed using the finite element method. From the simulation, we quantity how the electroviscous effect changes the general flow permeability in complex three-dimensional porous media. The porous media we consider are mostly generated artificially by connecting randomly dispersed cylindrical pores. Furthermore, we present results of electric driven two-phase immiscible flow in two dimensions. The simulations are performed by augmenting the above equations with a phase field model to handle and track the interaction between the two fluids (using parameters corresponding to oil-water interfaces, where oil non-polar). In particular, we consider the electro-osmotic effect on imbibition due to charged walls and electrolyte-solution.

An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation.

PubMed

Ilias, Miroslav; Saue, Trond

2007-02-14

The authors report the implementation of a simple one-step method for obtaining an infinite-order two-component (IOTC) relativistic Hamiltonian using matrix algebra. They apply the IOTC Hamiltonian to calculations of excitation and ionization energies as well as electric and magnetic properties of the radon atom. The results are compared to corresponding calculations using identical basis sets and based on the four-component Dirac-Coulomb Hamiltonian as well as Douglas-Kroll-Hess and zeroth-order regular approximation Hamiltonians, all implemented in the DIRAC program package, thus allowing a comprehensive comparison of relativistic Hamiltonians within the finite basis approximation.

Asymptotic expansions of solutions of the heat conduction equation in internally bounded cylindrical geometry

USGS Publications Warehouse

Ritchie, R.H.; Sakakura, A.Y.

1956-01-01

The formal solutions of problems involving transient heat conduction in infinite internally bounded cylindrical solids may be obtained by the Laplace transform method. Asymptotic series representing the solutions for large values of time are given in terms of functions related to the derivatives of the reciprocal gamma function. The results are applied to the case of the internally bounded infinite cylindrical medium with, (a) the boundary held at constant temperature; (b) with constant heat flow over the boundary; and (c) with the "radiation" boundary condition. A problem in the flow of gas through a porous medium is considered in detail.

Comparison of infinite and wedge fringe settings in Mach Zehnder interferometer for temperature field measurement

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

Haridas, Divya; P, Vibin Antony; Sajith, V.

2014-10-15

Interferometric method, which utilizes the interference of coherent light beams, is used to determine the temperature distribution in the vicinity of a vertical heater plate. The optical components are arranged so as to obtain wedge fringe and infinite fringe patterns and isotherms obtained in each case were compared. In wedge fringe setting, image processing techniques has been used for obtaining isotherms by digital subtraction of initial parallel fringe pattern from deformed fringe pattern. The experimental results obtained are compared with theoretical correlations. The merits and demerits of the fringe analysis techniques are discussed on the basis of the experimental results.

Generalizing the bms3 and 2D-conformal algebras by expanding the Virasoro algebra

NASA Astrophysics Data System (ADS)

Caroca, Ricardo; Concha, Patrick; Rodríguez, Evelyn; Salgado-Rebolledo, Patricio

2018-03-01

By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the bms3 algebra are obtained from the Virasoro algebra. We extend this result to construct new families of expanded Virasoro algebras that turn out to be infinite-dimensional lifts of the so-called Bk, Ck and Dk algebras recently introduced in the literature in the context of (super)gravity. We also show how some of these new infinite-dimensional symmetries can be obtained from expanded Kač-Moody algebras using modified Sugawara constructions. Applications in the context of three-dimensional gravity are briefly discussed.

Infinite variance in fermion quantum Monte Carlo calculations.

PubMed

Shi, Hao; Zhang, Shiwei

2016-03-01

For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.

Gauge invariance of excitonic linear and nonlinear optical response

NASA Astrophysics Data System (ADS)

Taghizadeh, Alireza; Pedersen, T. G.

2018-05-01

We study the equivalence of four different approaches to calculate the excitonic linear and nonlinear optical response of multiband semiconductors. These four methods derive from two choices of gauge, i.e., length and velocity gauges, and two ways of computing the current density, i.e., direct evaluation and evaluation via the time-derivative of the polarization density. The linear and quadratic response functions are obtained for all methods by employing a perturbative density-matrix approach within the mean-field approximation. The equivalence of all four methods is shown rigorously, when a correct interaction Hamiltonian is employed for the velocity gauge approaches. The correct interaction is written as a series of commutators containing the unperturbed Hamiltonian and position operators, which becomes equivalent to the conventional velocity gauge interaction in the limit of infinite Coulomb screening and infinitely many bands. As a case study, the theory is applied to hexagonal boron nitride monolayers, and the linear and nonlinear optical response found in different approaches are compared.

A Chebyshev matrix method for spatial modes of the Orr-Sommerfeld equation

NASA Technical Reports Server (NTRS)

Danabasoglu, G.; Biringen, S.

1989-01-01

The Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr-Sommerfeld equation for Poiseuille flow and the Blausius boundary layer. The problem is linearized by the companion matrix technique for semi-infinite domain using a mapping transformation. The method can be easily adapted to problems with different boundary conditions requiring different transformations.

Computational neural learning formalisms for manipulator inverse kinematics

NASA Technical Reports Server (NTRS)

Gulati, Sandeep; Barhen, Jacob; Iyengar, S. Sitharama

1989-01-01

An efficient, adaptive neural learning paradigm for addressing the inverse kinematics of redundant manipulators is presented. The proposed methodology exploits the infinite local stability of terminal attractors - a new class of mathematical constructs which provide unique information processing capabilities to artificial neural systems. For robotic applications, synaptic elements of such networks can rapidly acquire the kinematic invariances embedded within the presented samples. Subsequently, joint-space configurations, required to follow arbitrary end-effector trajectories, can readily be computed. In a significant departure from prior neuromorphic learning algorithms, this methodology provides mechanisms for incorporating an in-training skew to handle kinematics and environmental constraints.

A new antenna concept for satellite communications

NASA Technical Reports Server (NTRS)

Skahill, G.; Ciccolella, D.

1982-01-01

A novel antenna configuration of two reflecting surfaces and a phased array is examined for application to satellite communications and shown to be superior in every respect to earlier designs for service to the continental United States from synchronous orbit. The vignetting that afflicts other two reflector optical systems is eliminated by use of a reflecting field element. The remaining aberrations, predominantly coma, are isolated in the time delay distribution at the surface of the array and can be compensated by ordinary array techniques. The optics exhibits infinite bandwidth and the frequency range is limited only by the design of the array.

Regulation of AID, the B-cell genome mutator

PubMed Central

Keim, Celia; Kazadi, David; Rothschild, Gerson; Basu, Uttiya

2013-01-01

The mechanisms by which B cells somatically engineer their genomes to generate the vast diversity of antibodies required to challenge the nearly infinite number of antigens that immune systems encounter are of tremendous clinical and academic interest. The DNA cytidine deaminase activation-induced deaminase (AID) catalyzes two of these mechanisms: class switch recombination (CSR) and somatic hypermutation (SHM). Recent discoveries indicate a significant promiscuous targeting of this B-cell mutator enzyme genome-wide. Here we discuss the various regulatory elements that control AID activity and prevent AID from inducing genomic instability and thereby initiating oncogenesis. PMID:23307864

Numerical investigation of soil plugging effect inside sleeve of cast-in-place piles driven by vibratory hammers in clays.

PubMed

Xiao, Yong Jie; Chen, Fu Quan; Dong, Yi Zhi

2016-01-01

During driving sleeve of cast-in-place piles by vibratory hammers, soils were squeezed into sleeve and then soil plugging was formed. The physic-mechanical properties of the soil plug have direct influence on the load transmission between the sleeve wall and soil plug. Nevertheless, the researches on this issue are insufficient. In this study, finite element and infinite element coupling model was introduced, through the commercial code ABAQUS, to simulate the full penetration process of the sleeve driven from the ground surface to the desired depth by applying vibratory hammers. The research results indicated that the cyclic shearing action decreases both in soil shear strength and in granular cementation force when the sleeve is driven by vibratory hammers, which leads to a partially plugged mode of the soil plug inside the sleeve. Accordingly, the penetration resistance of sleeve driven by vibratory hammers is the smallest compared to those by other installation methods. When driving the sleeve, the annular soil arches forming in the soil plug at sleeve end induce a significant rise in the internal shaft resistance. Moreover, the influence of vibration frequencies, sleeve diameters, and soil layer properties on the soil plug was investigated in detail, and at the same time improved formulas were brought forward to describe the soil plug resistance inside vibratory driven sleeve.

Improved numerical methods for infinite spin chains with long-range interactions

NASA Astrophysics Data System (ADS)

Nebendahl, V.; Dür, W.

2013-02-01

We present several improvements of the infinite matrix product state (iMPS) algorithm for finding ground states of one-dimensional quantum systems with long-range interactions. As a main ingredient, we introduce the superposed multioptimization method, which allows an efficient optimization of exponentially many MPS of different lengths at different sites all in one step. Here, the algorithm becomes protected against position-dependent effects as caused by spontaneously broken translational invariance. So far, these have been a major obstacle to convergence for the iMPS algorithm if no prior knowledge of the system's translational symmetry was accessible. Further, we investigate some more general methods to speed up calculations and improve convergence, which might be partially interesting in a much broader context, too. As a more special problem, we also look into translational invariant states close to an invariance-breaking phase transition and show how to avoid convergence into wrong local minima for such systems. Finally, we apply these methods to polar bosons with long-range interactions. We calculate several detailed Devil's staircases with the corresponding phase diagrams and investigate some supersolid properties.

Analysis of the dominant vibration frequencies of rail bridges for structure-borne noise using a power flow method

NASA Astrophysics Data System (ADS)

Li, Q.; Wu, D. J.

2013-09-01

The use of concrete bridges in urban rail transit systems has raised many concerns regarding low-frequency (20-200 Hz) structure-borne noise due to the vibration of bridges when subjected to moving trains. Understanding the mechanism that determines the dominant frequencies of bridge vibrations is essential for both vibration and noise reduction. This paper presents a general procedure based on the force method to obtain the power flows within a coupled vehicle-track-bridge system, the point mobility of the system and the dynamic interaction forces connecting various components. The general coupling system consists of multi-rigid-bodies for the vehicles, infinite Euler beams representing the rails, two-dimensional or three-dimensional elements of the concrete bridges, and spring-dashpot pairs to model the wheel-rail contacts, the vehicle suspensions, the rail pads and the bridge bearings. The dynamic interaction of the coupled system is solved in the frequency domain by assuming the combined wheel-rail roughness moves forward relative to the stationary vehicles. The proposed procedure is first applied to a rail on discrete supports and then to a real urban rail transit U-shaped concrete bridge. The computed results show that the wheel-rail contact forces, the power flows to the rail/bridge subsystem and the accelerations of the bridge are primarily dominated by the contents around the natural frequency of a single wheel adhered to the elastically supported rail. If the ath node of the mth spring-dashpot pair and the bth node of the nth spring-dashpot pair are connected to the same rigid body, then δmnab(ω) can be expressed as δmnab(ω)=-{(}/{Mlω}, where Ml is the mass of the lth rigid body. If the ath node of the mth spring-dashpot pair and the bth node of the nth spring-dashpot pair are connected to the same infinite rail, δmnab(ω) can be expressed as [8] δmnab(ω)=-j{((e-je)}/{4EIk}, where xm and xn are the x-coordinates of the mth and nth spring-dashpot pairs respectively; E and I denote the elastic module and the bending moment of inertia of the infinite rail; and k is the wavenumber of the unsupported infinite rail k=(EI)1/4, where mr is the mass per unit length of the rail. If the ath node of the mth spring-dashpot pair and the bth node of the nth spring-dashpot pair are connected to the same bridge component, then δmnab(ω) can be obtained by applying the mode superposition method δmnab(ω)=∑i=1Nl{(ϕ}/{liaϕlibωli2-ω+2jξωω}, where ω and ξ are the damped natural frequency and damping ratio of the ith mode of the lth bridge component; ϕlia and ϕlib denote the generalised mode shape amplitudes of the the lth bridge component to which the ath and bth nodes of the two spring-dashpot pairs are connected; and Nl is the mode number of interest. It can be observed from Eqs. (2)-(7) that the theorem of reciprocal displacements is met as follows: δ(ω)=δ(ω). An external point excitation can be regarded as a force produced by a spring-dashpot pair with its first node connected to the excitation point and the second node fixed to the ground. Therefore, each element in vector ΔP(ω) can be easily attained using the first and last terms of Eq. (3): Δmp(ω)=δmp11(ω)+δmp21(ω), where the subscript p denotes the fictitious spring-dashpot pair used to simulate the external harmonic force. The dominant frequency of the wheel-rail contact forces and power input to the rail on elastic supports is found to be consistent with the natural frequency of the single wheel adhered to the elastically supported rail. The simple formula derived to predict this dominant frequency matches well with the numerical results. The acceleration response of the bridge is also dominated by the natural frequency of the single wheel adhered to the elastically supported rail. Although the vehicle speed has an insignificant effect on the dominant frequency of the bridge response, it does influence the magnitude of the response. The findings in this paper and the proposed method can be applied to mitigate the vibration and noise from rail bridges once a series of parametric analyses has been carried out.

Total decay and transition rates from LQCD

NASA Astrophysics Data System (ADS)

Hansen, Maxwell T.; Meyer, Harvey B.; Robaina, Daniel

2018-03-01

We present a new technique for extracting total transition rates into final states with any number of hadrons from lattice QCD. The method involves constructing a finite-volume Euclidean four-point function whose corresponding infinite-volume spectral function gives access to the decay and transition rates into all allowed final states. The inverse problem of calculating the spectral function is solved via the Backus-Gilbert method, which automatically includes a smoothing procedure. This smoothing is in fact required so that an infinite-volume limit of the spectral function exists. Using a numerical toy example we find that reasonable precision can be achieved with realistic lattice data. In addition, we discuss possible extensions of our approach and, as an example application, prospects for applying the formalism to study the onset of deep-inelastic scattering. More details are given in the published version of this work, Ref. [1].

Comptonization of X-rays by low-temperature electrons. [photon wavelength redistribution in cosmic sources

NASA Technical Reports Server (NTRS)

Illarionov, A.; Kallman, T.; Mccray, R.; Ross, R.

1979-01-01

A method is described for calculating the spectrum that results from the Compton scattering of a monochromatic source of X-rays by low-temperature electrons, both for initial-value relaxation problems and for steady-state spatial diffusion problems. The method gives an exact solution of the inital-value problem for evolution of the spectrum in an infinite homogeneous medium if Klein-Nishina corrections to the Thomson cross section are neglected. This, together with approximate solutions for problems in which Klein-Nishina corrections are significant and/or spatial diffusion occurs, shows spectral structure near the original photon wavelength that may be used to infer physical conditions in cosmic X-ray sources. Explicit results, shown for examples of time relaxation in an infinite medium and spatial diffusion through a uniform sphere, are compared with results obtained by Monte Carlo calculations and by solving the appropriate Fokker-Planck equation.

Spatio-Temporal Video Segmentation with Shape Growth or Shrinkage Constraint

NASA Technical Reports Server (NTRS)

Tarabalka, Yuliya; Charpiat, Guillaume; Brucker, Ludovic; Menze, Bjoern H.

2014-01-01

We propose a new method for joint segmentation of monotonously growing or shrinking shapes in a time sequence of noisy images. The task of segmenting the image time series is expressed as an optimization problem using the spatio-temporal graph of pixels, in which we are able to impose the constraint of shape growth or of shrinkage by introducing monodirectional infinite links connecting pixels at the same spatial locations in successive image frames. The globally optimal solution is computed with a graph cut. The performance of the proposed method is validated on three applications: segmentation of melting sea ice floes and of growing burned areas from time series of 2D satellite images, and segmentation of a growing brain tumor from sequences of 3D medical scans. In the latter application, we impose an additional intersequences inclusion constraint by adding directed infinite links between pixels of dependent image structures.

The new electromagnetic tetrads, infinite tetrad nesting and the non-trivial emergence of complex numbers in real theories of gravitation

NASA Astrophysics Data System (ADS)

Garat, Alcides

How complex numbers get into play in a non-trivial way in real theories of gravitation is relevant since in a unified structure they should be able to relate in a natural way with quantum theories. For a long time this issue has been lingering on both relativistic formulations and quantum theories. We will analyze this fundamental subject under the light of new group isomorphism theorems linking local internal groups of transformations and local groups of spacetime transformations. The bridge between these two kinds of transformations is represented by new tetrads introduced previously. It is precisely through these local tetrad structures that we will provide a non-trivial answer to this old issue. These new tetrads have two fundamental building components, the skeletons and the gauge vectors. It is these constructive elements that provide the mathematical support that allows to prove group isomorphism theorems. In addition to this, we will prove a unique new property, the infinite tetrad nesting, alternating the nesting with non-Abelian tetrads in the construction of the tetrad gauge vectors. As an application we will demonstrate an alternative proof of a new group isomorphism theorem.

Infinite-order sudden approximation for collisions involving molecules in Pi electronic states: a new derivation and calculations of rotationally inelastic cross sections for NO(x superscript 2 Pi) + He and Ar

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

Corey, G.C.; Alexander, M.H.

1986-11-15

A new derivation is presented of the infinite order sudden (IOS) approximation for rotationally inelastic collisions of a diatomic molecule in a Pi electronic state with a closed shell atom. This derivation clearly demonstrates the connection between the two sudden S functions for scattering off the adiabatic potential surface of A' and A symmetry, which would arise from an ab initio calculation on an atom + Pi-state molecule system, and the S matrix elements in diabatic basis, which are required in the quantum treatment of the collision dynamics. Coupled states and IOS calculations were carried out for collisions of NImore » X 2 Pi with helium and argon, based on a electron gas potential surface at total energies of 63, 150, and 300 meV. The IOS approximation is not reliable for collisions of NO with Ar, even at the highest collision energy considered here. However, for collisions with He at 150 and 300 meV, the IOS approximation is nearly quantitative for transitions both within and between the Omega = 1/2 and Omega = 3/2 manifolds.« less

Dynamics of heterogeneous oscillator ensembles in terms of collective variables

NASA Astrophysics Data System (ADS)

Pikovsky, Arkady; Rosenblum, Michael

2011-04-01

We consider general heterogeneous ensembles of phase oscillators, sine coupled to arbitrary external fields. Starting with the infinitely large ensembles, we extend the Watanabe-Strogatz theory, valid for identical oscillators, to cover the case of an arbitrary parameter distribution. The obtained equations yield the description of the ensemble dynamics in terms of collective variables and constants of motion. As a particular case of the general setup we consider hierarchically organized ensembles, consisting of a finite number of subpopulations, whereas the number of elements in a subpopulation can be both finite or infinite. Next, we link the Watanabe-Strogatz and Ott-Antonsen theories and demonstrate that the latter one corresponds to a particular choice of constants of motion. The approach is applied to the standard Kuramoto-Sakaguchi model, to its extension for the case of nonlinear coupling, and to the description of two interacting subpopulations, exhibiting a chimera state. With these examples we illustrate that, although the asymptotic dynamics can be found within the framework of the Ott-Antonsen theory, the transients depend on the constants of motion. The most dramatic effect is the dependence of the basins of attraction of different synchronous regimes on the initial configuration of phases.

Magneto-elastic modeling of composites containing chain-structured magnetostrictive particles

NASA Astrophysics Data System (ADS)

Yin, H. M.; Sun, L. Z.; Chen, J. S.

2006-05-01

Magneto-elastic behavior is investigated for two-phase composites containing chain-structured magnetostrictive particles under both magnetic and mechanical loading. To derive the local magnetic and elastic fields, three modified Green's functions are derived and explicitly integrated for the infinite domain containing a spherical inclusion with a prescribed magnetization, body force, and eigenstrain. A representative volume element containing a chain of infinite particles is introduced to solve averaged magnetic and elastic fields in the particles and the matrix. Effective magnetostriction of composites is derived by considering the particle's magnetostriction and the magnetic interaction force. It is shown that there exists an optimal choice of the Young's modulus of the matrix and the volume fraction of the particles to achieve the maximum effective magnetostriction. A transversely isotropic effective elasticity is derived at the infinitesimal deformation. Disregarding the interaction term, this model provides the same effective elasticity as Mori-Tanaka's model. Comparisons of model results with the experimental data and other models show the efficacy of the model and suggest that the particle interactions have a considerable effect on the effective magneto-elastic properties of composites even for a low particle volume fraction.

Analytical solution for the transient wave propagation of a buried cylindrical P-wave line source in a semi-infinite elastic medium with a fluid surface layer

NASA Astrophysics Data System (ADS)

Shan, Zhendong; Ling, Daosheng

2018-02-01

This article develops an analytical solution for the transient wave propagation of a cylindrical P-wave line source in a semi-infinite elastic solid with a fluid layer. The analytical solution is presented in a simple closed form in which each term represents a transient physical wave. The Scholte equation is derived, through which the Scholte wave velocity can be determined. The Scholte wave is the wave that propagates along the interface between the fluid and solid. To develop the analytical solution, the wave fields in the fluid and solid are defined, their analytical solutions in the Laplace domain are derived using the boundary and interface conditions, and the solutions are then decomposed into series form according to the power series expansion method. Each item of the series solution has a clear physical meaning and represents a transient wave path. Finally, by applying Cagniard's method and the convolution theorem, the analytical solutions are transformed into the time domain. Numerical examples are provided to illustrate some interesting features in the fluid layer, the interface and the semi-infinite solid. When the P-wave velocity in the fluid is higher than that in the solid, two head waves in the solid, one head wave in the fluid and a Scholte wave at the interface are observed for the cylindrical P-wave line source.

On the mechanism of bandgap formation in locally resonant finite elastic metamaterials

NASA Astrophysics Data System (ADS)

Sugino, Christopher; Leadenham, Stephen; Ruzzene, Massimo; Erturk, Alper

2016-10-01

Elastic/acoustic metamaterials made from locally resonant arrays can exhibit bandgaps at wavelengths much longer than the lattice size for various applications spanning from low-frequency vibration/sound attenuation to wave guiding and filtering in mechanical and electromechanical devices. For an effective use of such locally resonant metamaterial concepts in finite structures, it is required to bridge the gap between the lattice dispersion characteristics and modal behavior of the host structure with its resonators. To this end, we develop a novel argument for bandgap formation in finite-length elastic metamaterial beams, relying on the modal analysis and the assumption of infinitely many resonators. We show that the dual problem to wave propagation through an infinite periodic beam is the modal analysis of a finite beam with an infinite number of resonators. A simple formula that depends only on the resonator natural frequency and total mass ratio is derived for placing the bandgap in a desired frequency range, yielding an analytical insight and a rule of thumb for design purposes. A method for understanding the importance of a resonator location and mass is discussed in the context of a Riemann sum approximation of an integral, and a method for determining the optimal number of resonators for a given set of boundary conditions and target frequency is introduced. The simulations of the theoretical framework are validated by experiments for bending vibrations of a locally resonant cantilever beam.

Asymptotics of the monomer-dimer model on two-dimensional semi-infinite lattices

NASA Astrophysics Data System (ADS)

Kong, Yong

2007-05-01

By using the asymptotic theory of Pemantle and Wilson [R. Pemantle and M. C. Wilson, J. Comb. Theory, Ser. AJCBTA70097-316510.1006/jcta.2001.3201 97, 129 (2002)], asymptotic expansions of the free energy of the monomer-dimer model on two-dimensional semi-infinite ∞×n lattices in terms of dimer density are obtained for small values of n , at both high- and low-dimer-density limits. In the high-dimer-density limit, the theoretical results confirm the dependence of the free energy on the parity of n , a result obtained previously by computational methods by Y. Kong [Y. Kong, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.74.061102 74, 061102 (2006); Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.73.016106 73, 016106 (2006);Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.74.011102 74, 011102 (2006)]. In the low-dimer-density limit, the free energy on a cylinder ∞×n lattice strip has exactly the same first n terms in the series expansion as that of an infinite ∞×∞ lattice.

Infinite family of three-dimensional Floquet topological paramagnets

NASA Astrophysics Data System (ADS)

Potter, Andrew C.; Vishwanath, Ashvin; Fidkowski, Lukasz

2018-06-01

We uncover an infinite family of time-reversal symmetric 3 d interacting topological insulators of bosons or spins, in time-periodically driven systems, which we term Floquet topological paramagnets (FTPMs). These FTPM phases exhibit intrinsically dynamical properties that could not occur in thermal equilibrium and are governed by an infinite set of Z2-valued topological invariants, one for each prime number. The topological invariants are physically characterized by surface magnetic domain walls that act as unidirectional quantum channels, transferring quantized packets of information during each driving period. We construct exactly solvable models realizing each of these phases, and discuss the anomalous dynamics of their topologically protected surface states. Unlike previous encountered examples of Floquet SPT phases, these 3 d FTPMs are not captured by group cohomology methods and cannot be obtained from equilibrium classifications simply by treating the discrete time translation as an ordinary symmetry. The simplest such FTPM phase can feature anomalous Z2 (toric code) surface topological order, in which the gauge electric and magnetic excitations are exchanged in each Floquet period, which cannot occur in a pure 2 d system without breaking time reversal symmetry.

Edge effect on a vacancy state in semi-infinite graphene

NASA Astrophysics Data System (ADS)

Deng, Hai-Yao; Wakabayashi, Katsunori

2014-09-01

The edge effect on a single vacancy state of semi-infinite graphene (SIG) has been studied using Green's function method within the tight-binding model. In the case of infinite graphene, it is known that a vacancy induces a zero-energy resonance state, whose wave function decays inversely with distance (R) from the vacancy and is not normalizable. However, for SIG with an armchair edge, we find that the corresponding wave function decays as R-2 and hence becomes normalizable owing to the intervalley interference caused by the armchair edge. For SIG with a zigzag edge, the vacancy state depends on the sublattice of the vacancy. When the vacancy and the edge belong to different sublattices, the vacancy has no effect on the zero-energy vacancy state. In contrast, when the vacancy is located on the same sublattice as the edge, the resonance state disappears but the wave function at zero energy is strongly distorted near the vacancy. Our results reveal that the presence of edges crucially changes the vacancy state in graphene, and thus such a state can be used to probe the edge structure.

Computational Aspects of N-Mixture Models

PubMed Central

Dennis, Emily B; Morgan, Byron JT; Ridout, Martin S

2015-01-01

The N-mixture model is widely used to estimate the abundance of a population in the presence of unknown detection probability from only a set of counts subject to spatial and temporal replication (Royle, 2004, Biometrics 60, 105–115). We explain and exploit the equivalence of N-mixture and multivariate Poisson and negative-binomial models, which provides powerful new approaches for fitting these models. We show that particularly when detection probability and the number of sampling occasions are small, infinite estimates of abundance can arise. We propose a sample covariance as a diagnostic for this event, and demonstrate its good performance in the Poisson case. Infinite estimates may be missed in practice, due to numerical optimization procedures terminating at arbitrarily large values. It is shown that the use of a bound, K, for an infinite summation in the N-mixture likelihood can result in underestimation of abundance, so that default values of K in computer packages should be avoided. Instead we propose a simple automatic way to choose K. The methods are illustrated by analysis of data on Hermann's tortoise Testudo hermanni. PMID:25314629

Infinite dilution partial molar volumes of platinum(II) 2,4-pentanedionate in supercritical carbon dioxide.

PubMed

Kong, Chang Yi; Siratori, Tomoya; Funazukuri, Toshitaka; Wang, Guosheng

2014-10-03

The effects of temperature and density on retention of platinum(II) 2,4-pentanedionate in supercritical fluid chromatography were investigated at temperatures of 308.15-343.15K and pressure range from 8 to 40MPa by the chromatographic impulse response method with curve fitting. The retention factors were utilized to derive the infinite dilution partial molar volumes of platinum(II) 2,4-pentanedionate in supercritical carbon dioxide. The determined partial molar volumes were small and positive at high pressures but exhibited very large and negative values in the highly compressible near critical region of carbon dioxide. Copyright © 2014 Elsevier B.V. All rights reserved.

A review of spectral methods

NASA Technical Reports Server (NTRS)

Lustman, L.

1984-01-01

An outline for spectral methods for partial differential equations is presented. The basic spectral algorithm is defined, collocation are emphasized and the main advantage of the method, the infinite order of accuracy in problems with smooth solutions are discussed. Examples of theoretical numerical analysis of spectral calculations are presented. An application of spectral methods to transonic flow is presented. The full potential transonic equation is among the best understood among nonlinear equations.

Electromagnetic Scattering by Multiple Cavities Embedded in the Infinite 2D Ground Plane

DTIC Science & Technology

2014-07-01

Electromagnetic Scattering by Multiple Cavities Embedded in the Infinite 2D Ground Plane Peijun Li 1 and Aihua W. Wood 2 1 Department of...of the electromagnetic wave scattering by multiple open cavities, which are embedded in an infinite two-dimensional ground plane . By introducing a...equation, variational formulation. I. INTRODUCTION A cavity is referred to as a local perturbation of the infinite ground plane . Given the cavity

On-line Model Structure Selection for Estimation of Plasma Boundary in a Tokamak

NASA Astrophysics Data System (ADS)

Škvára, Vít; Šmídl, Václav; Urban, Jakub

2015-11-01

Control of the plasma field in the tokamak requires reliable estimation of the plasma boundary. The plasma boundary is given by a complex mathematical model and the only available measurements are responses of induction coils around the plasma. For the purpose of boundary estimation the model can be reduced to simple linear regression with potentially infinitely many elements. The number of elements must be selected manually and this choice significantly influences the resulting shape. In this paper, we investigate the use of formal model structure estimation techniques for the problem. Specifically, we formulate a sparse least squares estimator using the automatic relevance principle. The resulting algorithm is a repetitive evaluation of the least squares problem which could be computed in real time. Performance of the resulting algorithm is illustrated on simulated data and evaluated with respect to a more detailed and computationally costly model FREEBIE.

Transformation of measures in infinite-dimensional spaces by the flow induced by a stochastic differential equation

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

Pilipenko, A Yu

2003-04-30

Let {mu} be a Gaussian measure in the space X and H the Cameron-Martin space of the measure {mu}. Consider the stochastic differential equation d{xi}(u,t)=a{sub t}({xi}(u,t))dt+{sigma}{sub n}{sigma}{sub t}{sup n}({xi}(u,t))d{omega}{sub n}(t), t element of [0,T]; {xi}(u,0)=u,; where u element of X, a and {sigma}{sub n} are functions taking values in H, {omega}{sub n}(t), n{>=}1 are independent one-dimensional Wiener processes. Consider the easure-valued random process {mu}{sub t}:={mu}o{xi}( {center_dot} ,t){sup -1}. It is shown that under certain natural conditions on the coefficients of the initial equation the measures {mu}{sub t}({omega}) are equivalent to {mu} for almost all {omega}. Explicit expressions for their Radon-Nikodymmore » densities are obtained.« less

Representations of S{sub {infinity}} admissible with respect to Young subgroups

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

Nessonov, Nikolai I

2012-03-31

Let N be the set of positive integers and S{sub {infinity}} the set of finite permutations of N. For a partition {Pi} of the set N into infinite parts A{sub 1},A{sub 2},... we denote by S{sub {Pi}} the subgroup of S{sub {infinity}} whose elements leave invariant each of the sets A{sub j}. We set S{sub {infinity}}{sup (N)}={l_brace}s element of S{sub {infinity}:} s(i)=i for any i=1,2,...,N{r_brace}. A factor representation T of the group S{sub {infinity}} is said to be {Pi}-admissible if for some N it contains a nontrivial identity subrepresentation of the subgroup S{sub {Pi}} intersection S{sub {infinity}}{sup (N)}. In themore » paper, we obtain a classification of the {Pi}-admissible factor representations of S{sub {infinity}}. Bibliography: 14 titles.« less

Studies of Sound Absorption by and Transmission Through Layers of Elastic Noise Control Foams: Finite Element Modeling and Effects of Anisotropy

NASA Astrophysics Data System (ADS)

Kang, Yeon June

In this thesis an elastic-absorption finite element model of isotropic elastic porous noise control materials is first presented as a means of investigating the effects of finite dimension and edge constraints on the sound absorption by, and transmission through, layers of acoustical foams. Methods for coupling foam finite elements with conventional acoustic and structural finite elements are also described. The foam finite element model based on the Biot theory allows for the simultaneous propagation of the three types of waves known to exist in an elastic porous material. Various sets of boundary conditions appropriate for modeling open, membrane-sealed and panel-bonded foam surfaces are formulated and described. Good agreement was achieved when finite element predictions were compared with previously established analytical results for the plane wave absorption coefficient and transmission loss in the case of wave propagation both in foam-filled waveguides and through foam-lined double panel structures of infinite lateral extent. The primary effect of the edge constraints of a foam layer was found to be an acoustical stiffening of the foam. Constraining the ends of the facing panels in foam-lined double panel systems was also found to increase the sound transmission loss significantly in the low frequency range. In addition, a theoretical multi-dimensional model for wave propagation in anisotropic elastic porous materials was developed to study the effect of anisotropy on the sound transmission of foam-lined noise control treatments. The predictions of the theoretical anisotropic model have been compared with experimental measurements for the random incidence sound transmission through double panel structure lined with polyimide foam. The predictions were made by using the measured and estimated macroscopic physical parameters of polyimide foam samples which were known to be anisotropic. It has been found that the macroscopic physical parameters in the direction normal to the face of foam layer play the principal role in determining the acoustical behavior of polyimide foam layers, although more satisfactory agreement between experimental measurements and theoretical predictions of transmission loss is obtained when the anisotropic properties are allowed in the model.

Combining the spin-separated exact two-component relativistic Hamiltonian with the equation-of-motion coupled-cluster method for the treatment of spin-orbit splittings of light and heavy elements.

PubMed

Cao, Zhanli; Li, Zhendong; Wang, Fan; Liu, Wenjian

2017-02-01

The spin-separated exact two-component (X2C) relativistic Hamiltonian [sf-X2C+so-DKHn, J. Chem. Phys., 2012, 137, 154114] is combined with the equation-of-motion coupled-cluster method with singles and doubles (EOM-CCSD) for the treatment of spin-orbit splittings of open-shell molecular systems. Scalar relativistic effects are treated to infinite order from the outset via the spin-free part of the X2C Hamiltonian (sf-X2C), whereas the spin-orbit couplings (SOC) are handled at the CC level via the first-order Douglas-Kroll-Hess (DKH) type of spin-orbit operator (so-DKH1). Since the exponential of single excitations, i.e., exp(T 1 ), introduces sufficient spin orbital relaxations, the inclusion of SOC at the CC level is essentially the same in accuracy as the inclusion of SOC from the outset in terms of the two-component spinors determined variationally by the sf-X2C+so-DKH1 Hamiltonian, but is computationally more efficient. Therefore, such an approach (denoted as sf-X2C-EOM-CCSD(SOC)) can achieve uniform accuracy for the spin-orbit splittings of both light and heavy elements. For light elements, the treatment of SOC can even be postponed until the EOM step (denoted as sf-X2C-EOM(SOC)-CCSD), so as to further reduce the computational cost. To reveal the efficacy of sf-X2C-EOM-CCSD(SOC) and sf-X2C-EOM(SOC)-CCSD, the spin-orbit splittings of the 2 Π states of monohydrides up to the sixth row of the periodic table are investigated. The results show that sf-X2C-EOM-CCSD(SOC) predicts very accurate results (within 5%) for elements up to the fifth row, whereas sf-X2C-EOM(SOC)-CCSD is useful only for light elements (up to the third row but with some exceptions). For comparison, the sf-X2C-S-TD-DFT-SOC approach [spin-adapted open-shell time-dependent density functional theory, Mol. Phys., 2013, 111, 3741] is applied to the same systems. The overall accuracy (1-10%) is satisfactory.

Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping

NASA Astrophysics Data System (ADS)

Lu, Jianfeng; Zhou, Zhennan

2018-02-01

To accelerate the thermal equilibrium sampling of multi-level quantum systems, the infinite swapping limit of a recently proposed multi-level ring polymer representation is investigated. In the infinite swapping limit, the ring polymer evolves according to an averaged Hamiltonian with respect to all possible surface index configurations of the ring polymer and thus connects the surface hopping approach to the mean-field path-integral molecular dynamics. A multiscale integrator for the infinite swapping limit is also proposed to enable efficient sampling based on the limiting dynamics. Numerical results demonstrate the huge improvement of sampling efficiency of the infinite swapping compared with the direct simulation of path-integral molecular dynamics with surface hopping.

The infinite limit as an eliminable approximation for phase transitions

NASA Astrophysics Data System (ADS)

Ardourel, Vincent

2018-05-01

It is generally claimed that infinite idealizations are required for explaining phase transitions within statistical mechanics (e.g. Batterman 2011). Nevertheless, Menon and Callender (2013) have outlined theoretical approaches that describe phase transitions without using the infinite limit. This paper closely investigates one of these approaches, which consists of studying the complex zeros of the partition function (Borrmann et al., 2000). Based on this theory, I argue for the plausibility for eliminating the infinite limit for studying phase transitions. I offer a new account for phase transitions in finite systems, and I argue for the use of the infinite limit as an approximation for studying phase transitions in large systems.

Hybrid Numerical-Analytical Scheme for Calculating Elastic Wave Diffraction in Locally Inhomogeneous Waveguides

NASA Astrophysics Data System (ADS)

Glushkov, E. V.; Glushkova, N. V.; Evdokimov, A. A.

2018-01-01

Numerical simulation of traveling wave excitation, propagation, and diffraction in structures with local inhomogeneities (obstacles) is computationally expensive due to the need for mesh-based approximation of extended domains with the rigorous account for the radiation conditions at infinity. Therefore, hybrid numerical-analytic approaches are being developed based on the conjugation of a numerical solution in a local vicinity of the obstacle and/or source with an explicit analytic representation in the remaining semi-infinite external domain. However, in standard finite-element software, such a coupling with the external field, moreover, in the case of multimode expansion, is generally not provided. This work proposes a hybrid computational scheme that allows realization of such a conjugation using a standard software. The latter is used to construct a set of numerical solutions used as the basis for the sought solution in the local internal domain. The unknown expansion coefficients on this basis and on normal modes in the semi-infinite external domain are then determined from the conditions of displacement and stress continuity at the boundary between the two domains. We describe the implementation of this approach in the scalar and vector cases. To evaluate the reliability of the results and the efficiency of the algorithm, we compare it with a semianalytic solution to the problem of traveling wave diffraction by a horizontal obstacle, as well as with a finite-element solution obtained for a limited domain artificially restricted using absorbing boundaries. As an example, we consider the incidence of a fundamental antisymmetric Lamb wave onto surface and partially submerged elastic obstacles. It is noted that the proposed hybrid scheme can also be used to determine the eigenfrequencies and eigenforms of resonance scattering, as well as the characteristics of traveling waves in embedded waveguides.

Non-pairwise additivity of the leading-order dispersion energy

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

Hollett, Joshua W., E-mail: j.hollett@uwinnipeg.ca

2015-02-28

The leading-order (i.e., dipole-dipole) dispersion energy is calculated for one-dimensional (1D) and two-dimensional (2D) infinite lattices, and an infinite 1D array of infinitely long lines, of doubly occupied locally harmonic wells. The dispersion energy is decomposed into pairwise and non-pairwise additive components. By varying the force constant and separation of the wells, the non-pairwise additive contribution to the dispersion energy is shown to depend on the overlap of density between neighboring wells. As well separation is increased, the non-pairwise additivity of the dispersion energy decays. The different rates of decay for 1D and 2D lattices of wells is explained inmore » terms of a Jacobian effect that influences the number of nearest neighbors. For an array of infinitely long lines of wells spaced 5 bohrs apart, and an inter-well spacing of 3 bohrs within a line, the non-pairwise additive component of the leading-order dispersion energy is −0.11 kJ mol{sup −1} well{sup −1}, which is 7% of the total. The polarizability of the wells and the density overlap between them are small in comparison to that of the atomic densities that arise from the molecular density partitioning used in post-density-functional theory (DFT) damped dispersion corrections, or DFT-D methods. Therefore, the nonadditivity of the leading-order dispersion observed here is a conservative estimate of that in molecular clusters.« less

Full-Potential Modeling of Blade-Vortex Interactions. Degree awarded by George Washington Univ., Feb. 1987

NASA Technical Reports Server (NTRS)

Jones, Henry E.

1997-01-01

A study of the full-potential modeling of a blade-vortex interaction was made. A primary goal of this study was to investigate the effectiveness of the various methods of modeling the vortex. The model problem restricts the interaction to that of an infinite wing with an infinite line vortex moving parallel to its leading edge. This problem provides a convenient testing ground for the various methods of modeling the vortex while retaining the essential physics of the full three-dimensional interaction. A full-potential algorithm specifically tailored to solve the blade-vortex interaction (BVI) was developed to solve this problem. The basic algorithm was modified to include the effect of a vortex passing near the airfoil. Four different methods of modeling the vortex were used: (1) the angle-of-attack method, (2) the lifting-surface method, (3) the branch-cut method, and (4) the split-potential method. A side-by-side comparison of the four models was conducted. These comparisons included comparing generated velocity fields, a subcritical interaction, and a critical interaction. The subcritical and critical interactions are compared with experimentally generated results. The split-potential model was used to make a survey of some of the more critical parameters which affect the BVI.

Numerical computation of gravitational field for general axisymmetric objects

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2016-10-01

We developed a numerical method to compute the gravitational field of a general axisymmetric object. The method (I) numerically evaluates a double integral of the ring potential by the split quadrature method using the double exponential rules, and (II) derives the acceleration vector by numerically differentiating the numerically integrated potential by Ridder's algorithm. Numerical comparison with the analytical solutions for a finite uniform spheroid and an infinitely extended object of the Miyamoto-Nagai density distribution confirmed the 13- and 11-digit accuracy of the potential and the acceleration vector computed by the method, respectively. By using the method, we present the gravitational potential contour map and/or the rotation curve of various axisymmetric objects: (I) finite uniform objects covering rhombic spindles and circular toroids, (II) infinitely extended spheroids including Sérsic and Navarro-Frenk-White spheroids, and (III) other axisymmetric objects such as an X/peanut-shaped object like NGC 128, a power-law disc with a central hole like the protoplanetary disc of TW Hya, and a tear-drop-shaped toroid like an axisymmetric equilibrium solution of plasma charge distribution in an International Thermonuclear Experimental Reactor-like tokamak. The method is directly applicable to the electrostatic field and will be easily extended for the magnetostatic field. The FORTRAN 90 programs of the new method and some test results are electronically available.

Vector image method for the derivation of elastostatic solutions for point sources in a plane layered medium. Part 1: Derivation and simple examples

NASA Technical Reports Server (NTRS)

Fares, Nabil; Li, Victor C.

1986-01-01

An image method algorithm is presented for the derivation of elastostatic solutions for point sources in bonded halfspaces assuming the infinite space point source is known. Specific cases were worked out and shown to coincide with well known solutions in the literature.

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.

Electrodynamics, Differential Forms and the Method of Images

ERIC Educational Resources Information Center

Low, Robert J.

2011-01-01

This paper gives a brief description of how Maxwell's equations are expressed in the language of differential forms and use this to provide an elegant demonstration of how the method of images (well known in electrostatics) also works for electrodynamics in the presence of an infinite plane conducting boundary. The paper should be accessible to an…

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.

[A way of helping "Mr. Minotaur" and "Ms. Ariadne" to exit from the multiple morbidity labyrinth: the "master problems"].

PubMed

Turabián, J L; Pérez Franco, B

2016-01-01

Multiple morbidity seems to be "infinite" and so is not easy to make useful decisions. A new concept is introduced: the "master problems", as a qualitative method to facilitate the exit from this maze of multiple morbidity. Metaphors from the art world have been used to teach this concept. These "master problems" generally remain hidden and can only "unravel" between the interstices of multiple morbidity, when the details of the system that defines the problem are explained. A problem with "energy" or a "master problem" is complex, multiple and dramatic or theatrical--everything in the clinical history history make us look into that particular question. It is what gives us a blow to the stomach, which causes our hearts to beat faster, that moves us on many levels, which has a high "density of emotions", human elements, social symbols, and opens solutions in a patient. Copyright © 2015 Sociedad Española de Médicos de Atención Primaria (SEMERGEN). Publicado por Elsevier España, S.L.U. All rights reserved.

Analytic and numeric Green's functions for a two-dimensional electron gas in an orthogonal magnetic field

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

Cresti, Alessandro; Grosso, Giuseppe; Parravicini, Giuseppe Pastori

2006-05-15

We have derived closed analytic expressions for the Green's function of an electron in a two-dimensional electron gas threaded by a uniform perpendicular magnetic field, also in the presence of a uniform electric field and of a parabolic spatial confinement. A workable and powerful numerical procedure for the calculation of the Green's functions for a large infinitely extended quantum wire is considered exploiting a lattice model for the wire, the tight-binding representation for the corresponding matrix Green's function, and the Peierls phase factor in the Hamiltonian hopping matrix element to account for the magnetic field. The numerical evaluation of themore » Green's function has been performed by means of the decimation-renormalization method, and quite satisfactorily compared with the analytic results worked out in this paper. As an example of the versatility of the numerical and analytic tools here presented, the peculiar semilocal character of the magnetic Green's function is studied in detail because of its basic importance in determining magneto-transport properties in mesoscopic systems.« less

Optimization of a superconducting linear levitation system using a soft ferromagnet

NASA Astrophysics Data System (ADS)

Agramunt-Puig, Sebastia; Del-Valle, Nuria; Navau, Carles; Sanchez, Alvaro

2013-04-01

The use of guideways that combine permanent magnets and soft ferromagnetic materials is a common practice in magnetic levitation transport systems (maglevs) with bulk high-temperature superconductors. Theoretical tools to simulate in a realistic way both the behavior of all elements (permanent magnets, soft ferromagnet and superconductor) and their mutual effects are helpful to optimize the designs of real systems. Here we present a systematic study of the levitation of a maglev with translational symmetry consisting of a superconducting bar and a guideway with two identic permanent magnets and a soft ferromagnetic material between them. The system is simulated with a numerical model based on the energy minimization method that allows to analyze the mutual interaction of the superconductor, assumed to be in the critical state, and a soft ferromagnet with infinite susceptibility. Results indicate that introducing a soft ferromagnet within the permanent magnets not only increases the levitation force but also improves the stability. Besides, an estimation of the relative sizes and shapes of the soft ferromagnet, permanent magnets and the superconductor in order to obtain large levitation force with full stability is provided.

Numerical simulation on the seismic absorption effect of the cushion in rigid-pile composite foundation

NASA Astrophysics Data System (ADS)

Han, Xiaolei; Li, Yaokun; Ji, Jing; Ying, Junhao; Li, Weichen; Dai, Baicheng

2016-06-01

In order to quantitatively study the seismic absorption effect of the cushion on a superstructure, a numerical simulation and parametric study are carried out on the overall FEA model of a rigid-pile composite foundation in ABAQUS. A simulation of a shaking table test on a rigid mass block is first completed with ABAQUS and EERA, and the effectiveness of the Drucker-Prager constitutive model and the finite-infinite element coupling method is proved. Dynamic time-history analysis of the overall model under frequent and rare earthquakes is carried out using seismic waves from the El Centro, Kobe, and Bonds earthquakes. The different responses of rigid-pile composite foundations and pile-raft foundations are discussed. Furthermore, the influence of thickness and modulus of cushion, and ground acceleration on the seismic absorption effect of the cushion are analyzed. The results show that: 1) the seismic absorption effect of a cushion is good under rare earthquakes, with an absorption ratio of about 0.85; and 2) the seismic absorption effect is strongly affected by cushion thickness and ground acceleration.

Structure and Electrical Conductivity of AgTaS 3

NASA Astrophysics Data System (ADS)

Kim, Changkeun; Yun, Hoseop; Lee, Youngju; Shin, Heekyoon; Liou, Kwangkyoung

1997-09-01

Single crystals of the compound AgTaS 3have been prepared through reactions of the elements with halide mixtures. The structure of AgTaS 3has been analyzed by single-crystal X-ray diffraction methods. AgTaS 3crystallizes in the space group D172h- Cmcmof the orthorhombic system with four formula units in a cell of dimensions a=3.378(2), b=14.070(5), c=7.756(3) Å. The structure of AgTaS 3consists of two-dimensional 2∞[TaS -3] layers separated by Ag +cations. The layer is composed of Ta-centered bicapped trigonal prisms stacked on top of each other by sharing triangular faces. These chains are linked to form the infinite two-dimensional 2∞[TaS -3] slabs. These layers are held together through van der Waals interactions, and Ag +ions reside in the distorted octahedral sites between the layers. The temperature dependence of the electrical conductivity along the needle axis of AgTaS 3shows the typical behavior of an extrinsic semiconductor.

Quantum transverse-field Ising model on an infinite tree from matrix product states

NASA Astrophysics Data System (ADS)

Nagaj, Daniel; Farhi, Edward; Goldstone, Jeffrey; Shor, Peter; Sylvester, Igor

2008-06-01

We give a generalization to an infinite tree geometry of Vidal’s infinite time-evolving block decimation (iTEBD) algorithm [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)] for simulating an infinite line of quantum spins. We numerically investigate the quantum Ising model in a transverse field on the Bethe lattice using the matrix product state ansatz. We observe a second order phase transition, with certain key differences from the transverse field Ising model on an infinite spin chain. We also investigate a transverse field Ising model with a specific longitudinal field. When the transverse field is turned off, this model has a highly degenerate ground state as opposed to the pure Ising model whose ground state is only doubly degenerate.

Infinity: The Twilight Zone of Mathematics.

ERIC Educational Resources Information Center

Love, William P.

1989-01-01

The theorems and proofs presented are designed to enhance student understanding of the theory of infinity as developed by Cantor and others. Three transfinite numbers are defined to express the cardinality of infinite algebraic sets, infinite sets of geometric points and infinite sets of functions. (DC)

A simple model for closure temperature of a trace element in cooling bi-mineralic systems

NASA Astrophysics Data System (ADS)

Liang, Yan

2015-09-01

Closure temperature is defined as the lower temperature limit at which the element of interest effectively ceases diffusive exchange with its surrounding medium during cooling. Here we generalize the classic equation of Dodson (1973) for cooling mono-mineralic systems to cooling bi-mineralic aggregates by considering diffusive exchange of a trace element between the two minerals in a closed system. We present a simple analytical model that includes key parameters affecting the closure temperature of a trace element in cooling bi-mineralic systems: cooling rate, temperature-dependent diffusion coefficients for the trace element in the two minerals, temperature-dependent partition coefficient of the trace element between the two minerals, effective grain sizes of the two minerals, and volume proportions of the minerals in the system. We show that closure temperatures of a trace element in cooling bi-mineralic systems are bounded by the closure temperatures of the trace element in the two mono-mineralic systems and that our generalized model reduces to Dodson's equation when one of the mineral serves as "an effective infinite" reservoir to the other mineral. Application to closure temperatures of REE in orthopyroxene and clinopyroxene bi-mineralic systems highlights the importance of REE diffusion and partitioning in the pyroxenes as well as clinopyroxene modal abundance and grain size in the systems. Closure temperatures for REE in two-pyroxene bearing equigranular rocks are controlled primarily by diffusion in orthopyroxene unless the modal abundance of clinopyroxene is very small. This has important bearings on the interpretation of temperatures derived from the REE-in-two-pyroxene thermometer.

Simulation of Conformal Spiral Slot Antennas on Composite Platforms

NASA Technical Reports Server (NTRS)

Volakis, J. L.; Nurnberger, M. W.; Ozdemir,T.

1998-01-01

During the course of the grant, we wrote and distributed about 12 reports and an equal number of journal papers supported fully or in part by this grant. The list of reports (title & abstract) and papers are given in Appendices A and B. This grant has indeed been instrumental in developing a robust hybrid finite element method for the analysis of complex broadband antennas on doubly curved platforms. Previous to the grant, our capability was limited to simple printed patch antennas on mostly planar platforms. More specifically: (1) mixed element formulations were developed and new edge-based prisms were introduced; (2) these elements were important in permitting flexibility in geometry gridding for most antennas of interest; (3) new perfectly matched absorbers were introduced for mesh truncations associated with highly curved surfaces; (4) fast integral algorithms were introduced for boundary integral truncations reducing CPU time from O(N-2) down to O(N-1.5) or less; (5) frequency extrapolation schemes were developed for efficient broadband performance evaluations. This activity has been successfully continued by NASA researchers; (6) computer codes were developed and extensively tested for several broadband configurations. These include FEMA-CYL, FEMA-PRISM and FEMA-TETRA written by L. Kempel, T. Ozdemir and J. Gong, respectively; (7) a new infinite balun feed was designed nearly constant impedance over the 800-3000 MHz operational band; (8) a complete slot spiral antenna was developed, fabricated and tested at NASA Langley. This new design is a culmination of the projects goals and integrates the computational and experimental efforts. this antenna design resulted in a U.S. patent and was revised three times to achieve the desired bandwidth and gain requirements from 800-3000 MHz.

Two dimensional J-matrix approach to quantum scattering

NASA Astrophysics Data System (ADS)

Olumegbon, Ismail Adewale

We present an extension of the J-matrix method of scattering to two dimensions in cylindrical coordinates. In the J-matrix approach we select a zeroth order Hamiltonian, H0, which is exactly solvable in the sense that we select a square integrable basis set that enable us to have an infinite tridiagonal representation for H0. Expanding the wavefunction in this basis makes the wave equation equivalent to a three-term recursion relation for the expansion coefficients. Consequently, finding solutions of the recursion relation is equivalent to solving the original H0 problem (i.e., determining the expansion coefficients of the system's wavefunction). The part of the original potential interaction which cannot be brought to an exact tridiagonal form is cut in an NxN basis space and its matrix elements are computed numerically using Gauss quadrature approach. Hence, this approach embodies powerful tools in the analysis of solutions of the wave equation by exploiting the intimate connection and interplay between tridiagonal matrices and the theory of orthogonal polynomials. In such analysis, one is at liberty to employ a wide range of well established methods and numerical techniques associated with these settings such as quadrature approximation and continued fractions. To demonstrate the utility, usefulness, and accuracy of the extended method we use it to obtain the bound states for an illustrative short range potential problem.

Two dimensional J-matrix approach to quantum scattering

NASA Astrophysics Data System (ADS)

Olumegbon, Ismail Adewale

2013-01-01

We present an extension of the J-matrix method of scattering to two dimensions in cylindrical coordinates. In the J-matrix approach we select a zeroth order Hamiltonian, H0, which is exactly solvable in the sense that we select a square integrable basis set that enable us to have an infinite tridiagonal representation for H0. Expanding the wavefunction in this basis makes the wave equation equivalent to a three-term recursion relation for the expansion coefficients. Consequently, finding solutions of the recursion relation is equivalent to solving the original H0 problem (i.e., determining the expansion coefficients of the system's wavefunction). The part of the original potential interaction which cannot be brought to an exact tridiagonal form is cut in an NxN basis space and its matrix elements are computed numerically using Gauss quadrature approach. Hence, this approach embodies powerful tools in the analysis of solutions of the wave equation by exploiting the intimate connection and interplay between tridiagonal matrices and the theory of orthogonal polynomials. In such analysis, one is at liberty to employ a wide range of well established methods and numerical techniques associated with these settings such as quadrature approximation and continued fractions. To demonstrate the utility, usefulness, and accuracy of the extended method we use it to obtain the bound states for an illustrative short range potential problem.

Improving the Instruction of Infinite Series

ERIC Educational Resources Information Center

Lindaman, Brian; Gay, A. Susan

2012-01-01

Calculus instructors struggle to teach infinite series, and students have difficulty understanding series and related concepts. Four instructional strategies, prominently used during the calculus reform movement, were implemented during a 3-week unit on infinite series in one class of second-semester calculus students. A description of each…

Quantizing and sampling considerations in digital phased-locked loops

NASA Technical Reports Server (NTRS)

Hurst, G. T.; Gupta, S. C.

1974-01-01

The quantizer problem is first considered. The conditions under which the uniform white sequence model for the quantizer error is valid are established independent of the sampling rate. An equivalent spectral density is defined for the quantizer error resulting in an effective SNR value. This effective SNR may be used to determine quantized performance from infinitely fine quantized results. Attention is given to sampling rate considerations. Sampling rate characteristics of the digital phase-locked loop (DPLL) structure are investigated for the infinitely fine quantized system. The predicted phase error variance equation is examined as a function of the sampling rate. Simulation results are presented and a method is described which enables the minimum required sampling rate to be determined from the predicted phase error variance equations.

Ablative Rayleigh Taylor instability in the limit of an infinitely large density ratio

NASA Astrophysics Data System (ADS)

Clavin, Paul; Almarcha, Christophe

2005-05-01

The instability of ablation fronts strongly accelerated toward the dense medium under the conditions of inertial confinement fusion (ICF) is addressed in the limit of an infinitely large density ratio. The analysis serves to demonstrate that the flow is irrotational to first order, reducing the nonlinear analysis to solve a two-potential flows problem. Vorticity appears at the following orders in the perturbation analysis. This result simplifies greatly the analysis. The possibility for using boundary integral methods opens new perspectives in the nonlinear theory of the ablative RT instability in ICF. A few examples are given at the end of the Note. To cite this article: P. Clavin, C. Almarcha, C. R. Mecanique 333 (2005).

Exact solution for the Poisson field in a semi-infinite strip.

PubMed

Cohen, Yossi; Rothman, Daniel H

2017-04-01

The Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve the field in other intricate geometries. We show that the Poisson flux reveals an inverse square-root singularity at a tip of a slit, and identify a characteristic length scale in which a small perturbation, in a form of a new slit, is screened by the field. We suggest that this length scale expresses itself as a characteristic spacing between tips in real Poisson networks that grow in response to fluxes at tips.

Infinite Conservation Laws, Continuous Symmetries and Invariant Solutions of Some Discrete Integrable Equations

NASA Astrophysics Data System (ADS)

Zhang, Yu-Feng; Zhang, Xiang-Zhi; Dong, Huan-He

2017-12-01

Two new shift operators are introduced for which a few differential-difference equations are generated by applying the R-matrix method. These equations can be reduced to the standard Toda lattice equation and (1+1)-dimensional and (2+1)-dimensional Toda-type equations which have important applications in hydrodynamics, plasma physics, and so on. Based on these consequences, we deduce the Hamiltonian structures of two discrete systems. Finally, we obtain some new infinite conservation laws of two discrete equations and employ Lie-point transformation group to obtain some continuous symmetries and part of invariant solutions for the (1+1) and (2+1)-dimensional Toda-type equations. Supported by the Fundamental Research Funds for the Central University under Grant No. 2017XKZD11

Analytic theory of photoacoustic wave generation from a spheroidal droplet.

PubMed

Li, Yong; Fang, Hui; Min, Changjun; Yuan, Xiaocong

2014-08-25

In this paper, we develop an analytic theory for describing the photoacoustic wave generation from a spheroidal droplet and derive the first complete analytic solution. Our derivation is based on solving the photoacoustic Helmholtz equation in spheroidal coordinates with the separation-of-variables method. As the verification, besides carrying out the asymptotic analyses which recover the standard solutions for a sphere, an infinite cylinder and an infinite layer, we also confirm that the partial transmission and reflection model previously demonstrated for these three geometries still stands. We expect that this analytic solution will find broad practical uses in interpreting experiment results, considering that its building blocks, the spheroidal wave functions (SWFs), can be numerically calculated by the existing computer programs.

The Green's functions for peridynamic non-local diffusion.

PubMed

Wang, L J; Xu, J F; Wang, J X

2016-09-01

In this work, we develop the Green's function method for the solution of the peridynamic non-local diffusion model in which the spatial gradient of the generalized potential in the classical theory is replaced by an integral of a generalized response function in a horizon. We first show that the general solutions of the peridynamic non-local diffusion model can be expressed as functionals of the corresponding Green's functions for point sources, along with volume constraints for non-local diffusion. Then, we obtain the Green's functions by the Fourier transform method for unsteady and steady diffusions in infinite domains. We also demonstrate that the peridynamic non-local solutions converge to the classical differential solutions when the non-local length approaches zero. Finally, the peridynamic analytical solutions are applied to an infinite plate heated by a Gauss source, and the predicted variations of temperature are compared with the classical local solutions. The peridynamic non-local diffusion model predicts a lower rate of variation of the field quantities than that of the classical theory, which is consistent with experimental observations. The developed method is applicable to general diffusion-type problems.

Examining the accuracy of the infinite order sudden approximation using sensitivity analysis

NASA Astrophysics Data System (ADS)

Eno, Larry; Rabitz, Herschel

1981-08-01

A method is developed for assessing the accuracy of scattering observables calculated within the framework of the infinite order sudden (IOS) approximation. In particular, we focus on the energy sudden assumption of the IOS method and our approach involves the determination of the sensitivity of the IOS scattering matrix SIOS with respect to a parameter which reintroduces the internal energy operator ?0 into the IOS Hamiltonian. This procedure is an example of sensitivity analysis of missing model components (?0 in this case) in the reference Hamiltonian. In contrast to simple first-order perturbation theory a finite result is obtained for the effect of ?0 on SIOS. As an illustration, our method of analysis is applied to integral state-to-state cross sections for the scattering of an atom and rigid rotor. Results are generated within the He+H2 system and a comparison is made between IOS and coupled states cross sections and the corresponding IOS sensitivities. It is found that the sensitivity coefficients are very useful indicators of the accuracy of the IOS results. Finally, further developments and applications are discussed.

Optical binding with cold atoms

NASA Astrophysics Data System (ADS)

Máximo, C. E.; Bachelard, R.; Kaiser, R.

2018-04-01

Optical binding is a form of light-mediated forces between elements of matter which emerge in response to the collective scattering of light. Such a phenomenon has been studied mainly in the context of the equilibrium stability of dielectric sphere arrays which move amid dissipative media. In this article, we demonstrate that optically bounded states of a pair of cold atoms can exist, in the absence of nonradiative damping. We study the scaling laws for the unstable-stable phase transition at negative detuning and the unstable-metastable one for positive detuning. In addition, we show that angular momentum can lead to dynamical stabilization with infinite-range scaling.

Evaluation of Magnetoresistive RAM for Space Applications

NASA Technical Reports Server (NTRS)

Heidecker, Jason

2014-01-01

Magnetoresistive random-access memory (MRAM) is a non-volatile memory that exploits electronic spin, rather than charge, to store data. Instead of moving charge on and off a floating gate to alter the threshold voltage of a CMOS transistor (creating different bit states), MRAM uses magnetic fields to flip the polarization of a ferromagnetic material thus switching its resistance and bit state. These polarized states are immune to radiation-induced upset, thus making MRAM very attractive for space application. These magnetic memory elements also have infinite data retention and erase/program endurance. Presented here are results of reliability testing of two space-qualified MRAM products from Aeroflex and Honeywell.

Numerical solution of acoustic scattering by finite perforated elastic plates

PubMed Central

2016-01-01

We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k0 based on the plate length. However, at low k0, finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k0. The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k0 for perforated elastic plates. PMID:27274685

Numerical solution of acoustic scattering by finite perforated elastic plates.

PubMed

Cavalieri, A V G; Wolf, W R; Jaworski, J W

2016-04-01

We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k 0 based on the plate length. However, at low k 0 , finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k 0 . The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k 0 for perforated elastic plates.

Eigenenergies of a Relativistic Particle in an Infinite Range Linear Potential Using WKB Method

ERIC Educational Resources Information Center

Shivalingaswamy, T.; Kagali, B. A.

2011-01-01

Energy eigenvalues for a non-relativistic particle in a linear potential well are available. In this paper we obtain the eigenenergies for a relativistic spin less particle in a similar potential using an extension of the well-known WKB method treating the potential as the time component of a four-vector potential. Since genuine bound states do…

A Simple Geometric Method of Estimating the Error in Using Vieta's Product for [pi

ERIC Educational Resources Information Center

Osler, T. J.

2007-01-01

Vieta's famous product using factors that are nested radicals is the oldest infinite product as well as the first non-iterative method for finding [pi]. In this paper a simple geometric construction intimately related to this product is described. The construction provides the same approximations to [pi] as are given by partial products from…

Envisioning the Infinite by Projecting Finite Properties

ERIC Educational Resources Information Center

Ely, Robert

2011-01-01

We analyze interviews with 24 post-secondary students as they reason about infinite processes in the context of the tricky Tennis Ball Problem. By metaphorically projecting various properties from the finite states such as counting and indexing, participants envisioned widely varying final states for the infinite process. Depending on which…

Understanding the Behaviour of Infinite Ladder Circuits

ERIC Educational Resources Information Center

Ucak, C.; Yegin, K.

2008-01-01

Infinite ladder circuits are often encountered in undergraduate electrical engineering and physics curricula when dealing with series and parallel combination of impedances, as a part of filter design or wave propagation on transmission lines. The input impedance of such infinite ladder circuits is derived by assuming that the input impedance does…

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.

Determination of thermodynamic properties of isotactic poly(1-butene) at infinite dilution using density and inverse gas chromatography.

PubMed

Kozłowska, Marta Karolina; Domańska, Urszula; Lempert, Małgorzata; Rogalski, Marek

2005-03-18

The partial molar volumes, V1(M), and the molar volume of isotactic crystalline low-molecular-weight poly(1-butene), iPBu-1, V1, have been calculated from the measured density of {iPBu-1 + solvent (n-hexane, n-heptane, n-nonane, n-decane, p-xylene, cyclohexane and chloroform)} systems. Some of the thermodynamic quantities were also obtained for the iPBu-1 with eight hydrocarbons (n-octane, n-decane, n-undecane, n-dodecane, n-tridecane, o-xylene, m-xylene, p-xylene) by the method of inverse gas chromatography at various temperatures. The weight fraction activity coefficients of the solvent at infinite dilution, omega2(infinity) and the Flory-Huggins thermodynamic interaction parameters, chi21(infinity), between polymer and solvents were determined. The partial molar free energy, deltaG2(infinity), the partial molar heat of mixing, deltaH2(infinity), at infinite dilution and the polymer solubility parameter, delta1, were calculated. Additionally, the (solid + liquid) binary mixtures equilibria, SLE, of iPBu-1 with three hydrocarbons (n-octane, n-decane and m-xylene) were studied by a dynamic method. By performing these experiments over a large concentration range, the T-x phase diagrams of the polymer-solvent systems were constructed. The excess Gibbs energy models were used to describe the nonideal behaviour of the liquid phase. The omega2(infinity) were determined from the solubility measurements and were predicted by using the UNIFAC FV model.

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination

PubMed Central

Duarte, Belmiro P.M.; Wong, Weng Kee; Atkinson, Anthony C.

2016-01-01

T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization. PMID:27330230

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination.

PubMed

Duarte, Belmiro P M; Wong, Weng Kee; Atkinson, Anthony C

2015-03-01

T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization.

General image method in a plane-layered elastostatic medium

NASA Technical Reports Server (NTRS)

Fares, N.; Li, V. C.

1988-01-01

The general-image method presently used to obtain the elastostatic fields in plane-layered media relies on the use of potentials in order to represent elastic fields. For the case of a single interface, this method yields the displacement field in closed form, and is applicable to antiplane, plane, and three-dimensional problems. In the case of multiplane interfaces, the image method generates the displacement fields in terms of infinite series whose convergences can be accelerated to improve method efficiency.

Analysis of superconducting electromagnetic finite elements based on a magnetic vector potential variational principle

NASA Technical Reports Server (NTRS)

Schuler, James J.; Felippa, Carlos A.

1991-01-01

Electromagnetic finite elements are extended based on a variational principle that uses the electromagnetic four potential as primary variable. The variational principle is extended to include the ability to predict a nonlinear current distribution within a conductor. The extension of this theory is first done on a normal conductor and tested on two different problems. In both problems, the geometry remains the same, but the material properties are different. The geometry is that of a 1-D infinite wire. The first problem is merely a linear control case used to validate the new theory. The second problem is made up of linear conductors with varying conductivities. Both problems perform well and predict current densities that are accurate to within a few ten thousandths of a percent of the exact values. The fourth potential is then removed, leaving only the magnetic vector potential, and the variational principle is further extended to predict magnetic potentials, magnetic fields, the number of charge carriers, and the current densities within a superconductor. The new element produces good results for the mean magnetic field, the vector potential, and the number of superconducting charge carriers despite a relatively high system condition number. The element did not perform well in predicting the current density. Numerical problems inherent to this formulation are explored and possible remedies to produce better current predicting finite elements are presented.

Efficient modeling of interconnects and capacitive discontinuities in high-speed digital circuits. Thesis

NASA Technical Reports Server (NTRS)

Oh, K. S.; Schutt-Aine, J.

1995-01-01

Modeling of interconnects and associated discontinuities with the recent advances high-speed digital circuits has gained a considerable interest over the last decade although the theoretical bases for analyzing these structures were well-established as early as the 1960s. Ongoing research at the present time is focused on devising methods which can be applied to more general geometries than the ones considered in earlier days and, at the same time, improving the computational efficiency and accuracy of these methods. In this thesis, numerically efficient methods to compute the transmission line parameters of a multiconductor system and the equivalent capacitances of various strip discontinuities are presented based on the quasi-static approximation. The presented techniques are applicable to conductors embedded in an arbitrary number of dielectric layers with two possible locations of ground planes at the top and bottom of the dielectric layers. The cross-sections of conductors can be arbitrary as long as they can be described with polygons. An integral equation approach in conjunction with the collocation method is used in the presented methods. A closed-form Green's function is derived based on weighted real images thus avoiding nested infinite summations in the exact Green's function; therefore, this closed-form Green's function is numerically more efficient than the exact Green's function. All elements associated with the moment matrix are computed using the closed-form formulas. Various numerical examples are considered to verify the presented methods, and a comparison of the computed results with other published results showed good agreement.

Fundamental studies in isotope chemistry. Progress report, 1 August 1982-1 August 1983

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

Bigeleisen, J.

1983-01-01

Interest in a search for superheavy elements present in nature as a remnant of the big bang or through continuous production by cosmic rays has prompted us to study the isotope chemistry of superheavy elements. Calculations of the fractionation factors of superheavy elements of masses 10, 100, 1000, and in the form of isotopes of hydrogen, carbon, selenium and uranium against the light naturally occurring isotope of the element show that the superheavy isotope, even of infinite mass, will not be sufficiently fractionated in single stage natural processes to obscure its chemistry. Calculations have been made of the elementary separationmore » factors of superheavy isotopes of carbon and oxygen by fractional distillation of CO at 80/sup 0/K. The fractionation factors are discussed in terms of a model for liquid CO in good agreement with experimental data on /sup 13/C/sup 16/O and /sup 12/C/sup 18/O. Calculations for very heavy isotopic forms of CO reveal for the first time the coupling effect between translation and internal vibration in the liquid. It is shown that a 1ow temperature distillation plant, such as the Los Alamos COLA plant, has a significant potential for enrichment of superheavy isotopes of carbon. The maximum enrichment factor is 10/sup 55/.« less

Source Methodology for Turbofan Noise Prediction (SOURCE3D Technical Documentation)

NASA Technical Reports Server (NTRS)

Meyer, Harold D.

1999-01-01

This report provides the analytical documentation for the SOURCE3D Rotor Wake/Stator Interaction Code. It derives the equations for the rotor scattering coefficients and stator source vector and scattering coefficients that are needed for use in the TFANS (Theoretical Fan Noise Design/Prediction System). SOURCE3D treats the rotor and stator as isolated source elements. TFANS uses this information, along with scattering coefficients for inlet and exit elements, and provides complete noise solutions for turbofan engines. SOURCE3D is composed of a collection of FORTRAN programs that have been obtained by extending the approach of the earlier V072 Rotor Wake/Stator Interaction Code. Similar to V072, it treats the rotor and stator as a collection of blades and vanes having zero thickness and camber contained in an infinite, hardwall annular duct. SOURCE3D adds important features to the V072 capability-a rotor element, swirl flow and vorticity waves, actuator disks for flow turning, and combined rotor/actuator disk and stator/actuator disk elements. These items allow reflections from the rotor, frequency scattering, and mode trapping, thus providing more complete noise predictions than previously. The code has been thoroughly verified through comparison with D.B. Hanson's CUP2D two- dimensional code using a narrow annulus test case.

An Infinite Mixture Model for Coreference Resolution in Clinical Notes

PubMed Central

Liu, Sijia; Liu, Hongfang; Chaudhary, Vipin; Li, Dingcheng

2016-01-01

It is widely acknowledged that natural language processing is indispensable to process electronic health records (EHRs). However, poor performance in relation detection tasks, such as coreference (linguistic expressions pertaining to the same entity/event) may affect the quality of EHR processing. Hence, there is a critical need to advance the research for relation detection from EHRs. Most of the clinical coreference resolution systems are based on either supervised machine learning or rule-based methods. The need for manually annotated corpus hampers the use of such system in large scale. In this paper, we present an infinite mixture model method using definite sampling to resolve coreferent relations among mentions in clinical notes. A similarity measure function is proposed to determine the coreferent relations. Our system achieved a 0.847 F-measure for i2b2 2011 coreference corpus. This promising results and the unsupervised nature make it possible to apply the system in big-data clinical setting. PMID:27595047

Analytical and experimental investigation on transmission loss of clamped double panels: implication of boundary effects.

PubMed

Xin, F X; Lu, T J

2009-03-01

The air-borne sound insulation performance of a rectangular double-panel partition clamp mounted on an infinite acoustic rigid baffle is investigated both analytically and experimentally and compared with that of a simply supported one. With the clamped (or simply supported) boundary accounted for by using the method of modal function, a double series solution for the sound transmission loss (STL) of the structure is obtained by employing the weighted residual (Galerkin) method. Experimental measurements with Al double-panel partitions having air cavity are subsequently carried out to validate the theoretical model for both types of the boundary condition, and good overall agreement is achieved. A consistency check of the two different models (based separately on clamped modal function and simply supported modal function) is performed by extending the panel dimensions to infinite where no boundaries exist. The significant discrepancies between the two different boundary conditions are demonstrated in terms of the STL versus frequency plots as well as the panel deflection mode shapes.

Students' Conception of Infinite Series

ERIC Educational Resources Information Center

Martinez-Planell, Rafael; Gonzalez, Ana Carmen; DiCristina, Gladys; Acevedo, Vanessa

2012-01-01

This is a report of a study of students' understanding of infinite series. It has a three-fold purpose: to show that students may construct two essentially different notions of infinite series, to show that one of the constructions is particularly difficult for students, and to examine the way in which these two different constructions may be…

Fluctuations around equilibrium laws in ergodic continuous-time random walks.

PubMed

Schulz, Johannes H P; Barkai, Eli

2015-06-01

We study occupation time statistics in ergodic continuous-time random walks. Under thermal detailed balance conditions, the average occupation time is given by the Boltzmann-Gibbs canonical law. But close to the nonergodic phase, the finite-time fluctuations around this mean are large and nontrivial. They exhibit dual time scaling and distribution laws: the infinite density of large fluctuations complements the Lévy-stable density of bulk fluctuations. Neither of the two should be interpreted as a stand-alone limiting law, as each has its own deficiency: the infinite density has an infinite norm (despite particle conservation), while the stable distribution has an infinite variance (although occupation times are bounded). These unphysical divergences are remedied by consistent use and interpretation of both formulas. Interestingly, while the system's canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion, they also control the infinite and Lévy-stable densities of fluctuations. The duality of stable and infinite densities is in fact ubiquitous for these dynamics, as it concerns the time averages of general physical observables.

Calculating three loop ladder and V-topologies for massive operator matrix elements by computer algebra

NASA Astrophysics Data System (ADS)

Ablinger, J.; Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schneider, C.

2016-05-01

Three loop ladder and V-topology diagrams contributing to the massive operator matrix element AQg are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable N and the dimensional parameter ε. Given these representations, the desired Laurent series expansions in ε can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of N are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of V-topologies.

Gauge Factor and Stretchability of Silicon-on-Polymer Strain Gauges

PubMed Central

Yang, Shixuan; Lu, Nanshu

2013-01-01

Strain gauges are widely applied to measure mechanical deformation of structures and specimens. While metallic foil gauges usually have a gauge factor slightly over 2, single crystalline silicon demonstrates intrinsic gauge factors as high as 200. Although silicon is an intrinsically stiff and brittle material, flexible and even stretchable strain gauges have been achieved by integrating thin silicon strips on soft and deformable polymer substrates. To achieve a fundamental understanding of the large variance in gauge factor and stretchability of reported flexible/stretchable silicon-on-polymer strain gauges, finite element and analytically models are established to reveal the effects of the length of the silicon strip, and the thickness and modulus of the polymer substrate. Analytical results for two limiting cases, i.e., infinitely thick substrate and infinitely long strip, have found good agreement with FEM results. We have discovered that strains in silicon resistor can vary by orders of magnitude with different substrate materials whereas strip length or substrate thickness only affects the strain level mildly. While the average strain in silicon reflects the gauge factor, the maximum strain in silicon governs the stretchability of the system. The tradeoff between gauge factor and stretchability of silicon-on-polymer strain gauges has been proposed and discussed. PMID:23881128

The Comparison Study of Quadratic Infinite Beam Program on Optimization Instensity Modulated Radiation Therapy Treatment Planning (IMRTP) between Threshold and Exponential Scatter Method with CERR® In The Case of Lung Cancer

NASA Astrophysics Data System (ADS)

Hardiyanti, Y.; Haekal, M.; Waris, A.; Haryanto, F.

2016-08-01

This research compares the quadratic optimization program on Intensity Modulated Radiation Therapy Treatment Planning (IMRTP) with the Computational Environment for Radiotherapy Research (CERR) software. We assumed that the number of beams used for the treatment planner was about 9 and 13 beams. The case used the energy of 6 MV with Source Skin Distance (SSD) of 100 cm from target volume. Dose calculation used Quadratic Infinite beam (QIB) from CERR. CERR was used in the comparison study between Gauss Primary threshold method and Gauss Primary exponential method. In the case of lung cancer, the threshold variation of 0.01, and 0.004 was used. The output of the dose was distributed using an analysis in the form of DVH from CERR. The maximum dose distributions obtained were on the target volume (PTV) Planning Target Volume, (CTV) Clinical Target Volume, (GTV) Gross Tumor Volume, liver, and skin. It was obtained that if the dose calculation method used exponential and the number of beam 9. When the dose calculation method used the threshold and the number of beam 13, the maximum dose distributions obtained were on the target volume PTV, GTV, heart, and skin.

Galerkin finite element scheme for magnetostrictive structures and composites

NASA Astrophysics Data System (ADS)

Kannan, Kidambi Srinivasan

The ever increasing-role of magnetostrictives in actuation and sensing applications is an indication of their importance in the emerging field of smart structures technology. As newer, and more complex, applications are developed, there is a growing need for a reliable computational tool that can effectively address the magneto-mechanical interactions and other nonlinearities in these materials and in structures incorporating them. This thesis presents a continuum level quasi-static, three-dimensional finite element computational scheme for modeling the nonlinear behavior of bulk magnetostrictive materials and particulate magnetostrictive composites. Models for magnetostriction must deal with two sources of nonlinearities-nonlinear body forces/moments in equilibrium equations governing magneto-mechanical interactions in deformable and magnetized bodies; and nonlinear coupled magneto-mechanical constitutive models for the material of interest. In the present work, classical differential formulations for nonlinear magneto-mechanical interactions are recast in integral form using the weighted-residual method. A discretized finite element form is obtained by applying the Galerkin technique. The finite element formulation is based upon three dimensional eight-noded (isoparametric) brick element interpolation functions and magnetostatic infinite elements at the boundary. Two alternative possibilities are explored for establishing the nonlinear incremental constitutive model-characterization in terms of magnetic field or in terms of magnetization. The former methodology is the one most commonly used in the literature. In this work, a detailed comparative study of both methodologies is carried out. The computational scheme is validated, qualitatively and quantitatively, against experimental measurements published in the literature on structures incorporating the magnetostrictive material Terfenol-D. The influence of nonlinear body forces and body moments of magnetic origin, on the response of magnetostrictive structures to complex mechanical and magnetic loading conditions, is carefully examined. While monolithic magnetostrictive materials have been commercially-available since the late eighties, attention in the smart structures research community has recently focussed upon building and using magnetostrictive particulate composite structures for conventional actuation applications and novel sensing methodologies in structural health monitoring. A particulate magnetostrictive composite element has been developed in the present work to model such structures. This composite element incorporates interactions between magnetostrictive particles by combining a numerical micromechanical analysis based on magneto-mechanical Green's functions, with a homogenization scheme based upon the Mori-Tanaka approach. This element has been applied to the simulation of particulate actuators and sensors reported in the literature. Simulation results are compared to experimental data for validation purposes. The computational schemes developed, for bulk materials and for composites, are expected to be of great value to researchers and designers of novel applications based on magnetostrictives.

Interaction-stabilized steady states in the driven O (N ) model

NASA Astrophysics Data System (ADS)

Chandran, Anushya; Sondhi, S. L.

2016-05-01

We study periodically driven bosonic scalar field theories in the infinite N limit. It is well known that the free theory can undergo parametric resonance under monochromatic modulation of the mass term and thereby absorb energy indefinitely. Interactions in the infinite N limit terminate this increase for any choice of the UV cutoff and driving frequency. The steady state has nontrivial correlations and is synchronized with the drive. The O (N ) model at infinite N provides the first example of a clean interacting quantum system that does not heat to infinite temperature at any drive frequency.

Lyapunov exponents for infinite dimensional dynamical systems

NASA Technical Reports Server (NTRS)

Mhuiris, Nessan Mac Giolla

1987-01-01

Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.

An Application of the Difference Potentials Method to Solving External Problems in CFD

NASA Technical Reports Server (NTRS)

Ryaben 'Kii, Victor S.; Tsynkov, Semyon V.

1997-01-01

Numerical solution of infinite-domain boundary-value problems requires some special techniques that would make the problem available for treatment on the computer. Indeed, the problem must be discretized in a way that the computer operates with only finite amount of information. Therefore, the original infinite-domain formulation must be altered and/or augmented so that on one hand the solution is not changed (or changed slightly) and on the other hand the finite discrete formulation becomes available. One widely used approach to constructing such discretizations consists of truncating the unbounded original domain and then setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The role of the ABC's is to close the truncated problem and at the same time to ensure that the solution found inside the finite computational domain would be maximally close to (in the ideal case, exactly the same as) the corresponding fragment of the original infinite-domain solution. Let us emphasize that the proper treatment of artificial boundaries may have a profound impact on the overall quality and performance of numerical algorithms. The latter statement is corroborated by the numerous computational experiments and especially concerns the area of CFD, in which external problems present a wide class of practically important formulations. In this paper, we review some work that has been done over the recent years on constructing highly accurate nonlocal ABC's for calculation of compressible external flows. The approach is based on implementation of the generalized potentials and pseudodifferential boundary projection operators analogous to those proposed first by Calderon. The difference potentials method (DPM) by Ryaben'kii is used for the effective computation of the generalized potentials and projections. The resulting ABC's clearly outperform the existing methods from the standpoints of accuracy and robustness, in many cases noticeably speed up the multigrid convergence, and at the same time are quite comparable to other methods from the standpoints of geometric universality and simplicity of implementation.

Excitation of secondary Love and Rayleigh waves in athree-dimensional sedimentary basin evaluated by the direct boundary element method with normal modes

NASA Astrophysics Data System (ADS)

Hatayama, Ken; Fujiwara, Hiroyuki

1998-05-01

This paper aims to present a new method to calculate surface waves in 3-D sedimentary basin models, based on the direct boundary element method (BEM) with vertical boundaries and normal modes, and to evaluate the excitation of secondary surface waves observed remarkably in basins. Many authors have so far developed numerical techniques to calculate the total 3-D wavefield. However, the calculation of the total wavefield does not match our purpose, because the secondary surface waves excited on the basin boundaries will be contaminated by other undesirable waves. In this paper, we prove that, in principle, it is possible to extract surface waves excited on part of the basin boundaries from the total 3-D wavefield with a formulation that uses the reflection and transmission operators defined in the space domain. In realizing this extraction in the BEM algorithm, we encounter the problem arising from the lateral and vertical truncations of boundary surfaces extending infinitely in the half-space. To compensate the truncations, we first introduce an approximate algorithm using 2.5-D and 1-D wavefields for reference media, where a 2.5-D wavefield means a 3-D wavefield with a 2-D subsurface structure, and we then demonstrate the extraction. Finally, we calculate the secondary surface waves excited on the arc shape (horizontal section) of a vertical basin boundary subject to incident SH and SV plane waves propagating perpendicularly to the chord of the arc. As a result, we find that in the SH-incident case the Love waves are predominantly excited, rather than the Rayleigh waves and that in the SV-wave incident case the Love waves as well as the Rayleigh waves are excited. This suggests that the Love waves are more detectable than the Rayleigh waves in the horizontal components of observed recordings.

The University as an Infinite Game: Revitalising Activism in the Academy

ERIC Educational Resources Information Center

Harré, Niki; Grant, Barbara M.; Locke, Kirsten; Sturm, Sean

2017-01-01

We offer here a metaphor of the university as an "infinite game" in which we bring to life insight, imagination, and radical inclusion; and resist the "finite games" that can lead us astray. We suggest that keeping the infinite game alive within universities is a much-needed form of academic activism. We offer four vignettes…

Orthogonality preserving infinite dimensional quadratic stochastic operators

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

Akın, Hasan; Mukhamedov, Farrukh

In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.

Inspiring Examples in Rearrangements of Infinite Products

ERIC Educational Resources Information Center

Ramasinghe, W.

2007-01-01

It is well known that simple examples are really encouraging in the understanding of rearrangements of infinite series. In this paper a similar role is played by simple examples in the case of infinite products. Iterated products of double products seem to have a similar spirit of rearrangements of products, although they are not the same.…

Certain approximation problems for functions on the infinite-dimensional torus: Lipschitz spaces

NASA Astrophysics Data System (ADS)

Platonov, S. S.

2018-02-01

We consider some questions about the approximation of functions on the infinite-dimensional torus by trigonometric polynomials. Our main results are analogues of the direct and inverse theorems in the classical theory of approximation of periodic functions and a description of the Lipschitz spaces on the infinite-dimensional torus in terms of the best approximation.

A Comparison of Numerical and Analytical Radiative-Transfer Solutions for Plane Albedo of Natural Waters

EPA Science Inventory

Three numerical algorithms were compared to provide a solution of a radiative transfer equation (RTE) for plane albedo (hemispherical reflectance) in semi-infinite one-dimensional plane-parallel layer. Algorithms were based on the invariant imbedding method and two different var...

Enhanced global seismic resolution using proposed undersea cables

NASA Astrophysics Data System (ADS)

Ranasinghe, N. R.; Rowe, C. A.; Larmat, C. S.; Syracuse, E. M.; Begnaud, M. L.

2016-12-01

With the exception of a few isolated, near-shore deployments of Ocean-bottom seismometers (OBS's), most seismic instrumentation on the Earth is located on land, although two thirds of the Earth's surface is covered with oceans. Most large earthquakes are unevenly distributed along the Earth's subduction zones; hence, large areas of the Earth are unevenly sampled in terms of seismic rays. The goal of this work is to produce a comparison of seismic ray coverage of the Earth with today's seismic stations to that which might be possible in the future if densely-instrumented transoceanic cables are deployed.Our work is motivated by the planning of a Joint Task Force under the UN that is proposing to integrate seismic sensors at intervals as small as 75 km along the next generation of oceanic telecommunication cables. These sensors offer the potential to improve global geophysical models as well as reduce event detection thresholds and location uncertainties in poorly characterized regions. Data coverage is first estimated via an infinite-frequency ray-tracing utility (Pcalc) that is used to predict seismic propagation in support of the United States effort towards nuclear explosion monitoring. We have predicted P-wave raypaths from 1668 earthquakes to 4421 seismic stations to produce global raypath density images in the crust and mantle. We present the improvement in ray coverage achieved at crustal and mantle depths by the addition of 1382 sensors along the telecommunication cables and we discuss the areas in which our models and earthquake characterization benefits from these proposed instruments. Because the Earth's complex 3D structure can have frequency-dependent effects on seismic propagation, we also employ a spectral element method (SPECFEM3D) to compute finite-frequency kernels that include the first order of scattering produced by 3D anomalies, and we present progress on this effort to compare with our infinite-frequency predictions.

Study on the electromechanical coupling coefficient of Rayleigh-type surface acoustic waves in semi-infinite piezoelectrics/non-piezoelectrics superlattices.

PubMed

Chen, Shi; Zhang, Yinhong; Lin, Shuyu; Fu, Zhiqiang

2014-02-01

The electromechanical coupling coefficient of Rayleigh-type surface acoustic waves in semi-infinite piezoelectrics/non-piezoelectrics superlattices is investigated by the transfer matrix method. Research results show the high electromechanical coupling coefficient can be obtained in these systems. The optimization design of it is also discussed fully. It is significantly influenced by electrical boundary conditions on interfaces, thickness ratios of piezoelectric and non-piezoelectric layers, and material parameters (such as velocities of pure longitudinal and transversal bulk waves in non-piezoelectric layers). In order to obtain higher electromechanical coupling coefficient, shorted interfaces, non-piezoelectric materials with large velocities of longitudinal and transversal bulk waves, and proper thickness ratios should be chosen. Copyright © 2013 Elsevier B.V. All rights reserved.

Nonlinear damping model for flexible structures. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Zang, Weijian

1990-01-01

The study of nonlinear damping problem of flexible structures is addressed. Both passive and active damping, both finite dimensional and infinite dimensional models are studied. In the first part, the spectral density and the correlation function of a single DOF nonlinear damping model is investigated. A formula for the spectral density is established with O(Gamma(sub 2)) accuracy based upon Fokker-Planck technique and perturbation. The spectral density depends upon certain first order statistics which could be obtained if the stationary density is known. A method is proposed to find the approximate stationary density explicitly. In the second part, the spectral density of a multi-DOF nonlinear damping model is investigated. In the third part, energy type nonlinear damping model in an infinite dimensional setting is studied.

Two types of modes in finite size one-dimensional coaxial photonic crystals: General rules and experimental evidence

NASA Astrophysics Data System (ADS)

El Boudouti, E. H.; El Hassouani, Y.; Djafari-Rouhani, B.; Aynaou, H.

2007-08-01

We demonstrate analytically and experimentally the existence and behavior of two types of modes in finite size one-dimensional coaxial photonic crystals made of N cells with vanishing magnetic field on both sides. We highlight the existence of N-1 confined modes in each band and one mode by gap associated to either one or the other of the two surfaces surrounding the structure. The latter modes are independent of N . These results generalize our previous findings on the existence of surface modes in two semi-infinite superlattices obtained from the cleavage of an infinite superlattice between two cells. The analytical results are obtained by means of the Green’s function method, whereas the experiments are carried out using coaxial cables in the radio-frequency regime.

Love-type wave propagation in a pre-stressed viscoelastic medium influenced by smooth moving punch

NASA Astrophysics Data System (ADS)

Singh, A. K.; Parween, Z.; Chatterjee, M.; Chattopadhyay, A.

2015-04-01

In the present paper, a mathematical model studying the effect of smooth moving semi-infinite punch on the propagation of Love-type wave in an initially stressed viscoelastic strip is developed. The dynamic stress concentration due to the punch for the force of a constant intensity has been obtained in the closed form. Method based on Weiner-hopf technique which is indicated by Matczynski has been employed. The study manifests the significant effect of various affecting parameters viz. speed of moving punch associated with Love-type wave speed, horizontal compressive/tensile initial stress, vertical compressive/tensile initial stress, frequency parameter, and viscoelastic parameter on dynamic stress concentration due to semi-infinite punch. Moreover, some important peculiarities have been traced out and depicted by means of graphs.

Enhanced absorption of TM waves in conductive nanoparticles structure

NASA Astrophysics Data System (ADS)

Mousa, H. M.; Shabat, M. M.; Ouda, A. K.; Schaadt, D. M.

2018-05-01

This paper tackles anti-reflection coating structure for silicon solar cell where conductive nanoparticle (CNP) film is sandwiched between a semi-infinite glass cover and a semi-infinite silicon substrate. The transmission and reflection coefficients are derived by the transfer matrix method and simulated for values of unit cell sizes, gab widths in visible and near-infrared radiation. We also illustrated the dependence of the absorption, transmission and reflection coefficients on several angles of incidence of the transverse magnetic polarized (TM) waves. We found out that reflection decreases by the increase of incident angle to 50∘. If nanoparticles are suitably located and sized at gab width of 3.5 nm, unit cell of 250 nm and CNP layer thickness of 150 nm, the absorptivity of the structure achieves 100%.

Application of the trigonal curve to the Blaszak-Marciniak lattice hierarchy

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Zeng, Xin

2017-01-01

We develop a method for constructing algebro-geometric solutions of the Blaszak-Marciniak ( BM) lattice hierarchy based on the theory of trigonal curves. We first derive the BM lattice hierarchy associated with a discrete (3×3)- matrix spectral problem using Lenard recurrence relations. Using the characteristic polynomial of the Lax matrix for the BM lattice hierarchy, we introduce a trigonal curve with two infinite points, which we use to establish the associated Dubrovin-type equations. We then study the asymptotic properties of the algebraic function carrying the data of the divisor and the Baker-Akhiezer function near the two infinite points on the trigonal curve. We finally obtain algebro-geometric solutions of the entire BM lattice hierarchy in terms of the Riemann theta function.

On regularization and error estimates for the backward heat conduction problem with time-dependent thermal diffusivity factor

NASA Astrophysics Data System (ADS)

Karimi, Milad; Moradlou, Fridoun; Hajipour, Mojtaba

2018-10-01

This paper is concerned with a backward heat conduction problem with time-dependent thermal diffusivity factor in an infinite "strip". This problem is drastically ill-posed which is caused by the amplified infinitely growth in the frequency components. A new regularization method based on the Meyer wavelet technique is developed to solve the considered problem. Using the Meyer wavelet technique, some new stable estimates are proposed in the Hölder and Logarithmic types which are optimal in the sense of given by Tautenhahn. The stability and convergence rate of the proposed regularization technique are proved. The good performance and the high-accuracy of this technique is demonstrated through various one and two dimensional examples. Numerical simulations and some comparative results are presented.

Shear waves in elastic medium with void pores welded between vertically inhomogeneous and anisotropic magnetoelastic semi-infinite media

NASA Astrophysics Data System (ADS)

Gupta, Shishir; Ahmed, Mostaid; Pramanik, Abhijit

2017-03-01

The paper intends to study the propagation of horizontally polarized shear waves in an elastic medium with void pores constrained between a vertically inhomogeneous and an anisotropic magnetoelastic semi-infinite media. Elasto-dynamical equations of elastic medium with void pores and magnetoelastic solid have been employed to investigate the shear wave propagation in the proposed three-layered earth model. Method of separation of variables has been incorporated to deduce the dispersion relation. All possible special cases have been envisaged and they fairly comply with the corresponding results for classical cases. The role of inhomogeneity parameter, thickness of layer, angle with which the wave crosses the magnetic field and anisotropic magnetoelastic coupling parameter for three different materials has been elucidated and represented by graphs using MATHEMATICA.

Non-linear wave interaction in a magnetoplasma column. I - Theory. II Experiment

NASA Technical Reports Server (NTRS)

Larsen, J.-M.; Crawford, F. W.

1979-01-01

The paper presents an analysis of non-linear three-wave interaction for propagation along a cylindrical plasma column surrounded either by a metallic boundary, or by an infinite dielectric, and immersed in an infinite, static, axial magnetic field. An averaged Lagrangian method is used and the results are specialized to parametric amplification and mode conversion, assuming an undepleted pump wave. Computations are presented for a magneto-plasma column surrounded by free space, indicating that parametric growth rates of the order of a fraction of a decibel per centimeter should be obtainable for plausible laboratory plasma parameters. In addition, experiments on non-linear mode conversion in a cylindrical magnetoplasma column are described. The results are compared with the theoretical predictions and good qualitative agreement is demonstrated.

Crack turning in integrally stiffened aircraft structures

NASA Astrophysics Data System (ADS)

Pettit, Richard Glen

Current emphasis in the aircraft industry toward reducing manufacturing cost has created a renewed interest in integrally stiffened structures. Crack turning has been identified as an approach to improve the damage tolerance and fail-safety of this class of structures. A desired behavior is for skin cracks to turn before reaching a stiffener, instead of growing straight through. A crack in a pressurized fuselage encounters high T-stress as it nears the stiffener---a condition favorable to crack turning. Also, the tear resistance of aluminum alloys typically varies with crack orientation, a form of anisotropy that can influence the crack path. The present work addresses these issues with a study of crack turning in two-dimensions, including the effects of both T-stress and fracture anisotropy. Both effects are shown to have relation to the process zone size, an interaction that is central to this study. Following an introduction to the problem, the T-stress effect is studied for a slightly curved semi-infinite crack with a cohesive process zone, yielding a closed form expression for the future crack path in an infinite medium. For a given initial crack tip curvature and tensile T-stress, the crack path instability is found to increase with process zone size. Fracture orthotropy is treated using a simple function to interpolate between the two principal fracture resistance values in two-dimensions. An extension to three-dimensions interpolates between the six principal values of fracture resistance. Also discussed is the transition between mode I and mode II fracture in metals. For isotropic materials, there is evidence that the crack seeks out a direction of either local symmetry (pure mode I) or local asymmetry (pure mode II) growth. For orthotropic materials the favored states are not pure modal, and have mode mixity that is a function of crack orientation. Drawing upon these principles, two crack turning prediction approaches are extended to include fracture resistance orthotropy---a second-order linear elastic method with a characteristic length parameter to incorporate T-stress/process-zone effects, and an elastic-plastic method that uses the Crack Tip Opening Displacement (CTOD) to determine the failure response. Together with a novel method for obtaining enhanced accuracy T-stress calculations, these methods are incorporated into an adaptive-mesh, finite-element fracture simulation code. A total of 43 fracture tests using symmetrically and asymmetrically loaded double cantilever beam specimens were run to develop crack turning parameters and compare predicted and observed crack paths.

Control of single-photon routing in a T-shaped waveguide by another atom

NASA Astrophysics Data System (ADS)

Huang, Jin-Song; Wang, Jing-Wen; Wang, Yan; Li, Yan-Ling; Huang, You-Wen

2018-04-01

Quantum routers with a high routing rate of much more than 0.5 are of great importance for quantum networks. We provide a scheme to perform bidirectional high routing-rate transfer in a T-shaped coupled-resonator waveguide (CRW), which extends a recent unidirectional scheme proposed by Lu et al. (Opt Express 23:22955, 2015). By locating an extra two-level atom in the infinite CRW channel of the T-shaped CRW with a three-level system, an effective potential is generated. Our numerical results show that high routing capability from the infinite CRW channel to the semi-infinite channel can be achieved, and routing capability from the semi-infinite CRW channel to the infinite channel can also be significantly enhanced, with the help of the effective potential. Therefore, the proposed double-atom configuration could be utilized as a bidirectional quantum routing controller to implement high transfer rate routing of single photons.

Infinite index extensions of local nets and defects

NASA Astrophysics Data System (ADS)

Del Vecchio, Simone; Giorgetti, Luca

The subfactor theory provides a tool to analyze and construct extensions of Quantum Field Theories, once the latter are formulated as local nets of von Neumann algebras. We generalize some of the results of [62] to the case of extensions with infinite Jones index. This case naturally arises in physics, the canonical examples are given by global gauge theories with respect to a compact (non-finite) group of internal symmetries. Building on the works of Izumi-Longo-Popa [44] and Fidaleo-Isola [30], we consider generalized Q-systems (of intertwiners) for a semidiscrete inclusion of properly infinite von Neumann algebras, which generalize ordinary Q-systems introduced by Longo [58] to the infinite index case. We characterize inclusions which admit generalized Q-systems of intertwiners and define a braided product among the latter, hence we construct examples of QFTs with defects (phase boundaries) of infinite index, extending the family of boundaries in the grasp of [7].

Mutual Coupling Analysis for Conformal Microstrip Antennas.

DTIC Science & Technology

1984-12-01

6 0.001/ko, and the infinite integral is terminated at k 150 ko . 28*,-J ." . .. C. MUTUAL COUPLING ANALYSIS In this section, the moment method ...fact that it does provide an attractive alternative to the Green’s function method on which the analysis in later sections is based. In the present...by the moment method , the chosen set of expansion dipole modes plays a very important role. The efficiency as well as accuracy of the analysis depend

Introduction to the theory of infinite systems. Theory and practices

NASA Astrophysics Data System (ADS)

Fedorov, Foma M.

2017-11-01

A review of the author's work is given, which formed the basis for a new theory of general infinite systems. The Gaussian elimination and Cramer's rule have been extended to infinite systems. A special particular solution is obtained, it is called a strictly particular solution. Necessary and sufficient conditions for existence of the nontrivial solutions of homogeneous systems are given.

Confusing Aspects in the Calculation of the Electrostatic Potential of an Infinite Line of Charge

ERIC Educational Resources Information Center

Jimenez, J. L.; Campos, I.; Roa-Neri, J. A. E.

2012-01-01

In this work we discuss the trick of eliminating infinite potential of reference arguing that it corresponds to a constant of integration, in the problem of determining the electrostatic potential of an infinite line of charge with uniform density, and show how the problem must be tackled properly. The usual procedure is confusing for most…

Functors of White Noise Associated to Characters of the Infinite Symmetric Group

NASA Astrophysics Data System (ADS)

Bożejko, Marek; Guţă, Mădălin

The characters of the infinite symmetric group are extended to multiplicative positive definite functions on pair partitions by using an explicit representation due to Veršik and Kerov. The von Neumann algebra generated by the fields with f in an infinite dimensional real Hilbert space is infinite and the vacuum vector is not separating. For a family depending on an integer N< - 1 an ``exclusion principle'' is found allowing at most ``identical particles'' on the same state: The algebras are type factors. Functors of white noise are constructed and proved to be non-equivalent for different values of N.

Drift as a mechanism for cultural change: an example from baby names.

PubMed Central

Hahn, Matthew W; Bentley, R Alexander

2003-01-01

In the social sciences, there is currently no consensus on the mechanism by which cultural elements come and go in human society. For elements that are value-neutral, an appropriate null model may be one of random copying between individuals in the population. We show that the frequency distributions of baby names used in the United States in each decade of the twentieth century, for both males and females, obey a power law that is maintained over 100 years even though the population is growing, names are being introduced and lost every decade and large changes in the frequencies of specific names are common. We show that these distributions are satisfactorily explained by a simple process in which individuals randomly copy names from each other, a process that is analogous to the infinite-allele model of population genetics with random genetic drift. By its simplicity, this model provides a powerful null hypothesis for cultural change. It further explains why a few elements inevitably become highly popular, even if they have no intrinsic superiority over alternatives. Random copying could potentially explain power law distributions in other cultural realms, including the links on the World Wide Web. PMID:12952655

Three-dimensional earthquake analysis of roller-compacted concrete dams

NASA Astrophysics Data System (ADS)

Kartal, M. E.

2012-07-01

Ground motion effect on a roller-compacted concrete (RCC) dams in the earthquake zone should be taken into account for the most critical conditions. This study presents three-dimensional earthquake response of a RCC dam considering geometrical non-linearity. Besides, material and connection non-linearity are also taken into consideration in the time-history analyses. Bilinear and multilinear kinematic hardening material models are utilized in the materially non-linear analyses for concrete and foundation rock respectively. The contraction joints inside the dam blocks and dam-foundation-reservoir interaction are modeled by the contact elements. The hydrostatic and hydrodynamic pressures of the reservoir water are modeled with the fluid finite elements based on the Lagrangian approach. The gravity and hydrostatic pressure effects are employed as initial condition before the strong ground motion. In the earthquake analyses, viscous dampers are defined in the finite element model to represent infinite boundary conditions. According to numerical solutions, horizontal displacements increase under hydrodynamic pressure. Besides, those also increase in the materially non-linear analyses of the dam. In addition, while the principle stress components by the hydrodynamic pressure effect the reservoir water, those decrease in the materially non-linear time-history analyses.

Unsteady heat transfer in turbine blade ducts: Focus on combustor sources

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Huff, Ronald

1988-01-01

Thermal waves generated by either turbine rotor blades cutting through nonuniform combustor temperature fields or unsteady burning could lead to thermal fatigue cracking in the blades. To determine the magnitude of the thermal oscillation in blades with complex shapes and material compositions, a finite element Galerkin formulation has been developed to study combustor generated thermal wave propagation in a model two-dimensional duct with a uniform plug flow profile. The reflection and transmission of the thermal waves at the entrance and exit boundaries are determined by coupling the finite element solutions at the entrance and exit to the eigenfunctions of an infinitely long adiabatic duct. Example solutions are presented. In general, thermal wave propagation from an air passage into a metallic blade wall is small and not a problem. However, if a thermal barrier coating is applied to a metallic surface under conditions of a high heat transfer, a good impedance match is obtained and a significant portion of the thermal wave can pass into the blade material.

Ladder-structured photonic variable delay device

NASA Technical Reports Server (NTRS)

Yao, X. Steve (Inventor)

1998-01-01

An ladder-structured variable delay device for providing variable true time delay to multiple optical beams simultaneously. The device comprises multiple basic units stacked on top of each other resembling a ladder. Each basic unit comprises a polarization sensitive corner reflector formed by two polarization beamsplitters and a polarization rotator array placed parallel to the hypotenuse of the corner reflector. Controlling an array element of the polarization rotator array causes an optical beam passing through the array element to either go up to a basic unit above it or reflect back towards output. The beams going higher on the ladder experience longer optical path delay. Finally, the ladder-structured variable device can be cascaded with another multi-channel delay device to form a new device which combines the advantages of the two individual devices. This programmable optic device has the properties of high packing density, low loss, easy fabrication, and virtually infinite bandwidth. In addition, the delay is reversible so that the same delay device can be used for both antenna transmitting and receiving.

User manual for EXCALIBUR: A FE-BI numerical laboratory for cavity-backed antennas in a circular cylinder, version 1.2

NASA Technical Reports Server (NTRS)

Kempel, Leo C.

1994-01-01

The Finite Element-Boundary Integral (FE-BI) technique was used to analyze the scattering and radiation properties of cavity-backed patch antennas recessed in a metallic groundplane. A program, CAVITY3D, was written and found to yield accurate results for large arrays without the usual high memory and computational demand associated with competing formulations. Recently, the FE-BI approach was extended to cavity-backed antennas recessed in an infinite, metallic circular cylinder. EXCALIBUR is a computer program written in the Radiation Laboratory of the University of Michigan which implements this formulation. This user manual gives a brief introduction to EXCALIBUR and some hints as to its proper use. As with all computational electromagnetics programs (especially finite element programs), skilled use and best performance are only obtained through experience. However, several important aspects of the program such as portability, geometry generation, interpretation of results, and custom modification are addressed.

Finding Optimal Gains In Linear-Quadratic Control Problems

NASA Technical Reports Server (NTRS)

Milman, Mark H.; Scheid, Robert E., Jr.

1990-01-01

Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.

The Absolute Measurement of Beta Activities; SOBRE LA MEDIDA ABSOLUTA DE ACTIVIDADES BETA

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

Del Rio, C.S.; Reynaldo, O.J.; Mayquez, E.R.

1956-01-01

A new method for the absolute beta counting of solid samples is given. The measurements are made with an inside Geiger-Muller tube of new construction. The backscattering correction, when using an "infinite" thick mounting, is discussed and results for different materials given. (auth)

A Computer Simulation Study of Vntr Population Genetics: Constrained Recombination Rules Out the Infinite Alleles Model

PubMed Central

Harding, R. M.; Boyce, A. J.; Martinson, J. J.; Flint, J.; Clegg, J. B.

1993-01-01

Extensive allelic diversity in variable numbers of tandem repeats (VNTRs) has been discovered in the human genome. For population genetic studies of VNTRs, such as forensic applications, it is important to know whether a neutral mutation-drift balance of VNTR polymorphism can be represented by the infinite alleles model. The assumption of the infinite alleles model that each new mutant is unique is very likely to be violated by unequal sister chromatid exchange (USCE), the primary process believed to generate VNTR mutants. We show that increasing both mutation rates and misalignment constraint for intrachromosomal recombination in a computer simulation model reduces simulated VNTR diversity below the expectations of the infinite alleles model. Maximal constraint, represented as slippage of single repeats, reduces simulated VNTR diversity to levels expected from the stepwise mutation model. Although misalignment rule is the more important variable, mutation rate also has an effect. At moderate rates of USCE, simulated VNTR diversity fluctuates around infinite alleles expectation. However, if rates of USCE are high, as for hypervariable VNTRs, simulated VNTR diversity is consistently lower than predicted by the infinite alleles model. This has been observed for many VNTRs and accounted for by technical problems in distinguishing alleles of neighboring size classes. We use sampling theory to confirm the intrinsically poor fit to the infinite alleles model of both simulated VNTR diversity and observed VNTR polymorphisms sampled from two Papua New Guinean populations. PMID:8293988

A computer simulation study of VNTR population genetics: constrained recombination rules out the infinite alleles model.

PubMed

Harding, R M; Boyce, A J; Martinson, J J; Flint, J; Clegg, J B

1993-11-01

Extensive allelic diversity in variable numbers of tandem repeats (VNTRs) has been discovered in the human genome. For population genetic studies of VNTRs, such as forensic applications, it is important to know whether a neutral mutation-drift balance of VNTR polymorphism can be represented by the infinite alleles model. The assumption of the infinite alleles model that each new mutant is unique is very likely to be violated by unequal sister chromatid exchange (USCE), the primary process believed to generate VNTR mutants. We show that increasing both mutation rates and misalignment constraint for intrachromosomal recombination in a computer simulation model reduces simulated VNTR diversity below the expectations of the infinite alleles model. Maximal constraint, represented as slippage of single repeats, reduces simulated VNTR diversity to levels expected from the stepwise mutation model. Although misalignment rule is the more important variable, mutation rate also has an effect. At moderate rates of USCE, simulated VNTR diversity fluctuates around infinite alleles expectation. However, if rates of USCE are high, as for hypervariable VNTRs, simulated VNTR diversity is consistently lower than predicted by the infinite alleles model. This has been observed for many VNTRs and accounted for by technical problems in distinguishing alleles of neighboring size classes. We use sampling theory to confirm the intrinsically poor fit to the infinite alleles model of both simulated VNTR diversity and observed VNTR polymorphisms sampled from two Papua New Guinean populations.

A computer simulation study of VNTR population genetics: Constrained recombination rules out the infinite alleles model

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

Harding, R.M.; Martinson, J.J.; Flint, J.

1993-11-01

Extensive allelic diversity in variable numbers of tandem repeats (VNTRs) has been discovered in the human genome. For population genetic studies of VNTRs, such as forensic applications, it is important to know whether a neutral mutation-drift balance of VNTR polymorphism can be represented by the infinite alleles model. The assumption of the infinite alleles model that each new mutant is unique is very likely to be violated by unequal sister chromatid exchange (USCE), the primary process believed to generate VNTR mutants. The authors show that increasing both mutation rates and misalignment constraint for intrachromosomal recombination in a computer simulation modelmore » reduces simulated VNTR diversity below the expectations of the infinite alleles model. Maximal constraint, represented as slippage of single repeats, reduces simulated VNTR diversity to levels expected from the stepwise mutation model. Although misalignment rule is the more important variable, mutation rate also has an effect. At moderate rates of USCE, simulated VNTR diversity fluctuates around infinite alleles expectation. However, if rates of USCE are high, as for hypervariable VNTRs, simulated VNTR diversity is consistently lower than predicted by the infinite alleles model. This has been observed for many VNTRs and accounted for by technical problems in distinguishing alleles of neighboring size classes. The authors use sampling theory to confirm the intrinsically poor fit to the infinite model of both simulated VNTR diversity and observed VNTR polymorphisms sampled from two Papua New Guinean populations. 25 refs., 20 figs., 4 tabs.« less

Multifractality to Photonic Crystal & Self-Organization to Metamaterials through Anderson Localizations & Group/Gauge Theory

NASA Astrophysics Data System (ADS)

Hidajatullah-Maksoed, Widastra

2015-04-01

Arthur Cayley at least investigate by creating the theory of permutation group[F:∖∖Group_theory.htm] where in cell elements addressing of the lattice Qmf used a Cayley tree, the self-afine object Qmf is described by the combination of the finite groups of rotation & inversion and the infinite groups of translation & dilation[G Corso & LS Lacena: ``Multifractal lattice and group theory'', Physica A: Statistical Mechanics &Its Applications, 2005, v 357, issue I, h 64-70; http://www.sciencedirect.com/science/articel/pii/S0378437105005005 ] hence multifractal can be related to group theory. Many grateful Thanks to HE. Mr. Drs. P. SWANTORO & HE. Mr. Ir. SARWONO KUSUMAATMADJA.

Acoustic metric of the compressible draining bathtub

NASA Astrophysics Data System (ADS)

Cherubini, C.; Filippi, S.

2011-10-01

The draining bathtub flow, a cornerstone in the theory of acoustic black holes, is here extended to the case of exact solutions for compressible nonviscous flows characterized by a polytropic equation of state. Investigating the analytical configurations obtained for selected values of the polytropic index, it is found that each of them becomes nonphysical at the so called limiting circle. By studying the null geodesics structure of the corresponding acoustic line elements, it is shown that such a geometrical locus coincides with the acoustic event horizon. This region is characterized also by an infinite value of space-time curvature, so the acoustic analogy breaks down there. Possible applications for artificial and natural vortices are finally discussed.

Decoherence dynamics of interacting qubits coupled to a bath of local optical phonons

NASA Astrophysics Data System (ADS)

Lone, Muzaffar Qadir; Yarlagadda, S.

2016-04-01

We study decoherence in an interacting qubit system described by infinite range Heisenberg model (IRHM) in a situation where the system is coupled to a bath of local optical phonons. Using perturbation theory in polaron frame of reference, we derive an effective Hamiltonian that is valid in the regime of strong spin-phonon coupling under nonadiabatic conditions. It is shown that the effective Hamiltonian commutes with the IRHM upto leading orders of perturbation and thus has the same eigenstates as the IRHM. Using a quantum master equation with Markovian approximation of dynamical evolution, we show that the off-diagonal elements of the density matrix do not decay in the energy eigen basis of IRHM.

Modeling and control of flexible space structures

NASA Technical Reports Server (NTRS)

Wie, B.; Bryson, A. E., Jr.

1981-01-01

The effects of actuator and sensor locations on transfer function zeros are investigated, using uniform bars and beams as generic models of flexible space structures. It is shown how finite element codes may be used directly to calculate transfer function zeros. The impulse response predicted by finite-dimensional models is compared with the exact impulse response predicted by the infinite dimensional models. It is shown that some flexible structures behave as if there were a direct transmission between actuator and sensor (equal numbers of zeros and poles in the transfer function). Finally, natural damping models for a vibrating beam are investigated since natural damping has a strong influence on the appropriate active control logic for a flexible structure.

An accurate cost effective DFT approach to study the sensing behaviour of polypyrrole towards nitrate ions in gas and aqueous phases.

PubMed

Wasim, Fatima; Mahmood, Tariq; Ayub, Khurshid

2016-07-28

Density functional theory (DFT) calculations have been performed to study the response of polypyrrole towards nitrate ions in gas and aqueous phases. First, an accurate estimate of interaction energies is obtained by methods calibrated against the gold standard CCSD(T) method. Then, a number of low cost DFT methods are also evaluated for their ability to accurately estimate the binding energies of polymer-nitrate complexes. The low cost methods evaluated here include dispersion corrected potential (DCP), Grimme's D3 correction, counterpoise correction of the B3LYP method, and Minnesota functionals (M05-2X). The interaction energies calculated using the counterpoise (CP) correction and DCP methods at the B3LYP level are in better agreement with the interaction energies calculated using the calibrated methods. The interaction energies of an infinite polymer (polypyrrole) with nitrate ions are calculated by a variety of low cost methods in order to find the associated errors. The electronic and spectroscopic properties of polypyrrole oligomers nPy (where n = 1-9) and nPy-NO3(-) complexes are calculated, and then extrapolated for an infinite polymer through a second degree polynomial fit. Charge analysis, frontier molecular orbital (FMO) analysis and density of state studies also reveal the sensing ability of polypyrrole towards nitrate ions. Interaction energies, charge analysis and density of states analyses illustrate that the response of polypyrrole towards nitrate ions is considerably reduced in the aqueous medium (compared to the gas phase).

Examining the accuracy of the infinite order sudden approximation using sensitivity analysis

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

Eno, L.; Rabitz, H.

1981-08-15

A method is developed for assessing the accuracy of scattering observables calculated within the framework of the infinite order sudden (IOS) approximation. In particular, we focus on the energy sudden assumption of the IOS method and our approach involves the determination of the sensitivity of the IOS scattering matrix S/sup IOS/ with respect to a parameter which reintroduces the internal energy operator h/sub 0/ into the IOS Hamiltonian. This procedure is an example of sensitivity analysis of missing model components (h/sub 0/ in this case) in the reference Hamiltonian. In contrast to simple first-order perturbation theory a finite result ismore » obtained for the effect of h/sub 0/ on S/sup IOS/. As an illustration, our method of analysis is applied to integral state-to-state cross sections for the scattering of an atom and rigid rotor. Results are generated within the He+H/sub 2/ system and a comparison is made between IOS and coupled states cross sections and the corresponding IOS sensitivities. It is found that the sensitivity coefficients are very useful indicators of the accuracy of the IOS results. Finally, further developments and applications are discussed.« less

A New Method for Calculating Counts in Cells

NASA Astrophysics Data System (ADS)

Szapudi, István

1998-04-01

In the near future, a new generation of CCD-based galaxy surveys will enable high-precision determination of the N-point correlation functions. The resulting information will help to resolve the ambiguities associated with two-point correlation functions, thus constraining theories of structure formation, biasing, and Gaussianity of initial conditions independently of the value of Ω. As one of the most successful methods of extracting the amplitude of higher order correlations is based on measuring the distribution of counts in cells, this work presents an advanced way of measuring it with unprecedented accuracy. Szapudi & Colombi identified the main sources of theoretical errors in extracting counts in cells from galaxy catalogs. One of these sources, termed as measurement error, stems from the fact that conventional methods use a finite number of sampling cells to estimate counts in cells. This effect can be circumvented by using an infinite number of cells. This paper presents an algorithm, which in practice achieves this goal; that is, it is equivalent to throwing an infinite number of sampling cells in finite time. The errors associated with sampling cells are completely eliminated by this procedure, which will be essential for the accurate analysis of future surveys.

The Green’s functions for peridynamic non-local diffusion

PubMed Central

Wang, L. J.; Xu, J. F.

2016-01-01

In this work, we develop the Green’s function method for the solution of the peridynamic non-local diffusion model in which the spatial gradient of the generalized potential in the classical theory is replaced by an integral of a generalized response function in a horizon. We first show that the general solutions of the peridynamic non-local diffusion model can be expressed as functionals of the corresponding Green’s functions for point sources, along with volume constraints for non-local diffusion. Then, we obtain the Green’s functions by the Fourier transform method for unsteady and steady diffusions in infinite domains. We also demonstrate that the peridynamic non-local solutions converge to the classical differential solutions when the non-local length approaches zero. Finally, the peridynamic analytical solutions are applied to an infinite plate heated by a Gauss source, and the predicted variations of temperature are compared with the classical local solutions. The peridynamic non-local diffusion model predicts a lower rate of variation of the field quantities than that of the classical theory, which is consistent with experimental observations. The developed method is applicable to general diffusion-type problems. PMID:27713658

Wave envelope technique for multimode wave guide problems

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Sudharsanan, S. I.

1986-01-01

A fast method for solving wave guide problems is proposed. In particular, the guide is considered to be inhomogeneous allowing propagation of waves of higher order modes. Such problems have been handled successfully for acoustic wave propagation problems with single mode and finite length. This paper extends this concept to electromagnetic wave guides with several modes and infinite length. The method is described and results of computations are presented.

Solution of electromagnetic scattering problems using time domain techniques

NASA Technical Reports Server (NTRS)

Britt, Charles L.

1989-01-01

New methods are developed to calculate the electromagnetic diffraction or scattering characteristics of objects of arbitrary material and shape. The methods extend the efforts of previous researchers in the use of finite-difference and pulse response techniques. Examples are given of the scattering from infinite conducting and nonconducting cylinders, open channel, sphere, cone, cone sphere, coated disk, open boxes, and open and closed finite cylinders with axially incident waves.

Nonlinear Control Systems

DTIC Science & Technology

2009-11-18

J.M. Schumacher, Finite -dimensional regulators for a class of infinite dimensional systems . Systems and Control Letters, 3 (1983), 7-12. [39J J.M...for the control of certain examples or system classes us- ing particular feedback design methods ([20, 21, 16, 17, 19, 18]). Still, the control of...long time existence and asymptotic behavior for certain examples or system classes using particular feedback design methods (see, e.g., [20, 21, 16, 17

Generalized analytical solutions to sequentially coupled multi-species advective-dispersive transport equations in a finite domain subject to an arbitrary time-dependent source boundary condition

NASA Astrophysics Data System (ADS)

Chen, Jui-Sheng; Liu, Chen-Wuing; Liang, Ching-Ping; Lai, Keng-Hsin

2012-08-01

SummaryMulti-species advective-dispersive transport equations sequentially coupled with first-order decay reactions are widely used to describe the transport and fate of the decay chain contaminants such as radionuclide, chlorinated solvents, and nitrogen. Although researchers attempted to present various types of methods for analytically solving this transport equation system, the currently available solutions are mostly limited to an infinite or a semi-infinite domain. A generalized analytical solution for the coupled multi-species transport problem in a finite domain associated with an arbitrary time-dependent source boundary is not available in the published literature. In this study, we first derive generalized analytical solutions for this transport problem in a finite domain involving arbitrary number of species subject to an arbitrary time-dependent source boundary. Subsequently, we adopt these derived generalized analytical solutions to obtain explicit analytical solutions for a special-case transport scenario involving an exponentially decaying Bateman type time-dependent source boundary. We test the derived special-case solutions against the previously published coupled 4-species transport solution and the corresponding numerical solution with coupled 10-species transport to conduct the solution verification. Finally, we compare the new analytical solutions derived for a finite domain against the published analytical solutions derived for a semi-infinite domain to illustrate the effect of the exit boundary condition on coupled multi-species transport with an exponential decaying source boundary. The results show noticeable discrepancies between the breakthrough curves of all the species in the immediate vicinity of the exit boundary obtained from the analytical solutions for a finite domain and a semi-infinite domain for the dispersion-dominated condition.

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan's tau function.

PubMed

Milne, S C

1996-12-24

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi's (1829) 4 and 8 squares identities to 4n(2) or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan's tau function tau(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the eta-function identities in appendix I of Macdonald's work [Macdonald, I. G. (1972) Invent. Math. 15, 91-143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415-456] identities involving representing a positive integer by sums of 4n(2) or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson's C(l) nonterminating (6)phi(5) summation theorem, and Andrews' basic hypergeometric series proof of Jacobi's 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n(2) or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

A Gauss-Newton full-waveform inversion in PML-truncated domains using scalar probing waves

NASA Astrophysics Data System (ADS)

Pakravan, Alireza; Kang, Jun Won; Newtson, Craig M.

2017-12-01

This study considers the characterization of subsurface shear wave velocity profiles in semi-infinite media using scalar waves. Using surficial responses caused by probing waves, a reconstruction of the material profile is sought using a Gauss-Newton full-waveform inversion method in a two-dimensional domain truncated by perfectly matched layer (PML) wave-absorbing boundaries. The PML is introduced to limit the semi-infinite extent of the half-space and to prevent reflections from the truncated boundaries. A hybrid unsplit-field PML is formulated in the inversion framework to enable more efficient wave simulations than with a fully mixed PML. The full-waveform inversion method is based on a constrained optimization framework that is implemented using Karush-Kuhn-Tucker (KKT) optimality conditions to minimize the objective functional augmented by PML-endowed wave equations via Lagrange multipliers. The KKT conditions consist of state, adjoint, and control problems, and are solved iteratively to update the shear wave velocity profile of the PML-truncated domain. Numerical examples show that the developed Gauss-Newton inversion method is accurate enough and more efficient than another inversion method. The algorithm's performance is demonstrated by the numerical examples including the case of noisy measurement responses and the case of reduced number of sources and receivers.

Electromagnetic Scattering from Arbitrarily Shaped Aperture Backed by Rectangular Cavity Recessed in Infinite Ground Plane

NASA Technical Reports Server (NTRS)

Cockrell, C. R.; Beck, Fred B.

1997-01-01

The electromagnetic scattering from an arbitrarily shaped aperture backed by a rectangular cavity recessed in an infinite ground plane is analyzed by the integral equation approach. In this approach, the problem is split into two parts: exterior and interior. The electromagnetic fields in the exterior part are obtained from an equivalent magnetic surface current density assumed to be flowing over the aperture and backed by an infinite ground plane. The electromagnetic fields in the interior part are obtained in terms of rectangular cavity modal expansion functions. The modal amplitudes of cavity modes are determined by enforcing the continuity of the electric field across the aperture. The integral equation with the aperture magnetic current density as an unknown is obtained by enforcing the continuity of magnetic fields across the aperture. The integral equation is then solved for the magnetic current density by the method of moments. The electromagnetic scattering properties of an aperture backed by a rectangular cavity are determined from the magnetic current density. Numerical results on the backscatter radar cross-section (RCS) patterns of rectangular apertures backed by rectangular cavities are compared with earlier published results. Also numerical results on the backscatter RCS patterns of a circular aperture backed by a rectangular cavity are presented.

Convergence analysis of a monotonic penalty method for American option pricing

NASA Astrophysics Data System (ADS)

Zhang, Kai; Yang, Xiaoqi; Teo, Kok Lay

2008-12-01

This paper is devoted to study the convergence analysis of a monotonic penalty method for pricing American options. A monotonic penalty method is first proposed to solve the complementarity problem arising from the valuation of American options, which produces a nonlinear degenerated parabolic PDE with Black-Scholes operator. Based on the variational theory, the solvability and convergence properties of this penalty approach are established in a proper infinite dimensional space. Moreover, the convergence rate of the combination of two power penalty functions is obtained.

Automated Assume-Guarantee Reasoning for Omega-Regular Systems and Specifications

NASA Technical Reports Server (NTRS)

Chaki, Sagar; Gurfinkel, Arie

2010-01-01

We develop a learning-based automated Assume-Guarantee (AG) reasoning framework for verifying omega-regular properties of concurrent systems. We study the applicability of non-circular (AGNC) and circular (AG-C) AG proof rules in the context of systems with infinite behaviors. In particular, we show that AG-NC is incomplete when assumptions are restricted to strictly infinite behaviors, while AG-C remains complete. We present a general formalization, called LAG, of the learning based automated AG paradigm. We show how existing approaches for automated AG reasoning are special instances of LAG.We develop two learning algorithms for a class of systems, called infinite regular systems, that combine finite and infinite behaviors. We show that for infinity-regular systems, both AG-NC and AG-C are sound and complete. Finally, we show how to instantiate LAG to do automated AG reasoning for infinite regular, and omega-regular, systems using both AG-NC and AG-C as proof rules

SIApopr: a computational method to simulate evolutionary branching trees for analysis of tumor clonal evolution.

PubMed

McDonald, Thomas O; Michor, Franziska

2017-07-15

SIApopr (Simulating Infinite-Allele populations) is an R package to simulate time-homogeneous and inhomogeneous stochastic branching processes under a very flexible set of assumptions using the speed of C ++. The software simulates clonal evolution with the emergence of driver and passenger mutations under the infinite-allele assumption. The software is an application of the Gillespie Stochastic Simulation Algorithm expanded to a large number of cell types and scenarios, with the intention of allowing users to easily modify existing models or create their own. SIApopr is available as an R library on Github ( https://github.com/olliemcdonald/siapopr ). Supplementary data are available at Bioinformatics online. michor@jimmy.harvard.edu. © The Author (2017). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com

Analysis of an infinite array of rectangular microstrip patches with idealized probe feeds

NASA Technical Reports Server (NTRS)

Pozar, D. M.; Schaubert, D. H.

1984-01-01

A solution is presented to the problem of an infinite array of microstrip patches fed by idealized current probes. The input reflection coefficient is calculated versus scan angle in an arbitrary scan plane, and the effects of substrate parameters and grid spacing are considered. It is pointed out that even when a Galerkin method is used the impedance matrix is not symmetric due to phasing through a unit cell, as required for scanning. The mechanism by which scan blindness can occur is discussed. Measurement results are presented for the reflection coefficient magnitude variation with angle for E-plane, H-plane, and D-plane scans, for various substrate parameters. Measured results from waveguide simulators are also presented, and the scan blindness phenomenon is observed and discussed in terms of forced surface waves and a modified grating lobe diagram.

Heat and Mass Transfer on MHD Free convective flow of Second grade fluid through Porous medium over an infinite vertical plate

NASA Astrophysics Data System (ADS)

Dastagiri Babu, D.; Venkateswarlu, S.; Keshava Reddy, E.

2017-08-01

In this paper, we have considered the unsteady free convective two dimensional flow of a viscous incompressible electrically conducting second grade fluid over an infinite vertical porous plate under the influence of uniform transverse magnetic field with time dependent permeability, oscillatory suction. The governing equations of the flow field are solved by a regular perturbation method for small amplitude of the permeability. The closed form solutions for the velocity, temperature and concentration have been derived analytically and also its behavior is computationally discussed with reference to different flow parameters with the help of profiles. The skin fiction on the boundary, the heat flux in terms of the Nusselt number and rate of mass transfer in terms of Sherwood number are also obtained and their behavior computationally discussed.

NMR shifts for polycyclic aromatic hydrocarbons from first-principles

NASA Astrophysics Data System (ADS)

Thonhauser, T.; Ceresoli, Davide; Marzari, Nicola

We present first-principles, density-functional theory calculations of the NMR chemical shifts for polycyclic aromatic hydrocarbons, starting with benzene and increasing sizes up to the one- and two-dimensional infinite limits of graphene ribbons and sheets. Our calculations are performed using a combination of the recently developed theory of orbital magnetization in solids, and a novel approach to NMR calculations where chemical shifts are obtained from the derivative of the orbital magnetization with respect to a microscopic, localized magnetic dipole. Using these methods we study on equal footing the 1H and 13 shifts in benzene, pyrene, coronene, in naphthalene, anthracene, naphthacene, and pentacene, and finally in graphene, graphite, and an infinite graphene ribbon. Our results show very good agreement with experiments and allow us to characterize the trends for the chemical shifts as a function of system size.

Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques

NASA Technical Reports Server (NTRS)

Banks, H. T.; Wang, C.

1989-01-01

A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

Identities of Finitely Generated Algebras Over AN Infinite Field

NASA Astrophysics Data System (ADS)

Kemer, A. R.

1991-02-01

It is proved that for each finitely generated associative PI-algebra U over an infinite field F, there is a finite-dimensional F-algebra C such that the ideals of identities of the algebras U and C coincide. This yields a positive solution to the local problem of Specht for algebras over an infinite field: A finitely generated free associative algebra satisfies the maximum condition for T-ideals.

Chain of point-like potentials in Script R3 and infiniteness of the number of bound states

NASA Astrophysics Data System (ADS)

Boitsev, A. A.; Popov, I. Yu; Sokolov, O. V.

2014-10-01

Infinite chain of point-like potentials having the Hamiltonian with infinite number of eigenvalues below the continuous spectrum is constructed. The background of the model is the theory of self-adjoint extensions of symmetric operators in the Hilbert space. The analogous example of the Hamiltonian is obtained for the system of three-dimensional waveguides coupled through point-like windows.

Numerical Studies of Three-dimensional Breakdown in Trailing Vortex Wakes

NASA Technical Reports Server (NTRS)

Evans, P. F.; Hackett, J. E.

1976-01-01

Finite element, three dimensional relaxation methods are used to calculate the development of vortex wakes behind aircraft for a considerable downstream distance. The inclusion of a self-induction term in the solution, dependent upon local curvature and vortex core radius, permits calculation of finite lifetimes for systems for which infinite life would be predicted two dimensionally. The associated computer program is described together with single-pair, twin-pair, and multiple-pair studies carried out using it. It is found, in single-pair studies, that there is a lower limit to the wavelengths at which the Crow-type of instability can occur. Below this limit, self-induction effects cause the plane of the disturbance waves to rotate counter to the vortex direction. Self induction in two dimensionally generated twin spiral waves causes an increase in axial length which becomes more marked with decreasing initial wavelength. The time taken for vortex convergence toward the center plane is correspondingly increased. The limited parametric twin-pair study performed suggests that time-to-converge increases with increasing flap span. Limited studies of Boeing 747 configurations show correct qualitative response to removal of the outer flap and to gear deployment, as compared with wind tunnel and flight test experience.

Scattering of turbulent-jet wavepackets by a swept trailing edge.

PubMed

Piantanida, Selene; Jaunet, Vincent; Huber, Jérôme; Wolf, William R; Jordan, Peter; Cavalieri, André V G

2016-12-01

Installed jet noise is studied by means of a simplified configuration comprising a flat plate in the vicinity of a round jet. The effects of Mach number, jet-plate radial distance, and trailing-edge sweep angle are explored. Acoustic measurements are performed using a traversable 18-microphone azimuthal array, providing pressure data at 360 points on a cylindrical surface surrounding the jet-plate system. Key observations include a decrease, with increasing Mach number, of the relative level of the scattered field in comparison to the uninstalled jet; an exponential dependence of the scattered sound pressure level on the radial jet-plate separation; and considerable sideline noise reductions with increasing sweep angle, with which there is an overall reduction in acoustic efficiency. The measurements are compared with results obtained using a kinematic wavepacket source model, whose radiation is computed in two ways. A TGF for a semi-infinite flat plate is used to provide a low-order approximation of the scattering effect. Use of a more computationally intensive boundary element method provides additional precision. Good agreement between model predictions and experiment, encouraging from the perspective of low-cost prediction strategies, demonstrates that the models comprise the essential sound generation mechanisms.

GaAs Coupled Micro Resonators with Enhanced Sensitive Mass Detection

PubMed Central

Chopard, Tony; Lacour, Vivien; Leblois, Therese

2014-01-01

This work demonstrates the improvement of mass detection sensitivity and time response using a simple sensor structure. Indeed, complicated technological processes leading to very brittle sensing structures are often required to reach high sensitivity when we want to detect specific molecules in biological fields. These developments constitute an obstacle to the early diagnosis of diseases. An alternative is the design of coupled structures. In this study, the device is based on the piezoelectric excitation and detection of two GaAs microstructures vibrating in antisymmetric modes. GaAs is a crystal which has the advantage to be micromachined easily using typical clean room processes. Moreover, we showed its high potential in direct biofunctionalisation for use in the biological field. A specific design of the device was performed to improve the detection at low mass and an original detection method has been developed. The principle is to exploit the variation in amplitude at the initial resonance frequency which has in the vicinity of weak added mass the greatest slope. Therefore, we get a very good resolution for an infinitely weak mass: relative voltage variation of 8%/1 fg. The analysis is based on results obtained by finite element simulation. PMID:25474375

Differential pencil beam dose computation model for photons.

PubMed

Mohan, R; Chui, C; Lidofsky, L

1986-01-01

Differential pencil beam (DPB) is defined as the dose distribution relative to the position of the first collision, per unit collision density, for a monoenergetic pencil beam of photons in an infinite homogeneous medium of unit density. We have generated DPB dose distribution tables for a number of photon energies in water using the Monte Carlo method. The three-dimensional (3D) nature of the transport of photons and electrons is automatically incorporated in DPB dose distributions. Dose is computed by evaluating 3D integrals of DPB dose. The DPB dose computation model has been applied to calculate dose distributions for 60Co and accelerator beams. Calculations for the latter are performed using energy spectra generated with the Monte Carlo program. To predict dose distributions near the beam boundaries defined by the collimation system as well as blocks, we utilize the angular distribution of incident photons. Inhomogeneities are taken into account by attenuating the primary photon fluence exponentially utilizing the average total linear attenuation coefficient of intervening tissue, by multiplying photon fluence by the linear attenuation coefficient to yield the number of collisions in the scattering volume, and by scaling the path between the scattering volume element and the computation point by an effective density.

Transition to Turbulence in curved pipe

NASA Astrophysics Data System (ADS)

Hashemi, Amirreza; Loth, Francis

2014-11-01

Studies have shown that transitional turbulence in a curved pipe is delayed significantly compared with straight pipes. These analytical, numerical and experimental studies employed a helical geometry that is infinitely long such that the effect of the inlet and outlet can be neglected. The present study examined transition to turbulence in a finite curved pipe with a straight inlet/outlet and a 180 degrees curved pipe with a constant radius of curvature and diameter (D). We have employed the large scale direct numerical simulation (DNS) by using the spectral element method, nek5000, to simulate the flow field within curved pipe geometry with different curvature radii and Reynolds numbers to determine the point of the transition to turbulence. Long extensions for the inlet (5D) and outlet (20D) were used to diminish the effect of the boundary conditions. Our numerical results for radius of curvatures of 1.5D and 5D show transition turbulence is near Re = 3000. This is delayed compared with a straight pipe (Re = 2200) but still less that observed for helical geometries (Reynolds number less than 5000). Our research aims to describe the critical Reynolds number for transition to turbulence for a finite curved pipe at various curvature radii.

Direct numerical simulation of turbulence in a bent pipe

NASA Astrophysics Data System (ADS)

Schlatter, Philipp; Noorani, Azad

2013-11-01

A series of direct numerical simulations of turbulent flow in a bent pipe is presented. The setup employs periodic (cyclic) boundary conditions in the axial direction, leading to a nominally infinitely long pipe. The discretisation is based on the high-order spectral element method, using the code Nek5000. Four different curvatures, defined as the ratio between pipe radius and coil radius, are considered: κ = 0 (straight), 0.01 (mild curvature), 0.1 and 0.3 (strong curvature), at bulk Reynolds numbers of up to 11700 (corresponding to Reτ = 360 in the straight pipe case). The result show the turbulence-reducing effect of the curvature (similar to rotation), leading close to relaminarisation in the inner side; the outer side, however, remains fully turbulent. Prpoer orthogonal decomposition (POD) is used to extract the dominant modes, in an effort to explain low-frequency switching of sides inside the pipe. A number of additional interesting features are explored, which include sub-straight and sub-laminar drag for specific choices of curvature and Reynolds number: In particular the case with sub-laminar drag is investigated further, and our analysis shows the existence of a spanwise wave in the bent pipe, which in fact leads to lower overall pressure drop.

The Effect of the Pore Entrance on Particle Motion in Slit Pores: Implications for Ultrathin Membranes

PubMed Central

Delavari, Armin; Baltus, Ruth

2017-01-01

Membrane rejection models generally neglect the effect of the pore entrance on intrapore particle transport. However, entrance effects are expected to be particularly important with ultrathin membranes, where membrane thickness is typically comparable to pore size. In this work, a 2D model was developed to simulate particle motion for spherical particles moving at small Re and infinite Pe from the reservoir outside the pore into a slit pore. Using a finite element method, particles were tracked as they accelerated across the pore entrance until they reached a steady velocity in the pore. The axial position in the pore where particle motion becomes steady is defined as the particle entrance length (PEL). PELs were found to be comparable to the fluid entrance length, larger than the pore size and larger than the thickness typical of many ultrathin membranes. Results also show that, in the absence of particle diffusion, hydrodynamic particle–membrane interactions at the pore mouth result in particle “funneling” in the pore, yielding cross-pore particle concentration profiles focused at the pore centerline. The implications of these phenomena on rejection from ultrathin membranes are examined. PMID:28796197

Tungsten joining with copper alloy and its high heat load performance

NASA Astrophysics Data System (ADS)

Liu, Xiang; Lian, Youyun; Chen, Lei; Cheng, Zengkui; Chen, Jiming; Duan, Xuru; Song, Jioupeng; Yu, Yang

2014-12-01

W-CuCrZr joining technology by using low activation Cu-Mn filler metal was developed at Southwestern Institute of Physics (SWIP) for the manufacturing of divertor components of fusion experiment devices. In addition, a fast W coating technology by chemical vapor deposition (CVD) was also developed and CVD-W/CuCrZr and CVD-W/C mockups with a W coating thickness of 2 mm were prepared. In order to assess their high heat flux (HHF) performances, a 60 kW Electron-beam Material testing Scenario (EMS-60) equipped with a 150 keV electron beam welding gun was constructed at SWIP. Experimental results indicated that brazed W/CuCrZr mockups can withstand 8 MW/m2 heat flux for 1000 cycles without visible damages and CVD-W/CuCrZr mockups with W-Cu gradient interface can survive 1000 cycles under 11 MW/m2 heat flux. An ultrasonic inspection method for non-destructive tests (NDT) of brazed W/CuCrZr mockups was established and 2 mm defect can be detected. Infinite element analysis and heat load tests indicated that 5 mm defect had less noticeable influence on the heat transfer.

Fracture analysis for a penny-shaped crack problem of a superconducting cylinder in a parallel magnetic field

NASA Astrophysics Data System (ADS)

Gao, S. W.; Feng, W. J.; Fang, X. Q.; Zhang, G. L.

2014-11-01

In this work, the penny-shaped crack problem is investigated for an infinite long superconducting cylinder under electromagnetic forces. The distributions of magnetic flux density in the superconducting cylinder are obtained analytically for both the zero-field cooling (ZFC) and the field cooling (FC) activation processes, where the magnetically impermeable crack surface condition and the Bean model outside the crack region are adopted. Based on the finite element method (FEM), the stress intensity factor (SIF) and energy release rate (ERR) at the crack tips in the process of field descent are further numerically calculated. Numerical results obtained show that according to the maximal energy release rate criterion, the FC process is generally easier to enhance crack initiation and propagation than the ZFC activation process. On the other hand, for the FC activation process, the larger the maximal applied magnetic field, more likely the crack propagates. Additionally, crack size has important and slightly different effects on the crack extension forces for the ZFC and FC cases. Thus, all of the activation processes, the applied field and the diameter of the penny-shaped crack have significant effects on the intensity analysis and design of superconducting materials.

Problems encountered in the use of neutron methods for elemental analysis on planetary surfaces

USGS Publications Warehouse

Senftle, F.; Philbin, P.; Moxham, R.; Boynton, G.; Trombka, J.

1974-01-01

From experimental studies of gamma rays from fast and thermal neutron reactions in hydrogeneous and non-hydrogeneous, semi-infinite samples and from Monte Carlo calculations on soil of a composition which might typically be encountered on planetary surfaces, it is found that gamma rays from fast or inelastic scattering reactions would dominate the observed spectra. With the exception of gamma rays formed by inelastically scattered neutrons on oxygen, useful spectra would be limited to energies below 3 MeV. Other experiments were performed which show that if a gamma-ray detector were placed within 6 m of an isotopic neutron source in a spacecraft, it would be rendered useless for gamma-ray spectrometry below 3 MeV because of internal activation produced by neutron exposure during space travel. Adequate shielding is not practicable because of the size and weight constraints for planetary missions. Thus, it is required that the source be turned off or removed to a safe distance during non-measurement periods. In view of these results an accelerator or an off-on isotopic source would be desirable for practical gamma-ray spectral analysis on planetary surfaces containing but minor amounts of hydrogen. ?? 1974.

On the effect of boundary layer growth on the stability of compressible flows

NASA Technical Reports Server (NTRS)

El-Hady, N. M.

1981-01-01

The method of multiple scales is used to describe a formally correct method based on the nonparallel linear stability theory, that examines the two and three dimensional stability of compressible boundary layer flows. The method is applied to the supersonic flat plate layer at Mach number 4.5. The theoretical growth rates are in good agreement with experimental results. The method is also applied to the infinite-span swept wing transonic boundary layer with suction to evaluate the effect of the nonparallel flow on the development of crossflow disturbances.

AUDIO-LINGUAL METHODS IN THE LANGUAGE ARTS PROGRAM.

ERIC Educational Resources Information Center

PLAISTER, TED

WHEN CHILDREN ENTER ELEMENTARY SCHOOL, THEY POSSESS A LANGUAGE SYSTEM WHICH HAS BEEN INTUITED FROM WHAT THEY HEAR AND WHICH CAN PRODUCE FOR THEM AN INFINITE NUMBER OF SENTENCES REFLECTING EITHER STANDARD OR NONSTANDARD DIALECTS OF ENGLISH. THE ELEMENTARY TEACHER CAN EQUIP THOSE WHO SPEAK A DIVERGENT ENGLISH DIALECT WITH ANOTHER, MORE SOCIALLY…

Experimental method to account for structural compliance in nanoindentation measurements

Treesearch

Joseph E. Jakes; Charles R. Frihart; James F. Beecher; Robert J. Moon; D. S. Stone

2008-01-01

The standard Oliver–Pharr nanoindentation analysis tacitly assumes that the specimen is structurally rigid and that it is both semi-infinite and homogeneous. Many specimens violate these assumptions. We show that when the specimen flexes or possesses heterogeneities, such as free edges or interfaces between regions of different properties, artifacts arise...

Strong convergence of an extragradient-type algorithm for the multiple-sets split equality problem.

PubMed

Zhao, Ying; Shi, Luoyi

2017-01-01

This paper introduces a new extragradient-type method to solve the multiple-sets split equality problem (MSSEP). Under some suitable conditions, the strong convergence of an algorithm can be verified in the infinite-dimensional Hilbert spaces. Moreover, several numerical results are given to show the effectiveness of our algorithm.

The Hildebrand solubility parameters of ionic liquids-part 2.

PubMed

Marciniak, Andrzej

2011-01-01

The Hildebrand solubility parameters have been calculated for eight ionic liquids. Retention data from the inverse gas chromatography measurements of the activity coefficients at infinite dilution were used for the calculation. From the solubility parameters, the enthalpies of vaporization of ionic liquids were estimated. Results are compared with solubility parameters estimated by different methods.

Mathematical and computational studies of equilibrium capillary free surfaces

NASA Technical Reports Server (NTRS)

Albright, N.; Chen, N. F.; Concus, P.; Finn, R.

1977-01-01

The results of several independent studies are presented. The general question is considered of whether a wetting liquid always rises higher in a small capillary tube than in a larger one, when both are dipped vertically into an infinite reservoir. An analytical investigation is initiated to determine the qualitative behavior of the family of solutions of the equilibrium capillary free-surface equation that correspond to rotationally symmetric pendent liquid drops and the relationship of these solutions to the singular solution, which corresponds to an infinite spike of liquid extending downward to infinity. The block successive overrelaxation-Newton method and the generalized conjugate gradient method are investigated for solving the capillary equation on a uniform square mesh in a square domain, including the case for which the solution is unbounded at the corners. Capillary surfaces are calculated on the ellipse, on a circle with reentrant notches, and on other irregularly shaped domains using JASON, a general purpose program for solving nonlinear elliptic equations on a nonuniform quadrilaterial mesh. Analytical estimates for the nonexistence of solutions of the equilibrium capillary free-surface equation on the ellipse in zero gravity are evaluated.

Round-robin differential-phase-shift quantum key distribution with heralded pair-coherent sources

NASA Astrophysics Data System (ADS)

Wang, Le; Zhao, Shengmei

2017-04-01

Round-robin differential-phase-shift (RRDPS) quantum key distribution (QKD) scheme provides an effective way to overcome the signal disturbance from the transmission process. However, most RRDPS-QKD schemes use weak coherent pulses (WCPs) as the replacement of the perfect single-photon source. Considering the heralded pair-coherent source (HPCS) can efficiently remove the shortcomings of WCPs, we propose a RRDPS-QKD scheme with HPCS in this paper. Both infinite-intensity decoy-state method and practical three-intensity decoy-state method are adopted to discuss the tight bound of the key rate of the proposed scheme. The results show that HPCS is a better candidate for the replacement of the perfect single-photon source, and both the key rate and the transmission distance are greatly increased in comparison with those results with WCPs when the length of the pulse trains is small. Simultaneously, the performance of the proposed scheme using three-intensity decoy states is close to that result using infinite-intensity decoy states when the length of pulse trains is small.

SQDFT: Spectral Quadrature method for large-scale parallel O(N) Kohn-Sham calculations at high temperature

NASA Astrophysics Data System (ADS)

Suryanarayana, Phanish; Pratapa, Phanisri P.; Sharma, Abhiraj; Pask, John E.

2018-03-01

We present SQDFT: a large-scale parallel implementation of the Spectral Quadrature (SQ) method for O(N) Kohn-Sham Density Functional Theory (DFT) calculations at high temperature. Specifically, we develop an efficient and scalable finite-difference implementation of the infinite-cell Clenshaw-Curtis SQ approach, in which results for the infinite crystal are obtained by expressing quantities of interest as bilinear forms or sums of bilinear forms, that are then approximated by spatially localized Clenshaw-Curtis quadrature rules. We demonstrate the accuracy of SQDFT by showing systematic convergence of energies and atomic forces with respect to SQ parameters to reference diagonalization results, and convergence with discretization to established planewave results, for both metallic and insulating systems. We further demonstrate that SQDFT achieves excellent strong and weak parallel scaling on computer systems consisting of tens of thousands of processors, with near perfect O(N) scaling with system size and wall times as low as a few seconds per self-consistent field iteration. Finally, we verify the accuracy of SQDFT in large-scale quantum molecular dynamics simulations of aluminum at high temperature.

IMSF: Infinite Methodology Set Framework

NASA Astrophysics Data System (ADS)

Ota, Martin; Jelínek, Ivan

Software development is usually an integration task in enterprise environment - few software applications work autonomously now. It is usually a collaboration of heterogeneous and unstable teams. One serious problem is lack of resources, a popular result being outsourcing, ‘body shopping’, and indirectly team and team member fluctuation. Outsourced sub-deliveries easily become black boxes with no clear development method used, which has a negative impact on supportability. Such environments then often face the problems of quality assurance and enterprise know-how management. The used methodology is one of the key factors. Each methodology was created as a generalization of a number of solved projects, and each methodology is thus more or less connected with a set of task types. When the task type is not suitable, it causes problems that usually result in an undocumented ad-hoc solution. This was the motivation behind formalizing a simple process for collaborative software engineering. Infinite Methodology Set Framework (IMSF) defines the ICT business process of adaptive use of methods for classified types of tasks. The article introduces IMSF and briefly comments its meta-model.

Unification of field theory and maximum entropy methods for learning probability densities

NASA Astrophysics Data System (ADS)

Kinney, Justin B.

2015-09-01

The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such approaches. Both have origins in statistical physics, but the relationship between them has remained unclear. Here I unify these two methods by showing that every maximum entropy density estimate can be recovered in the infinite smoothness limit of an appropriate Bayesian field theory. I also show that Bayesian field theory estimation can be performed without imposing any boundary conditions on candidate densities, and that the infinite smoothness limit of these theories recovers the most common types of maximum entropy estimates. Bayesian field theory thus provides a natural test of the maximum entropy null hypothesis and, furthermore, returns an alternative (lower entropy) density estimate when the maximum entropy hypothesis is falsified. The computations necessary for this approach can be performed rapidly for one-dimensional data, and software for doing this is provided.

Coupled dynamics of a viscoelastically supported infinite string and a number of discrete mechanical systems moving with uniform speed

NASA Astrophysics Data System (ADS)

Roy, Soumyajit; Chakraborty, G.; DasGupta, Anirvan

2018-02-01

The mutual interaction between a number of multi degrees of freedom mechanical systems moving with uniform speed along an infinite taut string supported by a viscoelastic layer has been studied using the substructure synthesis method when base excitations of a common frequency are given to the mechanical systems. The mobility or impedance matrices of the string have been calculated analytically by Fourier transform method as well as wave propagation technique. The above matrices are used to calculate the response of the discrete mechanical systems. Special attention is paid to the contact forces between the discrete and the continuous systems which are estimated by numerical simulation. The effects of phase difference, the distance between the systems and different base excitation amplitudes on the collective behaviour of the mechanical systems are also studied. The present study has relevance to the coupled dynamic problem of more than one railway pantographs and an overhead catenary system where the pantographs are modelled as discrete systems and the catenary is modelled as a taut string supported by continuous viscoelastic layer.

Diffusiophoresis in one-dimensional solute gradients

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

Ault, Jesse T.; Warren, Patrick B.; Shin, Sangwoo

Here, the diffusiophoretic motion of suspended colloidal particles under one-dimensional solute gradients is solved using numerical and analytical techniques. Similarity solutions are developed for the injection and withdrawal dynamics of particles into semi-infinite pores. Furthermore, a method of characteristics formulation of the diffusion-free particle transport model is presented and integrated to realize particle trajectories. Analytical solutions are presented for the limit of small particle diffusiophoretic mobility Γ p relative to the solute diffusivity D s for particle motions in both semi-infinite and finite domains. Results confirm the build up of local maxima and minima in the propagating particle front dynamics.more » The method of characteristics is shown to successfully predict particle motions and the position of the particle front, although it fails to accurately predict suspended particle concentrations in the vicinity of sharp gradients, such as at the particle front peak seen in some injection cases, where particle diffusion inevitably plays an important role. Results inform the design of applications in which the use of applied solute gradients can greatly enhance particle injection into and withdrawal from pores.« less

New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies.

PubMed

Essa, Khalid S

2014-01-01

A new fast least-squares method is developed to estimate the shape factor (q-parameter) of a buried structure using normalized residual anomalies obtained from gravity data. The problem of shape factor estimation is transformed into a problem of finding a solution of a non-linear equation of the form f(q) = 0 by defining the anomaly value at the origin and at different points on the profile (N-value). Procedures are also formulated to estimate the depth (z-parameter) and the amplitude coefficient (A-parameter) of the buried structure. The method is simple and rapid for estimating parameters that produced gravity anomalies. This technique is used for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The technique is tested and verified on theoretical models with and without random errors. It is also successfully applied to real data sets from Senegal and India, and the inverted-parameters are in good agreement with the known actual values.

Phase diagram of the quantum Ising model with long-range interactions on an infinite-cylinder triangular lattice

NASA Astrophysics Data System (ADS)

Saadatmand, S. N.; Bartlett, S. D.; McCulloch, I. P.

2018-04-01

Obtaining quantitative ground-state behavior for geometrically-frustrated quantum magnets with long-range interactions is challenging for numerical methods. Here, we demonstrate that the ground states of these systems on two-dimensional lattices can be efficiently obtained using state-of-the-art translation-invariant variants of matrix product states and density-matrix renormalization-group algorithms. We use these methods to calculate the fully-quantitative ground-state phase diagram of the long-range interacting triangular Ising model with a transverse field on six-leg infinite-length cylinders and scrutinize the properties of the detected phases. We compare these results with those of the corresponding nearest neighbor model. Our results suggest that, for such long-range Hamiltonians, the long-range quantum fluctuations always lead to long-range correlations, where correlators exhibit power-law decays instead of the conventional exponential drops observed for short-range correlated gapped phases. Our results are relevant for comparisons with recent ion-trap quantum simulator experiments that demonstrate highly-controllable long-range spin couplings for several hundred ions.

Unification of field theory and maximum entropy methods for learning probability densities.

PubMed

Kinney, Justin B

2015-09-01

The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such approaches. Both have origins in statistical physics, but the relationship between them has remained unclear. Here I unify these two methods by showing that every maximum entropy density estimate can be recovered in the infinite smoothness limit of an appropriate Bayesian field theory. I also show that Bayesian field theory estimation can be performed without imposing any boundary conditions on candidate densities, and that the infinite smoothness limit of these theories recovers the most common types of maximum entropy estimates. Bayesian field theory thus provides a natural test of the maximum entropy null hypothesis and, furthermore, returns an alternative (lower entropy) density estimate when the maximum entropy hypothesis is falsified. The computations necessary for this approach can be performed rapidly for one-dimensional data, and software for doing this is provided.

New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies

PubMed Central

Essa, Khalid S.

2013-01-01

A new fast least-squares method is developed to estimate the shape factor (q-parameter) of a buried structure using normalized residual anomalies obtained from gravity data. The problem of shape factor estimation is transformed into a problem of finding a solution of a non-linear equation of the form f(q) = 0 by defining the anomaly value at the origin and at different points on the profile (N-value). Procedures are also formulated to estimate the depth (z-parameter) and the amplitude coefficient (A-parameter) of the buried structure. The method is simple and rapid for estimating parameters that produced gravity anomalies. This technique is used for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The technique is tested and verified on theoretical models with and without random errors. It is also successfully applied to real data sets from Senegal and India, and the inverted-parameters are in good agreement with the known actual values. PMID:25685472

Atomic approximation to the projection on electronic states in the Douglas-Kroll-Hess approach to the relativistic Kohn-Sham method.

PubMed

Matveev, Alexei V; Rösch, Notker

2008-06-28

We suggest an approximate relativistic model for economical all-electron calculations on molecular systems that exploits an atomic ansatz for the relativistic projection transformation. With such a choice, the projection transformation matrix is by definition both transferable and independent of the geometry. The formulation is flexible with regard to the level at which the projection transformation is approximated; we employ the free-particle Foldy-Wouthuysen and the second-order Douglas-Kroll-Hess variants. The (atomic) infinite-order decoupling scheme shows little effect on structural parameters in scalar-relativistic calculations; also, the use of a screened nuclear potential in the definition of the projection transformation shows hardly any effect in the context of the present work. Applications to structural and energetic parameters of various systems (diatomics AuH, AuCl, and Au(2), two structural isomers of Ir(4), and uranyl dication UO(2) (2+) solvated by 3-6 water ligands) show that the atomic approximation to the conventional second-order Douglas-Kroll-Hess projection (ADKH) transformation yields highly accurate results at substantial computational savings, in particular, when calculating energy derivatives of larger systems. The size-dependence of the intrinsic error of the ADKH method in extended systems of heavy elements is analyzed for the atomization energies of Pd(n) clusters (n

Programming of the complex logarithm function in the solution of the cracked anisotropic plate loaded by a point force

NASA Astrophysics Data System (ADS)

Zaal, K. J. J. M.

1991-06-01

In programming solutions of complex function theory, the complex logarithm function is replaced by the complex logarithmic function, introducing a discontinuity along the branch cut into the programmed solution which was not present in the mathematical solution. Recently, Liaw and Kamel presented their solution of the infinite anisotropic centrally cracked plate loaded by an arbitrary point force, which they used as Green's function in a boundary element method intended to evaluate the stress intensity factor at the tip of a crack originating from an elliptical home. Their solution may be used as Green's function of many more numerical methods involving anisotropic elasticity. In programming applications of Liaw and Kamel's solution, the standard definition of the logarithmic function with the branch cut at the nonpositive real axis cannot provide a reliable computation of the displacement field for Liaw and Kamel's solution. Either the branch cut should be redefined outside the domain of the logarithmic function, after proving that the domain is limited to a part of the plane, or the logarithmic function should be defined on its Riemann surface. A two dimensional line fractal can provide the link between all mesh points on the plane essential to evaluate the logarithm function on its Riemann surface. As an example, a two dimensional line fractal is defined for a mesh once used by Erdogan and Arin.

TH-AB-BRA-09: Stability Analysis of a Novel Dose Calculation Algorithm for MRI Guided Radiotherapy

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

Zelyak, O; Fallone, B; Cross Cancer Institute, Edmonton, AB

2016-06-15

Purpose: To determine the iterative deterministic solution stability of the Linear Boltzmann Transport Equation (LBTE) in the presence of magnetic fields. Methods: The LBTE with magnetic fields under investigation is derived using a discrete ordinates approach. The stability analysis is performed using analytical and numerical methods. Analytically, the spectral Fourier analysis is used to obtain the convergence rate of the source iteration procedures based on finding the largest eigenvalue of the iterative operator. This eigenvalue is a function of relevant physical parameters, such as magnetic field strength and material properties, and provides essential information about the domain of applicability requiredmore » for clinically optimal parameter selection and maximum speed of convergence. The analytical results are reinforced by numerical simulations performed using the same discrete ordinates method in angle, and a discontinuous finite element spatial approach. Results: The spectral radius for the source iteration technique of the time independent transport equation with isotropic and anisotropic scattering centers inside infinite 3D medium is equal to the ratio of differential and total cross sections. The result is confirmed numerically by solving LBTE and is in full agreement with previously published results. The addition of magnetic field reveals that the convergence becomes dependent on the strength of magnetic field, the energy group discretization, and the order of anisotropic expansion. Conclusion: The source iteration technique for solving the LBTE with magnetic fields with the discrete ordinates method leads to divergent solutions in the limiting cases of small energy discretizations and high magnetic field strengths. Future investigations into non-stationary Krylov subspace techniques as an iterative solver will be performed as this has been shown to produce greater stability than source iteration. Furthermore, a stability analysis of a discontinuous finite element space-angle approach (which has been shown to provide the greatest stability) will also be investigated. Dr. B Gino Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization)« less

Control optimization, stabilization and computer algorithms for aircraft applications

NASA Technical Reports Server (NTRS)

1975-01-01

Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.

Symplectic partitioned Runge-Kutta scheme for Maxwell's equations

NASA Astrophysics Data System (ADS)

Huang, Zhi-Xiang; Wu, Xian-Liang

Using the symplectic partitioned Runge-Kutta (PRK) method, we construct a new scheme for approximating the solution to infinite dimensional nonseparable Hamiltonian systems of Maxwell's equations for the first time. The scheme is obtained by discretizing the Maxwell's equations in the time direction based on symplectic PRK method, and then evaluating the equation in the spatial direction with a suitable finite difference approximation. Several numerical examples are presented to verify the efficiency of the scheme.

Nonlocal Theory for Fracturing of Quasibrittle Materials.

DTIC Science & Technology

1994-03-01

eigenstrain e* be applied to an ellipsoidal domain 0J contained * in this infinite body. The values of the cigenstrain t* are such that the stress is...affecting its stresses and deformation. Thus, the change of potential energy of the infinite body caused by the applied eigenstrain is the same as the...infinite body is subjected to external forces alone or eigenstrain a* alone, respectively. If plane-strain cases are considered, the ellipsoid becomes an

Classical simulation of infinite-size quantum lattice systems in two spatial dimensions.

PubMed

Jordan, J; Orús, R; Vidal, G; Verstraete, F; Cirac, J I

2008-12-19

We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems [F. Verstraete and J. I. Cirac, arxiv:cond-mat/0407066] and the infinite time-evolving block decimation algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)10.1103/PhysRevLett.98.070201]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition.

Graph determined symbolic dynamics and hybrid systems

NASA Astrophysics Data System (ADS)

Ayers, Kimberly Danielle

In this paper we explore the concept of symbolic dynamical systems whose structure is determined by a directed graph, and then discrete-continuous hybrid systems that arise from such dynamical systems. Typically, symbolic dynamics involve the study of a left shift of a bi-infinite sequence. We examine the case when the bi-infinite system is dictated by a graph; that is, the sequence is a bi-infinite path of a directed graph. We then use the concept to study a system of dynamical systems all on the same compact space M, where "switching" between the systems occurs as given by the bi-infinite sequence in question. The concepts of limit sets, chain recurrent sets, chaos, and Morse sets for these systems are explored.

Contribution of large scale coherence to wind turbine power: A large eddy simulation study in periodic wind farms

NASA Astrophysics Data System (ADS)

Chatterjee, Tanmoy; Peet, Yulia T.

2018-03-01

Length scales of eddies involved in the power generation of infinite wind farms are studied by analyzing the spectra of the turbulent flux of mean kinetic energy (MKE) from large eddy simulations (LES). Large-scale structures with an order of magnitude bigger than the turbine rotor diameter (D ) are shown to have substantial contribution to wind power. Varying dynamics in the intermediate scales (D -10 D ) are also observed from a parametric study involving interturbine distances and hub height of the turbines. Further insight about the eddies responsible for the power generation have been provided from the scaling analysis of two-dimensional premultiplied spectra of MKE flux. The LES code is developed in a high Reynolds number near-wall modeling framework, using an open-source spectral element code Nek5000, and the wind turbines have been modelled using a state-of-the-art actuator line model. The LES of infinite wind farms have been validated against the statistical results from the previous literature. The study is expected to improve our understanding of the complex multiscale dynamics in the domain of large wind farms and identify the length scales that contribute to the power. This information can be useful for design of wind farm layout and turbine placement that take advantage of the large-scale structures contributing to wind turbine power.