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Sample records for helmholtz equation exterior

  1. Implicit Boundary Integral Methods for the Helmholtz Equation in Exterior Domains

    DTIC Science & Technology

    2016-06-01

    differential equations on surfaces. SIAM J. Sci. Comput., 31(6):4330–4350, 2009. [13] A.-W. Maue. Zur Formulierung eines allgemeinen Beugungsproblems...Implicit boundary integral methods for the Helmholtz equation in exterior domains Chieh Chen and Richard Tsai∗ Abstract We propose a new algorithm...for solving Helmholtz equations in the exterior domain. The algorithm not only combines the advantages of implicit surface representation and the

  2. Active exterior cloaking for the 2D Laplace and Helmholtz equations.

    PubMed

    Vasquez, Fernando Guevara; Milton, Graeme W; Onofrei, Daniel

    2009-08-14

    A new cloaking method is presented for 2D quasistatics and the 2D Helmholtz equation that we speculate extends to other linear wave equations. For 2D quasistatics it is proven how a single active exterior cloaking device can be used to shield an object from surrounding fields, yet produce very small scattered fields. The problem is reduced to finding a polynomial which is close to 1 in a disk and close to 0 in another disk, and such a polynomial is constructed. For the 2D Helmholtz equation it is numerically shown that three exterior cloaking devices placed around the object suffice to hide it.

  3. On the Dirichlet problem for the dissipative Helmholtz equation in the exterior of non-closed Lipschitz surfaces

    NASA Astrophysics Data System (ADS)

    Krutitskii, P. A.

    2013-10-01

    The Dirichlet problem for the dissipative Helmholtz equation is considered in the exterior of non-closed Lipschitz surfaces in R3. Theorems on existence and uniqueness of a weak solution of the problem are proved. The problem is reduced to a uniquely solvable integral equation. The integral representation of a weak solution is obtained.

  4. A new method for true and spurious eigensolutions of arbitrary cavities using the combined Helmholtz exterior integral equation formulation method.

    PubMed

    Chen, I L; Chen, J T; Kuo, S R; Liang, M T

    2001-03-01

    Integral equation methods have been widely used to solve interior eigenproblems and exterior acoustic problems (radiation and scattering). It was recently found that the real-part boundary element method (BEM) for the interior problem results in spurious eigensolutions if the singular (UT) or the hypersingular (LM) equation is used alone. The real-part BEM results in spurious solutions for interior problems in a similar way that the singular integral equation (UT method) results in fictitious solutions for the exterior problem. To solve this problem, a Combined Helmholtz Exterior integral Equation Formulation method (CHEEF) is proposed. Based on the CHEEF method, the spurious solutions can be filtered out if additional constraints from the exterior points are chosen carefully. Finally, two examples for the eigensolutions of circular and rectangular cavities are considered. The optimum numbers and proper positions for selecting the points in the exterior domain are analytically studied. Also, numerical experiments were designed to verify the analytical results. It is worth pointing out that the nodal line of radiation mode of a circle can be rotated due to symmetry, while the nodal line of the rectangular is on a fixed position.

  5. Accelerated Schwarz iterations for Helmholtz equation

    NASA Astrophysics Data System (ADS)

    Nagid, Nabila; Belhadj, Hassan; Amattouch, Mohamed Ridouan

    2017-01-01

    In this paper, the Restricted additive Schwarz (RAS) method is applied to solve Helmholtz equation. To accelerate the RAS iterations, we propose to apply the vector ɛ-algorithm. Some convergence analysis of the proposed method is presented, and applied succeffully to Helmholtz problem. The obtained results show the efficiency of the proposed approach. Moreover, the algorithm yields much faster convergence than the classical Schwarz iterations.

  6. Preconditioning the Helmholtz Equation for Rigid Ducts

    NASA Technical Reports Server (NTRS)

    Baumeister, Kenneth J.; Kreider, Kevin L.

    1998-01-01

    An innovative hyperbolic preconditioning technique is developed for the numerical solution of the Helmholtz equation which governs acoustic propagation in ducts. Two pseudo-time parameters are used to produce an explicit iterative finite difference scheme. This scheme eliminates the large matrix storage requirements normally associated with numerical solutions to the Helmholtz equation. The solution procedure is very fast when compared to other transient and steady methods. Optimization and an error analysis of the preconditioning factors are present. For validation, the method is applied to sound propagation in a 2D semi-infinite hard wall duct.

  7. Robust iterative method for nonlinear Helmholtz equation

    NASA Astrophysics Data System (ADS)

    Yuan, Lijun; Lu, Ya Yan

    2017-08-01

    A new iterative method is developed for solving the two-dimensional nonlinear Helmholtz equation which governs polarized light in media with the optical Kerr nonlinearity. In the strongly nonlinear regime, the nonlinear Helmholtz equation could have multiple solutions related to phenomena such as optical bistability and symmetry breaking. The new method exhibits a much more robust convergence behavior than existing iterative methods, such as frozen-nonlinearity iteration, Newton's method and damped Newton's method, and it can be used to find solutions when good initial guesses are unavailable. Numerical results are presented for the scattering of light by a nonlinear circular cylinder based on the exact nonlocal boundary condition and a pseudospectral method in the polar coordinate system.

  8. Monopoles, instantons, and the Helmholtz equation

    NASA Astrophysics Data System (ADS)

    Franchetti, Guido; Maldonado, Rafael

    2016-07-01

    In this work we study the dimensional reduction of smooth circle invariant Yang-Mills instantons defined on 4-manifolds which asymptotically become circle fibrations over hyperbolic 3-space. A suitable choice of the 4-manifold metric within a specific conformal class gives rise to singular and smooth hyperbolic monopoles. A large class of monopoles is obtained if the conformal factor satisfies the Helmholtz equation on hyperbolic 3-space. We describe simple configurations and relate our results to the Jackiw-Nohl-Rebbi construction, for which we provide a geometric interpretation.

  9. Boundary regularized integral equation formulation of the Helmholtz equation in acoustics

    PubMed Central

    Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y. C.

    2015-01-01

    A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals. PMID:26064591

  10. Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.

    PubMed

    Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y C

    2015-01-01

    A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals.

  11. Iterative solution of the Helmholtz equation

    SciTech Connect

    Larsson, E.; Otto, K.

    1996-12-31

    We have shown that the numerical solution of the two-dimensional Helmholtz equation can be obtained in a very efficient way by using a preconditioned iterative method. We discretize the equation with second-order accurate finite difference operators and take special care to obtain non-reflecting boundary conditions. We solve the large, sparse system of equations that arises with the preconditioned restarted GMRES iteration. The preconditioner is of {open_quotes}fast Poisson type{close_quotes}, and is derived as a direct solver for a modified PDE problem.The arithmetic complexity for the preconditioner is O(n log{sub 2} n), where n is the number of grid points. As a test problem we use the propagation of sound waves in water in a duct with curved bottom. Numerical experiments show that the preconditioned iterative method is very efficient for this type of problem. The convergence rate does not decrease dramatically when the frequency increases. Compared to banded Gaussian elimination, which is a standard solution method for this type of problems, the iterative method shows significant gain in both storage requirement and arithmetic complexity. Furthermore, the relative gain increases when the frequency increases.

  12. Mosaic-skeleton method as applied to the numerical solution of three-dimensional Dirichlet problems for the Helmholtz equation in integral form

    NASA Astrophysics Data System (ADS)

    Kashirin, A. A.; Smagin, S. I.; Taltykina, M. Yu.

    2016-04-01

    Interior and exterior three-dimensional Dirichlet problems for the Helmholtz equation are solved numerically. They are formulated as equivalent boundary Fredholm integral equations of the first kind and are approximated by systems of linear algebraic equations, which are then solved numerically by applying an iteration method. The mosaic-skeleton method is used to speed up the solution procedure.

  13. Multigrid and cyclic reduction applied to the Helmholtz equation

    NASA Technical Reports Server (NTRS)

    Brackenridge, Kenneth

    1993-01-01

    We consider the Helmholtz equation with a discontinuous complex parameter and inhomogeneous Dirichlet boundary conditions in a rectangular domain. A variant of the direct method of cyclic reduction (CR) is employed to facilitate the design of improved multigrid (MG) components, resulting in the method of CR-MG. We demonstrate the improved convergence properties of this method.

  14. Bistable dark solitons of a cubic-quintic Helmholtz equation

    SciTech Connect

    Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.

    2010-05-15

    We provide a report on exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an investigation of the modulational instability characteristics of Helmholtz plane waves. We then derive a dark soliton by mapping the desired asymptotic form onto a uniform background field and obtain a more general solution by deploying rotational invariance laws in the laboratory frame. The geometry of the new soliton is explored in detail, and a range of new physical predictions is uncovered. Particular attention is paid to the unified phenomena of arbitrary-angle off-axis propagation and nondegenerate bistability. Crucially, the corresponding solution of paraxial theory emerges in a simultaneous multiple limit. We conclude with a set of computer simulations that examine the role of Helmholtz dark solitons as robust attractors.

  15. Transition between free-space Helmholtz equation solutions with plane sources and parabolic wave equation solutions.

    PubMed

    Mahillo-Isla, R; Gonźalez-Morales, M J; Dehesa-Martínez, C

    2011-06-01

    The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well.

  16. Galerkin Boundary Integral Analysis for the 3D Helmholtz Equation

    SciTech Connect

    Swager, Melissa; Gray, Leonard J; Nintcheu Fata, Sylvain

    2010-01-01

    A linear element Galerkin boundary integral analysis for the three-dimensional Helmholtz equation is presented. The emphasis is on solving acoustic scattering by an open (crack) surface, and to this end both a dual equation formulation and a symmetric hypersingular formulation have been developed. All singular integrals are defined and evaluated via a boundary limit process, facilitating the evaluation of the (finite) hypersingular Galerkin integral. This limit process is also the basis for the algorithm for post-processing of the surface gradient. The analytic integrations required by the limit process are carried out by employing a Taylor series expansion for the exponential factor in the Helmholtz fundamental solutions. For the open surface, the implementations are validated by comparing the numerical results obtained by using the two different methods.

  17. Volume integrals of ellipsoids associated with the inhomogeneous Helmholtz equation

    NASA Technical Reports Server (NTRS)

    Fu, L. S.; Mura, T.

    1982-01-01

    Problems of wave phenomena in the fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the inhomogeneous Helmholtz equation, for an ellipsoidal region. By using appropriate Taylor series expansions and the multinomial theorem, these volume integrals are obtained in series form for regions r greater than r-prime and r less than r-prime, where r and r-prime are the distances from the origin to the point of observation and the source. Derivatives of these integrals are easily evaluated. When the wavenumber approaches zero the results reduce directly to the potentials of ellipsoids of variable densities.

  18. Precise evaluation of the Helmholtz equation for optical propagation.

    PubMed

    Pond, John E; Sutton, George W

    2015-01-01

    A precise computational integration of the Helmholtz equation was performed for laser propagation of an electromagnetic wave with no approximations or linearization. This computation integration was performed using 64-bit processors. This is illustrated for a uniform monochromatic beam from a circular aperture that has a uniform intensity. It predicts many Arago spots and near-field intensity fluctuations for a large ratio of aperture size to wavelength and converges to the usual Airy pattern in the far field.

  19. An iterative solver for the 3D Helmholtz equation

    NASA Astrophysics Data System (ADS)

    Belonosov, Mikhail; Dmitriev, Maxim; Kostin, Victor; Neklyudov, Dmitry; Tcheverda, Vladimir

    2017-09-01

    We develop a frequency-domain iterative solver for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our solver has been verified by benchmarking against exact solutions and a time-domain solver.

  20. Exact nonparaxial beams of the scalar Helmholtz equation.

    PubMed

    Rodríguez-Morales, Gustavo; Chávez-Cerda, Sabino

    2004-03-01

    It is shown that three-dimensional nonparaxial beams are described by the oblate spheroidal exact solutions of the Helmholtz equation. For what is believed to be the first time, their beam behavior is investigated and their corresponding parameters are defined. Using the fact that the beam width of the family of paraxial Gaussian beams is described by a hyperbola, we formally establish the connection between the physical parameters of nonparaxial spheroidal beam solutions and those of paraxial beams. These results are also helpful for investigating exact vector nonparaxial beams.

  1. The Radially Symmetric Euler Equations as an Exterior Differential System

    NASA Astrophysics Data System (ADS)

    Baty, Roy; Ramsey, Scott; Schmidt, Joseph

    2016-11-01

    This work develops the Euler equations as an exterior differential system in radially symmetric coordinates. The Euler equations are studied for unsteady, compressible, inviscid fluids in one-dimensional, converging flow fields with a general equation of state. The basic geometrical constructions (for example, the differential forms, tangent planes, jet space, and differential ideal) used to define and analyze differential equations as systems of exterior forms are reviewed and discussed for converging flows. Application of the Frobenius theorem to the question of the existence of solutions to radially symmetric converging flows is also reviewed and discussed. The exterior differential system is further applied to derive and analyze the general family of characteristic vector fields associated with the one-dimensional inviscid flow equations.

  2. The analytic continuation of solutions of the generalized axially symmetric Helmholtz equation

    NASA Astrophysics Data System (ADS)

    Millar, R. F.

    1983-12-01

    The analytic continuation of a solution of the generalized axially symmetric Helmholtz equation u xx + u yy + (2α/ x) u x + k 2 u = 0is examined. A representation in terms of boundary data and the complex Riemann function is given for the continuation of the solution to an analytic boundary value problem; this also provides the solution of the analytic Cauchy problem on an analytic arc. Integral representations are found for the Riemann function, and the axial behaviour of the Riemann function is determined and used to recover a representation for the solution in terms of analytic axial data, as given originally by Henrici. For an exterior boundary value problem in which the axial values of the solution are defined on two disjoint, semi-infinite segments of the axis, it is shown that the two functions are not analytic continuations of one an-other and that a certain linear combination of them is an entire function. As an example, for α = 1/2 it is shown that the continuation of an exterior solution for a prolate spheroidal boundary is logarithmically infinite on the interfocal segment. A further special case, one that involves wave scattering by slender bodies of revolution for which the solution may be represented as a superposition over axial singularities, is briefly examined; properties of the axial values which are forced by this representation are determined and, where comparison is possible, shown to be consistent with the present work.

  3. A double-sweeping preconditioner for the Helmholtz equation

    NASA Astrophysics Data System (ADS)

    Eslaminia, Mehran; Guddati, Murthy N.

    2016-06-01

    A new preconditioner is developed to increase the efficiency of iterative solution of the Helmholtz equation. The key idea of the proposed preconditioner is to split the domain of interest into smaller subdomains and sequentially approximate the forward and backward components of the solution. The sequential solution is facilitated by approximate interface conditions that ignore the effect of multiple reflections. The efficiency of the proposed method is tested using various 2-D heterogeneous media. We observe that the proposed preconditioner results in good convergence, with number of iterations growing very slowly with increasing frequency. We also note that the mesh size and number of subdomains do not affect the convergence rate. Finally, we find that the overall computational time is much smaller than that of the sweeping preconditioner.

  4. Inverse medium scattering for the Helmholtz equation at fixed frequency

    NASA Astrophysics Data System (ADS)

    Bao, Gang; Li, Peijun

    2005-10-01

    Consider a time-harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain in \\bb{R}^2 . In this paper, existence and uniqueness of the variational problem for the direct scattering are established. An energy estimate for the scattered field is obtained on which the Born approximation is based. The Fréchet differentiability of the scattering map is examined. A new continuation method for the inverse medium scattering, which reconstructs the scatterer of an inhomogeneous medium from the boundary measurements of the scattered waves, is developed. The algorithm requires only single-frequency scattering data. Using an initial guess from the Born approximation, each update is obtained via recursive linearization on the spatial frequency of a one-parameter family of plane waves by solving one forward and one adjoint problem of the Helmholtz equation.

  5. 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.

  6. First-order system least-squares for the Helmholtz equation

    SciTech Connect

    Lee, B.; Manteuffel, T.; McCormick, S.; Ruge, J.

    1996-12-31

    We apply the FOSLS methodology to the exterior Helmholtz equation {Delta}p + k{sup 2}p = 0. Several least-squares functionals, some of which include both H{sup -1}({Omega}) and L{sup 2}({Omega}) terms, are examined. We show that in a special subspace of [H(div; {Omega}) {intersection} H(curl; {Omega})] x H{sup 1}({Omega}), each of these functionals are equivalent independent of k to a scaled H{sup 1}({Omega}) norm of p and u = {del}p. This special subspace does not include the oscillatory near-nullspace components ce{sup ik}({sup {alpha}x+{beta}y)}, where c is a complex vector and where {alpha}{sub 2} + {beta}{sup 2} = 1. These components are eliminated by applying a non-standard coarsening scheme. We achieve this scheme by introducing {open_quotes}ray{close_quotes} basis functions which depend on the parameter pair ({alpha}, {beta}), and which approximate ce{sup ik}({sup {alpha}x+{beta}y)} well on the coarser levels where bilinears cannot. We use several pairs of these parameters on each of these coarser levels so that several coarse grid problems are spun off from the finer levels. Some extensions of this theory to the transverse electric wave solution for Maxwell`s equations will also be presented.

  7. An invariant shape representation using the anisotropic Helmholtz equation.

    PubMed

    Joshi, A A; Ashrafulla, S; Shattuck, D W; Damasio, H; Leahy, R M

    2012-01-01

    Analyzing geometry of sulcal curves on the human cortical surface requires a shape representation invariant to Euclidean motion. We present a novel shape representation that characterizes the shape of a curve in terms of a coordinate system based on the eigensystem of the anisotropic Helmholtz equation. This representation has many desirable properties: stability, uniqueness and invariance to scaling and isometric transformation. Under this representation, we can find a point-wise shape distance between curves as well as a bijective smooth point-to-point correspondence. When the curves are sampled irregularly, we also present a fast and accurate computational method for solving the eigensystem using a finite element formulation. This shape representation is used to find symmetries between corresponding sulcal shapes between cortical hemispheres. For this purpose, we automatically generate 26 sulcal curves for 24 subject brains and then compute their invariant shape representation. Left-right sulcal shape symmetry as measured by the shape representation's metric demonstrates the utility of the presented invariant representation for shape analysis of the cortical folding pattern.

  8. A spectral boundary integral equation method for the 2-D Helmholtz equation

    NASA Technical Reports Server (NTRS)

    Hu, Fang Q.

    1994-01-01

    In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.

  9. SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES.

    PubMed

    Wan, Xiaohai; Li, Zhilin

    2012-06-01

    Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size.

  10. SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES

    PubMed Central

    Wan, Xiaohai; Li, Zhilin

    2012-01-01

    Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size. PMID:22701346

  11. Convergence analysis of a balalncing domain decomposition method for solving interior Helmholtz equations

    SciTech Connect

    Li,Jing; Tu, Xuemin

    2008-12-10

    A variant of balancing domain decomposition method by constraints (BDDC) is proposed for solving a class of indefinite system of linear equations, which arises from the finite element discretization of the Helmholtz equation of time-harmonic wave propagation in a bounded interior domain. The proposed BDDC algorithm is closely related to the dual-primal finite element tearing and interconnecting algorithm for solving Helmholtz equations (FETI-DPH). Under the condition that the diameters of the subdomains are small enough, the rate of convergence is established which depends polylogarithmically on the dimension of the individual subdomain problems and which improves with the decrease of the subdomain diameters. These results are supported by numerical experiments of solving a Helmholtz equation on a two-dimensional square domain.

  12. Wavenumber Explicit Analysis for a DPG Method for the Multidimensional Helmholtz Equation

    DTIC Science & Technology

    2011-07-01

    Application to the Helmholtz equation. We consider a bounded domain Ω ⊂ Rn (n ≥ 2) with Lipschitz boundary. Let f ∈ L2(Ω) and g ∈ H−1/2(∂Ω). We...Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?, SIAM Rev., 42 (2000), pp. 451–484 ( electronic ...equations, Electron . Trans. Numer. Anal., 6 (1997), pp. 162–181 ( electronic ). Special issue on multilevel methods (Copper Mountain, CO, 1997). [4] O

  13. Accelerated over relaxation iterative method using triangle element approximation for solving 2D Helmholtz Equations

    NASA Astrophysics Data System (ADS)

    Akhir, M. K. M.; Sulaiman, J.

    2017-09-01

    Weighted iterative methods particularly Accelerated Over Relaxation (AOR) method are used to solve linear system generated from triangle finite element approximation equation in solving 2D Helmholtz equation. The development of the AOR iterative method were also presented. Numerical experiments have been carried out and the results obtained confirm the superiority of the proposed iterative method

  14. The Two Dimensional Euler Equations on Singular Exterior Domains

    NASA Astrophysics Data System (ADS)

    Gérard-Varet, David; Lacave, Christophe

    2015-12-01

    This paper is a follow-up of Gérard-Varet and Lacave (Arch Ration Mech Anal 209(1):131-170, 2013), on the existence of global weak solutions to the two dimensional Euler equations in singular domains. In Gérard-Varet and Lacave (Arch Ration Mech Anal 209(1):131-170, 2013), we have established the existence of weak solutions for a large class of bounded domains, with initial vorticity in L p ( p > 1). For unbounded domains, we have proved a similar result only when the initial vorticity is in {Lpc} ( p > 2) and when the domain is the exterior of a single obstacle. The goal here is to retrieve these two restrictions: we consider general initial vorticity in {L1 {\\cap} Lp} ( p > 1), outside an arbitrary number of obstacles (not reduced to points).

  15. Azimuthal anisotropy at Valhall: The Helmholtz equation approach

    NASA Astrophysics Data System (ADS)

    Mordret, AuréLien; Shapiro, Nikolai M.; Singh, Satish; Roux, Philippe; Montagner, Jean-Paul; Barkved, Olav. I.

    2013-06-01

    We used 6 h of continuous vertical records from 2320 sensors of the Valhall Life of Fields Seismic network to compute 2,690,040 cross-correlation functions between the full set of sensor pair combinations. We applied the "Helmholtz tomography" approach combined with the ambient noise correlation method to track the wave front across the network with every station considered as a virtual source. The gradient of the interpolated phase travel time gives us an estimate of the local phase speed and of the direction of wave propagation. By combining the individual measurements for every station, we estimated the distribution of Scholte's wave phase speeds with respect to azimuth. The observed cosine pattern indicates the presence of azimuthal anisotropy. The elliptic shape of the fast anisotropy direction is consistent with results of previous shear wave splitting studies and reflects the strong seafloor subsidence due to the hydrocarbon reservoir depletion at depth and is in good agreement with geomechanical modeling.

  16. Volume integrals associated with the inhomogeneous Helmholtz equation. Part 1: Ellipsoidal region

    NASA Technical Reports Server (NTRS)

    Fu, L. S.; Mura, T.

    1983-01-01

    Problems of wave phenomena in fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) to alpha(2), for the case of an ellipsoidal region. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r 4' and r r', where r and r' are distances from the origin to the point of observation and source, respectively. Derivatives of these integrals are easily evaluated. When the wave number approaches zero, the results reduce directly to the potentials of variable densities.

  17. Resolution of coupled Helmholtz equation in the inhomogeneous coaxial waveguides by the finite element method

    NASA Astrophysics Data System (ADS)

    Bour, M.; Toumanari, A.; Khatib, D.

    2007-04-01

    This paper presents the application of the Finite Element Method FEM to the resolution of system Helmholtz coupled equations that has been obtained in the coaxial waveguides containing magnetic anisotropic materials with loss. This application is based on variational method which necessitates the construction of functional stationary written in the form of integral equation and dependent on the electromagnetic fields. After being minimized, this functional leads to algebraic equation system to which we can apply many numerical resolution algorithms. The electromagnetic study of the waveguide led us to a system of Helmholtz coupled equations which is difficult to be solved analytically. Our software code allows us to determine the electromagnetic field distribution in all points of the coaxial waveguide. The result has been validated when the coaxial waveguide was entirely loaded with air. This software has later been applied when the waveguide was partially filled with a magnetic anisotropic material with loss (\\varepsilon_r, overline{overline{μ_r}}).

  18. On the solution of the Helmholtz equation on regions with corners.

    PubMed

    Serkh, Kirill; Rokhlin, Vladimir

    2016-08-16

    In this paper we solve several boundary value problems for the Helmholtz equation on polygonal domains. We observe that when the problems are formulated as the boundary integral equations of potential theory, the solutions are representable by series of appropriately chosen Bessel functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.

  19. Inverse scattering for the one-dimensional Helmholtz equation: fast numerical method.

    PubMed

    Belai, Oleg V; Frumin, Leonid L; Podivilov, Evgeny V; Shapiro, David A

    2008-09-15

    The inverse scattering problem for the one-dimensional Helmholtz wave equation is studied. The equation is reduced to a Fresnel set that describes multiple bulk reflection and is similar to the coupled-wave equations. The inverse scattering problem is equivalent to coupled Gel'fand-Levitan-Marchenko integral equations. In the discrete representation its matrix has Töplitz symmetry, and the fast inner bordering method can be applied for its inversion. Previously the method was developed for the design of fiber Bragg gratings. The testing example of a short Bragg reflector with deep modulation demonstrates the high efficiency of refractive-index reconstruction.

  20. A High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions

    NASA Technical Reports Server (NTRS)

    Sun, Xian-He; Zhuang, Yu

    1997-01-01

    In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments are then introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern, and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.

  1. The arithmetic mean iterative method for solving 2D Helmholtz equation

    NASA Astrophysics Data System (ADS)

    Muthuvalu, Mohana Sundaram; Akhir, Mohd Kamalrulzaman Md; Sulaiman, Jumat; Suleiman, Mohamed; Dass, Sarat Chandra; Singh, Narinderjit Singh Sawaran

    2014-10-01

    In this paper, application of the Arithmetic Mean (AM) iterative method is extended by solving second order finite difference algebraic equations. The performance of AM method in solving second order finite difference algebraic equations is comparatively studied by their application on two-dimensional Helmholtz equation. Numerical results of AM method in solving two test problems are included and compared with the standard Gauss-Seidel (GS) method. Based on the numerical results obtained, the results show that AM method is better than GS method in the sense of number of iterations and CPU time.

  2. A convergent Born series for solving the inhomogeneous Helmholtz equation in arbitrarily large media

    NASA Astrophysics Data System (ADS)

    Osnabrugge, Gerwin; Leedumrongwatthanakun, Saroch; Vellekoop, Ivo M.

    2016-10-01

    We present a fast method for numerically solving the inhomogeneous Helmholtz equation. Our iterative method is based on the Born series, which we modified to achieve convergence for scattering media of arbitrary size and scattering strength. Compared to pseudospectral time-domain simulations, our modified Born approach is two orders of magnitude faster and nine orders of magnitude more accurate in benchmark tests in 1, 2, and 3-dimensional systems.

  3. Green function of the inhomogeneous Helmholtz equation with nonuniform refraction index, using quaternion analysis

    SciTech Connect

    Fathi, S. M. Saberi

    2010-12-15

    In this paper we first show in the framework of quaternion analysis how the fundamental solutions of the Dirac operators with vector potential can be obtained. Then, we use the obtained results to present a derivation of the exact analytic Green function for the Helmholtz equation, i.e., ({Delta}+|a(x)|{sup 2})G{sub 0}(x)={delta}(x), for the case a(x) is a monogenic (analytic) vector potential.

  4. A symmetric Trefftz-DG formulation based on a local boundary element method for the solution of the Helmholtz equation

    NASA Astrophysics Data System (ADS)

    Barucq, H.; Bendali, A.; Fares, M.; Mattesi, V.; Tordeux, S.

    2017-02-01

    A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly its outstanding ability to reduce the instabilities known as the "pollution effect" in the literature on numerical simulations of long-range wave propagation.

  5. Combined Helmholtz equation-least squares method for reconstructing acoustic radiation from arbitrarily shaped objects.

    PubMed

    Wu, Sean F; Zhao, Xiang

    2002-07-01

    A combined Helmholtz equation-least squares (CHELS) method is developed for reconstructing acoustic radiation from an arbitrary object. This method combines the advantages of both the HELS method and the Helmholtz integral theory based near-field acoustic holography (NAH). As such it allows for reconstruction of the acoustic field radiated from an arbitrary object with relatively few measurements, thus significantly enhancing the reconstruction efficiency. The first step in the CHELS method is to establish the HELS formulations based on a finite number of acoustic pressure measurements taken on or beyond a hypothetical spherical surface that encloses the object under consideration. Next enough field acoustic pressures are generated using the HELS formulations and taken as the input to the Helmholtz integral formulations implemented through the boundary element method (BEM). The acoustic pressure and normal component of the velocity at the discretized nodes on the surface are then determined by solving two matrix equations using singular value decomposition (SVD) and regularization techniques. Also presented are in-depth analyses of the advantages and limitations of the CHELS method. Examples of reconstructing acoustic radiation from separable and nonseparable surfaces are demonstrated.

  6. Combined Helmholtz equation-least squares method for reconstructing acoustic radiation from arbitrarily shaped objects

    NASA Astrophysics Data System (ADS)

    Wu, Sean F.; Zhao, Xiang

    2002-07-01

    A combined Helmholtz equation-least squares (CHELS) method is developed for reconstructing acoustic radiation from an arbitrary object. This method combines the advantages of both the HELS method and the Helmholtz integral theory based near-field acoustic holography (NAH). As such it allows for reconstruction of the acoustic field radiated from an arbitrary object with relatively few measurements, thus significantly enhancing the reconstruction efficiency. The first step in the CHELS method is to establish the HELS formulations based on a finite number of acoustic pressure measurements taken on or beyond a hypothetical spherical surface that encloses the object under consideration. Next enough field acoustic pressures are generated using the HELS formulations and taken as the input to the Helmholtz integral formulations implemented through the boundary element method (BEM). The acoustic pressure and normal component of the velocity at the discretized nodes on the surface are then determined by solving two matrix equations using singular value decomposition (SVD) and regularization techniques. Also presented are in-depth analyses of the advantages and limitations of the CHELS method. Examples of reconstructing acoustic radiation from separable and nonseparable surfaces are demonstrated. copyright 2002 Acoustical Society of America.

  7. Solutions of the Helmholtz equation with boundary conditions for force-free magnetic fields

    NASA Technical Reports Server (NTRS)

    Rasband, S. N.; Turner, L.

    1981-01-01

    It is shown that the solution, with one ignorable coordinate, for the Taylor minimum energy state (resulting in a force-free magnetic field) in either a straight cylindrical or a toroidal geometry with arbitrary cross section can be reduced to the solution of either an inhomogeneous Helmholtz equation or a Grad-Shafranov equation with simple boundary conditions. Standard Green's function theory is, therefore, applicable. Detailed solutions are presented for the Taylor state in toroidal and cylindrical domains having a rectangular cross section. The focus is on solutions corresponding to the continuous eigenvalue spectra. Singular behavior at 90 deg corners is explored in detail.

  8. Diffusion phenomenon for linear dissipative wave equations in an exterior domain

    NASA Astrophysics Data System (ADS)

    Ikehata, Ryo

    Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

  9. Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions

    NASA Technical Reports Server (NTRS)

    Hodge, Steve L.; Zorumski, William E.; Watson, Willie R.

    1995-01-01

    The Helmholtz equation is solved within a three-dimensional rectangular duct with a nonlocal radiation boundary condition at the duct exit plane. This condition accurately models the acoustic admittance at an arbitrarily-located computational boundary plane. A linear system of equations is constructed with second-order central differences for the Helmholtz operator and second-order backward differences for both local admittance conditions and the gradient term in the nonlocal radiation boundary condition. The resulting matrix equation is large, sparse, and non-Hermitian. The size and structure of the matrix makes direct solution techniques impractical; as a result, a nonstationary iterative technique is used for its solution. The theory behind the nonstationary technique is reviewed, and numerical results are presented for radiation from both a point source and a planar acoustic source. The solutions with the nonlocal boundary conditions are invariant to the location of the computational boundary, and the same nonlocal conditions are valid for all solutions. The nonlocal conditions thus provide a means of minimizing the size of three-dimensional computational domains.

  10. Vortex lattices generated by the Kelvin-Helmholtz instability in the Gross-Pitaevskii equation

    SciTech Connect

    Ohta, A.; Kashiwa, R.; Sakaguchi, H.

    2010-11-15

    Vortex streets are formed from sheared initial conditions in classical fluids even without viscosity, which is called the Kelvin-Helmholtz instability. We demonstrate that similar vortex streets are generated from sheared initial conditions by the direct numerical simulation of the Gross-Pitaevskii (GP) equation which describes the dynamics of the Bose-Einstein condensates. Furthermore, we show the vortex-lattice formation from sheared initial conditions analogous to the rigid-body rotation in the GP equation under a rotating harmonic potential. The vortex-lattice formation by the dynamical instability in the system without energy dissipation differs from the vortex-lattice formation process by the imaginary time evolution of the GP equation where the lowest energy state is obtained.

  11. A numerical scheme for nonlinear Helmholtz equations with strong nonlinear optical effects.

    PubMed

    Xu, Zhengfu; Bao, Gang

    2010-11-01

    A numerical scheme is presented to solve the nonlinear Helmholtz (NLH) equation modeling second-harmonic generation (SHG) in photonic bandgap material doped with a nonlinear χ((2)) effect and the NLH equation modeling wave propagation in Kerr type gratings with a nonlinear χ((3)) effect in the one-dimensional case. Both of these nonlinear phenomena arise as a result of the combination of high electromagnetic mode density and nonlinear reaction from the medium. When the mode intensity of the incident wave is significantly strong, which makes the nonlinear effect non-negligible, numerical methods based on the linearization of the essentially nonlinear problem will become inadequate. In this work, a robust, stable numerical scheme is designed to simulate the NLH equations with strong nonlinearity.

  12. A broadband fast multipole accelerated boundary element method for the three dimensional Helmholtz equation.

    PubMed

    Gumerov, Nail A; Duraiswami, Ramani

    2009-01-01

    The development of a fast multipole method (FMM) accelerated iterative solution of the boundary element method (BEM) for the Helmholtz equations in three dimensions is described. The FMM for the Helmholtz equation is significantly different for problems with low and high kD (where k is the wavenumber and D the domain size), and for large problems the method must be switched between levels of the hierarchy. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements), and these errors must be balanced against approximations introduced by the FMM and the convergence criterion for iterative solution. These different errors must all be chosen in a way that, on the one hand, excess work is not done and, on the other, that the error achieved by the overall computation is acceptable. Details of translation operators for low and high kD, choice of representations, and BEM quadrature schemes, all consistent with these approximations, are described. A novel preconditioner using a low accuracy FMM accelerated solver as a right preconditioner is also described. Results of the developed solvers for large boundary value problems with 0.0001 less, similarkD less, similar500 are presented and shown to perform close to theoretical expectations.

  13. Accelerating the shifted Laplace preconditioner for the Helmholtz equation by multilevel deflation

    NASA Astrophysics Data System (ADS)

    Sheikh, A. H.; Lahaye, D.; Garcia Ramos, L.; Nabben, R.; Vuik, C.

    2016-10-01

    Many important physical phenomena can be described by the Helmholtz equation. We investigate to what extent the convergence of the shifted Laplacian preconditioner for the Helmholtz equation can be accelerated using deflation with multigrid vectors. We therefore present a unified framework for two published algorithms. The first deflates the preconditioned operator and requires no further preconditioning. The second deflates the original operator and combines deflation and preconditioning in a multiplicative fashion. We pursue two scientific contributions. First we show, using a model problem analysis, that both algorithms cluster the eigenvalues. The new and key insight here is that the near-kernel of the coarse grid operator causes a limited set of eigenvalues to shift away from the center of the cluster with a distance proportional to the wave number. This effect is less pronounced in the first algorithmic variant at the expense of a higher computational cost. In the second contribution we quantify for the first time the large amount of reduction in CPU-time that results from the clustering of eigenvalues and the reduction in iteration count. We report to this end on the findings of an implementation in PETSc on two and three-dimensional problems with constant and variable wave number.

  14. Preconditioning based on Calderon's formulae for periodic fast multipole methods for Helmholtz' equation

    NASA Astrophysics Data System (ADS)

    Niino, Kazuki; Nishimura, Naoshi

    2012-01-01

    Solution of periodic boundary value problems is of interest in various branches of science and engineering such as optics, electromagnetics and mechanics. In our previous studies we have developed a periodic fast multipole method (FMM) as a fast solver of wave problems in periodic domains. It has been found, however, that the convergence of the iterative solvers for linear equations slows down when the solutions show anomalies related to the periodicity of the problems. In this paper, we propose preconditioning schemes based on Calderon's formulae to accelerate convergence of iterative solvers in the periodic FMM for Helmholtz' equations. The proposed preconditioners can be implemented more easily than conventional ones. We present several numerical examples to test the performance of the proposed preconditioners. We show that the effectiveness of these preconditioners is definite even near anomalies.

  15. Stability of a modified Peaceman–Rachford method for the paraxial Helmholtz equation on adaptive grids

    SciTech Connect

    Sheng, Qin; Sun, Hai-wei

    2016-11-15

    This study concerns the asymptotic stability of an eikonal, or ray, transformation based Peaceman–Rachford splitting method for solving the paraxial Helmholtz equation with high wave numbers. Arbitrary nonuniform grids are considered in transverse and beam propagation directions. The differential equation targeted has been used for modeling propagations of high intensity laser pulses over a long distance without diffractions. Self-focusing of high intensity beams may be balanced with the de-focusing effect of created ionized plasma channel in the situation, and applications of grid adaptations are frequently essential. It is shown rigorously that the fully discretized oscillation-free decomposition method on arbitrary adaptive grids is asymptotically stable with a stability index one. Simulation experiments are carried out to illustrate our concern and conclusions.

  16. Stability of a modified Peaceman-Rachford method for the paraxial Helmholtz equation on adaptive grids

    NASA Astrophysics Data System (ADS)

    Sheng, Qin; Sun, Hai-wei

    2016-11-01

    This study concerns the asymptotic stability of an eikonal, or ray, transformation based Peaceman-Rachford splitting method for solving the paraxial Helmholtz equation with high wave numbers. Arbitrary nonuniform grids are considered in transverse and beam propagation directions. The differential equation targeted has been used for modeling propagations of high intensity laser pulses over a long distance without diffractions. Self-focusing of high intensity beams may be balanced with the de-focusing effect of created ionized plasma channel in the situation, and applications of grid adaptations are frequently essential. It is shown rigorously that the fully discretized oscillation-free decomposition method on arbitrary adaptive grids is asymptotically stable with a stability index one. Simulation experiments are carried out to illustrate our concern and conclusions.

  17. Fast Huygens sweeping methods for Helmholtz equations in inhomogeneous media in the high frequency regime

    NASA Astrophysics Data System (ADS)

    Luo, Songting; Qian, Jianliang; Burridge, Robert

    2014-08-01

    In some applications, it is reasonable to assume that geodesics (rays) have a consistent orientation so that the Helmholtz equation may be viewed as an evolution equation in one of the spatial directions. With such applications in mind, we propose a new Eulerian computational geometrical-optics method, dubbed the fast Huygens sweeping method, for computing Green functions of Helmholtz equations in inhomogeneous media in the high-frequency regime and in the presence of caustics. The first novelty of the new method is that the Huygens-Kirchhoff secondary source principle is used to integrate many locally valid asymptotic solutions to yield a globally valid asymptotic solution so that caustics associated with the usual geometrical-optics ansatz can be treated automatically. The second novelty is that a butterfly algorithm is adapted to carry out the matrix-vector products induced by the Huygens-Kirchhoff integration in O(Nlog N) operations, where N is the total number of mesh points, and the proportionality constant depends on the desired accuracy and is independent of the frequency parameter. To reduce the storage of the resulting traveltime and amplitude tables, we compress each table into a linear combination of tensor-product based multivariate Chebyshev polynomials so that the information of each table is encoded into a small number of Chebyshev coefficients. The new method enjoys the following desired features: (1) it precomputes a set of local traveltime and amplitude tables; (2) it automatically takes care of caustics; (3) it constructs Green functions of the Helmholtz equation for arbitrary frequencies and for many point sources; (4) for a specified number of points per wavelength it constructs each Green function in nearly optimal complexity in terms of the total number of mesh points, where the prefactor of the complexity only depends on the specified accuracy and is independent of the frequency parameter. Both two-dimensional (2-D) and three-dimensional (3

  18. On reconstruction of acoustic pressure fields using the Helmholtz equation least squares method

    PubMed

    Wu

    2000-05-01

    This paper presents analyses and implementation of the reconstruction of acoustic pressure fields radiated from a general, three-dimensional complex vibrating structure using the Helmholtz equation least-squares (HELS) method. The structure under consideration emulates a full-size four-cylinder engine. To simulate sound radiation from a vibrating structure, harmonic excitations are assumed to act on arbitrarily selected surfaces. The resulting vibration responses are solved by the commercial FEM (finite element method) software I-DEAS. Once the normal component of the surface velocity distribution is determined, the surface acoustic pressures are calculated using standard boundary element method (BEM) codes. The radiated acoustic pressures over several planar surfaces at certain distances from the source are calculated by the Helmholtz integral formulation. These field pressures are taken as the input to the HELS formulation to reconstruct acoustic pressures on the entire source surface, as well as in the field. The reconstructed acoustic pressures thus obtained are then compared with benchmark values. Numerical results demonstrate that good agreements can be obtained with relatively few expansion functions. The HELS method is shown to be very effective in the low-to-mid frequency regime, and can potentially become a powerful noise diagnostic tool.

  19. Babich's expansion and the fast Huygens sweeping method for the Helmholtz wave equation at high frequencies

    NASA Astrophysics Data System (ADS)

    Lu, Wangtao; Qian, Jianliang; Burridge, Robert

    2016-05-01

    In some applications, it is reasonable to assume that geodesics (rays) have a consistent orientation so that the Helmholtz equation can be viewed as an evolution equation in one of the spatial directions. With such applications in mind, starting from Babich's expansion, we develop a new high-order asymptotic method, which we dub the fast Huygens sweeping method, for solving point-source Helmholtz equations in inhomogeneous media in the high-frequency regime and in the presence of caustics. The first novelty of this method is that we develop a new Eulerian approach to compute the asymptotics, i.e. the traveltime function and amplitude coefficients that arise in Babich's expansion, yielding a locally valid solution, which is accurate close enough to the source. The second novelty is that we utilize the Huygens-Kirchhoff integral to integrate many locally valid wavefields to construct globally valid wavefields. This automatically treats caustics and yields uniformly accurate solutions both near the source and remote from it. The third novelty is that the butterfly algorithm is adapted to accelerate the Huygens-Kirchhoff summation, achieving nearly optimal complexity O (Nlog ⁡ N), where N is the number of mesh points; the complexity prefactor depends on the desired accuracy and is independent of the frequency. To reduce the storage of the resulting tables of asymptotics in Babich's expansion, we use the multivariable Chebyshev series expansion to compress each table by encoding the information into a small number of coefficients. The new method enjoys the following desired features. First, it precomputes the asymptotics in Babich's expansion, such as traveltime and amplitudes. Second, it takes care of caustics automatically. Third, it can compute the point-source Helmholtz solution for many different sources at many frequencies simultaneously. Fourth, for a specified number of points per wavelength, it can construct the wavefield in nearly optimal complexity in terms

  20. Global existence of solutions for semilinear damped wave equation in 2-D exterior domain

    NASA Astrophysics Data System (ADS)

    Ikehata, Ryo

    We consider a mixed problem of a damped wave equation utt-Δ u+ ut=| u| p in the two dimensional exterior domain case. Small global in time solutions can be constructed in the case when the power p on the nonlinear term | u| p satisfies p ∗=2exterior domain. A new device developed in Ikehata-Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

  1. Two reconstruction procedures for a 3D phaseless inverse scattering problem for the generalized Helmholtz equation

    NASA Astrophysics Data System (ADS)

    Klibanov, Michael V.; Romanov, Vladimir G.

    2016-01-01

    The 3D inverse scattering problem of the reconstruction of the unknown dielectric permittivity in the generalized Helmholtz equation is considered. Applications are in imaging of nanostructures and biological cells. The main difference with the conventional inverse scattering problems is that only the modulus of the scattering wave field is measured. The phase is not measured. The initializing wave field is the incident plane wave. On the other hand, in the previous recent works of the authors about the ‘phaseless topic’ the case of the point source was considered (Klibanov and Romanov 2015 J. Inverse Ill-Posed Problem 23 415-28 J. Inverse Ill-Posed Problem 23 187-93). Two reconstruction procedures are developed.

  2. A fast Fourier transform on multipoles (FFTM) algorithm for solving Helmholtz equation in acoustics analysis.

    PubMed

    Ong, Eng Teo; Lee, Heow Pueh; Lim, Kian Meng

    2004-09-01

    This article presents a fast algorithm for the efficient solution of the Helmholtz equation. The method is based on the translation theory of the multipole expansions. Here, the speedup comes from the convolution nature of the translation operators, which can be evaluated rapidly using fast Fourier transform algorithms. Also, the computations of the translation operators are accelerated by using the recursive formulas developed recently by Gumerov and Duraiswami [SIAM J. Sci. Comput. 25, 1344-1381(2003)]. It is demonstrated that the algorithm can produce good accuracy with a relatively low order of expansion. Efficiency analyses of the algorithm reveal that it has computational complexities of O(Na), where a ranges from 1.05 to 1.24. However, this method requires substantially more memory to store the translation operators as compared to the fast multipole method. Hence, despite its simplicity in implementation, this memory requirement issue may limit the application of this algorithm to solving very large-scale problems.

  3. Bessel-Gauss beams as rigorous solutions of the Helmholtz equation.

    PubMed

    April, Alexandre

    2011-10-01

    The study of the nonparaxial propagation of optical beams has received considerable attention. In particular, the so-called complex-source/sink model can be used to describe strongly focused beams near the beam waist, but this method has not yet been applied to the Bessel-Gauss (BG) beam. In this paper, the complex-source/sink solution for the nonparaxial BG beam is expressed as a superposition of nonparaxial elegant Laguerre-Gaussian beams. This provides a direct way to write the explicit expression for a tightly focused BG beam that is an exact solution of the Helmholtz equation. It reduces correctly to the paraxial BG beam, the nonparaxial Gaussian beam, and the Bessel beam in the appropriate limits. The analytical expression can be used to calculate the field of a BG beam near its waist, and it may be useful in investigating the features of BG beams under tight focusing conditions.

  4. Absence of Critical Points of Solutions to the Helmholtz Equation in 3D

    NASA Astrophysics Data System (ADS)

    Alberti, Giovanni S.

    2016-11-01

    The focus of this paper is to show the absence of critical points for the solutions to the Helmholtz equation in a bounded domain {Ωsubset{R}3} , given by { div(a nabla u_{ω}g)-ω qu_{ω}g=0&quad{in Ω,} u_{ω}g=g quad{on partialΩ.} We prove that for an admissible g there exists a finite set of frequencies K in a given interval and an open cover {overline{Ω}=\\cup_{ωin K} Ω_{ω}} such that {|nabla u_{ω}g(x)| > 0} for every {ωin K} and {xinΩ_{ω}} . The set K is explicitly constructed. If the spectrum of this problem is simple, which is true for a generic domain {Ω} , the admissibility condition on g is a generic property.

  5. A numerical method for inverse source problems for Poisson and Helmholtz equations

    NASA Astrophysics Data System (ADS)

    Hamad, A.; Tadi, M.

    2016-11-01

    This paper is concerned with an iterative algorithm for inverse evaluation of the source function for two elliptic systems. The algorithm starts with an initial guess for the unknown source function, obtains a background field and, obtains the working equations for the error field. The correction to the assumed value appears as a source term for the error field. It formulates two well-posed problems for the error field which makes it possible to obtain the correction term. The algorithm can also recover the source function with partial data at the boundary. We consider 2-D as well as 3-D domains. The method can be applied to both Poisson and Helmholtz operators. Numerical results indicate that the algorithm can recover close estimates of the unknown source functions based on measurements collected at the boundary.

  6. Effect of triangular element orientation on finite element solutions of the Helmholtz equation

    NASA Technical Reports Server (NTRS)

    Baumeister, K. J.

    1986-01-01

    The Galerkin finite element solutions for the scalar homogeneous Helmholtz equation are presented for no reflection, hard wall, and potential relief exit terminations with a variety of triangular element orientations. For this group of problems, the correlation between the accuracy of the solution and the orientation of the linear triangle is examined. Nonsymmetric element patterns are found to give generally poor results in the model problems investigated, particularly for cases where standing waves exist. For a fixed number of vertical elements, the results showed that symmetric element patterns give much better agreement with corresponding exact analytical results. In laminated wave guide application, the symmetric pyramid pattern is convenient to use and is shown to give excellent results.

  7. Seafloor identification in sonar imagery via simulations of Helmholtz equations and discrete optimization

    NASA Astrophysics Data System (ADS)

    Engquist, Björn; Frederick, Christina; Huynh, Quyen; Zhou, Haomin

    2017-06-01

    We present a multiscale approach for identifying features in ocean beds by solving inverse problems in high frequency seafloor acoustics. The setting is based on Sound Navigation And Ranging (SONAR) imaging used in scientific, commercial, and military applications. The forward model incorporates multiscale simulations, by coupling Helmholtz equations and geometrical optics for a wide range of spatial scales in the seafloor geometry. This allows for detailed recovery of seafloor parameters including material type. Simulated backscattered data is generated using numerical microlocal analysis techniques. In order to lower the computational cost of the large-scale simulations in the inversion process, we take advantage of a pre-computed library of representative acoustic responses from various seafloor parameterizations.

  8. Wave chaos in the stadium: Statistical properties of short-wave solutions of the Helmholtz equation

    SciTech Connect

    McDonald, S.W.; Kaufman, A.N.

    1988-04-15

    We numerically investigate statistical properties of short-wavelength normal modes and the spectrum for the Helmholtz equation in a two-dimensional stadium-shaped region. As the geometrical optics rays within this boundary (billiards) are nonintegrable, this wave problem serves as a simple model for the study of quantum chaos. The local spatial correlation function and the probability distribution P/sub n/(psi) of wave amplitude for normal modes psi/sub n/ are computed and compared with predictions based on semiclassical arguments applied to this nonintegrable Hamiltonian. The spectrum is analyzed in terms of the probability P(..delta..E) of neighboring energy-eigenvalue separations, which is shown to be similar to a Wigner distribution for the eigenvalues of a random matrix

  9. Wave Gradiometry and Helmholtz Equation Solutions Applied to USArray across the Contiguous U.S.

    NASA Astrophysics Data System (ADS)

    Liu, Y.; Holt, W. E.

    2015-12-01

    Wave gradiometry is an array processing technique utilizing the shape of seismic wavefields captured by USArray TA stations to determine fundamental wave propagation characteristics. We first explore a compatibility relation that links spatial gradients of the wavefield with the displacements and the time derivatives of displacements through two unknown coefficients Aand B, which are solved through iterative, damped least-square inversion, to provide estimates of phase velocity, back-azimuth, radiation pattern and geometrical spreading. We show that the A-coefficient corresponds to the gradient of logarithmic amplitude and the B-coefficient corresponds approximately to the local dynamic phase velocity. These vector fields are interpolated to explore a second compatibility relation through solutions to the Helmholtz equation. For most wavefields passing through the eastern U.S., we show that the A-coefficients are generally orthogonal to the B-coefficients. Where they are not completely orthogonal, there is a strong positive correlation between the gradients of B-coefficients and changes in geometrical spreading, which can be further linked with areas of strong energy focusing and defocusing. We then obtain isotropic phase velocity maps across the contiguous United States for 20 - 150 s Rayleigh wave by stacking results from 700 earthquakes. The strong velocity variations in the western U.S. correlate well with known geological features and the am- plitude correction terms from Helmholtz equation solutions generally improve the resolution of small-scale structures for all periods analyzed. We also observe a velocity change along the approximate boundary of the early Paleozoic continental margin in the eastern U.S and two significant low velocity anomalies within the central Appalachians, one centered where Eocene basaltic volcanism has occurred, and the other within the northeastern U.S., possibly associated with the Great Meteor Hotspot track.

  10. Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation.

    PubMed

    Baydoun, Ibrahim; Baresch, Diego; Pierrat, Romain; Derode, Arnaud

    2016-11-01

    Heterogeneity can be accounted for by a random potential in the wave equation. For acoustic waves in a fluid with fluctuations of both density and compressibility (as well as for electromagnetic waves in a medium with fluctuation of both permittivity and permeability) the random potential entails a scalar and an operator contribution. For simplicity, the latter is usually overlooked in multiple scattering theory: whatever the type of waves, this simplification amounts to considering the Helmholtz equation with a sound speed c depending on position r. In this work, a radiative transfer equation is derived from the wave equation, in order to study energy transport through a multiple scattering medium. In particular, the influence of the operator term on various transport parameters is studied, based on the diagrammatic approach of multiple scattering. Analytical results are obtained for fundamental quantities of transport theory such as the transport mean-free path ℓ^{*}, scattering phase function f, and anisotropy factor g. Discarding the operator term in the wave equation is shown to have a significant impact on f and g, yet limited to the low-frequency regime, i.e., when the correlation length of the disorder ℓ_{c} is smaller than or comparable to the wavelength λ. More surprisingly, discarding the operator part has a significant impact on the transport mean-free path ℓ^{*} whatever the frequency regime. When the scalar and operator terms have identical amplitudes, the discrepancy on the transport mean-free path is around 300% in the low-frequency regime, and still above 30% for ℓ_{c}/λ=10^{3} no matter how weak fluctuations of the disorder are. Analytical results are supported by numerical simulations of the wave equation and Monte Carlo simulations.

  11. Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation

    NASA Astrophysics Data System (ADS)

    Baydoun, Ibrahim; Baresch, Diego; Pierrat, Romain; Derode, Arnaud

    2016-11-01

    Heterogeneity can be accounted for by a random potential in the wave equation. For acoustic waves in a fluid with fluctuations of both density and compressibility (as well as for electromagnetic waves in a medium with fluctuation of both permittivity and permeability) the random potential entails a scalar and an operator contribution. For simplicity, the latter is usually overlooked in multiple scattering theory: whatever the type of waves, this simplification amounts to considering the Helmholtz equation with a sound speed c depending on position r . In this work, a radiative transfer equation is derived from the wave equation, in order to study energy transport through a multiple scattering medium. In particular, the influence of the operator term on various transport parameters is studied, based on the diagrammatic approach of multiple scattering. Analytical results are obtained for fundamental quantities of transport theory such as the transport mean-free path ℓ*, scattering phase function f , and anisotropy factor g . Discarding the operator term in the wave equation is shown to have a significant impact on f and g , yet limited to the low-frequency regime, i.e., when the correlation length of the disorder ℓc is smaller than or comparable to the wavelength λ . More surprisingly, discarding the operator part has a significant impact on the transport mean-free path ℓ* whatever the frequency regime. When the scalar and operator terms have identical amplitudes, the discrepancy on the transport mean-free path is around 300 % in the low-frequency regime, and still above 30 % for ℓc/λ =103 no matter how weak fluctuations of the disorder are. Analytical results are supported by numerical simulations of the wave equation and Monte Carlo simulations.

  12. Radiation boundary condition and anisotropy correction for finite difference solutions of the Helmholtz equation

    NASA Technical Reports Server (NTRS)

    Tam, Christopher K. W.; Webb, Jay C.

    1994-01-01

    In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The

  13. Radiation boundary condition and anisotropy correction for finite difference solutions of the Helmholtz equation

    NASA Technical Reports Server (NTRS)

    Tam, Christopher K. W.; Webb, Jay C.

    1994-01-01

    In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The

  14. Helmholtz and parabolic equation solutions to a benchmark problem in ocean acoustics.

    PubMed

    Larsson, Elisabeth; Abrahamsson, Leif

    2003-05-01

    The Helmholtz equation (HE) describes wave propagation in applications such as acoustics and electromagnetics. For realistic problems, solving the HE is often too expensive. Instead, approximations like the parabolic wave equation (PE) are used. For low-frequency shallow-water environments, one persistent problem is to assess the accuracy of the PE model. In this work, a recently developed HE solver that can handle a smoothly varying bathymetry, variable material properties, and layered materials, is used for an investigation of the errors in PE solutions. In the HE solver, a preconditioned Krylov subspace method is applied to the discretized equations. The preconditioner combines domain decomposition and fast transform techniques. A benchmark problem with upslope-downslope propagation over a penetrable lossy seamount is solved. The numerical experiments show that, for the same bathymetry, a soft and slow bottom gives very similar HE and PE solutions, whereas the PE model is far from accurate for a hard and fast bottom. A first attempt to estimate the error is made by computing the relative deviation from the energy balance for the PE solution. This measure gives an indication of the magnitude of the error, but cannot be used as a strict error bound.

  15. The Dirichlet problem for the diffusion equation in the exterior of non-closed Lipschitz surfaces

    NASA Astrophysics Data System (ADS)

    Krutitskii, P. A.

    2012-09-01

    We study the Dirichlet problem for the stationary diffusion equation in the exterior of non-closed Lipschitz surfaces in R3. The Dirichlet problem for a Laplace equation is a particular case of our problem. Theorems on existence and uniqueness of a weak solution of the problem are proved. The integral representation for a solution is obtained in the form of single layer potential. The density in the potential is defined as a solution of the operator (integral) equation, which is uniquely solvable.

  16. Lie Symmetry Analysis of the Inhomogeneous Toda Lattice Equation via Semi-Discrete Exterior Calculus

    NASA Astrophysics Data System (ADS)

    Liu, Jiang; Wang, Deng-Shan; Yin, Yan-Bin

    2017-06-01

    In this work, the Lie point symmetries of the inhomogeneous Toda lattice equation are obtained by semi-discrete exterior calculus, which is a semi-discrete version of Harrison and Estabrook’s geometric approach. A four-dimensional Lie algebra and its one-, two- and three-dimensional subalgebras are given. Two similarity reductions of the inhomogeneous Toda lattice equation are obtained by using the symmetry vectors. Supported by National Natural Science Foundation of China under Grant Nos. 11375030, 11472315, and Department of Science and Technology of Henan Province under Grant No. 162300410223 and Beijing Finance Funds of Natural Science Program for Excellent Talents under Grant No. 2014000026833ZK19

  17. Numerical modeling of Kelvin-Helmholtz instability by using potential equation

    NASA Astrophysics Data System (ADS)

    Ahmadi, Somayeh

    2012-11-01

    This paper presents a potential flow numerical solution for the Kelvin-Helmholtz Instability (KHI) problem of an incompressible two-phase immiscible fluid in a stratified shear flow. As a problem: the two-fluid model becomes illposed when the slip velocity exceeds a critical value, and computations can be quite unstable before the flow reaches the ill-posed condition. In this work, computational stability of various convection schemes together with the potential equation method for the time derivatives in conjunction with the two-fluid model is analyzed. The normal stress balance (with the normal viscous stress) at the interface for the two-fluid model is carefully implemented to minimize its effect on numerical stability. Von Neumann stability analysis shows that: stability condition for two-fluid with equal kinematic viscosity ratio and inviscid flow, supply numerical stability. Excellent agreement has obtained according to analytical result that existing of imaginary part in solution which specialized this method. The numerical algorithm presented in this work can easily handle two-phase fluid flow with various density and viscosity ratios in rectangular channel. Simulation of this model has implemented by writing a code in FORTRAN programming.

  18. The method of polarized traces for the 2D Helmholtz equation

    NASA Astrophysics Data System (ADS)

    Zepeda-Núñez, Leonardo; Demanet, Laurent

    2016-03-01

    We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media, with online parallel complexity that scales optimally as O (N/L), where N is the number of volume unknowns, and L is the number of processors, as long as L grows at most like a small fractional power of N. The solver decomposes the domain into layers, and uses transmission conditions in boundary integral form to explicitly define "polarized traces", i.e., up- and down-going waves sampled at interfaces. Local direct solvers are used in each layer to precompute traces of local Green's functions in an embarrassingly parallel way (the offline part), and incomplete Green's formulas are used to propagate interface data in a sweeping fashion, as a preconditioner inside a GMRES loop (the online part). Adaptive low-rank partitioning of the integral kernels is used to speed up their application to interface data. The method uses second-order finite differences. The complexity scalings are empirical but motivated by an analysis of ranks of off-diagonal blocks of oscillatory integrals. They continue to hold in the context of standard geophysical community models such as BP and Marmousi 2, where convergence occurs in 5 to 10 GMRES iterations. While the parallelism in this paper stems from decomposing the domain, we do not explore the alternative of parallelizing the systems solves with distributed linear algebra routines.

  19. On the choice of expansion functions in the Helmholtz equation least-squares method.

    PubMed

    Semenova, Tatiana; Wu, Sean F

    2005-02-01

    This paper examines the performance of Helmholtz equation least-squares (HELS) method in reconstructing acoustic radiation from an arbitrary source by using three different expansions, namely, localized spherical waves (LSW), distributed spherical waves (DSW), and distributed point sources (DPS), under the same set of measurements. The reconstructed acoustic pressures are validated against the benchmark data measured at the same locations as reconstruction points for frequencies up to 3275 Hz. Reconstruction is obtained by using Tikhonov regularization or its modification with the regularization parameter selected by error-free parameter-choice methods. The impact of the number of measurement points on the resultant reconstruction accuracy under different expansion functions is investigated. Results demonstrate that DSW leads to a better-conditioned transfer matrix, yields more accurate reconstruction than both LSW and DPS, and is not affected as much by the change in measurement points. Also, it is possible to obtain optimal locations of the auxiliary sources for DSW, LSW, and DPS by taking an independent layer of measurements. Use of these auxiliary sources and an optimal combination of regularization and error-free parameter choice methods can yield a satisfactory reconstruction of acoustic quantities on the source surfaces as well as in the field in the most cost-effective manner.

  20. Reconstruction of vibroacoustic responses of a highly nonspherical structure using Helmholtz equation least-squares method.

    PubMed

    Lu, Huancai; Wu, Sean F

    2009-03-01

    The vibroacoustic responses of a highly nonspherical vibrating object are reconstructed using Helmholtz equation least-squares (HELS) method. The objectives of this study are to examine the accuracy of reconstruction and the impacts of various parameters involved in reconstruction using HELS. The test object is a simply supported and baffled thin plate. The reason for selecting this object is that it represents a class of structures that cannot be exactly described by the spherical Hankel functions and spherical harmonics, which are taken as the basis functions in the HELS formulation, yet the analytic solutions to vibroacoustic responses of a baffled plate are readily available so the accuracy of reconstruction can be checked accurately. The input field acoustic pressures for reconstruction are generated by the Rayleigh integral. The reconstructed normal surface velocities are validated against the benchmark values, and the out-of-plane vibration patterns at several natural frequencies are compared with the natural modes of a simply supported plate. The impacts of various parameters such as number of measurement points, measurement distance, location of the origin of the coordinate system, microphone spacing, and ratio of measurement aperture size to the area of source surface of reconstruction on the resultant accuracy of reconstruction are examined.

  1. Scattering mean free path in continuous complex media: beyond the Helmholtz equation.

    PubMed

    Baydoun, Ibrahim; Baresch, Diego; Pierrat, Romain; Derode, Arnaud

    2015-09-01

    We present theoretical calculations of the ensemble-averaged (or effective or coherent) wave field propagating in a heterogeneous medium considered as one realization of a random process. In the literature, it is usually assumed that heterogeneity can be accounted for by a random scalar function of the space coordinates, termed the potential. Physically, this amounts to replacing the constant wave speed in Helmholtz' equation by a space-dependent speed. In the case of acoustic waves, we show that this approach leads to incorrect results for the scattering mean free path, no matter how weak the fluctuations. The detailed calculation of the coherent wave field must take into account both a scalar and an operator part in the random potential. When both terms have identical amplitudes, the correct value for the scattering mean free paths is shown to be more than 4 times smaller (13/3, precisely) in the low-frequency limit, whatever the shape of the correlation function. Based on the diagrammatic approach of multiple scattering, theoretical results are obtained for the self-energy and mean free path within Bourret's and on-shell approximations. They are confirmed by numerical experiments.

  2. Scattering mean free path in continuous complex media: Beyond the Helmholtz equation

    NASA Astrophysics Data System (ADS)

    Baydoun, Ibrahim; Baresch, Diego; Pierrat, Romain; Derode, Arnaud

    2015-09-01

    We present theoretical calculations of the ensemble-averaged (or effective or coherent) wave field propagating in a heterogeneous medium considered as one realization of a random process. In the literature, it is usually assumed that heterogeneity can be accounted for by a random scalar function of the space coordinates, termed the potential. Physically, this amounts to replacing the constant wave speed in Helmholtz' equation by a space-dependent speed. In the case of acoustic waves, we show that this approach leads to incorrect results for the scattering mean free path, no matter how weak the fluctuations. The detailed calculation of the coherent wave field must take into account both a scalar and an operator part in the random potential. When both terms have identical amplitudes, the correct value for the scattering mean free paths is shown to be more than 4 times smaller (13/3, precisely) in the low-frequency limit, whatever the shape of the correlation function. Based on the diagrammatic approach of multiple scattering, theoretical results are obtained for the self-energy and mean free path within Bourret's and on-shell approximations. They are confirmed by numerical experiments.

  3. Simulations of incompressible Navier Stokes equations on curved surfaces using discrete exterior calculus

    NASA Astrophysics Data System (ADS)

    Samtaney, Ravi; Mohamed, Mamdouh; Hirani, Anil

    2015-11-01

    We present examples of numerical solutions of incompressible flow on 2D curved domains. The Navier-Stokes equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. A conservative discretization of Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). The discretization is then carried out by substituting the corresponding discrete operators based on the DEC framework. By construction, the method is conservative in that both the discrete divergence and circulation are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step. Numerical examples include Taylor vortices on a sphere, Stuart vortices on a sphere, and flow past a cylinder on domains with varying curvature. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01.

  4. Regularized Transformation-Optics Cloaking for the Helmholtz Equation: From Partial Cloak to Full Cloak

    NASA Astrophysics Data System (ADS)

    Li, Jingzhi; Liu, Hongyu; Rondi, Luca; Uhlmann, Gunther

    2015-04-01

    We develop a very general theory on the regularized approximate invisibility cloaking for the wave scattering governed by the Helmholtz equation in any space dimensions via the approach of transformation optics. There are four major ingredients in our proposed theory: (1) The non-singular cloaking medium is obtained by the push-forwarding construction through a transformation that blows up a subset in the virtual space, where is an asymptotic regularization parameter. will degenerate to K 0 as , and in our theory K 0 could be any convex compact set in , or any set whose boundary consists of Lipschitz hypersurfaces, or a finite combination of those sets. (2) A general lossy layer with the material parameters satisfying certain compatibility integral conditions is employed right between the cloaked and cloaking regions. (3) The contents being cloaked could also be extremely general, possibly including, at the same time, generic mediums and, sound-soft, sound-hard and impedance-type obstacles, as well as some sources or sinks. (4) In order to achieve a cloaking device of compact size, particularly for the case when is not "uniformly small", an assembly-by-components, the (ABC) geometry is developed for both the virtual and physical spaces and the blow-up construction is based on concatenating different components. Within the proposed framework, we show that the scattered wave field corresponding to a cloaking problem will converge to u 0 as , with u 0 being the scattered wave field corresponding to a sound-hard K 0. The convergence result is used to theoretically justify the approximate full and partial invisibility cloaks, depending on the geometry of K 0. On the other hand, the convergence results are conducted in a much more general setting than what is needed for the invisibility cloaking, so they are of significant mathematical interest for their own sake. As for applications, we construct three types of full and partial cloaks. Some numerical experiments are

  5. An investigation in acoustic holography using the Helmholtz equation-least squares method

    NASA Astrophysics Data System (ADS)

    Rayess, Nassif Elias

    2001-10-01

    An investigation is undertaken to validate the Helmholtz Equation-Least Squares (HELS) method, a novel approach in acoustic holography. The HELS method, like other acoustic holography methods, allows for 3-D reconstruction of the radiated sound field based on 2-D measurements of acoustic pressure signals. It does so by assuming the pressure field to be written as a series expansion in spherical wave functions and uses the collocation method to solve for the expansion coefficients. This expansion is shown to be valid for non-spherical objects as long as the aspect ratio is not very high. Also, the parameters of the expansion are investigated, namely the number of functions used and the number and locations of measurements. It is found that the number of expansion functions is dependent on the frequency, size of object and measurement distance. Meanwhile, the number of measurements must exceed the number of functions by more than half for the reconstruction to be accurate. Also, the HELS method is found to be able to accurately reconstruct the pressure field based on partial planar measurements. The HELS method is validated experimentally on a bowling ball, a vehicle front end and an engine block. In the vehicle front end case, the pressure is measured on two planes parallel to the object surfaces. The coefficients obtained from employing the HELS method on the data from the plane farther away are used to reconstruct the acoustic pressure on the plane nearer to the surface where a comparison takes place with very good results. The intensity and the far field pressure are calculated for the case of the engine block and shown to be accurate. A prototype of a holography system based on this method is developed and validated. This prototype uses a 16 microphone array and a data acquisition and processing modules interfaced with the HELS algorithm. This holography system based on the HELS method is found to improve efficiency and functionality of the holography procedure.

  6. A mapping relationship based near-field acoustic holography with spherical fundamental solutions for Helmholtz equation

    NASA Astrophysics Data System (ADS)

    Wu, Haijun; Jiang, Weikang; Zhang, Haibin

    2016-07-01

    In the procedure of the near-field acoustic holography (NAH) based on the fundamental solutions for Helmholtz equation (FS), the number of FS and the measurement setup to obtain their coefficients are two crucial issues to the successful reconstruction. The current work is motivated to develop a framework for the NAH which supplies a guideline to the determination of the number of FS as well as an optimized measurement setup. A mapping relationship between modes on surfaces of boundary and hologram is analytically derived by adopting the modes as FS in spherical coordinates. Thus, reconstruction is converted to obtain the coefficients of participant modes on holograms. In addition, an integral identity is firstly to be derived for the modes on convex surfaces, which is useful in determining the inefficient or evanescent modes for acoustic radiation in free space. To determine the number of FS adopted in the mapping relationship based NAH (MRS-based NAH), two approaches are proposed to supply reasonable estimations with criteria of point-wise pressure and energy, respectively. A technique to approximate a specific degree of mode on patches by a set of locally orthogonal patterns is explored for three widely used holograms, such as planar, cylindrical and spherical holograms, which results in an automatic determinations of the number and position of experimental setup for a given tolerance. Numerical examples are set up to validate the theory and techniques in the MRS-based NAH. Reconstructions of a cubic model demonstrate the potential of the proposed method for regular models even with corners and shapers. Worse results for the elongated cylinder with two spherical caps reveal the deficiency of the MRS-based NAH for irregular models which is largely due to the adopted modes are FS in spherical coordinates. The NAH framework pursued in the current work provides a new insight to the reconstruction procedure based on the FS in spherical coordinates.

  7. Solution of the modified Helmholtz equation in a triangular domain and an application to diffusion-limited coalescence.

    PubMed

    ben-Avraham, D; Fokas, A S

    2001-07-01

    A new transform method for solving boundary value problems for linear and integrable nonlinear partial differential equations recently introduced in the literature is used here to obtain the solution of the modified Helmholtz equation q(xx)(x,y)+q(yy)(x,y)-4 beta(2)q(x,y)=0 in the triangular domain 0< or =x< or =L-y< or =L, with mixed boundary conditions. This solution is applied to the problem of diffusion-limited coalescence, A+A<==>A, in the segment (-L/2,L/2), with traps at the edges.

  8. Helmholtz dark solitons.

    PubMed

    Chamorro-Posada, P; McDonald, G S

    2003-05-15

    A general dark-soliton solution of the Helmholtz equation (with defocusing Kerr nonlinearity) that has on- and off-axis, gray and black, paraxial and Helmholtz solitons as particular solutions, is reported. Modifications to soliton transverse velocity, width, phase period, and existence conditions are derived and explained in geometrical terms. Simulations verify analytical predictions and also demonstrate spontaneous formation of Helmholtz solitons and transparency of their interactions.

  9. Structure borne noise analysis using Helmholtz equation least squares based forced vibro acoustic components

    NASA Astrophysics Data System (ADS)

    Natarajan, Logesh Kumar

    This dissertation presents a structure-borne noise analysis technology that is focused on providing a cost-effective noise reduction strategy. Structure-borne sound is generated or transmitted through structural vibration; however, only a small portion of the vibration can effectively produce sound and radiate it to the far-field. Therefore, cost-effective noise reduction is reliant on identifying and suppressing the critical vibration components that are directly responsible for an undesired sound. However, current technologies cannot successfully identify these critical vibration components from the point of view of direct contribution to sound radiation and hence cannot guarantee the best cost-effective noise reduction. The technology developed here provides a strategy towards identifying the critical vibration components and methodically suppressing them to achieve a cost-effective noise reduction. The core of this technology is Helmholtz equation least squares (HELS) based nearfield acoustic holography method. In this study, the HELS formulations derived in spherical co-ordinates using spherical wave expansion functions utilize the input data of acoustic pressures measured in the nearfield of a vibrating object to reconstruct the vibro-acoustic responses on the source surface and acoustic quantities in the far field. Using these formulations, three steps were taken to achieve the goal. First, hybrid regularization techniques were developed to improve the reconstruction accuracy of normal surface velocity of the original HELS method. Second, correlations between the surface vibro-acoustic responses and acoustic radiation were factorized using singular value decomposition to obtain orthogonal basis known here as the forced vibro-acoustic components (F-VACs). The F-VACs enables one to identify the critical vibration components for sound radiation in a similar manner that modal decomposition identifies the critical natural modes in a structural vibration. Finally

  10. Tomographic systems for the Helmholtz equation with extended Born field models using conjugate gradient inversion methods

    NASA Astrophysics Data System (ADS)

    Olsen, Scott Charles

    In this dissertation, new inverse scattering algorithms are derived for the Helmholtz equation using the Extended Born field model (eikonal rescattered field), and the angular spectrum (parabolic) layered field model. These two field models performed the 'best' of all the field models evaluated. Algorithms are solved with conjugate gradient methods. An advanced ultrasonic data acquisition system is also designed. Many different field models for use in a reconstruction algorithm are investigated. 'Layered' field models that mathematically partition the field calculation in layers in space possess the advantage that the field in layer n is calculated from the field in layer n - 1. Several of the 'layered' field models are investigated in terms of accuracy and computational complexity. Field model accuracy using field rescattering is also tested. The models investigated are the eikonal field model, the angular spectrum (AS) field model, and the parabolic field models known as the Split-Step Fast-Fourier Transform and the Crank-Nicolson algorithms. All of the 'layered' field models can be referred to as Extended Born field models since the 'layered' field models are more accurate than the Born approximated total field. The Rescattered Extended Born (eikonal rescattered field) Transmission Mode (REBTM) algorithm with the AS field model and the Nonrescattered AS Reconstruction (NASR) algorithm are tested with several types of objects: a single-layer cylinder, double-layer cylinders, two double-layer cylinders and the breast model. Both algorithms, REBTM and NASR work well; however, the NASR algorithm is faster and more accurate than the REBTM algorithm. The NASR algorithm is matched well with the requirements of breast model reconstructions. A major purpose of new scanner development is to collect both transmission and reflection data from multiple ultrasonic transducer arrays to test the next generation of reconstruction algorithms. The data acquisition system advanced

  11. A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional

    SciTech Connect

    Ciraolo, Giulio Gargano, Francesco Sciacca, Vincenzo

    2013-08-01

    We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.

  12. Simulations of the nonlinear Helmholtz equation: arrest of beam collapse, nonparaxial solitons and counter-propagating beams.

    PubMed

    Baruch, G; Fibich, G; Tsynkov, Semyon

    2008-08-18

    We solve the (2+1)D nonlinear Helmholtz equation (NLH) for input beams that collapse in the simpler NLS model. Thereby, we provide the first ever numerical evidence that nonparaxiality and backscattering can arrest the collapse. We also solve the (1+1)D NLH and show that solitons with radius of only half the wavelength can propagate over forty diffraction lengths with no distortions. In both cases we calculate the backscattered field, which has not been done previously. Finally, we compute the dynamics of counter-propagating solitons using the NLH model, which is more comprehensive than the previously used coupled NLS model.

  13. A Rationale for p-Refinement with the Vector Helmholtz Equation and Two Dimensional Vector Finite Elements

    DTIC Science & Technology

    2004-07-02

    Helmholtz equation was introduced by Nedelec in 1980 [5]. These functions maintain tangential cell-to-cell continuity and are known as curl...Forghani functions [8], but have been modified to satisfy the Nedelec conditions [5]. Functions have been included up to order 4/5. For source-free...satisfy the Nedelec conditions. In Table 1, functions of degrees 3 and 4 are constructed using polynomial products such as (3L1 – L2) (L1 – L2) (L1

  14. Helmholtz-Manakov solitons.

    PubMed

    Christian, J M; McDonald, G S; Chamorro-Posada, P

    2006-12-01

    A different spatial soliton-bearing wave equation is introduced, the Helmholtz-Manakov (HM) equation, for describing the evolution of broad multicomponent self-trapped beams in Kerr-type media. By omitting the slowly varying envelope approximation, the HM equation can describe accurately vector solitons propagating and interacting at arbitrarily large angles with respect to the reference direction. The HM equation is solved using Hirota's method, yielding four different classes of Helmholtz soliton that are vector generalizations of their scalar counterparts. General and particular forms of the three invariants of the HM system are also reported.

  15. An exterior Poisson solver using fast direct methods and boundary integral equations with applications to nonlinear potential flow

    NASA Technical Reports Server (NTRS)

    Young, D. P.; Woo, A. C.; Bussoletti, J. E.; Johnson, F. T.

    1986-01-01

    A general method is developed combining fast direct methods and boundary integral equation methods to solve Poisson's equation on irregular exterior regions. The method requires O(N log N) operations where N is the number of grid points. Error estimates are given that hold for regions with corners and other boundary irregularities. Computational results are given in the context of computational aerodynamics for a two-dimensional lifting airfoil. Solutions of boundary integral equations for lifting and nonlifting aerodynamic configurations using preconditioned conjugate gradient are examined for varying degrees of thinness.

  16. The stationary Navier-Stokes equations in 3D exterior domains. An approach in anisotropically weighted L spaces

    NASA Astrophysics Data System (ADS)

    Razafison, Ulrich

    We consider the three-dimensional exterior problem for stationary Navier-Stokes equations. We prove, under assumptions of smallness of the data, existence and uniqueness of solutions. By setting the problem in weighted spaces where the weights reflect the anisotropic decay properties of the fundamental solution of Oseen, we show the better decay of the solutions outside the wake region. Moreover, the solutions we obtained have a finite Dirichlet integral and under additional assumptions on the weights they are also PR-solutions in the sense of Finn [R. Finn, On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems, Arch. Ration. Mech. Anal. 19 (1965) 363-406]. The study relies on an L-theory for 1

  17. Existence of global decaying solutions to the exterior problem for the Klein-Gordon equation with a nonlinear localized dissipation and a derivative nonlinearity

    NASA Astrophysics Data System (ADS)

    Nakao, Mitsuhiro

    We prove the existence of global decaying solutions to the exterior problem for the Klein-Gordon equation with a nonlinear localized dissipation and a derivative nonlinearity. To derive the required estimates of solutions we employ a 'loan' method.

  18. Upscaling of Helmholtz Equation Originating in Transmission through Metallic Gratings in Metamaterials.

    PubMed

    Mahato, Hari Shankar

    2016-01-01

    We investigate the transmission properties of a metallic layer with narrow slits. We consider (time-harmonic) Maxwell's equations in the H-parallel case with a fixed incident wavelength. We denote η > 0 as the typical size of the complex structure and obtain the effective equations by letting η → 0. For metallic permittivities with negative real part, plasmonic waves can be excited on the surfaces of the slits. For the waves to be in resonance with the height of the metallic layer, the corresponding results can be perfect transmission through the layer.

  19. Wave propagation through random media: A local method of small perturbations based on the Helmholtz equation

    NASA Technical Reports Server (NTRS)

    Grosse, Ralf

    1990-01-01

    Propagation of sound through the turbulent atmosphere is a statistical problem. The randomness of the refractive index field causes sound pressure fluctuations. Although no general theory to predict sound pressure statistics from given refractive index statistics exists, there are several approximate solutions to the problem. The most common approximation is the parabolic equation method. Results obtained by this method are restricted to small refractive index fluctuations and to small wave lengths. While the first condition is generally met in the atmosphere, it is desirable to overcome the second. A generalization of the parabolic equation method with respect to the small wave length restriction is presented.

  20. Upscaling of Helmholtz Equation Originating in Transmission through Metallic Gratings in Metamaterials

    PubMed Central

    2016-01-01

    We investigate the transmission properties of a metallic layer with narrow slits. We consider (time-harmonic) Maxwell's equations in the H-parallel case with a fixed incident wavelength. We denote η > 0 as the typical size of the complex structure and obtain the effective equations by letting η → 0. For metallic permittivities with negative real part, plasmonic waves can be excited on the surfaces of the slits. For the waves to be in resonance with the height of the metallic layer, the corresponding results can be perfect transmission through the layer. PMID:27738650

  1. A coordinate transformation approach for efficient repeated solution of Helmholtz equation pertaining to obstacle scattering by shape deformations

    NASA Astrophysics Data System (ADS)

    Ozgun, Ozlem; Kuzuoglu, Mustafa

    2014-06-01

    A computational model is developed for efficient solutions of electromagnetic scattering from obstacles having random surface deformations or irregularities (such as roughness or randomly-positioned bump on the surface), by combining the Monte Carlo method with the principles of transformation electromagnetics in the context of finite element method. In conventional implementation of the Monte Carlo technique in such problems, a set of random rough surfaces is defined from a given probability distribution; a mesh is generated anew for each surface realization; and the problem is solved for each surface. Hence, this repeated mesh generation process places a heavy burden on CPU time. In the proposed approach, a single mesh is created assuming smooth surface, and a transformation medium is designed on the smooth surface of the object. Constitutive parameters of the medium are obtained by the coordinate transformation technique combined with the form-invariance property of Maxwell's equations. At each surface realization, only the material parameters are modified according to the geometry of the deformed surface, thereby avoiding repeated mesh generation process. In this way, a simple, single and uniform mesh is employed; and CPU time is reduced to a great extent. The technique is demonstrated via various finite element simulations for the solution of two-dimensional, Helmholtz-type and transverse magnetic scattering problems.

  2. Wave gradiometry and its link with Helmholtz equation solutions applied to USArray in the eastern U.S.

    NASA Astrophysics Data System (ADS)

    Liu, Yuanyuan; Holt, William E.

    2015-08-01

    Wave gradiometry is an array processing technique utilizing the shape of seismic wavefields captured by USArray TA stations to determine fundamental wave propagation characteristics. We first explore a compatibility relation that links the displacement spatial gradients to seismogram displacements and velocities through two unknown coefficients, A→ and B→. These coefficients are solved for through iterative, damped least squares inversion to provide estimates of phase velocity, back azimuth, radiation pattern, and geometrical spreading. We show that the A→ coefficient corresponds to the gradient of logarithmic amplitude, and the B→ coefficient corresponds approximately to the local wave slowness. A→ and B→ vector fields are interpolated to explore a second compatibility relation through solutions to the Helmholtz equation. For most wavefields passing through the eastern U.S., we show that the A→ coefficients are generally orthogonal to the B→ coefficients. Where they are not completely orthogonal, there is a strong positive correlation between ∇·B→ and changes in geometrical spreading, which can be further linked with areas of strong energy focusing and defocusing. We finally obtain isotropic Rayleigh wave phase velocity maps for 15 periods between 20 and 150 s, by stacking results from 37 earthquakes, which show a velocity change along the approximate boundary of the early Paleozoic continental margin. We also observe two low-velocity anomalies, one centered over the central Appalachians where Eocene basaltic volcanism has occurred and the other within the northeastern U.S., possibly associated with the Great Meteor Hotspot track.

  3. Computational issues and applications of line-elements to model subsurface flow governed by the modified Helmholtz equation

    NASA Astrophysics Data System (ADS)

    Bakker, Mark; Kuhlman, Kristopher L.

    2011-09-01

    Two new approaches are presented for the accurate computation of the potential due to line elements that satisfy the modified Helmholtz equation with complex parameters. The first approach is based on fundamental solutions in elliptical coordinates and results in products of Mathieu functions. The second approach is based on the integration of modified Bessel functions. Both approaches allow evaluation of the potential at any distance from the element. The computational approaches are applied to model transient flow with the Laplace transform analytic element method. The Laplace domain solution is computed using a combination of point elements and the presented line elements. The time domain solution is obtained through a numerical inversion. Two applications are presented to transient flow fields, which could not be modeled with the Laplace transform analytic element method prior to this work. The first application concerns transient single-aquifer flow to wells near impermeable walls modeled with line-doublets. The second application concerns transient two-aquifer flow to a well near a stream modeled with line-sinks.

  4. Reconstructing the vibro-acoustic quantities on a highly non-spherical surface using the Helmholtz equation least squares method.

    PubMed

    Natarajan, Logesh Kumar; Wu, Sean F

    2012-06-01

    This paper presents helpful guidelines and strategies for reconstructing the vibro-acoustic quantities on a highly non-spherical surface by using the Helmholtz equation least squares (HELS). This study highlights that a computationally simple code based on the spherical wave functions can produce an accurate reconstruction of the acoustic pressure and normal surface velocity on planar surfaces. The key is to select the optimal origin of the coordinate system behind the planar surface, choose a target structural wavelength to be reconstructed, set an appropriate stand-off distance and microphone spacing, use a hybrid regularization scheme to determine the optimal number of the expansion functions, etc. The reconstructed vibro-acoustic quantities are validated rigorously via experiments by comparing the reconstructed normal surface velocity spectra and distributions with the benchmark data obtained by scanning a laser vibrometer over the plate surface. Results confirm that following the proposed guidelines and strategies can ensure the accuracy in reconstructing the normal surface velocity up to the target structural wavelength, and produce much more satisfactory results than a straight application of the original HELS formulations. Experiment validations on a baffled, square plate were conducted inside a fully anechoic chamber.

  5. Spectral Solution of the Helmholtz and Paraxial Wave Equations and Classical Diffraction Formulae

    DTIC Science & Technology

    2004-03-01

    Traité de la lumière (completed in 1678, published in Leyden, 1690). 7. Kirchoff, G. “Zur Theorie der Lichtstrahlen ,” Wiedemann Ann. 1896, 18(2...4 3. A Précis of Classical Scalar Diffraction Theory 5 3.1 History...derivation of the paraxial wave equation. Section 3 briefly reviews the salient results of classical scalar diffraction theory . In sections 4 and 5

  6. An exact solution for a constant-strength line-sink satisfying the modified Helmholtz equation for groundwater flow

    NASA Astrophysics Data System (ADS)

    Gusyev, M. A.; Haitjema, H. M.

    2011-04-01

    We obtained an exact solution in terms of the discharge potential for a constant-strength line-sink that satisfies the modified Helmholtz equation for groundwater flow, for example for semi-confined flow and transient flow. The solution is obtained by integrating the potential for a point sink (well) along a straight line element. The potential for the point-sink is the modified Bessel function of the second kind and zero order K0. Since K0 cannot be integrated directly (in closed form) along a line-element, earlier solutions for a line-sink have been obtained by integrating polynomial approximations to K0. These approximations, however, are only valid up to a certain distance from the well and consequently impose a limit on the length of the line-sink. In this paper we integrate an exact series representation for K0 that is valid at any distance from the well, thus allowing integration along line-elements of any length, at least in theory. Numerical difficulties arise when evaluating our expressions at large distances from the line-sink, but these are shown to be of little consequence in practice. We made use of Wirtinger calculus to facilitate integration and also to allow us to arrive at exact expressions for the integrated flux over a poly-line and the total leakage over a domain. These properties are essential when using the solution in the context of the Analytic Element Method (AEM). We demonstrate our solution for the case of semi-confined flow (with leakage) and for the case of transient flow in the context of the Laplace Transform Analytic Element Method (LT-AEM).

  7. On an exterior boundary value problem for the Laplace equation with boundary operator of fractional order

    NASA Astrophysics Data System (ADS)

    Turmetov, B. Kh.

    2016-12-01

    In the paper in a class of regular harmonic functions we study properties of some integro-differential operators that generalize the operators of fractional differentiation in Hadamard sense. These operators transfer regular harmonic functions to the same function, and are inverse to the regular harmonic functions. Boundary value problem with the boundary operator of fractional order is studied in the exterior of the unit sphere. The considered problem generalizes the well-known Neumann problem on boundary operators of fractional order. We prove a theorem on existence and uniqueness of solutions of the problem. Moreover, an integral representation of the problem solution is obtained.

  8. A new Green's function Monte Carlo algorithm for the estimation of the derivative of the solution of Helmholtz equation subject to Neumann and mixed boundary conditions

    NASA Astrophysics Data System (ADS)

    Chatterjee, Kausik

    2016-06-01

    The objective of this paper is the extension and application of a newly-developed Green's function Monte Carlo (GFMC) algorithm to the estimation of the derivative of the solution of the one-dimensional (1D) Helmholtz equation subject to Neumann and mixed boundary conditions problems. The traditional GFMC approach for the solution of partial differential equations subject to these boundary conditions involves "reflecting boundaries" resulting in relatively large computational times. My work, inspired by the work of K.K. Sabelfeld is philosophically different in that there is no requirement for reflection at these boundaries. The underlying feature of this algorithm is the elimination of the use of reflecting boundaries through the use of novel Green's functions that mimic the boundary conditions of the problem of interest. My past work has involved the application of this algorithm to the estimation of the solution of the 1D Laplace equation, the Helmholtz equation and the modified Helmholtz equation. In this work, this algorithm has been adapted to the estimation of the derivative of the solution which is a very important development. In the traditional approach involving reflection, to estimate the derivative at a certain number of points, one has to a priori estimate the solution at a larger number of points. In the case of a one-dimensional problem for instance, to obtain the derivative of the solution at a point, one has to obtain the solution at two points, one on each side of the point of interest. These points have to be close enough so that the validity of the first-order approximation for the derivative operator is justified and at the same time, the actual difference between the solutions at these two points has to be at least an order of magnitude higher than the statistical error in the estimation of the solution, thus requiring a significantly larger number of random-walks than that required for the estimation of the solution. In this new approach

  9. Optical Helmholtz resonators

    NASA Astrophysics Data System (ADS)

    Chevalier, Paul; Bouchon, Patrick; Haïdar, Riad; Pardo, Fabrice

    2014-08-01

    Helmholtz resonators are widely used acoustic components able to select a single frequency. Here, based on an analogy between acoustics and electromagnetism wave equations, we present an electromagnetic 2D Helmholtz resonator made of a metallic slit-box structure. At the resonance, the light is funneled in the λ/800 apertures, and is subsequently absorbed in the cavity. As in acoustics, there is no higher order of resonance, which is an appealing feature for applications such as photodetection or thermal emission. Eventually, we demonstrate that the slit is of capacitive nature while the box behaves inductively. We derive an analytical formula for the resonance wavelength, which does not rely on wave propagation and therefore does not depend on the permittivity of the material filling the box. Besides, in contrast with half-wavelength resonators, the resonance wavelength can be engineered by both the slit aspect ratio and the box area.

  10. On the Dirichlet problem for the Helmholtz equation on the plane with boundary conditions on an almost closed curve

    SciTech Connect

    Gadyl'shin, R R

    2000-06-30

    In this article the two-dimensional Dirichlet boundary-value problem is considered for the Helmholtz operator with boundary conditions on an almost closed curve {gamma}{sub {epsilon}} where {epsilon}<<1 is the distance between the end-points of the curve. A complete asymptotic expression is constructed for a pole of the analytic continuation of the Green's function of this problem as the pole converges to a simple eigenfrequency of the limiting interior problem in the case when the corresponding eigenfunction of the limiting problem has a second-order zero at the centre of contraction of the gap. The influence of symmetry of the gap on the absolute value of the imaginary parts of the poles is investigated.

  11. High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences

    NASA Astrophysics Data System (ADS)

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

    2016-05-01

    We apply second order finite differences to calculate the lowest eigenvalues of the Helmholtz equation, for complicated non-tensor domains in the plane, using different grids which sample exactly the border of the domain. We show that the results obtained applying Richardson and Padé-Richardson extrapolations to a set of finite difference eigenvalues corresponding to different grids allow us to obtain extremely precise values. When possible we have assessed the precision of our extrapolations comparing them with the highly precise results obtained using the method of particular solutions. Our empirical findings suggest an asymptotic nature of the FD series. In all the cases studied, we are able to report numerical results which are more precise than those available in the literature.

  12. Finite Element Solution to the Helmholtz Equation with High Wave Number. Part 1. The h-Version of the FEM

    DTIC Science & Technology

    1993-11-01

    methou, mn: A.K. Aziz (ed.), The mathematical foundations of tile finite element, method with applicai.4ons to partial differential equations , Academic...nonlinear differential equations and problems in linear and nonlinear algebra. "* To help bridge gaps between computational directions in engineering, physics...Life of Contract Equation with High Wave Number Part 1: The h-Version of the FEM 7. Au TNO R(a)COTATO ATgUSAs Frank Ihlenburgi - Ivo Babuska 2 2ONR

  13. Measurement of Helmholtz wave fields

    PubMed

    Alonso

    2000-07-01

    A simple formalism is found for the measurement of wave fields that satisfy the Helmholtz equation in free space. This formalism turns out to be analogous to the well-known theory of measurements for quantum-mechanical wave functions: A measurement corresponds to the squared magnitude of the inner product (in a suitable Hilbert space) of the wave field and a field that is associated with the detector. The measurement can also be expressed as an overlap in phase space of a special form of the Wigner function that is tailored for Helmholtz wave fields.

  14. Nonlinear electrostatic drift Kelvin-Helmholtz instability

    NASA Technical Reports Server (NTRS)

    Sharma, Avadhesh C.; Srivastava, Krishna M.

    1993-01-01

    Nonlinear analysis of electrostatic drift Kelvin-Helmholtz instability is performed. It is shown that the analysis leads to the propagation of the weakly nonlinear dispersive waves, and the nonlinear behavior is governed by the nonlinear Burger's equation.

  15. [Hermann von Helmholtz--a physicist in medicine].

    PubMed

    Omerbasić, A

    1999-01-01

    Helmholtz left an indelible mark in science. He was a predecessor to the multidisciplinary scientific approach, and his contribution to physics (The Law on Energy Sustainability, Helmholtz's Free Energy, Gibs-Helmholtz's Equationes, Helmholtz Theory of Rotational Liquids Flow, Helmholtz's Oscillatory Cycle, Helmholtz's Waves Equation) and to medicine (Ophthalmoscope, Young-Helmholtz's Theory of Colours, Sight Theory, Speed of Impulse Transfer, Speech and Tone of Voice, The Sound Transfer to Nerves) was indispensable. Helmholtz was surrounded by the respect and love of his contemporaries, appreciated and respected by his followers for the results he left. As a respectable professor of anatomy, physiology and physics at the most eminent universities, "he used to give lectures in such a clear and concise way that they could have been, without any changes, published in a form of a textbook" (Ostwald).

  16. Experiments with Helmholtz Resonators.

    ERIC Educational Resources Information Center

    Greenslade, Thomas B., Jr.

    1996-01-01

    Presents experiments that use Helmholtz resonators and have been designed for a sophomore-level course in oscillations and waves. Discusses the theory of the Helmholtz resonator and resonance curves. (JRH)

  17. Conformal mapping for the Helmholtz equation: acoustic wave scattering by a two dimensional inclusion with irregular shape in an ideal fluid.

    PubMed

    Liu, Gang; Jayathilake, Pahala G; Khoo, Boo Cheong; Han, Feng; Liu, Dian Kui

    2012-02-01

    The complex variables method with mapping function was extended to solve the linear acoustic wave scattering by an inclusion with sharp/smooth corners in an infinite ideal fluid domain. The improved solutions of Helmholtz equation, shown as Bessel function with mapping function as the argument and fractional order Bessel function, were analytically obtained. Based on the mapping function, the initial geometry as well as the original physical vector can be transformed into the corresponding expressions inside the mapping plane. As all the physical vectors are calculated in the mapping plane (η,η), this method can lead to potential vast savings of computational resources and memory. In this work, the results are validated against several published works in the literature. The different geometries of the inclusion with sharp corners based on the proposed mapping functions for irregular polygons are studied and discussed. The findings show that the variation of angles and frequencies of the incident waves have significant influence on the bistatic scattering pattern and the far-field form factor for the pressure in the fluid.

  18. Northeastern Exterior, Northwestern Exterior, & Southwestern Exterior Elevations, Northeastern Interior, ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Northeastern Exterior, Northwestern Exterior, & Southwestern Exterior Elevations, Northeastern Interior, Southeastern Interior, & Southwestern Interior Elevations, Floor Plan, and Eastern Corner Detail - Manatoc Reservation, Vale Edge Adirondack, 1075 Truxell Road, Peninsula, Summit County, OH

  19. Gradient Theory simulations of pure fluid interfaces using a generalized expression for influence parameters and a Helmholtz energy equation of state for fundamentally consistent two-phase calculations.

    PubMed

    Dahms, Rainer N

    2015-05-01

    The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phase components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. The new model preserves the accuracy of previous temperature

  20. Gradient Theory simulations of pure fluid interfaces using a generalized expression for influence parameters and a Helmholtz energy equation of state for fundamentally consistent two-phase calculations

    SciTech Connect

    Dahms, Rainer N.

    2014-12-31

    The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phase components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. As a result, the new model preserves the accuracy of previous

  1. Gradient Theory simulations of pure fluid interfaces using a generalized expression for influence parameters and a Helmholtz energy equation of state for fundamentally consistent two-phase calculations

    DOE PAGES

    Dahms, Rainer N.

    2014-12-31

    The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phasemore » components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. As a result, the new model preserves the accuracy of

  2. Visualizing interior and exterior jet aircraft noise

    NASA Astrophysics Data System (ADS)

    Moondra, Manmohan S.

    In today's competitive aerospace industry, the quest for quiet has drawn significant attention to both the interior and exterior design of an airplane. Understanding the noise generation mechanisms of a jet aircraft is a crucial first step toward developing the most cost-effective noise and vibrations abatement methods. In this investigation, the Helmholtz Equation Least Squares (HELS) based nearfield acoustic holography will be used to understand noise transmission caused by jet engine and turbulence into the fuselage of a jet aircraft cruising at 30,000 ft. Modern propulsive jet engines produce exterior noise sources with a high amplitude noise field and complicated characteristics, which makes them very difficult to characterize. In particular, there are turbulent eddies that are moving through the jet at high speeds along the jet boundary. These turbulent eddies in the shear layer produce a directional and frequency dependent noise. The original HELS approach assumes a spherical source at the origin and computes the acoustic field based on spherical emission from this source. This assumption of one source at the origin is not sufficient to characterize a complex source like a jet. As such, a modified HELS approach is introduced that will help improve the source characterization as it is not dependent on a single source at the origin but a number of virtual sources throughout the space. Custom microphones are created to take acoustic pressure measurements around the jet engine. These measured acoustic pressures are then taken as input to the modified HELS algorithm to visualize the noise pattern of a subsonic jet engine.

  3. Solution of exterior acoustic problems by the boundary element method

    NASA Astrophysics Data System (ADS)

    Kirkup, Stephen Martin

    The boundary element method is described and investigated, especially in respect of its application to exterior two-dimensional Laplace problems. Both empirical and algebraic analyses (including the effects of approximation of the boundary and boundary functions and the precision of the evaluation of the discrete forms) are developed. Methods for the automatic evaluation of the discrete forms of the Laplace and Helmholtz integral operators are reviewed and extended. Boundary element methods for the solution of exterior Helmholtz problems with general (but most importantly Neumann) boundary conditions are reviewed and some are explicitly stated using a new notation. Boundary element methods based on the boundary integral equations introduced by Brakhage and Werner/Leis/Panich/Kussmaul (indirect) and Burton and Miller (direct) are given prime consideration and implemented for three-dimensional problems. The influence of the choice of weighting parameter on the performance of the methods is explored and further guidance is given. The application of boundary element methods and methods based on the Rayleigh integral to acoustic radiation problems are considered. Methods for speeding up their solution via the boundary element method are developed. Library subroutines for the solution of acoustic radiation problems are described and demonstrated. Computational techniques for the problem of predicting the noise produced by a running engine are reviewed and appraised. The application of the boundary element method to low-noise engine design and in the design of noise shields is considered. The boundary element method is applied to the Ricardo crankcase simulation rig, which is an engine-like structure. A comparison of predicted and measured sound power spectra is given.

  4. Solution of Exterior Acoustic Problems by the Boundary Element Method.

    NASA Astrophysics Data System (ADS)

    Kirkup, Stephen Martin

    Available from UMI in association with The British Library. The boundary element method is described and investigated, especially in respect of its application to exterior two -dimensional Laplace problems. Both empirical and algebraic analyses (including the effects of approximation of the boundary and boundary functions and the precision of the evaluation of the discrete forms) are developed. Methods for the automatic evaluation of the discrete forms of the Laplace and Helmholtz integral operators are reviewed and extended. Boundary element methods for the solution of exterior Helmholtz problems with general (but most importantly Neumann) boundary conditions are reviewed and some are explicitly stated using a new notation. Boundary element methods based on the boundary integral equations introduced by Brakhage & Werner/ Leis/ Panich/ Kussmaul (indirect) and Burton & Miller (direct) are given prime consideration and implemented for three -dimensional problems. The influence of the choice of weighting parameter on the performance of the methods is explored and further guidance is given. The application of boundary element methods and methods based on the Rayleigh integral to acoustic radiation problems are considered. Methods for speeding up their solution via the boundary element method are developed. Library subroutines for the solution of acoustic radiation problems are described and demonstrated. Computational techniques for the problem of predicting the noise produced by a running engine are reviewed and appraised. The application of the boundary element method to low-noise engine design and in the design of noise shields is considered. The boundary element method is applied to the Ricardo crankcase simulation rig, which is an engine -like structure. A comparison of predicted and measured sound power spectra is given.

  5. Inverse scattering for an exterior Dirichlet problem. [due to metallic cylinder

    NASA Technical Reports Server (NTRS)

    Hariharan, S. I.

    1982-01-01

    Scattering caused by a metallic cylinder in the field of a wire carrying a periodic current is studied, with a view to determining the location and shape of the cylinder in light of far field measurements between the cylinder and the wire. The associated direct problem is the exterior Dirichlet problem for the Helmholtz equation in two dimensions, and an improved low frequency estimate for its solution by integral equation methods is shown by inverse scattering calculations to be accurate to this estimate. The far field measurements are related to low frequency boundary integral equations whose solutions may be expressed in terms of a mapping function for the exterior of the unknown curve onto the exterior of a unit disk. The conformal transformation's Laurent expansion coefficients can be related to those of the far field, the first of which leads to the calculation of the distance between the source and the cylinder, while the other coefficients are determined by placing the source in a different location.

  6. Inverse scattering for an exterior Dirichlet problem. [due to metallic cylinder

    NASA Technical Reports Server (NTRS)

    Hariharan, S. I.

    1982-01-01

    Scattering caused by a metallic cylinder in the field of a wire carrying a periodic current is studied, with a view to determining the location and shape of the cylinder in light of far field measurements between the cylinder and the wire. The associated direct problem is the exterior Dirichlet problem for the Helmholtz equation in two dimensions, and an improved low frequency estimate for its solution by integral equation methods is shown by inverse scattering calculations to be accurate to this estimate. The far field measurements are related to low frequency boundary integral equations whose solutions may be expressed in terms of a mapping function for the exterior of the unknown curve onto the exterior of a unit disk. The conformal transformation's Laurent expansion coefficients can be related to those of the far field, the first of which leads to the calculation of the distance between the source and the cylinder, while the other coefficients are determined by placing the source in a different location.

  7. Fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain

    NASA Astrophysics Data System (ADS)

    Ryo, Ikehata

    Uniform energy and L2 decay of solutions for linear wave equations with localized dissipation will be given. In order to derive the L2-decay property of the solution, a useful device whose idea comes from Ikehata-Matsuyama (Sci. Math. Japon. 55 (2002) 33) is used. In fact, we shall show that the L2-norm and the total energy of solutions, respectively, decay like O(1/ t) and O(1/ t2) as t→+∞ for a kind of the weighted initial data.

  8. On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions

    NASA Technical Reports Server (NTRS)

    Hagstrom, Thomas; Hariharan, S. I.; Maccamy, R. C.

    1993-01-01

    We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.

  9. The ophthalmoscope: Helmholtz's Augenspiegel.

    PubMed

    Pearce, J M S

    2009-01-01

    The origins of Helmholtz's invention of the ophthalmoscope are found in the ancient observation that the back of the eye appeared black. In 1703, Jean Méry reported that the luminosity of the cat's eye could be seen when the animal was held under water, and Mariotte observed that a dog's eye was luminous but erroneously thought this was because its choroid was white. Prévost made a breakthrough when he deduced it was incident light and not light coming out of the eye. Purkinje and von Brucke used lenses to attempt to see the fundus and almost succeeded. However, it was Helmholtz who created the first useable ophthalmoscope, whose development and clinical application are traced in this paper. One of the greatest physical scientists in many spheres of learning, his biography is briefly sketched.

  10. Fully adaptive algorithms for multivariate integral equations using the non-standard form and multiwavelets with applications to the Poisson and bound-state Helmholtz kernels in three dimensions

    NASA Astrophysics Data System (ADS)

    Frediani, Luca; Fossgaard, Eirik; Flå, Tor; Ruud, Kenneth

    2013-07-01

    We have developed and implemented a general formalism for fast numerical solution of time-independent linear partial differential equations as well as integral equations through the application of numerically separable integral operators in d ≥ 1 dimensions using the non-standard (NS) form. The proposed formalism is universal, compact and oriented towards the practical implementation into a working code using multiwavelets. The formalism is applied to the case of Poisson and bound-state Helmholtz operators in d = 3. Our algorithms are fully adaptive in the sense that the grid supporting each function is obtained on the fly while the function is being computed. In particular, when the function g = O f is obtained by applying an integral operator O, the corresponding grid is not obtained by transferring the grid from the input function f. This aspect has significant implications that will be discussed in the numerical section. The operator kernels are represented in a separated form with finite but arbitrary precision using Gaussian functions. Such a representation combined with the NS form allows us to build a sparse, banded representation of Green's operator kernel. We have implemented a code for the application of such operators in a separated NS form to a multivariate function in a finite but, in principle, arbitrary number of dimensions. The error of the method is controlled, while the low complexity of the numerical algorithm is kept. The implemented code explicitly computes all the 22d components of the d-dimensional operator. Our algorithms are described in detail in the paper through pseudo-code examples. The final goal of our work is to be able to apply this method to build a fast and accurate Kohn-Sham solver for density functional theory.

  11. Error and Complexity Analysis for a Collocation-Grid-Projection Plus Precorrected-FFT Algorithm for Solving Potential Integral Equations with LaPlace or Helmholtz Kernels

    NASA Technical Reports Server (NTRS)

    Phillips, J. R.

    1996-01-01

    In this paper we derive error bounds for a collocation-grid-projection scheme tuned for use in multilevel methods for solving boundary-element discretizations of potential integral equations. The grid-projection scheme is then combined with a precorrected FFT style multilevel method for solving potential integral equations with 1/r and e(sup ikr)/r kernels. A complexity analysis of this combined method is given to show that for homogeneous problems, the method is order n natural log n nearly independent of the kernel. In addition, it is shown analytically and experimentally that for an inhomogeneity generated by a very finely discretized surface, the combined method slows to order n(sup 4/3). Finally, examples are given to show that the collocation-based grid-projection plus precorrected-FFT scheme is competitive with fast-multipole algorithms when considering realistic problems and 1/r kernels, but can be used over a range of spatial frequencies with only a small performance penalty.

  12. Vector Helmholtz-Gauss and vector Laplace-Gauss beams.

    PubMed

    Bandres, Miguel A; Gutiérrez-Vega, Julio C

    2005-08-15

    We demonstrate the existence of vector Helmholtz-Gauss (vHzG) and vector Laplace-Gauss beams that constitute two general families of localized vector beam solutions of the Maxwell equations in the paraxial approximation. The electromagnetic components are determined starting from the scalar solutions of the two-dimensional Helmholtz and Laplace equations, respectively. Special cases of the vHzG beams are TE and TM Gaussian vector beams, nondiffracting vector Bessel beams, polarized Bessel-Gauss beams, modes in cylindrical waveguides and cavities, and scalar Helmholtz-Gauss beams. The general expression of the vHzG beams can be used straightforwardly to obtain vector Mathieu-Gauss and vector parabolic-Gauss beams, which to our knowledge have not yet been reported.

  13. Stabilization of time domain acoustic boundary element method for the exterior problem avoiding the nonuniqueness.

    PubMed

    Jang, Hae-Won; Ih, Jeong-Guon

    2013-03-01

    The time domain boundary element method (TBEM) to calculate the exterior sound field using the Kirchhoff integral has difficulties in non-uniqueness and exponential divergence. In this work, a method to stabilize TBEM calculation for the exterior problem is suggested. The time domain CHIEF (Combined Helmholtz Integral Equation Formulation) method is newly formulated to suppress low order fictitious internal modes. This method constrains the surface Kirchhoff integral by forcing the pressures at the additional interior points to be zero when the shortest retarded time between boundary nodes and an interior point elapses. However, even after using the CHIEF method, the TBEM calculation suffers the exponential divergence due to the remaining unstable high order fictitious modes at frequencies higher than the frequency limit of the boundary element model. For complete stabilization, such troublesome modes are selectively adjusted by projecting the time response onto the eigenspace. In a test example for a transiently pulsating sphere, the final average error norm of the stabilized response compared to the analytic solution is 2.5%.

  14. Optical structure based on the acoustic Helmholtz resonator

    NASA Astrophysics Data System (ADS)

    Chevalier, Paul; Bouchon, Patrick; Pelouard, Jean-Luc; Pardo, Fabrice; Haidar, Riad

    2015-02-01

    Here, based on an analogy between acoustics and electromagnetism wave equations, we present an electromagnetic resonator analogous to the Helmholtz resonator in acoustics. This structure is made of a tiny slit above a box and exhibits appealing properties for applications such as thermal emission, bio-sensing or spectroscopy.

  15. Helmholtz solitons in power-law optical materials

    SciTech Connect

    Christian, J. M.; McDonald, G. S.; Potton, R. J.; Chamorro-Posada, P.

    2007-09-15

    A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures the evolution of broad beams at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses, and liquid crystals. Exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three general conservation laws are also reported. Analysis and numerical simulations examine the stability of the Helmholtz power-law solitons. A propagation feature, associated with spatial solitons in power-law media, constituting a class of oscillatory solution, is identified.

  16. Bistable Helmholtz solitons in cubic-quintic materials

    SciTech Connect

    Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.

    2007-09-15

    We propose a nonlinear Helmholtz equation for modeling the evolution of broad optical beams in media with a cubic-quintic intensity-dependent refractive index. This type of nonlinearity is appropriate for some semiconductor materials, glasses, and polymers. Exact analytical soliton solutions are presented that describe self-trapped nonparaxial beams propagating at any angle with respect to the reference direction. These spatially symmetric solutions are, to the best of our knowledge, the first bistable Helmholtz solitons to be derived. Accompanying conservation laws (both integral and particular forms) are also reported. Numerical simulations investigate the stability of the solitons, which appear to be remarkably robust against perturbations.

  17. Kelvin-Helmholtz versus Hall magnetoshear instability in astrophysical flows.

    PubMed

    Gómez, Daniel O; Bejarano, Cecilia; Mininni, Pablo D

    2014-05-01

    We study the stability of shear flows in a fully ionized plasma. Kelvin-Helmholtz is a well-known macroscopic and ideal shear-driven instability. In sufficiently low-density plasmas, also the microscopic Hall magnetoshear instability can take place. We performed three-dimensional simulations of the Hall-magnetohydrodynamic equations where these two instabilities are present, and carried out a comparative study. We find that when the shear flow is so intense that its vorticity surpasses the ion-cyclotron frequency of the plasma, the Hall magnetoshear instability is not only non-negligible, but it actually displays growth rates larger than those of the Kelvin-Helmholtz instability.

  18. Exterior metric approach to a charged axially symmetric celestial body: the fourth-order approximate solutions of Einstein--Maxwell equations

    SciTech Connect

    Zhou Qi-huang

    1988-12-01

    Starting with the general expression of a static state axisymmetric metric and using the principle of equivalence and the Maccullagh formula, the Einstein--Maxwell equations of a charged axisymmetric celestial body are obtained. Next, using the method of undetermined coefficients these equations are solved up to fourth-order approximate. These sets of solutions are generally appropriate for all kinds of charged axisymmetric celestial bodies.

  19. Analysis of Kelvin Helmholtz Instabilities of Plasma Jets

    NASA Technical Reports Server (NTRS)

    Friedman, Mark J.; Hollingsworth, Blane J.

    1999-01-01

    Ulysses data indicates density fluctuations which axe theorized to be the result of shear between a solar jet and its ambient. The MHD Kelvin-Helmholtz ("KH") instability causes such fluctuations as observed by Ulysses. A new dispersion relationship which accounts for this KH instability is derived via the linearization of the MHD equations. This generalizes an earlier result by Hardee. This dispersion relationship has the form of eight non-linear equations with nine unknowns.

  20. Analysis of Kelvin Helmholtz Instabilities of Plasma Jets

    NASA Technical Reports Server (NTRS)

    Friedman, Mark J.; Hollingsworth, Blane J.

    1999-01-01

    Ulysses data indicates density fluctuations which are theorized to be the result of shear between a solar jet and its ambient. The MHD Kelvin-Helmholtz ("KH") instability causes such fluctuations as observed by Ulysses. A new dispersion relationship which accounts for this KH instability is derived via the linearization of the MHD equations. This generalizes an earlier result by Hardee. This dispersion relationship has the form of eight non-linear equations with nine unknowns.

  1. 28. EXTERIOR CAN CONVEYOR Exterior section of empty can ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    28. EXTERIOR - CAN CONVEYOR Exterior section of empty can conveyor which transported cans from the third floor of the main warehouse (right) to the canning area. - Hovden Cannery, 886 Cannery Row, Monterey, Monterey County, CA

  2. The possibility of Kelvin-Helmholtz instability in solar spicules

    NASA Astrophysics Data System (ADS)

    Ajabshirizadeh, A.; Ebadi, H.; Vekalati, R. E.; Molaverdikhani, K.

    2015-05-01

    Transversal oscillations of spicules axes may be related to the propagation of magnetohydrodynamic waves along them. These waves may become unstable and the instability can be of the Kelvin-Helmholtz type. We use the dispersion relation of kink mode derived from linearized magnetohydrodynamic equations. The input parameters of the derived dispersion equation, namely, spicules and their ambient medium densities ratios as well as their corresponding magnetic fields ratios, are considered to be within the range 0-1. By solving the dispersion equation numerically, we show that for higher densities and lower magnetic fields ratios within the range mentioned, the KHI onset in type ii spicules conditions is possible. This possibility decreases with an increase in Alfvén velocity inside spicules. A rough criterion for appearing of Kelvin-Helmholtz instability is obtained. We also drive a more reliable and exact criterion for KHI onset of kink waves.

  3. Improvement Of The Helmholtz Absorber

    NASA Technical Reports Server (NTRS)

    Morrow, Duane L.

    1992-01-01

    Helmholtz-resonator system improved to enable it to absorb sound at more than one frequency without appreciable loss of effectiveness at primary frequency. Addition of annular cavities enables absorption of sound at harmonic frequencies in addition to primary frequency. Improved absorber designed for use on structures of high transmission loss. Applied to such machines as fixed-speed engines and fans.

  4. An intrinsic and exterior form of the Bianchi identities

    NASA Astrophysics Data System (ADS)

    Do, Thoan; Prince, Geoff

    2017-09-01

    We give an elegant formulation of the structure equations (of Cartan) and the Bianchi identities in terms of exterior calculus without reference to a particular basis and without the exterior covariant derivative. This approach allows both structure equations and the Bianchi identities to be expressed in terms of forms of arbitrary degree. We demonstrate the relationship with both the conventional vector version of the Bianchi identities and to the exterior covariant derivative approach. Contact manifolds, codimension one foliations and the Cartan form of classical mechanics are studied as examples of its flexibility and utility.

  5. Helmholtz-Smoluchowski velocity for viscoelastic electroosmotic flows.

    PubMed

    Park, H M; Lee, W M

    2008-01-15

    Many biofluids such as blood and DNA solutions are viscoelastic and exhibit extraordinary flow behaviors, not existing in Newtonian fluids. Adopting appropriate constitutive equations these exotic flow behaviors can be modeled and predicted reasonably using various numerical methods. However, the governing equations for viscoelastic flows are not easily solvable, especially for electroosmotic flows where the streamwise velocity varies rapidly from zero at the wall to a nearly uniform velocity at the outside of the very thin electric double layer. In the present investigation, we have devised a simple method to find the volumetric flow rate of viscoelastic electroosmotic flows through microchannels. It is based on the concept of the Helmholtz-Smoluchowski velocity which is widely adopted in the electroosmotic flows of Newtonian fluids. It is shown that the Helmholtz-Smoluchowski velocity for viscoelastic fluids can be found by solving a simple cubic algebraic equation. The volumetric flow rate obtained using this Helmholtz-Smoluchowski velocity is found to be almost the same as that obtained by solving the governing partial differential equations for various viscoelastic fluids.

  6. Comment on the Exterior Solutions and Their Geometry in Scalar-Tensor Theories of Gravity

    NASA Astrophysics Data System (ADS)

    Tsuchida, T.; Watanabe, K.

    1999-01-01

    We study series of stationary solutions with asymptotic flatness properties in the Einstein-Maxwell-free scalar system because they are locally equivalent to the exterior solutions in some class of scalar-tensor theories of gravity. First, we classify spherical exterior solutions into two types of solutions, an apparently black hole type solution and an apparently worm hole type solution. The solutions contain three parameters, and we clarify their physical significance. Second, we reduce the field equations for the axisymmetric exterior solutions. We find that the reduced equations are partially the same as the Ernst equations. As simple examples, we derive new series of static, axisymmetric exterior solutions, which correspond to Voorhees's solutions. We then establish a non-trivial relation between the spherical exterior solutions and our new solutions. Finally, since null geodesics have conformally invariant properties, we study the local geometry of the exterior solutions by using the optical scalar equations and find some anomalous behavior of the null geodesics.

  7. The Poisson-Helmholtz-Boltzmann model.

    PubMed

    Bohinc, K; Shrestha, A; May, S

    2011-10-01

    We present a mean-field model of a one-component electrolyte solution where the mobile ions interact not only via Coulomb interactions but also through a repulsive non-electrostatic Yukawa potential. Our choice of the Yukawa potential represents a simple model for solvent-mediated interactions between ions. We employ a local formulation of the mean-field free energy through the use of two auxiliary potentials, an electrostatic and a non-electrostatic potential. Functional minimization of the mean-field free energy leads to two coupled local differential equations, the Poisson-Boltzmann equation and the Helmholtz-Boltzmann equation. Their boundary conditions account for the sources of both the electrostatic and non-electrostatic interactions on the surface of all macroions that reside in the solution. We analyze a specific example, two like-charged planar surfaces with their mobile counterions forming the electrolyte solution. For this system we calculate the pressure between the two surfaces, and we analyze its dependence on the strength of the Yukawa potential and on the non-electrostatic interactions of the mobile ions with the planar macroion surfaces. In addition, we demonstrate that our mean-field model is consistent with the contact theorem, and we outline its generalization to arbitrary interaction potentials through the use of a Laplace transformation.

  8. Spiking neuron network Helmholtz machine.

    PubMed

    Sountsov, Pavel; Miller, Paul

    2015-01-01

    An increasing amount of behavioral and neurophysiological data suggests that the brain performs optimal (or near-optimal) probabilistic inference and learning during perception and other tasks. Although many machine learning algorithms exist that perform inference and learning in an optimal way, the complete description of how one of those algorithms (or a novel algorithm) can be implemented in the brain is currently incomplete. There have been many proposed solutions that address how neurons can perform optimal inference but the question of how synaptic plasticity can implement optimal learning is rarely addressed. This paper aims to unify the two fields of probabilistic inference and synaptic plasticity by using a neuronal network of realistic model spiking neurons to implement a well-studied computational model called the Helmholtz Machine. The Helmholtz Machine is amenable to neural implementation as the algorithm it uses to learn its parameters, called the wake-sleep algorithm, uses a local delta learning rule. Our spiking-neuron network implements both the delta rule and a small example of a Helmholtz machine. This neuronal network can learn an internal model of continuous-valued training data sets without supervision. The network can also perform inference on the learned internal models. We show how various biophysical features of the neural implementation constrain the parameters of the wake-sleep algorithm, such as the duration of the wake and sleep phases of learning and the minimal sample duration. We examine the deviations from optimal performance and tie them to the properties of the synaptic plasticity rule.

  9. Spiking neuron network Helmholtz machine

    PubMed Central

    Sountsov, Pavel; Miller, Paul

    2015-01-01

    An increasing amount of behavioral and neurophysiological data suggests that the brain performs optimal (or near-optimal) probabilistic inference and learning during perception and other tasks. Although many machine learning algorithms exist that perform inference and learning in an optimal way, the complete description of how one of those algorithms (or a novel algorithm) can be implemented in the brain is currently incomplete. There have been many proposed solutions that address how neurons can perform optimal inference but the question of how synaptic plasticity can implement optimal learning is rarely addressed. This paper aims to unify the two fields of probabilistic inference and synaptic plasticity by using a neuronal network of realistic model spiking neurons to implement a well-studied computational model called the Helmholtz Machine. The Helmholtz Machine is amenable to neural implementation as the algorithm it uses to learn its parameters, called the wake-sleep algorithm, uses a local delta learning rule. Our spiking-neuron network implements both the delta rule and a small example of a Helmholtz machine. This neuronal network can learn an internal model of continuous-valued training data sets without supervision. The network can also perform inference on the learned internal models. We show how various biophysical features of the neural implementation constrain the parameters of the wake-sleep algorithm, such as the duration of the wake and sleep phases of learning and the minimal sample duration. We examine the deviations from optimal performance and tie them to the properties of the synaptic plasticity rule. PMID:25954191

  10. Nonlinear behavior of Helmholtz resonators

    NASA Astrophysics Data System (ADS)

    Hersh, A. S.

    1990-10-01

    A semi-empirical fluid mechanical model has been derived to predict the nonlinear acoustic behavior of thin-walled, single-orifice Helmholtz resonators. The model assumed that the sound particle velocity field approaches the resonator in a spherically symmetric manner. The incident and cavity sound pressure fields are connected in terms of an orifice discharge coefficient and an end correction parameter whose values are determined empirically. The accuracy of the model was verified by comparing predicted with measured impedance over a wide range of sound amplitudes and frequencies for two different resonator geometries and with measurements conducted by Ingard and Ising.

  11. Sunshade for building exteriors

    DOEpatents

    Braunstein, Richard; McKenna, Gregory B.; Hewitt, David W.; Harper, Randolph S.

    2002-01-01

    A sunshade for shading window exteriors includes at least one connecting bracket for attachment to a window mullion, a blade support strut attached to the connecting bracket at a first joint, and a plurality of louvered blades supported by the blade support strut at a second joint. The pivot angle at the first joint may be varied to extend the louvered blades a desired distance from the window mullion. The louvered blades are positioned at a preselected fixed profile angle on the second joint in order to optimize shading at the latitude where the sunshade is installed. In a preferred embodiment, the louvered blades have top walls supporting photovoltaic cells and the sunshade includes electric cables for connecting the photovoltaic cells to an electric circuit.

  12. Integral equations with modified fundamental solution in time-harmonic electromagnetic scattering

    NASA Astrophysics Data System (ADS)

    Jost, Gabriele

    The exterior boundary-value problem for time-harmonic EM reflection from a perfect conductor is investigated analytically. The technique developed by Ursell (1973 and 1974) and Jones (1974) for the scalar Helmholtz equation, based on the addition of outgoing waves to the fundamental free-space solution, is extended to overcome the problem of nonuniqueness in the case of the reduced Maxwell equations. The reduction of the boundary-value problem to a Fredholm integral equation of the second kind and the coefficient selection criteria are explained in detail, and numerical results showing the dependence of the condition number on the frequency are presented in extensive graphs. The present approach is found to be well suited to small wave numbers.

  13. A full-wave Helmholtz model for continuous-wave ultrasound transmission.

    PubMed

    Huttunen, Tomi; Malinen, Matti; Kaipio, Jari P; White, Phillip Jason; Hynynen, Kullervo

    2005-03-01

    A full-wave Helmholtz model of continuous-wave (CW) ultrasound fields may offer several attractive features over widely used partial-wave approximations. For example, many full-wave techniques can be easily adjusted for complex geometries, and multiple reflections of sound are automatically taken into account in the model. To date, however, the full-wave modeling of CW fields in general 3D geometries has been avoided due to the large computational cost associated with the numerical approximation of the Helmholtz equation. Recent developments in computing capacity together with improvements in finite element type modeling techniques are making possible wave simulations in 3D geometries which reach over tens of wavelengths. The aim of this study is to investigate the feasibility of a full-wave solution of the 3D Helmholtz equation for modeling of continuous-wave ultrasound fields in an inhomogeneous medium. The numerical approximation of the Helmholtz equation is computed using the ultraweak variational formulation (UWVF) method. In addition, an inverse problem technique is utilized to reconstruct the velocity distribution on the transducer which is used to model the sound source in the UWVF scheme. The modeling method is verified by comparing simulated and measured fields in the case of transmission of 531 kHz CW fields through layered plastic plates. The comparison shows a reasonable agreement between simulations and measurements at low angles of incidence but, due to mode conversion, the Helmholtz model becomes insufficient for simulating ultrasound fields in plates at large angles of incidence.

  14. Leakage effect in Helmholtz resonators.

    PubMed

    Selamet, Ahmet; Kim, Hyunsu; Huff, Norman T

    2009-09-01

    The effect of leakage in Helmholtz resonators has been investigated in this predominantly experimental study combined with a computational effort. A prototype has been built with varying levels of intentional leakage due to holes in the baffle and gaps between the baffle and the housing. The transmission loss is then measured with different combinations of holes and/or gaps. Such openings, even though their cross-sectional areas are small, are found to have a significant impact on transmission loss. The effect of holes versus gaps is also compared as a function of the leakage area. The present study illustrates the critical need to account for such leakages at the design stage for the proper tuning of these resonators.

  15. Fluid mechanical model of the Helmholtz resonator

    NASA Technical Reports Server (NTRS)

    Hersh, A. S.; Walker, B.

    1977-01-01

    A semi-empirical fluid mechanical model of the acoustic behavior of Helmholtz resonators is presented which predicts impedance as a function of the amplitude and frequency of the incident sound pressure field and resonator geometry. The model assumes that the particle velocity approaches the orifice in a spherical manner. The incident and cavity sound fields are connected by solving the governing oscillating mass and momentum conservation equations. The model is in agreement with the Rayleigh slug-mass model at low values of incident sound pressure level. At high values, resistance is predicted to be independent of frequency, proportional to the square root of the amplitude of the incident sound pressure field, and virtually independent of resonator geometry. Reactance is predicted to depend in a very complicated way upon resonator geometry, incident sound pressure level, and frequency. Nondimensional parameters are defined that divide resonator impedance into three categories corresponding to low, moderately low, and intense incident sound pressure amplitudes. The two-microphone method was used to measure the impedance of a variety of resonators. The data were used to refine and verify the model.

  16. Exterior dimension of fat fractals

    NASA Technical Reports Server (NTRS)

    Grebogi, C.; Mcdonald, S. W.; Ott, E.; Yorke, J. A.

    1985-01-01

    Geometric scaling properties of fat fractal sets (fractals with finite volume) are discussed and characterized via the introduction of a new dimension-like quantity which is called the exterior dimension. In addition, it is shown that the exterior dimension is related to the 'uncertainty exponent' previously used in studies of fractal basin boundaries, and it is shown how this connection can be exploited to determine the exterior dimension. Three illustrative applications are described, two in nonlinear dynamics and one dealing with blood flow in the body. Possible relevance to porous materials and ballistic driven aggregation is also noted.

  17. Helmholtz's Kant revisited (Once more). The all-pervasive nature of Helmholtz's struggle with Kant's Anschauung.

    PubMed

    De Kock, Liesbet

    2016-04-01

    In this analysis, the classical problem of Hermann von Helmholtz's (1821-1894) Kantianism is explored from a particular vantage point, that to my knowledge, has not received the attention it deserves notwithstanding its possible key role in disentangling Helmholtz's relation to Kant's critical project. More particularly, we will focus on Helmholtz's critical engagement with Kant's concept of intuition [Anschauung] and (the related issue of) his dissatisfaction with Kant's doctrinal dualism. In doing so, it soon becomes clear that both (i) crucially mediated Helmholtz's idiosyncratic appropriation and criticism of (certain aspects of) Kant's critical project, and (ii) can be considered as a common denominator in a variety of issues that are usually addressed separately under the general header of (the problem of) Helmholtz's Kantianism. The perspective offered in this analysis can not only shed interesting new light on some interpretive issues that have become commonplace in discussions on Helmholtz's Kantianism, but also offers a particular way of connecting seemingly unrelated dimensions of Helmholtz's engagement with Kant's critical project (e.g. Helmholtz's views on causality and space). Furthermore, it amounts to the rather surprising conclusion that Helmholtz's most drastic revision of Kant's project pertains to his assumption of free will as a formal condition of experience and knowledge. Copyright © 2015 Elsevier Ltd. All rights reserved.

  18. The Magnetic Field of Helmholtz Coils

    ERIC Educational Resources Information Center

    Berridge, H. J. J.

    1975-01-01

    Describes the magnetic field of Helmholtz coils qualitatively and then provides the basis for a quantitative expression. Since the mathematical calculations are very involved, a computer program for solving the mathematical expression is presented and explained. (GS)

  19. A transverse Kelvin-Helmholtz instability in a magnetized plasma

    NASA Technical Reports Server (NTRS)

    Kintner, P.; Dangelo, N.

    1977-01-01

    An analysis is conducted of the transverse Kelvin-Helmholtz instability in a magnetized plasma for unstable flute modes. The analysis makes use of a two-fluid model. Details regarding the instability calculation are discussed, taking into account the ion continuity and momentum equations, the solution of a zero-order and a first-order component, and the properties of the solution. It is expected that the linear calculation conducted will apply to situations in which the plasma has experienced no more than a few growth periods.

  20. Parametric design of tri-axial nested Helmholtz coils.

    PubMed

    Abbott, Jake J

    2015-05-01

    This paper provides an optimal parametric design for tri-axial nested Helmholtz coils, which are used to generate a uniform magnetic field with controllable magnitude and direction. Circular and square coils, both with square cross section, are considered. Practical considerations such as wire selection, wire-wrapping efficiency, wire bending radius, choice of power supply, and inductance and time response are included. Using the equations provided, a designer can quickly create an optimal set of custom coils to generate a specified field magnitude in the uniform-field region while maintaining specified accessibility to the central workspace. An example case study is included.

  1. Drift Kelvin-Helmholtz instabilities in space plasmas

    NASA Technical Reports Server (NTRS)

    Sharma, Avadhesh C.; Srivastava, Krishna M.

    1992-01-01

    Drift Kelvin-Helmholtz instabilities of a finite-beta plasma in equilibrium electric and magnetic fields which are perpendicular to each other are studied using two fluid equations. Three types of these instabilities are considered including the magnetosonic instability of a finite beta-homogeneous plasma, the electrostatic drift instability of an inhomogeneous low-beta plasma, and the magneto-acoustic instability of a high-beta inhomogeneous isothermal plasma. It is shown that the electric field has either stabilizing or destabilizing effect depending on conditions under consideration.

  2. Fully vectorial accelerating diffraction-free Helmholtz beams.

    PubMed

    Aleahmad, Parinaz; Miri, Mohammad-Ali; Mills, Matthew S; Kaminer, Ido; Segev, Mordechai; Christodoulides, Demetrios N

    2012-11-16

    We show that new families of diffraction-free nonparaxial accelerating optical beams can be generated by considering the symmetries of the underlying vectorial Helmholtz equation. Both two-dimensional transverse electric and magnetic accelerating wave fronts are possible, capable of moving along elliptic trajectories. Experimental results corroborate these predictions when these waves are launched from either the major or minor axis of the ellipse. In addition, three-dimensional spherical nondiffracting field configurations are presented along with their evolution dynamics. Finally, fully vectorial self-similar accelerating optical wave solutions are obtained via oblate-prolate spheroidal wave functions. In all occasions, these effects are illustrated via pertinent examples.

  3. Parametric design of tri-axial nested Helmholtz coils

    SciTech Connect

    Abbott, Jake J.

    2015-05-15

    This paper provides an optimal parametric design for tri-axial nested Helmholtz coils, which are used to generate a uniform magnetic field with controllable magnitude and direction. Circular and square coils, both with square cross section, are considered. Practical considerations such as wire selection, wire-wrapping efficiency, wire bending radius, choice of power supply, and inductance and time response are included. Using the equations provided, a designer can quickly create an optimal set of custom coils to generate a specified field magnitude in the uniform-field region while maintaining specified accessibility to the central workspace. An example case study is included.

  4. A tunable electromechanical Helmholtz resonator

    NASA Astrophysics Data System (ADS)

    Liu, Fei

    Acoustic liners are used in turbofan engine nacelles for the suppression of engine noise. For a given engine, there are different optimum impedance distributions associated with take-off, cut-back, and approach flight conditions. The impedance of conventional acoustic liners is fixed for a given geometry, and conventional active liner approaches are impractical. This project addresses the need for a tunable impedance through the development of an electromechanical Helmholtz resonator (EMHR). The device consists of a Helmholtz resonator with the standard rigid backplate replaced by a compliant piezoelectric composite. Analytical models (i.e., a lumped element model (LEM) and a transfer matrix (TM) representation of the EMHR) are developed to predict the acoustic behavior of the EMHR. The EMHR is experimentally investigated using the standard two-microphone method (TMM). The measurement results validate both the LEM and the TM of the EMHR. Good agreement between predicted and measured impedance is obtained. Short- and open-circuit loads define the limits of the tuning range using resistive and capacitive loads. There is approximately a 9% tuning limit under these conditions for the non-optimized resonator configuration studied. Inductive shunt loads result in a 3 degree-of-freedom (DOF) system and an enhanced tuning range of over 47% that is not restricted by the short- and open-circuit limits. Damping coefficient measurements for a piezoelectric backplate in a vacuum chamber are performed and indicate that the damping is dominated by structural damping losses. A Pareto optimization design based on models of the EMHR is performed with non-inductive loads. The EMHR with non-inductive loads has 2DOF and two resonant frequencies. The tuning ranges of the two resonant frequencies of the EMHR with non-inductive loads cannot be optimized simultaneously, so a trade-off (Pareto solution) must be reached. The Pareto solution shows how design trade-offs can be used to satisfy

  5. Laplace-Gauss and Helmholtz-Gauss paraxial modes in media with quadratic refraction index.

    PubMed

    Kiselev, Aleksei P; Plachenov, Alexandr B

    2016-04-01

    The scalar theory of paraxial wave propagation in an axisymmetric medium where the refraction index quadratically depends on transverse variables is addressed. Exact solutions of the corresponding parabolic equation are presented, generalizing the Laplace-Gauss and Helmholtz-Gauss modes earlier known for homogeneous media. Also, a generalization of a zero-order asymmetric Bessel-Gauss beam is given.

  6. Extraordinary acoustic transmission mediated by Helmholtz resonators

    SciTech Connect

    Koju, Vijay; Rowe, Ebony; Robertson, William M.

    2014-07-15

    We demonstrate perfect transmission of sound through a rigid barrier embedded with Helmholtz resonators. The resonators are confined within a waveguide and they are oriented such that one neck protrudes onto each side of the barrier. Perfect sound transmission occurs even though the open area of the necks is less than 3% of the barrier area. Maximum transmission occurs at the resonant frequency of the Helmholtz resonator. Because the dimensions of the Helmholtz resonators are much smaller than the resonant wavelength, the transmission is independent of the direction of sound on the barrier and of the relative placement of the necks. Further, we show that the transmitted sound experiences a continuous phase transition of π radians as a function of frequency through resonance. In simulations of adjacent resonators with slightly offset resonance frequencies, the phase difference leads to destructive interference. By expanding the simulation to a linear array of tuned Helmholtz resonators we show that it is possible to create an acoustic lens. The ability of Helmholtz resonator arrays to manipulate the phase of a plane acoustic wave enables a new class of sonic beam-forming devices analogous to diffractive optics.

  7. Extraordinary acoustic transmission mediated by Helmholtz resonators

    NASA Astrophysics Data System (ADS)

    Koju, Vijay; Rowe, Ebony; Robertson, William M.

    2014-07-01

    We demonstrate perfect transmission of sound through a rigid barrier embedded with Helmholtz resonators. The resonators are confined within a waveguide and they are oriented such that one neck protrudes onto each side of the barrier. Perfect sound transmission occurs even though the open area of the necks is less than 3% of the barrier area. Maximum transmission occurs at the resonant frequency of the Helmholtz resonator. Because the dimensions of the Helmholtz resonators are much smaller than the resonant wavelength, the transmission is independent of the direction of sound on the barrier and of the relative placement of the necks. Further, we show that the transmitted sound experiences a continuous phase transition of π radians as a function of frequency through resonance. In simulations of adjacent resonators with slightly offset resonance frequencies, the phase difference leads to destructive interference. By expanding the simulation to a linear array of tuned Helmholtz resonators we show that it is possible to create an acoustic lens. The ability of Helmholtz resonator arrays to manipulate the phase of a plane acoustic wave enables a new class of sonic beam-forming devices analogous to diffractive optics.

  8. New exact solution for the exterior gravitational field of a spinning mass

    SciTech Connect

    Manko, V.S. Department of Theoretical Physics, Peoples' Friendship University, Ordzhonikidze Street 3, Moscow 117198, U.S.S.R. )

    1990-04-02

    An exact asymptotically flat solution of the vacuum Einstein equations representing the exterior gravitational field of a stationary axisymmetric mass with an arbitrary mass-multipole structure is presented.

  9. New exact solution for the exterior gravitational field of a charged spinning mass

    SciTech Connect

    Chamorro, A. ); Manko, V.S. ); Denisova, T.E. )

    1991-11-15

    An exact asymptotically flat solution of the Einstein-Maxwell equations describing the exterior gravitational field of a charged rotating axisymmetric mass possessing an arbitrary set of multipole moments is presented explicitly.

  10. Helmholtz and the psychophysiology of time.

    PubMed

    Debru, C

    2001-09-01

    After having measured the velocity of the nervous impulse in the 1850s, Helmholtz began doing research on the temporal dimensions of visual perception. Experiments dealing with the velocity of propagation in nerves (as well as with aspects of perception) were carried out occasionally for some fifteen years until their final publication in 1871. Although the temporal dimension of perception seems to have interested Helmholtz less than problems of geometry and space, his experiments on the time of perception were technically rather subtle and seminal, especially compared with experiments performed by his contemporaries, such as Sigmund Exner, William James, Rudolf Hermann Lotze, Ernst Mach, Wilhelm Volkmann, and Wilhelm Wundt. Helmholtz's conception of the temporal aspects of perception reflects the continuity that holds between psychophysiological research and the Kantian philosophical background.

  11. Preserving the Helmholtz dispersion relation: One-way acoustic wave propagation using matrix square roots

    NASA Astrophysics Data System (ADS)

    Keefe, Laurence

    2016-11-01

    Parabolized acoustic propagation in transversely inhomogeneous media is described by the operator update equation U (x , y , z + Δz) =eik0 (- 1 +√{ 1 + Z }) U (x , y , z) for evolution of the envelope of a wavetrain solution to the original Helmholtz equation. Here the operator, Z =∇T2 + (n2 - 1) , involves the transverse Laplacian and the refractive index distribution. Standard expansion techniques (on the assumption Z << 1)) produce pdes that approximate, to greater or lesser extent, the full dispersion relation of the original Helmholtz equation, except that none of them describe evanescent/damped waves without special modifications to the expansion coefficients. Alternatively, a discretization of both the envelope and the operator converts the operator update equation into a matrix multiply, and existing theorems on matrix functions demonstrate that the complete (discrete) Helmholtz dispersion relation, including evanescent/damped waves, is preserved by this discretization. Propagation-constant/damping-rates contour comparisons for the operator equation and various approximations demonstrate this point, and how poorly the lowest-order, textbook, parabolized equation describes propagation in lined ducts.

  12. Cladding Attachment Over Thick Exterior Insulating Sheathing

    SciTech Connect

    Baker, P.; Eng, P.; Lepage, R.

    2014-01-01

    The addition of insulation to the exterior of buildings is an effective means of increasing the thermal resistance of both wood framed walls as well as mass masonry wall assemblies. For thick layers of exterior insulation (levels greater than 1.5 inches), the use of wood furring strips attached through the insulation back to the structure has been used by many contractors and designers as a means to provide a convenient cladding attachment location (Straube and Smegal 2009, Pettit 2009, Joyce 2009, Ueno 2010). The research presented in this report is intended to help develop a better understanding of the system mechanics involved and the potential for environmental exposure induced movement between the furring strip and the framing. BSC sought to address the following research questions: 1.What are the relative roles of the mechanisms and the magnitudes of the force that influence the vertical displacement resistance of the system? 2.Can the capacity at a specified deflection be reliably calculated using mechanics based equations? 3.What are the impacts of environmental exposure on the vertical displacement of furring strips attached directly through insulation back to a wood structure?

  13. Cladding Attachment Over Thick Exterior Insulating Sheathing

    SciTech Connect

    Baker, P.; Eng, P.; Lepage, R.

    2014-01-01

    The addition of insulation to the exterior of buildings is an effective means of increasing the thermal resistance of both wood framed walls as well as mass masonry wall assemblies. For thick layers of exterior insulation (levels greater than 1.5 inches), the use of wood furring strips attached through the insulation back to the structure has been used by many contractors and designers as a means to provide a convenient cladding attachment location (Straube and Smegal 2009, Pettit 2009, Joyce 2009, Ueno 2010). The research presented in this report is intended to help develop a better understanding of the system mechanics involved and the potential for environmental exposure induced movement between the furring strip and the framing. BSC sought to address the following research questions: 1. What are the relative roles of the mechanisms and the magnitudes of the force that influence the vertical displacement resistance of the system? 2. Can the capacity at a specified deflection be reliably calculated using mechanics based equations? 3. What are the impacts of environmental exposure on the vertical displacement of furring strips attached directly through insulation back to a wood structure?

  14. Extension of the Helmholtz-Smoluchowski velocity to the hydrophobic microchannels with velocity slip.

    PubMed

    Park, H M; Kim, T W

    2009-01-21

    Electrokinetic flows through hydrophobic microchannels experience velocity slip at the microchannel wall, which affects volumetric flow rate and solute retention time. The usual method of predicting the volumetric flow rate and velocity profile for hydrophobic microchannels is to solve the Navier-Stokes equation and the Poisson-Boltzmann equation for the electric potential with the boundary condition of velocity slip expressed by the Navier slip coefficient, which is computationally demanding and defies analytic solutions. In the present investigation, we have devised a simple method of predicting the velocity profiles and volumetric flow rates of electrokinetic flows by extending the concept of the Helmholtz-Smoluchowski velocity to microchannels with Navier slip. The extended Helmholtz-Smoluchowski velocity is simple to use and yields accurate results as compared to the exact solutions. Employing the extended Helmholtz-Smoluchowski velocity, the analytical expressions for volumetric flow rate and velocity profile for electrokinetic flows through rectangular microchannels with Navier slip have been obtained at high values of zeta potential. The range of validity of the extended Helmholtz-Smoluchowski velocity is also investigated.

  15. Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

    NASA Astrophysics Data System (ADS)

    Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

    2015-05-01

    We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.

  16. Helmholtz Hodge decomposition of scalar optical fields.

    PubMed

    Bahl, Monika; Senthilkumaran, P

    2012-11-01

    It is shown that the vector field decomposition method, namely, the Helmholtz Hodge decomposition, can also be applied to analyze scalar optical fields that are ubiquitously present in interference and diffraction optics. A phase gradient field that depicts the propagation and Poynting vector directions can hence be separated into solenoidal and irrotational components.

  17. Hermann von Helmholtz's empirico-transcendentalism reconsidered: construction and constitution in Helmholtz's psychology of the object.

    PubMed

    De Kock, Liesbet

    2014-12-01

    This paper aims at contributing to the ongoing efforts to get a firmer grasp of the systematic significance of the entanglement of idealism and empiricism in Helmholtz's work. Contrary to existing analyses, however, the focal point of the present exposition is Helmholtz's attempt to articulate a psychological account of objectification. Helmholtz's motive, as well as his solution to the problem of the object are outlined, and interpreted against the background of his scientific practice on the one hand, and that of empiricist and (transcendental) idealist analyses of experience on the other. The specifically psychological angle taken, not only prompts us to consider figures who have hitherto been treated as having only minor import for Helmholtz interpretation (most importantly J.S. Mill and J.G. Fichte), it furthermore sheds new light on some central tenets of the latter's psychological stance that have hitherto remained underappreciated. For one thing, this analysis reveals an explicit voluntarist tendency in Helmholtz's psychological theory. In conclusion, it is argued that the systematic significance of Helmholtz's empirico-transcendentalism with respect to questions of the mind is best understood as an attempt to found his empirical theory of perception in a second order, normative account of epistemic subjectivity.

  18. [Kelvin-Helmholtz instability in protostellar jets

    NASA Technical Reports Server (NTRS)

    Stone, James; Hardee, Philip

    1996-01-01

    NASA grant NAG 5 2866, funded by the Astrophysics Theory Program, enabled the study the Kelvin-Helmholtz instability in protostellar jets. In collaboration with co-investigator Philip Hardee, the PI derived the analytic dispersion relation for the instability in including a cooling term in the energy equation which was modeled as one of two different power laws. Numerical solutions to this dispersion relation over a wide range of perturbation frequencies, and for a variety of parameter values characterizing the jet (such as Mach number, and density ratio) were found It was found that the growth rates and wavelengths associated with unstable roots of the dispersion relation in cooling jets are significantly different than those associated with adiabatic jets, which have been studied previously. In collaboration with graduate student Jianjun Xu (funded as a research associate under this grant), hydrodynamical simulations were used to follow the growth of the instability into the nonlinear regime. It was found that asymmetric surface waves lead to large amplitude, sinusoidal distortions of the jet, and ultimately to disruption Asymmetric body waves, on the other hand, result in the formation of shocks in the jet beam in the nonlinear regime. In cooling jets, these shocks lead to the formation of dense knots and filaments of gas within the jet. For sufficiently high perturbation frequencies, however, the jet cannot respond and it remains symmetric. Applying these results to observed systems, such as the Herbig-Haro jets HH34, HH111 and HH47 which have been observed with the Hubble Space Telescope, we predicted that some of the asymmetric structures observed in these systems could be attributed to the K-H modes, but that perturbations on timescales associated with the inner disk (about 1 year) would be too rapid to cause disruption. Moreover, it was discovered that weak shock 'spurs' in the ambient gas produced by ripples in the jet surface due to nonlinear, modes of

  19. Accurate boundary conditions for exterior problems in gas dynamics

    NASA Technical Reports Server (NTRS)

    Hagstrom, Thomas; Hariharan, S. I.

    1988-01-01

    The numerical solution of exterior problems is typically accomplished by introducing an artificial, far-field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far-field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.

  20. Accurate boundary conditions for exterior problems in gas dynamics

    NASA Technical Reports Server (NTRS)

    Hagstrom, Thomas; Hariharan, S. I.

    1988-01-01

    The numerical solution of exterior problems is typically accomplished by introducing an artificial, far field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.

  1. Analogues of the Helmholtz resonator in homogenization theory

    SciTech Connect

    Gadyl'shin, R R

    2002-12-31

    Perturbed two-dimensional boundary-value problems are considered for Helmholtz's equation with Dirichlet and Neumann boundary conditions on a family of arcs obtained from the boundary of a bounded domain {omega} by cutting out a large number of small holes distributed almost periodically and close to one another. Relations between the sizes of the openings and of the boundary ensuring that the solution of the perturbed problem converges to the solutions of the Dirichlet or the Neumann problem in {omega} and outside {omega}-bar are established. In the case when {omega} is a disc, the holes are periodically distributed and the homogenized problems are Dirichlet problems, asymptotic formulae with respect to a small parameter {epsilon} (characterizing the sizes of the openings and the distance between them) are constructed for the poles with small imaginary parts of the analytic continuation of the solution of the perturbed problem and their resonance behaviour is demonstrated.

  2. Hermann von Helmholtz and his students

    NASA Astrophysics Data System (ADS)

    Mulligan, Joseph F.

    1989-01-01

    During the years 1871-1888, when Hermann von Helmholtz was professor of physics at the University of Berlin, physicists from all over the world flocked to Berlin to study and do research with him. Among these were the German physicists Max Planck, Heinrich Kayser, Eugen Goldstein, Wilhelm Wien, and Heinrich Hertz, and Americans Henry Rowland, A. A. Michelson, and Michael Pupin. Examples of Helmholtz's scientific and personal interactions with these students and research associates show why he is justly considered the outstanding physics mentor of the 19th century. Both his ideas and his students played a major role in the development of physics in the late 19th and early 20th centuries.

  3. Porogranular materials composed of elastic Helmholtz resonators for acoustic wave absorption.

    PubMed

    Griffiths, Stéphane; Nennig, Benoit; Job, Stéphane

    2017-01-01

    A theoretical and experimental study of the acoustic absorption of granular porous media made of non-cohesive piles of spherical shells is presented. These shells are either rigid or elastic, possibly drilled with a neck (Helmholtz resonators), and either porous or impervious. A description is given of acoustic propagation through these media using the effective medium models proposed by Johnson (rigid particles) and Boutin (rigid Helmholtz resonators), which are extended to the configurations studied in this work. A solution is given for the local equation of elasticity of a shell coupled to the viscous flow of air through the neck and the micropores. The models and the simulations are compared to absorption spectra measured in reflection in an impedance tube. The effective medium models and the measurements show excellent agreement for configurations made of rigid particles and rigid Helmholtz resonators that induce an additional peak of absorption at low frequency. A shift of the Helmholtz resonance toward low frequencies, due to the softness of the shells is revealed by the experiments for elastic shells made of soft elastomer and is well reproduced by the simulations. It is shown that microporous shells enhance and broaden acoustic absorption compared to stiff or elastic resonators.

  4. The Kelvin–Helmholtz instability at Venus: What is the unstable boundary?

    PubMed Central

    Möstl, Ute V.; Erkaev, Nikolay V.; Zellinger, Michael; Lammer, Helmut; Gröller, Hannes; Biernat, Helfried K.; Korovinskiy, Daniil

    2011-01-01

    The Kelvin–Helmholtz instability gained scientific attention after observations at Venus by the spacecraft Pioneer Venus Orbiter gave rise to speculations that the instability contributes to the loss of planetary ions through the formation of plasma clouds. Since then, a handful of studies were devoted to the Kelvin–Helmholtz instability at the ionopause and its implications for Venus. The aim of this study is to investigate the stability of the two instability-relevant boundary layers around Venus: the induced magnetopause and the ionopause. We solve the 2D magnetohydrodynamic equations with the total variation diminishing Lax–Friedrichs algorithm and perform simulation runs with different initial conditions representing the situation at the boundary layers around Venus. Our results show that the Kelvin–Helmholtz instability does not seem to be able to reach its nonlinear vortex phase at the ionopause due to the very effective stabilizing effect of a large density jump across this boundary layer. This seems also to be true for the induced magnetopause for low solar activity. During high solar activity, however, there could occur conditions at the induced magnetopause which are in favour of the nonlinear evolution of the instability. For this situation, we estimated roughly a growth rate for planetary oxygen ions of about 7.6 × 1025 s−1, which should be regarded as an upper limit for loss due to the Kelvin–Helmholtz instability. PMID:22347723

  5. Subcritical Kelvin-Helmholtz instability in a Hele-Shaw cell.

    PubMed

    Meignin, L; Gondret, P; Ruyer-Quil, C; Rabaud, M

    2003-06-13

    We investigate experimentally the subcritical behavior of the Kelvin-Helmholtz instability for a gas-liquid shearing flow in a Hele-Shaw cell. The subcritical curve separating the solutions of a stable plane interface and a fully saturated nonlinear wave train is determined. Experimental results are fitted by a fifth order complex Ginzburg-Landau equation whose linear coefficients are compared to theoretical ones.

  6. Divergence Boundary Conditions for Vector Helmholtz Equations with Divergence Constraints

    NASA Technical Reports Server (NTRS)

    Kangro, Urve; Nicolaides, Roy

    1997-01-01

    The idea of replacing a divergence constraint by a divergence boundary condition is investigated. The connections between the formulations are considered in detail. It is shown that the most common methods of using divergence boundary conditions do not always work properly. Necessary and sufficient conditions for the equivalence of the formulations are given.

  7. Helmholtz's early empiricism and the Erhaltung der Kraft.

    PubMed

    Jurkowitz, Edward

    2010-01-01

    Hermann Helmholtz has often been understood to have started research under the influence of Kant, and then to have made a transition to a later mature empiricist phase. Without claiming that in 1847 Helmholtz held the same positions that he later espoused, I suggest that already in his 1847 'Uber die Erhaltung der Kraft' one may find important aspects of his later empiricism. I highlight the ways in which, from early on, Helmholtz turned Kant to use in developing an empirical program of inquiry into possible basic natural causes. To that end, I indicate how, throughout his arguments, Helmholtz employed, sometimes explicitly, but often tacitly, an empiricist logic, one that ran contrary to any form of transcendental deduction, and even to all a priori knowledge. Instead of deriving aspects about the ultimate constituents of nature, Helmholtz aimed to define the proper project for physical natural science. The first part of the paper describes the context of discussion in which Helmholtz entered. The bulk of the paper then analyzes Helmholtz's arguments in order to make space between (1) Kantian, and other, deductions of characteristics that must be true of nature and (2) Helmholtz's delineation of empirically determinable characteristics of presumed ultimate elements of nature, ones that he meant to be specified and delimited through future experimental research. The paper highlights that throughout his discussion Helmholtz meant to define the proper project for physical natural science, a project rife with empiricist aspects.

  8. An acoustic double fishnet using Helmholtz resonators.

    PubMed

    Murray, A R J; Summers, I R; Sambles, J R; Hibbins, A P

    2014-09-01

    The acoustic transmission of a closely spaced pair of patterned and perforated rigid plates is explored in air. The structure resembles an acoustic double fishnet design, with each plate modified such that the gap between them acts as an array of Helmholtz resonators. This allows the center frequency of the stop band to be reduced by a factor greater than 2 from the value obtained for the conventional acoustic double fishnet design. Experimental results accord well with the predictions of a finite element model.

  9. Measuring the acoustic response of Helmholtz resonators

    NASA Astrophysics Data System (ADS)

    Monteiro, Martín; Marti, Arturo C.; Vogt, Patrik; Kasper, Lutz; Quarthal, Dominik

    2015-04-01

    Many experiments have been proposed to investigate acoustic phenomena in college and early undergraduate levels, in particular the speed of sound,1-9 by means of different methods, such as time of flight, transit time, or resonance in tubes. In this paper we propose to measure the acoustic response curves of a glass beaker filled with different gases, used as an acoustic resonator. We show that these curves expose many interesting peaks and features, one of which matches the resonance peak predicted for a Helmholtz resonator fairly well, and gives a decent estimate for the speed of sound in some cases. The measures are obtained thanks to the capabilities of smartphones.

  10. Extraordinary transmission in optical Helmholtz resonators.

    PubMed

    Chevalier, Paul; Bouchon, Patrick; Sakat, Emilie; Pelouard, Jean-Luc; Pardo, Fabrice; Haïdar, Riad

    2015-06-15

    Optical Helmholtz resonators (OHRs) have been adapted from acoustics designs for light absorbing structures, exhibiting extreme light confinement. Here, extraordinary transmission of light is theoretically demonstrated through symmetric OHRs, comprising a cavity with two λ/500 narrow slits on either side. This device has appealing features to act as a spectral bandpass filter in the context of multispectral imaging, in particular its high angular tolerance because of the localized nature of the resonance. Besides, the cavity can be modeled as an inductor and the two slits can be modeled as capacitors, the whole design acting as a LC circuit thus preventing any harmonic features.

  11. Giant field enhancement in electromagnetic Helmholtz nanoantenna

    NASA Astrophysics Data System (ADS)

    Chevalier, Paul; Bouchon, Patrick; Greffet, Jean-Jacques; Pelouard, Jean-Luc; Haïdar, Riad; Pardo, Fabrice

    2014-11-01

    Inspired by the acoustic Helmholtz resonator, we propose a slit-box electromagnetic nanoantenna able to concentrate the energy of an incident beam into surfaces a thousand times smaller than with a classical lens. This design produces a giant electric field enhancement throughout the slit. The intensity enhancement reaches 104 in the visible range up to 108 in the THz range even with focused beams, thanks to an omnidirectional reception. These properties could target applications requiring extreme light concentration, such as surface-enhanced infrared absorption, nonlinear optics, and biophotonics.

  12. Poisson-Helmholtz-Boltzmann model of the electric double layer: analysis of monovalent ionic mixtures.

    PubMed

    Bohinc, Klemen; Shrestha, Ahis; Brumen, Milan; May, Sylvio

    2012-03-01

    In the classical mean-field description of the electric double layer, known as the Poisson-Boltzmann model, ions interact exclusively through their Coulomb potential. Ion specificity can arise through solvent-mediated, nonelectrostatic interactions between ions. We employ the Yukawa pair potential to model the presence of nonelectrostatic interactions. The combination of Yukawa and Coulomb potential on the mean-field level leads to the Poisson-Helmholtz-Boltzmann model, which employs two auxiliary potentials: one electrostatic and the other nonelectrostatic. In the present work we apply the Poisson-Helmholtz-Boltzmann model to ionic mixtures, consisting of monovalent cations and anions that exhibit different Yukawa interaction strengths. As a specific example we consider a single charged surface in contact with a symmetric monovalent electrolyte. From the minimization of the mean-field free energy we derive the Poisson-Boltzmann and Helmholtz-Boltzmann equations. These nonlinear equations can be solved analytically in the weak perturbation limit. This together with numerical solutions in the nonlinear regime suggests an intricate interplay between electrostatic and nonelectrostatic interactions. The structure and free energy of the electric double layer depends sensitively on the Yukawa interaction strengths between the different ion types and on the nonelectrostatic interactions of the mobile ions with the surface.

  13. Formation and destabilization of Kelvin-Helmholtz billows in stably stratified turbulence

    NASA Astrophysics Data System (ADS)

    Kimura, Yoshifumi; Herring, Jackson

    2013-11-01

    We investigate the formation and destabilization of Kelvin-Helmholtz billows in stably stratified turbulence using the pseudo-spectral DNS of the Navier-Stokes equations under the Boussinesq approximation with 20483 grid points. Our method is to integrate the equations from the zero total energy initial condition with horizontal forcing imposed in a narrow wave number band. In the course of developments, the horizontal spectra first show a single steep power-law (k ? 4 , 5, where k is the horizontal wavenumber), and then the tail part of the spectrum begins to rise to show the Kolmogorov-type slope (k ? 5 / 3). From the viewpoint of vortex formation, we first observe that many wedge vortices are produced which move horizontally (like dipoles) in random directions. As time goes on, the wings of the wedges become thinner and thinner while translating, and finally detach to be almost independent vortex layers. This thinning mechanism makes the vertical shear stronger and eventually the local Richardson number small enough to produce Kelvin-Helmholtz billows. We will demonstrate that the transition in the horizontal energy spectra has a close relation with the destabilizing process of the Kelvin-Helmholtz billows.

  14. 24 CFR 3285.801 - Exterior close-up.

    Code of Federal Regulations, 2012 CFR

    2012-04-01

    ... DEVELOPMENT MODEL MANUFACTURED HOME INSTALLATION STANDARDS Exterior and Interior Close-Up § 3285.801 Exterior... section). (b) Joints and seams. All joints and seams in exterior wall coverings that were disturbed...

  15. Asymmetric liberations in exterior resonances

    NASA Astrophysics Data System (ADS)

    Beauge, C.

    1994-10-01

    The purpose of this paper is to present a general analysis of the planar circular restricted problem of three bodies in the case of exterior mean-motion resonances. Particularly, our aim is to map the phase space of various commensurabilities and determine the singular solutions of the averaged system, comparing them to the well-known case of interior resonances. In some commensurabilities (e.g. 1/2, 1/3) we show the existence of asymmetric librations; that is, librations in which the stationary value of the critical angle theta = (p+q) lambda1-p lambda-q pi is not equal to either zero or pi. The origin, stability and morphogenesis of these solutions are discussed and compared to symmetric librations. However, in some other resonances (e.g. 2/3, 3/4), these fixed points of the mean system seem to be absent. Librations in such cases are restricted to theta = O mod(pi). Asymmetric singular solutions of the plane circular problem are unknown in the case of interior resonances and cannot be reproduced by the reduced Andoyer Hamiltonian known as the Second Fundamental Model for Resonance. However, we show that the extended version of this Hamiltonian function, in which harmonics up to order two are considered, can reproduce fairly well the principal topological characteristics of the phase space and thereby constitutes a simple and useful analytical approximation for these resonances.

  16. Upstate Windows and Exteriors Information Sheet

    EPA Pesticide Factsheets

    Upstate Windows and Exteriors (the Company) is located in Greenville, South Carolina. The settlement involves renovation activities conducted at properties constructed prior to 1978, located in Greenville and Easley, South Carolina.

  17. Helmholtz decomposition coupling rotational to irrotational flow of a viscous fluid

    PubMed Central

    Joseph, Daniel D.

    2006-01-01

    In this work, I present the form of the Navier–Stokes equations implied by the Helmholtz decomposition in which the relation of the irrotational and rotational velocity fields is made explicit. The idea of self-equilibration of irrotational viscous stresses is introduced. The decomposition is constructed by first selecting the irrotational flow compatible with the flow boundaries and other prescribed conditions. The rotational component of velocity is then the difference between the solution of the Navier–Stokes equations and the selected irrotational flow. To satisfy the boundary conditions, the irrotational field is required, and it depends on the viscosity. Five unknown fields are determined by the decomposed form of the Navier–Stokes equations for an incompressible fluid: the rotational component of velocity, the pressure, and the harmonic potential. These five fields may be readily identified in analytic solutions available in the literature. It is clear from these exact solutions that potential flow of a viscous fluid is required to satisfy prescribed conditions, like the no-slip condition at the boundary of a solid or continuity conditions across a two-fluid boundary. It can be said that equations governing the Helmholtz decomposition describe the modification of irrotational flow due to vorticity, but the analysis shows the two fields are coupled and cannot be completely determined independently. PMID:16983077

  18. Numerical modeling of nonlinear acoustic waves in a tube connected with Helmholtz resonators

    NASA Astrophysics Data System (ADS)

    Lombard, Bruno; Mercier, Jean-François

    2014-02-01

    Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a nonlinear PDE describing nonlinear acoustic waves, and a linear ODE describing the oscillations in the Helmholtz resonators. The thermal and viscous losses in the tube and in the necks of the resonators are modeled by fractional derivatives. A diffusive representation is followed: the convolution kernels are replaced by a finite number of memory variables that satisfy local ordinary differential equations. A splitting method is then applied to the evolution equations: their propagative part is solved using a standard TVD scheme for hyperbolic equations, whereas their diffusive part is solved exactly. Various strategies are examined to compute the coefficients of the diffusive representation; finally, an optimization method is preferred to the usual quadrature rules. The numerical model is validated by comparisons with exact solutions. The properties of the full nonlinear solutions are investigated numerically. In particular, the existence of acoustic solitary waves is confirmed.

  19. Nonlinear MHD Kelvin-Helmholtz instability in a pipe

    NASA Astrophysics Data System (ADS)

    Leshan, Chen; Fu, Xu

    1989-05-01

    Nonlinear MHD Kelvin-Helmholtz (K-H) instability in a pipe is treated with the derivative expansion method in the present paper. The linear stability problem was discussed in the past by Chandrasekhar (1961)[1] and Xu et al. (1981).[6]Nagano (1979)[3] discussed the nonlinear MHD K-H instability with infinite depth. He used the singular perturbation method and extrapolated the obtained second order modifier of amplitude vs. frequency to seek the nonlinear effect on the instability growth rate γ. However, in our view, such an extrapolation is inappropriate. Because when the instability sets in, the growth rates of higher order terms on the right hand side of equations will exceed the corresponding secular producing terms, so the expansion will still become meaningless even if the secular producing terms are eliminated. Mathematically speaking, it's impossible to derive formula (39) when γ{0/2} is negative in Nagano's paper.[3]Moreover, even as early as γ{0/2}→ O+, the expansion becomes invalid because the 2nd order modifier γ2 (in his formula (56)) tends to infinity. This weakness is removed in this paper, and the result is extended to the case of a pipe with finite depth.

  20. Cardiac video analysis using Hodge-Helmholtz field decomposition.

    PubMed

    Guo, Qinghong; Mandal, Mrinal K; Liu, Gang; Kavanagh, Katherine M

    2006-01-01

    The critical points (also known as phase singularities) in the heart reflect the pathological change of the heart tissue, and hence can be used to describe and analyze the dynamics of the cardiac electrical activity. As a result, the detection of these critical points can lead to correct understanding and effective therapy of the tachycardia. In this paper, we propose a novel approach to address this problem. The proposed approach includes four stages: image smoothing, motion estimation, motion decomposition, and detection of the critical points. In the image smoothing stage, the noisy cardiac optical data are smoothed using anisotropic diffusion equation. The conduction velocity fields of the cardiac electrical patterns can then be estimated from two consecutive smoothed images. Using the recently developed discrete Hodge-Helmholtz motion decomposition technique, the curl-free and divergence-free potential surfaces of an estimated velocity field are extracted. Finally, hierarchically searching the minima and maxima on the potential surfaces, the sources, sinks, and rotational centers are located with high accuracy. Experimental results with four real cardiac videos show that the proposed approach performs satisfactorily, especially for the cardiac electrical patterns with simple propagations.

  1. Modelling discontinuities and Kelvin Helmholtz instabilities in SPH

    NASA Astrophysics Data System (ADS)

    Price, Daniel J.

    2008-12-01

    In this paper we discuss the treatment of discontinuities in smoothed particle hydrodynamics (SPH) simulations. In particular we discuss the difference between integral and differential representations of the fluid equations in an SPH context and how this relates to the formulation of dissipative terms for the capture of shocks and other discontinuities. This has important implications for many problems, in particular related to recently highlighted problems in treating Kelvin Helmholtz instabilities across entropy gradients in SPH. The specific problems pointed out by Agertz et al. [O. Agertz, B. Moore, J. Stadel, D. Potter, F. Miniati, J. Read, L. Mayer, A. Gawryszczak, A. Kravtsov, Å. Nordlund, F. Pearce, V. Quilis, D. Rudd, V. Springel, J. Stone, E. Tasker, R. Teyssier, J. Wadsley, R. Walder, Fundamental differences between SPH and grid methods, MNRAS 380 (2007) 963 978] are shown to be related in particular to the (lack of) treatment of contact discontinuities in standard SPH formulations which can be cured by the simple application of an artificial thermal conductivity term. We propose a new formulation of artificial thermal conductivity in SPH which minimises dissipation away from discontinuities and can therefore be applied quite generally in SPH calculations.

  2. The Goos-Hanchen shift in Helmholtz-Gauss beams

    NASA Astrophysics Data System (ADS)

    Jezzini, Moises A.; Gutierrez-Vega, Julio C.

    2006-08-01

    We present a study of the total internal reflection of a Helmholtz-Gauss beam at a plane interface between two dielectric media. The derivation is based on the decomposition of the Helmholtz-Gauss beams in terms of its constituent plane waves components. We determine the shift predicted by the classical theory of the Goos- Hänchen shift and analyze the transverse intensity patterns of the reflected waves for a variety of Helmholtz-Gauss beam including Bessel-Gauss and Cosine-Gauss beams.

  3. 7 CFR 1980.315 - Escrow accounts for exterior development.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 7 Agriculture 14 2014-01-01 2014-01-01 false Escrow accounts for exterior development. 1980.315... Escrow accounts for exterior development. When proposed exterior development work cannot be completed... escrow account for exterior development only may be established by the originating lender if the...

  4. 7 CFR 1980.315 - Escrow accounts for exterior development.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 7 Agriculture 14 2013-01-01 2013-01-01 false Escrow accounts for exterior development. 1980.315... Escrow accounts for exterior development. When proposed exterior development work cannot be completed... escrow account for exterior development only may be established by the originating lender if the...

  5. 7 CFR 1980.315 - Escrow accounts for exterior development.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 7 Agriculture 14 2012-01-01 2012-01-01 false Escrow accounts for exterior development. 1980.315... Escrow accounts for exterior development. When proposed exterior development work cannot be completed... escrow account for exterior development only may be established by the originating lender if the...

  6. 7 CFR 1980.315 - Escrow accounts for exterior development.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 14 2010-01-01 2009-01-01 true Escrow accounts for exterior development. 1980.315... Escrow accounts for exterior development. When proposed exterior development work cannot be completed... escrow account for exterior development only may be established by the originating lender if the...

  7. 7 CFR 1980.315 - Escrow accounts for exterior development.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 7 Agriculture 14 2011-01-01 2011-01-01 false Escrow accounts for exterior development. 1980.315... Escrow accounts for exterior development. When proposed exterior development work cannot be completed... escrow account for exterior development only may be established by the originating lender if the...

  8. 24 CFR 3280.105 - Exit facilities; exterior doors.

    Code of Federal Regulations, 2010 CFR

    2010-04-01

    ... construction. (1) Exterior swinging doors shall be constructed in accordance with § 3280.405 the “Standard for Swinging Exterior Passage Doors for Use in Manufactured Homes”. Exterior sliding glass doors shall be... Manufactured Homes”. (2) All exterior swinging doors shall provide a minimum 28 inch wide by 74 inch high...

  9. 24 CFR 3280.105 - Exit facilities; exterior doors.

    Code of Federal Regulations, 2011 CFR

    2011-04-01

    ... construction. (1) Exterior swinging doors shall be constructed in accordance with § 3280.405 the “Standard for Swinging Exterior Passage Doors for Use in Manufactured Homes”. Exterior sliding glass doors shall be... Manufactured Homes”. (2) All exterior swinging doors shall provide a minimum 28 inch wide by 74 inch high...

  10. Loss-improved electroacoustical modeling of small Helmholtz resonators.

    PubMed

    Starecki, Tomasz

    2007-10-01

    Modeling of small Helmholtz resonators based on electroacoustical analogies often results in significant disagreement with measurements, as existing models do not take into account some losses that are observed in practical implementations of such acoustical circuits, e.g., in photoacoustic Helmholtz cells. The paper presents a method which introduces loss corrections to the transmission line model, resulting in substantial improvement of simulations. Values of the loss corrections obtained from comparison of frequency responses of practically implemented resonators with computer simulations are presented in tabular and graphical form. A simple analytical function that can be used for interpolation or extrapolation of the loss corrections for other dimensions of the Helmholtz resonators is also given. Verification of such a modeling method against an open two-cavity Helmholtz structure shows very good agreement between measurements and simulations.

  11. Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green’s function

    SciTech Connect

    Linton, C. M.

    2015-01-15

    A class of two-dimensional phase modulated lattice sums in which the denominator is an indefinite quadratic polynomial Q is expressed in terms of a single, exponentially convergent series of elementary functions. This expression provides an extremely efficient method for the computation of the quasi-periodic Green’s function for the Helmholtz equation that arises in a number of physical contexts when studying wave propagation through a doubly periodic medium. For a class of sums in which Q is positive definite, our new result can be used to generate representations in terms of θ-functions which are significant generalisations of known results.

  12. Kelvin-Helmholtz instability in an Alfven resonant layer of a solar coronal loop

    NASA Technical Reports Server (NTRS)

    Uchimoto, E.; Strauss, H. R.; Lawson, W. S.

    1991-01-01

    A Kelvin-Helmholtz instability has been identified numerically on an azimuthally symmetric Alfven resonant layer in an axially bounded, straight cylindrical coronal loop. The set of equations is solved numerically as an initial value problem. The linear growth rate of this instability is shown to be approximately proportional to the Alfven driving amplitude and inversely proportional to the width of the Alfven resonant layer. It is also shown that the linear growth rate increases linearly with m - 1 up to a certain m, reaches its maximum value for the mode whose half wavelength is comparable to the Alfven resonant layer width, and decreases at higher azimuthal mode number.

  13. Kingfish striations and the Kelvin-Helmholtz instability. Part 1

    SciTech Connect

    Hunter, J.H. Jr.

    1985-10-01

    The role of the Kelvin-Helmholtz instability in initiating the formation of the density striations observed in the Kingfish fireball is examined. Two idealized models are proposed for the velocity shear layer on the sides of the fireball, each of which includes essential characteristics of the Kingfish event insofar as the development of Kelvin-Helmholtz instabilities is concerned. A complete linear analysis is presented for each model.

  14. 75 FR 34170 - Plastic Omnium Automotive Exteriors, LLC, Anderson, SC; Plastic Omnium Automotive Exteriors, LLC...

    Federal Register 2010, 2011, 2012, 2013, 2014

    2010-06-16

    ... Employment and Training Administration Plastic Omnium Automotive Exteriors, LLC, Anderson, SC; Plastic Omnium... Assistance on March 18, 2010, applicable to workers of Plastic Omnium Automotive Exteriors, LLC, Anderson... have occurred involving workers in support of the Anderson, South Carolina location of Plastic Omnium...

  15. Experimental realization of extraordinary acoustic transmission using Helmholtz resonators

    SciTech Connect

    Crow, Brian C.; Cullen, Jordan M.; McKenzie, William W.; Koju, Vijay; Robertson, William M.

    2015-02-15

    The phenomenon of extraordinary acoustic transmission through a solid barrier with an embedded Helmholtz resonator (HR) is demonstrated. The Helmholtz resonator consists of an embedded cavity and two necks that protrude, one on each side of the barrier. Extraordinary transmission occurs for a narrow spectral range encompassing the resonant frequency of the Helmholtz resonator. We show that an amplitude transmission of 97.5% is achieved through a resonator whose neck creates an open area of 6.25% of the total barrier area. In addition to the enhanced transmission, we show that there is a smooth, continuous phase transition in the transmitted sound as a function of frequency. The frequency dependent phase transition is used to experimentally realize slow wave propagation for a narrow-band Gaussian wave packet centered at the maximum transmission frequency. The use of parallel pairs of Helmholtz resonators tuned to different resonant frequencies is experimentally explored as a means of increasing the transmission bandwidth. These experiments show that because of the phase transition, there is always a frequency between the two Helmholtz resonant frequencies at which destructive interference occurs whether the resonances are close or far apart. Finally, we explain how the phase transition associated with Helmholtz-resonator-mediated extraordinary acoustic transmission can be exploited to produce diffractive acoustic components including sub-wavelength thickness acoustic lenses.

  16. Experimental realization of extraordinary acoustic transmission using Helmholtz resonators

    NASA Astrophysics Data System (ADS)

    Crow, Brian C.; Cullen, Jordan M.; McKenzie, William W.; Koju, Vijay; Robertson, William M.

    2015-02-01

    The phenomenon of extraordinary acoustic transmission through a solid barrier with an embedded Helmholtz resonator (HR) is demonstrated. The Helmholtz resonator consists of an embedded cavity and two necks that protrude, one on each side of the barrier. Extraordinary transmission occurs for a narrow spectral range encompassing the resonant frequency of the Helmholtz resonator. We show that an amplitude transmission of 97.5% is achieved through a resonator whose neck creates an open area of 6.25% of the total barrier area. In addition to the enhanced transmission, we show that there is a smooth, continuous phase transition in the transmitted sound as a function of frequency. The frequency dependent phase transition is used to experimentally realize slow wave propagation for a narrow-band Gaussian wave packet centered at the maximum transmission frequency. The use of parallel pairs of Helmholtz resonators tuned to different resonant frequencies is experimentally explored as a means of increasing the transmission bandwidth. These experiments show that because of the phase transition, there is always a frequency between the two Helmholtz resonant frequencies at which destructive interference occurs whether the resonances are close or far apart. Finally, we explain how the phase transition associated with Helmholtz-resonator-mediated extraordinary acoustic transmission can be exploited to produce diffractive acoustic components including sub-wavelength thickness acoustic lenses.

  17. Tuned passive control of combustion instabilities using multiple Helmholtz resonators

    NASA Astrophysics Data System (ADS)

    Zhao, Dan; Morgans, A. S.

    2009-03-01

    In this work, tuned passive control is used to damp unstable combustion systems, with particular emphasis on systems which exhibit multiple unstable modes. Helmholtz resonators are used as passive dampers. The frequency at which they offer maximum damping is varied by altering their geometry; in this work, geometry changes are achieved by varying the area of the Helmholtz resonator neck. For each unstable mode exhibited by the combustion system, a separate Helmholtz resonator has its neck area tuned. Two algorithms are developed, one for identifying the characteristics of all modes present in real time, and another for tuning the neck areas of the Helmholtz resonators. These algorithms are successfully implemented in numerical simulations of a longitudinal combustor exhibiting two unstable modes. The algorithms result in both modes being stabilised as long as two Helmholtz resonators are used. Experiments are then conducted on a Rijke tube with its upper part split into two branches of differing lengths, shaped like a 'Y'. The differing lengths give rise to two unstable modes at different frequencies. A Helmholtz resonator is attached to each branch; the neck area of both can be varied by means of an 'iris' valve, which opens and closes like a camera lens. On implementing the procedure for tuning the neck areas, both unstable modes are stabilised, and stability is maintained for large changes in operating condition. This confirms that the procedure developed is sufficiently robust for use in real combustion systems exhibiting multiple unstable modes.

  18. Dust Dynamics in Kelvin-Helmholtz Instabilities

    NASA Astrophysics Data System (ADS)

    Hendrix, Tom; Keppens, Rony

    2013-04-01

    The Kelvin-Helmholtz instability (KHI) is a fluid instability which arises when two contacting flows have different tangential velocities. As shearing flows are very common in all sorts of (astro)physical fluid setups, the KHI is frequently encountered. In many astrophysical fluids the gas fluid in loaded with additional dust particles. Here we study the influence of these dust particles on the initiation of the KHI, as well as the effect the KHI has on the density distribution of dust species in a range of different particle sizes. This redistribution by the instability is of importance in the formation of dust structures in astrophysical fluids. To study the effect of dust on the linear and nonlinear phase of the KHI, we use the multi-fluid dust + gas module of the MPI-AMRVAC [1] code to perform 2D and 3D simulations of KHI in setups with physical quantities relevant to astrophysical fluids. A clear dependency on dust sizes is seen, with larger dust particles displaying significantly more clumping than smaller ones.

  19. The Helmholtz Total Artificial Heart Labtype.

    PubMed

    Kaufmann, R; Reul, H; Rau, G

    1994-07-01

    To perform the first experimental tests for validation of a new gear unit concept, the pump chamber, diaphragm, and pusher plate design of an orthotopic electromechanical total artificial heart (TAH) (Helmholtz Labtype) was manufactured. In its early stage of development, it provides some of the most important features of the conceptual final artificial heart. The new gear unit transforms a uniform unidirectional rotational motor movement into translatory pusher plate movements, with resting phase in the end-diastolic position, and the angled pump chamber orientation determines the available space for the motor and gear unit. Furthermore, this labtype provides flexibility with regard to use of different types of structural parts for experimental investigations. The first in vitro test results, obtained with specially designed circulatory mockloops that simulate physiological preload and afterload conditions, are presented. They comprise pressure and flow generation, motor performance, efficiency, and energy consumption. The results prove the feasibility of the new gear unit concept for an electromechanical artificial heart and allow a reliable determination of the necessary performance of the future brushless DC motor for the first in vivo TAH model.

  20. Spectral properties of the Dirichlet-to-Neumann operator for the exterior Helmholtz problem and its applications to scattering theory

    NASA Astrophysics Data System (ADS)

    L, Lakshtanov E.

    2010-03-01

    We prove that the Dirichlet-to-Neumann operator (DtN) has no spectrum in the lower half of the complex plane. We find several applications of this fact in scattering by obstacles with impedance boundary conditions. In particular, we find an upper bound for the gradient of the scattering amplitude and for the total cross section. We justify numerical approximations by providing bounds for the difference between theoretical and approximated solutions without using any a priori unknown constants.

  1. STABILITY OF ROTATING MAGNETIZED JETS IN THE SOLAR ATMOSPHERE. I. KELVIN–HELMHOLTZ INSTABILITY

    SciTech Connect

    Zaqarashvili, Teimuraz V.; Zhelyazkov, Ivan; Ofman, Leon

    2015-11-10

    Observations show various jets in the solar atmosphere with significant rotational motions, which may undergo instabilities leading to heat ambient plasma. We study the Kelvin–Helmholtz instability (KHI) of twisted and rotating jets caused by the velocity jumps near the jet surface. We derive a dispersion equation with appropriate boundary conditions for total pressure (including centrifugal force of tube rotation), which governs the dynamics of incompressible jets. Then, we obtain analytical instability criteria of KHI in various cases, which were verified by numerical solutions to the dispersion equation. We find that twisted and rotating jets are unstable to KHI when the kinetic energy of rotation is more than the magnetic energy of the twist. Our analysis shows that the azimuthal magnetic field of 1–5 G can stabilize observed rotations in spicule/macrospicules and X-ray/extreme-ultraviolet (EUV) jets. On the other hand, nontwisted jets are always unstable to KHI. In this case, the instability growth time is several seconds for spicule/macrospicules and a few minutes (or less) for EUV/X-ray jets. We also find that standing kink and torsional Alfvén waves are always unstable near the antinodes, owing to the jump of azimuthal velocity at the surface, while the propagating waves are generally stable. Kelvin–Helmholtz (KH) vortices may lead to enhanced turbulence development and heating of surrounding plasma; therefore, rotating jets may provide energy for chromospheric and coronal heating.

  2. Stability of Rotating Magnetized Jets in the Solar Atmosphere. I. Kelvin-Helmholtz Instability

    NASA Astrophysics Data System (ADS)

    Zaqarashvili, Teimuraz V.; Zhelyazkov, Ivan; Ofman, Leon

    2015-11-01

    Observations show various jets in the solar atmosphere with significant rotational motions, which may undergo instabilities leading to heat ambient plasma. We study the Kelvin-Helmholtz instability (KHI) of twisted and rotating jets caused by the velocity jumps near the jet surface. We derive a dispersion equation with appropriate boundary conditions for total pressure (including centrifugal force of tube rotation), which governs the dynamics of incompressible jets. Then, we obtain analytical instability criteria of KHI in various cases, which were verified by numerical solutions to the dispersion equation. We find that twisted and rotating jets are unstable to KHI when the kinetic energy of rotation is more than the magnetic energy of the twist. Our analysis shows that the azimuthal magnetic field of 1-5 G can stabilize observed rotations in spicule/macrospicules and X-ray/extreme-ultraviolet (EUV) jets. On the other hand, nontwisted jets are always unstable to KHI. In this case, the instability growth time is several seconds for spicule/macrospicules and a few minutes (or less) for EUV/X-ray jets. We also find that standing kink and torsional Alfvén waves are always unstable near the antinodes, owing to the jump of azimuthal velocity at the surface, while the propagating waves are generally stable. Kelvin-Helmholtz (KH) vortices may lead to enhanced turbulence development and heating of surrounding plasma therefore, rotating jets may provide energy for chromospheric and coronal heating.

  3. [Hermann von Helmholtz and Carl Stumpf on consonance and dissonance].

    PubMed

    Kursell, Julia

    2008-06-01

    The article juxtaposes Hermann von Helmholtz's work in the experimental physiology of hearing and Carl Stumpf's tone psychology, focusing on the problem of consonance and dissonance in music. It argues that the experimental set-up plays a major role in the approaches to hearing of both Helmholtz and Stumpf, shaping their redefinition of the musical concepts of consonance and dissonance. Helmholtz, however, explains dissonance as resulting from the beats that are heard when sound waves interfere, while Stumpf explains consonance from the fusion (Verschmelzung) of sounds, noting that two tones, depending on their distance cannot always be recognized as two but are heard as one single tone. Helmholtz's definition of dissonance eventually threatens his own theory of hearing, which is based on the mechanical principle of resonance and considers sound to be composed of sinusoidal waves. Both the physical and the mathematical tools he uses cannot easily be brought into accordance with his experimental findings on beats, which ask for a discrimination of fast changes in intensity. Dissonance thus becomes "unrecomendable" for Helmholtz, because it overstrains the ear. Stumpf's research, in contrast, has its point of departure in the historically given set of intervals and tries to find a principle that would explain this choice. His tests with experimental subjects who have no conscious knowledge of musical harmony and prove incapable to follow or reproduce music reveals to him a difference between the unity and multiplicity of tones.

  4. Evaluation of commercially available exterior digital VMDs

    SciTech Connect

    Ringler, C.E.; Hoover, C.E.

    1995-06-01

    This report discusses the testing and evaluation of thirteen commercially available exterior digital video motion detection (VMD) systems. The systems were evaluated for use in a specific outdoor application. The report focuses primarily on the testing parameters, each system`s advertised features, and the nuisance alarm and detection test results.

  5. Quantifying Kelvin-Helmholtz instability dynamics observed in noctilucent clouds: 1. Methods and observations

    NASA Astrophysics Data System (ADS)

    Baumgarten, Gerd; Fritts, David C.

    2014-08-01

    Noctilucent clouds (NLCs) have been imaged during two nights in summer 2009 from northern Germany (Kühlungsborn, 54°N) and middle Norway (Trondheim, 64°N). For the first time a horizontal resolution of 10 to 20 m at the altitude of the clouds (about 83 km) and a temporal resolution of about 1 s was achieved. Additional imaging using a coarser resolution provided monitoring of the larger-scale (~100 km) structures observed in the clouds. Two series of NLC images are described that reveal apparent Kelvin-Helmholtz (KH) billow structures having very different morphologies and apparent transitions to turbulence and mixing. One series exhibits deep KH billows and apparent secondary instabilities in the billow exteriors having streamwise alignment (and spanwise wave number), suggesting a small initial Richardson number (Ri). A second series of images suggests a larger and less unstable Ri, a slower KH billow evolution, shallower billows, and turbulence and mixing confined to the billow cores. We suggest that systematic exploration of these dynamics employing NLC imaging may enable characterization and quantification of KH instability occurrence statistics and of their contributions to turbulence and mixing in the summer mesopause environment with unique sensitivity to their small-scale dynamics.

  6. 68. Detail view, exterior, south bay of east facade. This ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    68. Detail view, exterior, south bay of east facade. This view was taken following cleaning and repointing of the exterior stonework during the fall 2001. - John Bartram House & Garden, House, 54th Street & Lindbergh Boulevard, Philadelphia, Philadelphia County, PA

  7. EXTERIOR, A view looking east at the west elevation of ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR, A view looking east at the west elevation of the building, including an exterior staircase that leads to the roof - Department of Energy, Mound Facility, Hydrolysis House Building (HH Building), One Mound Road, Miamisburg, Montgomery County, OH

  8. 9. Interior view of unoccupied space; showing opened exterior garage ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    9. Interior view of unoccupied space; showing opened exterior garage door, opened doorway to adjoining rooms, and closed exterior doorway; near southeast corner of building; view to southwest. - Ellsworth Air Force Base, Warehouse, 789 Twining Street, Blackhawk, Meade County, SD

  9. EXTERIOR, A view looking south toward the northwest corner of ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR, A view looking south toward the northwest corner of the building including an exterior staircase that leads to the roof - Department of Energy, Mound Facility, B Building, One Mound Road, Miamisburg, Montgomery County, OH

  10. 24 CFR 3280.105 - Exit facilities; exterior doors.

    Code of Federal Regulations, 2012 CFR

    2012-04-01

    ... opening. (3) Each swinging exterior door other than screen or storm doors shall have a key-operated lock... the use of a key for operation from the inside. (4) All exterior doors, including storm and screen...

  11. Exterior view of north and east exterior walls of LongTerm ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Exterior view of north and east exterior walls of Long-Term Oxidizer Silo (T-28B), looking south. Silo was designed to assess long-term environmental impacts on storage of the Titan II's oxidizer (nitrogen tetroxide). The shorter Oxidizer Conditioning Structure (T-28D) is located behind and to the immediate left of T-28B - Air Force Plant PJKS, Systems Integration Laboratory, Long-Term Oxidizer Silo, Waterton Canyon Road & Colorado Highway 121, Lakewood, Jefferson County, CO

  12. On realizations of exterior calculus with dN = 0

    NASA Astrophysics Data System (ADS)

    Abramov, V.

    1998-11-01

    We study realizations of the q-exterior calculus with exterior differential d satisfying d N = 0, N > 2 on the free associative algebra with one generator and on the generalized Clifford algebras. Analogs of the notions of connection and curvature are discussed in the case of the q-exterior calculus on the generalized Clifford algebra. We show that the q-exterior calculus on the free associative algebra with one generator is related to q-calculus on the braided line.

  13. Self-similar wave produced by local perturbation of the Kelvin-Helmholtz shear-layer instability.

    PubMed

    Hoepffner, Jérôme; Blumenthal, Ralf; Zaleski, Stéphane

    2011-03-11

    We show that the Kelvin-Helmholtz instability excited by a localized perturbation yields a self-similar wave. The instability of the mixing layer was first conceived by Helmholtz as the inevitable growth of any localized irregularity into a spiral, but the search and uncovering of the resulting self-similar evolution was hindered by the technical success of Kelvin's wavelike perturbation theory. The identification of a self-similar solution is useful since its specific structure is witness of a subtle nonlinear equilibrium among the forces involved. By simulating numerically the Navier-Stokes equations, we analyze the properties of the wave: growth rate, propagation speed and the dependency of its shape upon the density ratio of the two phases of the mixing layer.

  14. 36 CFR 910.38 - Building exterior illumination.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 36 Parks, Forests, and Public Property 3 2010-07-01 2010-07-01 false Building exterior... PENNSYLVANIA AVENUE DEVELOPMENT AREA Standards Uniformly Applicable to the Development Area § 910.38 Building exterior illumination. Exterior illumination of a building shall be in conformance with the...

  15. 36 CFR 910.38 - Building exterior illumination.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... 36 Parks, Forests, and Public Property 3 2011-07-01 2011-07-01 false Building exterior... PENNSYLVANIA AVENUE DEVELOPMENT AREA Standards Uniformly Applicable to the Development Area § 910.38 Building exterior illumination. Exterior illumination of a building shall be in conformance with the...

  16. 24 CFR 3285.801 - Exterior close-up.

    Code of Federal Regulations, 2010 CFR

    2010-04-01

    .... All home installers must ensure that all field installed trim, windows, doors, and other openings are... DEVELOPMENT MODEL MANUFACTURED HOME INSTALLATION STANDARDS Exterior and Interior Close-Up § 3285.801 Exterior close-up. (a) Exterior siding and roofing necessary to join all sections of the home must be installed...

  17. 36 CFR § 910.38 - Building exterior illumination.

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... 36 Parks, Forests, and Public Property 3 2013-07-01 2012-07-01 true Building exterior illumination... PENNSYLVANIA AVENUE DEVELOPMENT AREA Standards Uniformly Applicable to the Development Area § 910.38 Building exterior illumination. Exterior illumination of a building shall be in conformance with the standards...

  18. 36 CFR 910.38 - Building exterior illumination.

    Code of Federal Regulations, 2012 CFR

    2012-07-01

    ... 36 Parks, Forests, and Public Property 3 2012-07-01 2012-07-01 false Building exterior... PENNSYLVANIA AVENUE DEVELOPMENT AREA Standards Uniformly Applicable to the Development Area § 910.38 Building exterior illumination. Exterior illumination of a building shall be in conformance with the standards...

  19. 36 CFR 910.38 - Building exterior illumination.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... 36 Parks, Forests, and Public Property 3 2014-07-01 2014-07-01 false Building exterior... PENNSYLVANIA AVENUE DEVELOPMENT AREA Standards Uniformly Applicable to the Development Area § 910.38 Building exterior illumination. Exterior illumination of a building shall be in conformance with the standards...

  20. Comments on the "Meshless Helmholtz-Hodge decomposition".

    PubMed

    Bhatia, Harsh; Norgard, Gregory; Pascucci, Valerio; Bremer, Peer-Timo

    2013-03-01

    The Helmholtz-Hodge decomposition (HHD) is one of the fundamental theorems of fluids describing the decomposition of a flow field into its divergence-free, curl-free, and harmonic components. Solving for the HHD is intimately connected to the choice of boundary conditions which determine the uniqueness and orthogonality of the decomposition. This article points out that one of the boundary conditions used in a recent paper "Meshless Helmholtz-Hodge Decomposition" is, in general, invalid and provides an analytical example demonstrating the problem. We hope that this clarification on the theory will foster further research in this area and prevent undue problems in applying and extending the original approach.

  1. Solution of the General Helmholtz Equation Starting from Laplace’s Equation

    DTIC Science & Technology

    2002-11-01

    infinity for the two dimensional case. For the 3D the general form case, this term does not exist, as the potential at infinity is zero. Hence the Green’s...companies. She has assisted the Comisi6n the Living System Laboratory, Interministerial de Ciencia y Tecnologia (National LG Electronics, From 1998 to 2000

  2. Maxwell Equations and the Redundant Gauge Degree of Freedom

    ERIC Educational Resources Information Center

    Wong, Chun Wa

    2009-01-01

    On transformation to the Fourier space (k,[omega]), the partial differential Maxwell equations simplify to algebraic equations, and the Helmholtz theorem of vector calculus reduces to vector algebraic projections. Maxwell equations and their solutions can then be separated readily into longitudinal and transverse components relative to the…

  3. Maxwell Equations and the Redundant Gauge Degree of Freedom

    ERIC Educational Resources Information Center

    Wong, Chun Wa

    2009-01-01

    On transformation to the Fourier space (k,[omega]), the partial differential Maxwell equations simplify to algebraic equations, and the Helmholtz theorem of vector calculus reduces to vector algebraic projections. Maxwell equations and their solutions can then be separated readily into longitudinal and transverse components relative to the…

  4. A perturbation method for the Ornstein-Zernike equation and the generic van der Waals equation of state for a square well potential model.

    PubMed

    Eu, Byung Chan; Qin, Yuan

    2007-04-12

    We calculate the generic van der Waals parameters A and B for a square well model by means of a perturbation theory. To calculate the pair distribution function or the cavity function necessary for the calculation of A and B, we have used the Percus-Yevick integral equation, which is put into an equivalent form by means of the Wiener-Hopf method. This latter method produces a pair of integral equations, which are solved by a perturbation method treating the Mayer function or the well width or the functions in the square well region exterior to the hard core as the perturbation. In the end, the Mayer function times the well width is identified as the perturbation parameter in the present method. In this sense, the present perturbation method is distinct from the existing thermodynamic perturbation theory, which expands the Helmholtz free energy in a perturbation series with the inverse temperature treated as an expansion parameter. The generic van der Waals parameters are explicitly calculated in analytic form as functions of reduced temperature and density. The van der Waals parameters are recovered from them in the limits of vanishing density and high temperature. The equation of state thus obtained is tested against Monte Carlo simulation results and found reliable, provided that the temperature is in the supercritical regime. By scaling the packing fraction with a temperature-dependent hard core, it is suggested to construct an equation of state for fluids with a temperature-dependent hard core that mimicks a soft core repulsive force on the basis of the equation of state derived for the square well model.

  5. Exterior LED Lighting Projects at Princeton University

    SciTech Connect

    Davis, Robert G.; Evans, William; Murphy, Arthur T.; Perrin, Tess E.

    2015-10-01

    For this report, PNNL / the U.S. Department of Energy (DOE) studied a series of past exterior lighting projects at Princeton, in order to document Princeton’s experiences with solid-state lighting (SSL) and the lessons learned along the way, and to show how their approach to SSL projects evolved as their own learning expanded and as the products available improved in performance and sophistication.

  6. Excavationless Exterior Foundation Insulation Exploratory Study

    SciTech Connect

    Mosiman, G.; Wagner, R.; Schirber, T.

    2013-02-01

    The key objective of this exploratory study was to investigate the feasibility of the development or adoption of technologies that would enable a large percentage of existing homes in cold climates to apply a combination 'excavationless' soil removal process with appropriate insulation and water management on the exterior of existing foundations at a low cost. Our approach was to explore existing excavation and material technologies and systems to discover whether potential successful combinations existed.

  7. Excavationless Exterior Foundation Insulation Exploratory Study

    SciTech Connect

    Mosimann, Garrett; Wagner, Rachel; Schirber, Tom

    2013-02-01

    The key objective of this exploratory study was to investigate the feasibility of the development or adoption of technologies that would enable a large percentage of existing homes in cold climates to apply a combination 'excavationless' soil removal process with appropriate insulation and water management on the exterior of existing foundations at a low cost. Our approach was to explore existing excavation and material technologies and systems to discover whether potential successful combinations existed.

  8. Spectral methods for exterior elliptic problems

    NASA Technical Reports Server (NTRS)

    Canuto, C.; Hariharan, S. I.; Lustman, L.

    1984-01-01

    Spectral approximations for exterior elliptic problems in two dimensions are discussed. As in the conventional finite difference or finite element methods, the accuracy of the numerical solutions is limited by the order of the numerical farfield conditions. A spectral boundary treatment is introduced at infinity which is compatible with the infinite order interior spectral scheme. Computational results are presented to demonstrate the spectral accuracy attainable. Although a simple Laplace problem is examined, the analysis covers more complex and general cases.

  9. Excavationless Exterior Foundation Insulation Field Study

    SciTech Connect

    Schirber, T.; Mosiman, G.; Ojczyk, C.

    2014-09-01

    Building science research supports installing exterior (soil side) foundation insulation as the optimal method to enhance the hygrothermal performance of new homes. With exterior foundation insulation, water management strategies are maximized while insulating the basement space and ensuring a more even temperature at the foundation wall. However, such an approach can be very costly and disruptive when applied to an existing home, requiring deep excavation around the entire house. The NorthernSTAR Building America Partnership team implemented an innovative, minimally invasive foundation insulation upgrade technique on an existing home. The approach consisted of using hydrovac excavation technology combined with liquid insulating foam. The team was able to excavate a continuous 4 inches wide by 4 feet to 5 feet deep trench around the entire house, 128 linear feet, except for one small part under the stoop that was obstructed with concrete debris. The combination pressure washer and vacuum extraction technology also enabled the elimination of large trenches and soil stockpiles normally produced by backhoe excavation. The resulting trench was filled with liquid insulating foam, which also served as a water-control layer of the assembly. The insulation was brought above grade using a liquid foam/rigid foam hybrid system and terminated at the top of the rim joist. Cost savings over the traditional excavation process ranged from 23% to 50%. The excavationless process could result in even greater savings since replacement of building structures, exterior features, utility meters, and landscaping would be minimal or non-existent in an excavationless process.

  10. Excavationless Exterior Foundation Insulation Field Study

    SciTech Connect

    Schirber, T.; Mosiman, G.; Ojczyk, C.

    2014-10-01

    Building science research supports installing exterior (soil side) foundation insulation as the optimal method to enhance the hygrothermal performance of new homes. With exterior foundation insulation, water management strategies are maximized while insulating the basement space and ensuring a more even temperature at the foundation wall. However, such an approach can be very costly and disruptive when applied to an existing home, requiring deep excavation around the entire house. The NorthernSTAR Building America Partnership team implemented an innovative, minimally invasive foundation insulation upgrade technique on an existing home. The approach consisted of using hydrovac excavation technology combined with a liquid insulating foam. The team was able to excavate a continuous 4" wide by 4' to 5' deep trench around the entire house, 128 linear feet, except for one small part under the stoop that was obstructed with concrete debris. The combination pressure washer and vacuum extraction technology also enabled the elimination of large trenches and soil stockpiles normally produced by backhoe excavation. The resulting trench was filled with liquid insulating foam, which also served as a water-control layer of the assembly. The insulation was brought above grade using a liquid foam/rigid foam hybrid system and terminated at the top of the rim joist. Cost savings over the traditional excavation process ranged from 23% to 50%. The excavationless process could result in even greater savings since replacement of building structures, exterior features, utility meters, and landscaping would be minimal or non-existent in an excavationless process.

  11. A WELL-POSED KELVIN-HELMHOLTZ INSTABILITY TEST AND COMPARISON

    SciTech Connect

    McNally, Colin P.; Lyra, Wladimir; Passy, Jean-Claude E-mail: wlyra@jpl.nasa.gov

    2012-08-01

    Recently, there has been a significant level of discussion of the correct treatment of Kelvin-Helmholtz instability (KHI) in the astrophysical community. This discussion relies largely on how the KHI test is posed and analyzed. We pose a stringent test of the initial growth of the instability. The goal is to provide a rigorous methodology for verifying a code on two-dimensional KHI. We ran the problem in the Pencil Code, Athena, Enzo, NDSPMHD, and Phurbas. A strict comparison, judgment, or ranking, between codes is beyond the scope of this work, though this work provides the mathematical framework needed for such a study. Nonetheless, how the test is posed circumvents the issues raised by tests starting from a sharp contact discontinuity yet it still shows the poor performance of smoothed particle hydrodynamics (SPH). We then comment on the connection between this behavior to the underlying lack of zeroth-order consistency in SPH interpolation. We comment on the tendency of some methods, particularly those with very low numerical diffusion, to produce secondary Kelvin-Helmholtz billows on similar tests. Though the lack of a fixed, physical diffusive scale in the Euler equations lies at the root of the issue, we suggest that in some methods an extra diffusion operator should be used to damp the growth of instabilities arising from grid noise. This statement applies particularly to moving-mesh tessellation codes, but also to fixed-grid Godunov schemes.

  12. Quantitative Reappraisal of the Helmholtz-Guyton Resonance Theory of Frequency Tuning in the Cochlea

    PubMed Central

    Babbs, Charles F.

    2011-01-01

    To explore the fundamental biomechanics of sound frequency transduction in the cochlea, a two-dimensional analytical model of the basilar membrane was constructed from first principles. Quantitative analysis showed that axial forces along the membrane are negligible, condensing the problem to a set of ordered one-dimensional models in the radial dimension, for which all parameters can be specified from experimental data. Solutions of the radial models for asymmetrical boundary conditions produce realistic deformation patterns. The resulting second-order differential equations, based on the original concepts of Helmholtz and Guyton, and including viscoelastic restoring forces, predict a frequency map and amplitudes of deflections that are consistent with classical observations. They also predict the effects of an observation hole drilled in the surrounding bone, the effects of curvature of the cochlear spiral, as well as apparent traveling waves under a variety of experimental conditions. A quantitative rendition of the classical Helmholtz-Guyton model captures the essence of cochlear mechanics and unifies the competing resonance and traveling wave theories. PMID:22028708

  13. Quantitative reappraisal of the helmholtz-guyton resonance theory of frequency tuning in the cochlea.

    PubMed

    Babbs, Charles F

    2011-01-01

    To explore the fundamental biomechanics of sound frequency transduction in the cochlea, a two-dimensional analytical model of the basilar membrane was constructed from first principles. Quantitative analysis showed that axial forces along the membrane are negligible, condensing the problem to a set of ordered one-dimensional models in the radial dimension, for which all parameters can be specified from experimental data. Solutions of the radial models for asymmetrical boundary conditions produce realistic deformation patterns. The resulting second-order differential equations, based on the original concepts of Helmholtz and Guyton, and including viscoelastic restoring forces, predict a frequency map and amplitudes of deflections that are consistent with classical observations. They also predict the effects of an observation hole drilled in the surrounding bone, the effects of curvature of the cochlear spiral, as well as apparent traveling waves under a variety of experimental conditions. A quantitative rendition of the classical Helmholtz-Guyton model captures the essence of cochlear mechanics and unifies the competing resonance and traveling wave theories.

  14. Suppression of Helmholtz resonance using inside acoustic liner

    NASA Astrophysics Data System (ADS)

    Hong, Zhiliang; Dai, Xiwen; Zhou, Nianfa; Sun, Xiaofeng; Jing, Xiaodong

    2014-08-01

    When a Helmholtz resonator is exposed to grazing flow, an unstable shear layer at the opening can cause the occurrence of acoustic resonance under appropriate conditions. In this paper, in order to suppress the flow-induced resonance, the effects of inside acoustic liners placed on the side wall or the bottom of a Helmholtz resonator are investigated. Based on the one-dimensional sound propagation theory, the time domain impedance model of a Helmholtz resonator with inside acoustic liner is derived, and then combined with a discrete vortex model the resonant behavior of the resonator under grazing flow is simulated. Besides, an experiment is conducted to validate the present model, showing significant reduction of the peak sound pressure level achieved by the use of the side-wall liners. And the simulation results match reasonably well with the experimental data. The present results reveal that the inside acoustic liner can not only absorb the resonant sound pressure, but also suppress the fluctuation motion of the shear layer over the opening of the resonator. In all, the impact of the acoustic liners is to dampen the instability of the flow-acoustic coupled system. This demonstrates that it is a convenient and effective method for suppressing Helmholtz resonance by using inside acoustic liner.

  15. Design for a High Energy Density Kelvin-Helmholtz Experiment

    SciTech Connect

    Hurricane, O A

    2007-10-29

    While many high energy density physics (HEDP) Rayleigh-Taylor and Richtmyer-Meshkov instability experiments have been fielded as part of basic HEDP and astrophysics studies, not one HEDP Kelvin-Helmholtz (KH) experiment has been successfully performed. Herein, a design for a novel HEDP x-ray driven KH experiment is presented along with supporting radiation-hydrodynamic simulation and theory.

  16. Directional organization and shape formation: new illusions and Helmholtz's Square

    PubMed Central

    Pinna, Baingio

    2015-01-01

    According to Helmholtz's Square illusion, a square appears wider when it is filled with vertical lines and higher when filled with horizontal lines (Helmholtz von, 1866). Recently, Pinna (2010a) demonstrated that the grouping of small squares on the basis of the similarity principle influences also perception of their shape and of the whole emerging shapes. The direction imparted by grouping is the main attribute that influences the shape by polarizing it in the same direction both globally and locally. The rectangle illusion is opposite to what expected on the basis of Helmholtz's Square illusion. Aim of this work is to solve the antinomy between the two sets of illusions and to demonstrate a common explanation based on the interaction between different sources of directional organization. This was accomplished by introducing some new phenomena and through phenomenological experiments proving the role played by the directional shape organization in shape formation. According to our results, Helmholtz's square illusion shows at least two synergistic sources of directional organization: the direction of the grouping of the lines due to their similarity of the luminance contrast and the direction of the grouping of the lines due to the good continuation. PMID:25784870

  17. Hydraulic pressure energy harvester enhanced by Helmholtz resonator

    NASA Astrophysics Data System (ADS)

    Skow, Ellen; Koontz, Zachary; Cunefare, Kenneth; Erturk, Alper

    2015-04-01

    Hydraulic pressure energy harvesters (HPEH) are devices that convert the dynamic pressure within hydraulic systems into usable electrical power through axially loaded piezoelectric stacks excited off-resonance by the fluid. Within hydraulic systems, the dominant frequency is typically a harmonic of the pump operating frequency. The pressure fluctuations coupled with the piezoelectric stack can be amplified by creating a housing design that includes a Helmholtz resonator tuned to the dominant frequency of the fluid excitation. A Helmholtz resonator is an acoustic device that consists of a cavity coupled to a fluid medium via a neck, or in this case a port connection to the fluid flow, that acts as an amplifier when within the bandwidth of its resonance. The implementation of a piezoelectric stack within the HPEH allows for a Helmholtz resonator to be included within the fluidic environment despite the significantly higher than air static pressures typical of fluid hydraulic systems (on the order of one to tens of MPa). The resistive losses within the system, such as from energy harvesting and viscous losses, can also be used to increase the bandwidth of the resonance; thus increasing the utility of the device. This paper investigates the design, modeling, and performance of hydraulic pressure energy harvesters utilizing a Helmholtz resonator design.

  18. FUNDAMENTAL AREAS OF PHENOMENOLOGY (INCLUDING APPLICATIONS): Numerical Simulation of Electromagnetic Waves Scattering by Discrete Exterior Calculus

    NASA Astrophysics Data System (ADS)

    Ye, Zheng; Xie, Zheng; Ma, Yu-Jie

    2009-08-01

    We show how to construct discrete Maxwell equations by discrete exterior calculus. The new scheme has many virtues compared to the traditional Yee's scheme: it is a multisymplectic scheme and keeps geometric properties. Moreover, it can be applied on triangular mesh and thus is more adaptive to handle domains with irregular shapes. We have implemented this scheme on a Java platform successfully and our experimental results show that this scheme works well.

  19. ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS: Numerical Simulation of Antennae by Discrete Exterior Calculus

    NASA Astrophysics Data System (ADS)

    Xie, Zheng; Ye, Zheng; Ma, Yu-Jie

    2009-12-01

    Numerical simulation of antennae is a topic in computational electromagnetism, which is concerned with the numerical study of Maxwell equations. By discrete exterior calculus and the lattice gauge theory with coefficient R, we obtain the Bianchi identity on prism lattice. By defining an inner product of discrete differential forms, we derive the source equation and continuity equation. Those equations compose the discrete Maxwell equations in vacuum case on discrete manifold, which are implemented on Java development platform to simulate the Gaussian pulse radiation on antennaes.

  20. Numerical simulation of the excitation of a Helmholtz resonator by a grazing flow.

    PubMed

    Mallick, S; Shock, R; Yakhot, V

    2003-10-01

    The process of noise generation in a flow-excited Helmholtz resonator involves strong interaction between a time-dependent fluid flow and acoustic resonance. Quantitative prediction of this effect, requiring accurate prediction of time-dependent features of a flow over complex three-dimensional bodies, turbulence modeling, compressibility and Mach number effects, is one of the major challenges to computational fluid dynamics. In this paper a numerical procedure based on the lattice kinetic equation, combined with the RNG turbulence model, is applied to describe a well-controlled experiment on acoustic resonance excitation by a grazing flow [Nelson et al., J. Sound Vib. 78, 15-27 (1981)]. The achieved agreement between numerical and physical experiments is very good. The simulations reveal a universality transformation enabling comparison of the data for different inlet conditions.

  1. A new correlation effect in the Helmholtz and surface potentials of the electrical double layer.

    PubMed

    González-Tovar, Enrique; Jiménez-Angeles, Felipe; Messina, René; Lozada-Cassou, Marcelo

    2004-05-22

    The restricted primitive model of an electrical double layer around a spherical macroparticle is studied by using integral equation theories and Monte Carlo simulations. The resulting theoretical curves for the Helmholtz and surface potentials versus the macroparticle charge show an unexpected positive curvature when the ionic size of uni- and divalent electrolyte species is increased. This is a novel effect that is confirmed here by computer experiments. An explanation of this phenomenon is advanced in terms of the adsorption and layering of the electrolytic species and of the compactness of the diffuse double layer. It is claimed that the interplay between electrostatic and ionic size correlation effects, absent in the classical Poisson-Boltzmann view, is responsible for this singularity.

  2. Numerical simulations of magnetic Kelvin-Helmholtz instability at a twisted solar flux tube

    NASA Astrophysics Data System (ADS)

    Murawski, K.; Chmielewski, P.; Zaqarashvili, T. V.; Khomenko, E.

    2016-07-01

    The paper aims to study the response of a solar small-scale and weak magnetic flux tube to photospheric twisting motions. We numerically solve three-dimensional ideal magnetohydrodynamic equations to describe the evolution of the perturbation within the initially static flux tube, excited by twists in the azimuthal component of the velocity. These twists produce rotation of the magnetic field lines. Perturbation of magnetic field lines propagates upwardly, driving vertical and azimuthal flow as well as plasma compressions and rarefactions in the form of eddies. We conclude that these eddies result from the sheared azimuthal flow which seeds Kelvin-Helmholtz instability (KHI) between the flux tube and the ambient medium. Numerically obtained properties of the KHI confirm the analytical predictions for the occurrence of the instability.

  3. Exterior of Opportunity Heat Shield, Sol 344

    NASA Technical Reports Server (NTRS)

    2005-01-01

    NASA's Mars Exploration Rover Opportunity took a detailed look at what was once the exterior of its heat shield. Hitting the martian surface inverted the heat shield, making it difficult to photograph the outside where evidence of any atmospheric effects may be found.

    Engineers sought this image to help determine how the heat shield weathered the intense frictional heat created as it passed through the martian atmosphere.

    This is an approximately true-color rendering of the scene acquired around 12:47 p.m. local solar time on Opportunity's sol 344 (Jan. 11, 2005) using panoramic camera filters at wavelengths of 750, 530, and 430 nanometers.

  4. Design of an autonomous exterior security robot

    NASA Technical Reports Server (NTRS)

    Myers, Scott D.

    1994-01-01

    This paper discusses the requirements and preliminary design of robotic vehicle designed for performing autonomous exterior perimeter security patrols around warehouse areas, ammunition supply depots, and industrial parks for the U.S. Department of Defense. The preliminary design allows for the operation of up to eight vehicles in a six kilometer by six kilometer zone with autonomous navigation and obstacle avoidance. In addition to detection of crawling intruders at 100 meters, the system must perform real-time inventory checking and database comparisons using a microwave tags system.

  5. Acoustic superlens using Helmholtz-resonator-based metamaterials

    SciTech Connect

    Yang, Xishan; Yin, Jing; Yu, Gaokun Peng, Linhui; Wang, Ning

    2015-11-09

    Acoustic superlens provides a way to overcome the diffraction limit with respect to the wavelength of the bulk wave in air. However, the operating frequency range of subwavelength imaging is quite narrow. Here, an acoustic superlens is designed using Helmholtz-resonator-based metamaterials to broaden the bandwidth of super-resolution. An experiment is carried out to verify subwavelength imaging of double slits, the imaging of which can be well resolved in the frequency range from 570 to 650 Hz. Different from previous works based on the Fabry-Pérot resonance, the corresponding mechanism of subwavelength imaging is the Fano resonance, and the strong coupling between the neighbouring Helmholtz resonators separated at the subwavelength interval leads to the enhanced sound transmission over a relatively wide frequency range.

  6. Helmholtz-like resonators for thermoacoustic prime movers.

    PubMed

    Andersen, Bonnie J; Symko, Orest G

    2009-02-01

    In a thermoacoustic prime mover, high acoustic output power can be achieved with a large-diameter stack and with a cavity with a large volume attached at the open end of the resonator containing the stack. The combination of resonator and cavity makes the device Helmholtz-like, with special characteristics of the resonant frequencies and quality factor, Q. Analysis of its acoustic behavior based on a model of a closed bottle presents features that are useful for the development of such prime movers for energy conversion from heat to sound. In particular, the arrangement produces in the cavity a high sound level, which is determined by the Q of the system. Comparison with a half-wave resonator type of prime mover, closed at both ends, shows the advantages of the Helmholtz-like device.

  7. Acoustic superlens using Helmholtz-resonator-based metamaterials

    NASA Astrophysics Data System (ADS)

    Yang, Xishan; Yin, Jing; Yu, Gaokun; Peng, Linhui; Wang, Ning

    2015-11-01

    Acoustic superlens provides a way to overcome the diffraction limit with respect to the wavelength of the bulk wave in air. However, the operating frequency range of subwavelength imaging is quite narrow. Here, an acoustic superlens is designed using Helmholtz-resonator-based metamaterials to broaden the bandwidth of super-resolution. An experiment is carried out to verify subwavelength imaging of double slits, the imaging of which can be well resolved in the frequency range from 570 to 650 Hz. Different from previous works based on the Fabry-Pérot resonance, the corresponding mechanism of subwavelength imaging is the Fano resonance, and the strong coupling between the neighbouring Helmholtz resonators separated at the subwavelength interval leads to the enhanced sound transmission over a relatively wide frequency range.

  8. Voluntarism in early psychology: the case of Hermann von Helmholtz.

    PubMed

    De Kock, Liesbet

    2014-05-01

    The failure to recognize the programmatic similarity between (post-)Kantian German philosophy and early psychology has impoverished psychology's historical self-understanding to a great extent. This article aims to contribute to recent efforts to overcome the gaps in the historiography of contemporary psychology, which are the result of an empiricist bias. To this end, we present an analysis of the way in which Hermann von Helmholtz's theory of perception resonates with Johann Gottlieb Fichte's Ego-doctrine. It will be argued that this indebtedness is particularly clear when focusing on the foundation of the differential awareness of subject and object in perception. In doing so, the widespread reception of Helmholtz's work as proto-positivist or strictly empiricist is challenged, in favor of the claim that important elements of his theorizing can only be understood properly against the background of Fichte's Ego-doctrine. PsycINFO Database Record (c) 2014 APA, all rights reserved.

  9. 1. EXTERIOR OF CENTRAL HEATING STATION, BUILDING 102, LOOKING NORTH. ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. EXTERIOR OF CENTRAL HEATING STATION, BUILDING 102, LOOKING NORTH. - Mill Valley Air Force Station, Central Heating Station, East Ridgecrest Boulevard, Mount Tamalpais, Mill Valley, Marin County, CA

  10. 1. GENERAL EXTERIOR VIEW LOOKING SOUTHEAST AT DOWNSTREAM FACE OF ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. GENERAL EXTERIOR VIEW LOOKING SOUTHEAST AT DOWNSTREAM FACE OF DAM/SPILLWAY. VIEW TAKEN FROM WASHINGTON SHORELINE. - Bonneville Project, Bonneville Dam, Columbia River, Bonneville, Multnomah County, OR

  11. 11. Exterior detail view of northeast corner, showing stucco finish ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    11. Exterior detail view of northeast corner, showing stucco finish and woodwork details - American Railway Express Company Freight Building, 1060 Northeast Division Street, Bend, Deschutes County, OR

  12. 1. EXTERIOR, SIDE OF PICKLE BARREL RESTAURANT AND ADJOINING STORE ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. EXTERIOR, SIDE OF PICKLE BARREL RESTAURANT AND ADJOINING STORE - Silverton Historic District, East Thirteenth & Green Streets (Commercial Building), East Thirteenh & Green Streets, Silverton, San Juan County, CO

  13. View of exterior circumferential path at northeast side of building ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    View of exterior circumferential path at northeast side of building beneath trellis, looking southeast - National Zoological Park, Bird House, 3001 Connecticut Avenue NW, Washington, District of Columbia, DC

  14. EXTERIOR ELEVATION AND OBLIQUE PERSPECTIVE, LOOKING NORTH, WITH DRIVE WHEELS ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR ELEVATION AND OBLIQUE PERSPECTIVE, LOOKING NORTH, WITH DRIVE WHEELS IN FOREGROUND. - Norfolk & Southern Steam Locomotive No. 1218, Norris Yards, East of Ruffner Road, Irondale, Jefferson County, AL

  15. 1. EXTERIOR OF BUILDING 402, CIVIL ENGINEERING STORAGE, LOOKING SOUTH. ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. EXTERIOR OF BUILDING 402, CIVIL ENGINEERING STORAGE, LOOKING SOUTH. - Mill Valley Air Force Station, Civil Engineering Storage, East Ridgecrest Boulevard, Mount Tamalpais, Mill Valley, Marin County, CA

  16. Midplate seismicity exterior to former rift-basins

    USGS Publications Warehouse

    Dewey, J.W.

    1988-01-01

    Midplate seismicity associated with some former rift-zones is distributed diffusely near, but exterior to, the rift basins. This "basin-exterior' seismicity cannot be attributed to reactivation of major basin-border faults on which uppercrustal extension was concentrated at the time of rifting, because the border faults dip beneath the basins. The seismicity may nonetheless represent reactivation of minor faults that were active at the time of rifting but that were located outside of the principal zones of upper-crustal extension; the occurrence of basin-exterior seismicity in some present-day rift-zones supports the existence of such minor basin-exterior faults. Other hypotheses for seismicity exterior to former rift-basins are that the seismicity reflects lobes of high stress due to lithospheric-bending that is centered on the axis of the rift, that the seismicity is localized on the exteriors of rift-basins by basin-interiors that are less deformable in the current epoch than the basin exteriors, and that seismicity is localized on the basin-exteriors by the concentration of tectonic stress in the highly elastic basin-exterior upper-crust. -from Author

  17. Radiative feedback in Helmholtz resonators with more than one opening.

    PubMed

    Dosch, Hans Günter

    2016-11-01

    The resonance frequency of a Helmholtz resonator with several openings is derived, taking into account the radiation feedback between the different holes. This is done under the assumption that the distance between the openings is large as compared to their linear dimensions. The effect of a finite wall thickness of the resonator is also discussed. The radiation feedback can lead to a shift of the resonance position by more than 10%.

  18. Extended variational theory of complex rays in heterogeneous Helmholtz problem

    NASA Astrophysics Data System (ADS)

    Li, Hao; Ladeveze, Pierre; Riou, Hervé

    2017-02-01

    In the past years, a numerical technique method called Variational Theory of Complex Rays (VTCR) has been developed for vibration problems in medium frequency. It is a Trefftz Discontinuous Galerkin method which uses plane wave functions as shape functions. However this method is only well developed in homogeneous case. In this paper, VTCR is extended to the heterogeneous Helmholtz problem by creating a new base of shape functions. Numerical examples give a scope of the performances of such an extension of VTCR.

  19. Kelvin-Helmholtz wave generation beneath hovercraft skirts

    NASA Astrophysics Data System (ADS)

    Sullivan, P. A.; Walsh, C.; Hinchey, M. J.

    1993-05-01

    When a hovercraft is hovering over water, the air flow beneath its skirts can interact with the water surface and generate waves. These, in turn, can cause the hovercraft to undergo violent self-excited heave motions. This note shows that the wave generation is due to the classical Kelvin-Helmholtz mechanism where, beyond a certain air flow rate, small waves at the air water interface extract energy from the air stream and grow.

  20. Wavelet Helmholtz decomposition for weak lensing mass map reconstruction

    NASA Astrophysics Data System (ADS)

    Deriaz, E.; Starck, J.-L.; Pires, S.

    2012-04-01

    To derive the convergence field from the gravitational shear γ of the background galaxy images, the classical methods require a convolution of the shear to be performed over the entire sky, usually expressed by the fast Fourier transform (FFT). However, it is not optimal for an imperfect geometry survey. Furthermore, FFT implicitly uses periodic conditions that introduce errors into the reconstruction. A method has been proposed that relies on computation of an intermediate field u that combines the derivatives of γ and on convolution with a Green kernel. In this paper, we study the wavelet Helmholtz decomposition as a new approach to reconstructing the dark matter mass map. We show that a link exists between the Helmholtz decomposition and the electric and magnetic component separation. We introduce a new wavelet construction that has a property that gives us more flexibility in handling the border problem, and we propose a new method of reconstructing the dark matter mass map in the wavelet space. A set of experiments based on noise-free images illustrates that this Wavelet Helmholtz decomposition reconstructs the borders better than all other existing methods.

  1. Calculation of the Kirchhoff coefficients for the Helmholtz resonator

    NASA Astrophysics Data System (ADS)

    Brüning, J.; Martin, G.; Pavlov, B.

    2009-06-01

    A Helmholtz resonator is a shell Ωshell separating a compact cavity Ωint from a noncompact outer domain Ωout. A small opening Ω δ in the shell connects the cavity with the outer domain, causing the transformation of real eigenfrequencies of the Neumann Laplacian in the cavity into the complex scattering frequencies of the full spectral problem for the Neumann Laplacian on Ω = ℝ3Ωshell. The Kirchhoff model of 1882, see [21], gives a convenient ansatz Ψ _{out} (x,ν ,λ ) = Ψ _{out}^N (x,ν ,λ ) + A_{out} G_{out}^N (x,a,λ ), x in Ω _{out} , for the approximate calculation of the outer component of the scattered wave of the full spectral problem on Ω in terms of the scattered wave Ψ{out/ N } ( x, ν, λ) and the Green function G {out/ N }( x, a, λ) of the Neumann Laplacian on the outer domain, with a pole at the pointwise opening Ω δ ≈ a. In this paper, we suggest an explicit formula for the Kirchhoff coefficient A out, based on the construction of a fitted solvable model for the Helmholtz resonator with a narrow short channel Ω δ connecting the cavity with the outer domain. The correcting term of the scattering matrix of the model serves as a rational approximation, on a certain spectral interval, for the correcting term of the full scattering matrix of the Helmholtz resonator.

  2. Optimization of numerical orbitals using the Helmholtz kernel.

    PubMed

    Solala, Eelis; Losilla, Sergio A; Sundholm, Dage; Xu, Wenhua; Parkkinen, Pauli

    2017-02-28

    We present an integration scheme for optimizing the orbitals in numerical electronic structure calculations on general molecules. The orbital optimization is performed by integrating the Helmholtz kernel in the double bubble and cube basis, where bubbles represent the steep part of the functions in the vicinity of the nuclei, whereas the remaining cube part is expanded on an equidistant three-dimensional grid. The bubbles' part is treated by using one-center expansions of the Helmholtz kernel in spherical harmonics multiplied with modified spherical Bessel functions of the first and second kinds. The angular part of the bubble functions can be integrated analytically, whereas the radial part is integrated numerically. The cube part is integrated using a similar method as we previously implemented for numerically integrating two-electron potentials. The behavior of the integrand of the auxiliary dimension introduced by the integral transformation of the Helmholtz kernel has also been investigated. The correctness of the implementation has been checked by performing Hartree-Fock self-consistent-field calculations on H2, H2O, and CO. The obtained energies are compared with reference values in the literature showing that an accuracy of 10(-4) to 10(-7) Eh can be obtained with our approach.

  3. Optimization of numerical orbitals using the Helmholtz kernel

    NASA Astrophysics Data System (ADS)

    Solala, Eelis; Losilla, Sergio A.; Sundholm, Dage; Xu, Wenhua; Parkkinen, Pauli

    2017-02-01

    We present an integration scheme for optimizing the orbitals in numerical electronic structure calculations on general molecules. The orbital optimization is performed by integrating the Helmholtz kernel in the double bubble and cube basis, where bubbles represent the steep part of the functions in the vicinity of the nuclei, whereas the remaining cube part is expanded on an equidistant three-dimensional grid. The bubbles' part is treated by using one-center expansions of the Helmholtz kernel in spherical harmonics multiplied with modified spherical Bessel functions of the first and second kinds. The angular part of the bubble functions can be integrated analytically, whereas the radial part is integrated numerically. The cube part is integrated using a similar method as we previously implemented for numerically integrating two-electron potentials. The behavior of the integrand of the auxiliary dimension introduced by the integral transformation of the Helmholtz kernel has also been investigated. The correctness of the implementation has been checked by performing Hartree-Fock self-consistent-field calculations on H2, H2O, and CO. The obtained energies are compared with reference values in the literature showing that an accuracy of 10-4 to 10-7 Eh can be obtained with our approach.

  4. 10 CFR 434.516 - Building exterior envelope.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 10 Energy 3 2014-01-01 2014-01-01 false Building exterior envelope. 434.516 Section 434.516 Energy DEPARTMENT OF ENERGY ENERGY CONSERVATION ENERGY CODE FOR NEW FEDERAL COMMERCIAL AND MULTI-FAMILY HIGH RISE RESIDENTIAL BUILDINGS Building Energy Cost Compliance Alternative § 434.516 Building exterior envelope. 516.1...

  5. 70. Detail view, exterior, south bay of east facade. This ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    70. Detail view, exterior, south bay of east facade. This view was taken following the cleaning and repointing of the exterior stonework during the fall 2001 (Similar to HALS PA-1-A-69). - John Bartram House & Garden, House, 54th Street & Lindbergh Boulevard, Philadelphia, Philadelphia County, PA

  6. 18. DETAIL OF EXTERIOR WALL CONSTRUCTION, VIEW TOWARD EAST, THIRD ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    18. DETAIL OF EXTERIOR WALL CONSTRUCTION, VIEW TOWARD EAST, THIRD BAY Showing furring strips, kraft faced cellulose fiber insulation, and asphalt felt applied to interior of exterior wall studs. - U.S. Military Academy, Ice House, Mills Road at Howze Place, West Point, Orange County, NY

  7. 17. DETAIL OF INTERIOR AND EXTERIOR WALL CONSTRUCTION, VIEW TOWARD ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    17. DETAIL OF INTERIOR AND EXTERIOR WALL CONSTRUCTION, VIEW TOWARD NORTHEAST CORNER, THIRD BAY Showing insulated exterior wall at right; asphalt felt on interior separation wall at left; sill beam, stud, and concrete foundation detailing of interior wall. - U.S. Military Academy, Ice House, Mills Road at Howze Place, West Point, Orange County, NY

  8. 5. EXTERIOR OF WEST (REAR) SIDE OF BUILDING 103 SHOWING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    5. EXTERIOR OF WEST (REAR) SIDE OF BUILDING 103 SHOWING TALL RUSTIC STYLE CHIMNEY WITH GABLE FRAME, AND CONCRETE STEPS TO SIDE ENTRY DOOR AT PHOTO RIGHT. CHANGE IN EXTERIOR WALL DELINEATING 1946 BEDROOM ADDITION AND REMODELED WINDOW TO BATHROOM ARE VISIBLE AT PHOTO LEFT. VIEW TO NORTHEAST. - Rush Creek Hydroelectric System, Worker Cottage, Rush Creek, June Lake, Mono County, CA

  9. 8. Interior view of unoccupied office space; showing exterior windows, ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    8. Interior view of unoccupied office space; showing exterior windows, exterior door at far left, and opened doorway to corridor; north end of east wing on top floor; view to southeast. - Ellsworth Air Force Base, Group Administration & Secure Storage Building, 2372 Westover Avenue, Blackhawk, Meade County, SD

  10. Exterior differentiation in the Regge calculus

    SciTech Connect

    Brewin, L.

    1986-01-01

    Regge manifolds are piecewise continuous manifolds constructed from a finite number of basic building blocks. On such manifolds piecewise continuous forms can be defined in a way similar to differential forms on a differentiable manifold. Regge manifolds are used extensively in the construction of space-times in numerical general relativity. In this paper a definition of exterior differentiation suitable for use on piecewise continuous forms on a Regge manifold is presented. It is shown that this definition leads to a version of Stokes' theorem and also to the usual result that d/sup 2/ = 0. This is preceded by a discussion of certain geometrical properties of the Regge manifolds. It is shown that the version of Stokes' theorem presented here coincides with the usual definition when the Regge manifold is refined, by increasing the number of cells while keeping the total volume constant, to a smooth manifold.

  11. Magnetic field uniformity of the practical tri-axial Helmholtz coils systems.

    PubMed

    Beiranvand, R

    2014-05-01

    In this paper, effects of the assembly misalignments and the manufacturing mismatches on the magnetic field uniformity of a practical tri-axial Helmholtz coils system have been modeled mathematically. These undesired effects regularly occur in any practical tri-axial Helmholtz coils system. To confirm the mathematical calculations, a tri-axial Helmholtz coils system has been constructed and the uniformity of its magnetic field has been measured under different conditions. The experimental results are in good agreement with the mathematical analyses.

  12. A comparison of high-order polynomial and wave-based methods for Helmholtz problems

    NASA Astrophysics Data System (ADS)

    Lieu, Alice; Gabard, Gwénaël; Bériot, Hadrien

    2016-09-01

    The application of computational modelling to wave propagation problems is hindered by the dispersion error introduced by the discretisation. Two common strategies to address this issue are to use high-order polynomial shape functions (e.g. hp-FEM), or to use physics-based, or Trefftz, methods where the shape functions are local solutions of the problem (typically plane waves). Both strategies have been actively developed over the past decades and both have demonstrated their benefits compared to conventional finite-element methods, but they have yet to be compared. In this paper a high-order polynomial method (p-FEM with Lobatto polynomials) and the wave-based discontinuous Galerkin method are compared for two-dimensional Helmholtz problems. A number of different benchmark problems are used to perform a detailed and systematic assessment of the relative merits of these two methods in terms of interpolation properties, performance and conditioning. It is generally assumed that a wave-based method naturally provides better accuracy compared to polynomial methods since the plane waves or Bessel functions used in these methods are exact solutions of the Helmholtz equation. Results indicate that this expectation does not necessarily translate into a clear benefit, and that the differences in performance, accuracy and conditioning are more nuanced than generally assumed. The high-order polynomial method can in fact deliver comparable, and in some cases superior, performance compared to the wave-based DGM. In addition to benchmarking the intrinsic computational performance of these methods, a number of practical issues associated with realistic applications are also discussed.

  13. Helmholtz and Zoellner: nineteenth-century empiricism, spiritism, and the theory of space perception.

    PubMed

    Stromberg, W H

    1989-10-01

    J. K. F. Zoellner began writing on "experimental proofs" of a fourth spatial dimension, and of the existence of spirits, in 1878. His arguments caused strong controversy, with rebuttal essays by Wilhelm Wundt and others. The author argues that Zoellner's case that these matters are experimental questions rested on arguments which Hermann von Helmholtz, inveighing against rationalist views of space and space perception, had recently published. Zoellner's use of Helmholtz's arguments to advance and defend his spiritist views occasioned strong criticism of Helmholtz, affected careers and reputations of scholars in Berlin and Leipzig, and caused enduring controversy over the credibility of Helmholtz's empiricist theory of space perception.

  14. Testing of a Helmholtz Microcoil in a Diamond Anvil Cell NMR

    NASA Astrophysics Data System (ADS)

    Lin, Ching; Weir, Sam; Evans, William; Chantel, A.; Vohra, Y.; Samudrala, G.; Crocker, J.; Shockley, A.; Curro, Nicholas

    2012-02-01

    A new designed, multi-turn tungsten Helmholtz micro-coil has been constructed and tested on the solid-state bulk NMR experiment. A Helmholtz micro-coil with diameter 950 μm is embedded on diamond culet and produces a nearly uniform AC magnetic field inside a sample space. A Fluorine polycrystal will be used to test our Helmholtz micro-coil, and the measured NMR data will be compared with the ones produced by other type of diamond anvil cell coils. The Helmholtz micro-coil will be used for high pressure NMR and future investigation of magnetic properties of heavy fermion superconductors.

  15. Black and gray Helmholtz-Kerr soliton refraction

    SciTech Connect

    Sanchez-Curto, Julio; Chamorro-Posada, Pedro; McDonald, Graham S.

    2011-01-15

    Refraction of black and gray solitons at boundaries separating different defocusing Kerr media is analyzed within a Helmholtz framework. A universal nonlinear Snell's law is derived that describes gray soliton refraction, in addition to capturing the behavior of bright and black Kerr solitons at interfaces. Key regimes, defined by beam and interface characteristics, are identified, and predictions are verified by full numerical simulations. The existence of a unique total nonrefraction angle for gray solitons is reported; both internal and external refraction at a single interface is shown possible (dependent only on incidence angle). This, in turn, leads to the proposal of positive or negative lensing operations on soliton arrays at planar boundaries.

  16. Noise control zone for a periodic ducted Helmholtz resonator system.

    PubMed

    Cai, Chenzhi; Mak, Cheuk Ming

    2016-12-01

    This paper presents a theoretical study of the dispersion characteristics of sound wave propagation in a periodic ducted Helmholtz resonator (HR) system. The predicted result fits well with a numerical simulation using a finite element method. This study indicates that for the same system, no matter how many HRs are connected or what the periodic distance is, the area under average transmission loss T L¯ curves is always the same. The broader the noise attenuation band, the lower the peak attenuation amplitude. A noise control zone compromising the attenuation bandwidth or peak amplitude is proposed for noise control optimization.

  17. Martian cave air-movement via Helmholtz resonance

    USGS Publications Warehouse

    Williams, Kaj; Titus, Timothy N.; Okubo, Chris; Cushing, Glen

    2017-01-01

    Infrasonic resonance has previously been measured in terrestrial caves by other researchers, where Helmholtz resonance has been suggested as the plausible mechanism resulting in periodic wind reversals within cave entrances. We extend this reasoning to possible Martian caves, where we examine the characteristics of four atypical pit craters (APCs) on Tharsis, suggested as candidate cave entrance locations. The results show that, for several possible cave air movement periods, we are able to infer the approximate cave volumes. The utility of inferring cave volumes for planetary cave exploration is discussed.

  18. The Helmholtz-Kirchhoff integral relation as a framework for developing algorithms for sound propagation through inhomogeneous moving media

    NASA Technical Reports Server (NTRS)

    Pierce, Allan D.

    1989-01-01

    Transient sound propagation in an inhomogeneous moving medium is considered. For circumstances in which the medium is slowly varying over distances of a wavelength but possibly varying substantially over the propagation distance, a derivation is given of a new wave equation, which implicitly allows for diffraction and scattering and which also is consistent with earlier geometrical acoustics formulations. This wave equation is used as a starting point to derive a version of the Helmholtz-Kirchhoff integral relation that applies to inhomogeneous moving medium. It is suggested that a good approximation to the Green's function that appears in this relation is that derived from geometrical acoustics, the approximation becoming progressively better the shorter the distance between surfaces in the computation. It should also be at least as good as conventional ray acoustics, but can account for diffraction effects, such as at caustics.

  19. Nonlinear dynamics of the interface between fluids at the suppression of Kelvin-Helmholtz instability by a tangential electric field

    NASA Astrophysics Data System (ADS)

    Zubarev, N. M.; Kochurin, E. A.

    2016-08-01

    The nonlinear dynamics of the interface between ideal dielectric fluids in the presence of tangential discontinuity of the velocity at the interface and the stabilizing action of the horizontal electric field is examined. It is shown that the regime of motion of the interface where liquids move along the field lines occurs in the state of neutral equilibrium where electrostatic forces suppress Kelvin-Helmholtz instability. The equations of motion of the interface describing this regime can be reduced to an arbitrary number of ordinary differential equations describing the propagation and interaction of structurally stable solitary waves, viz. rational solitons. It is shown that weakly interacting solitary waves recover their shape and velocity after collision, whereas strongly interacting solitary waves can form a wave packet (breather).

  20. Acoustic impedance characterization via numerical resolution of the inverse Helmholtz problem

    NASA Astrophysics Data System (ADS)

    Scalo, Carlo; Patel, Danish; Gupta, Prateek

    2016-11-01

    Impedance boundary conditions (IBCs) regulate the relative phasing and amplitudes of pressure and velocity fluctuations and, therefore, the acoustic energy flux. We present a numerical method to determine the acoustic impedance at the surface of an arbitrarily shaped cavity as seen by a generically oriented incident external harmonic planar wave. The proposed method (conceptually) inverts the usual eigenvalue-solving procedure underlying Helmholtz solvers: the impedance at one or multiple (but not all) boundaries is an output of the calculation and is obtained via implicit reconstruction the linear acoustic waveform at the frequency of the incident wave. The linearized governing equations are discretized via a mixed finite-difference/finite-volume approach and are closed with a generalized equation of state. Results are validated against quasi one-dimensional cases derived via direct application of Rott's linear thermoacoustic theory and by comparison against fully compressible Navier-Stokes simulations. This work is motivated by the need to develop a comprehensive suite of predictive tools capable of performing high-fidelity simulations of compressible boundary layers over assigned IBCs, accurately representing the acoustic response of arbitrarily shaped porous cavities.

  1. Autonomous navigation for structured exterior environments

    SciTech Connect

    Pletta, J B

    1993-12-01

    The Telemanaged Mobile Security Station (TMSS) was developed at Sandia National Laboratories to investigate the role of mobile robotics in exterior perimeter security systems. A major feature of the system is its capability to perform autonomous patrols of the security site`s network of roads. Perimeter security sites are well known, structured environments; the locations of the roads, buildings, and fences are relatively static. A security robot has the advantage of being able to learn its new environment prior to autonomous travel. The TMSS robot combines information from a microwave beacon system and on-board dead reckoning sensors to determine its location within the site. The operator is required to teleoperate the robot in a teach mode over all desired paths before autonomous operations can commence. During this teach phase, TMSS stores points from its position location system at two meter intervals. This map data base is used for planning paths and for reference during path following. Details of the position location and path following systems will be described along with system performance and recommendations for future enhancements.

  2. The Common Data Acquisition Platform in the Helmholtz Association

    NASA Astrophysics Data System (ADS)

    Kaever, P.; Balzer, M.; Kopmann, A.; Zimmer, M.; Rongen, H.

    2017-04-01

    Various centres of the German Helmholtz Association (HGF) started in 2012 to develop a modular data acquisition (DAQ) platform, covering the entire range from detector readout to data transfer into parallel computing environments. This platform integrates generic hardware components like the multi-purpose HGF-Advanced Mezzanine Card or a smart scientific camera framework, adding user value with Linux drivers and board support packages. Technically the scope comprises the DAQ-chain from FPGA-modules to computing servers, notably frontend-electronics-interfaces, microcontrollers and GPUs with their software plus high-performance data transmission links. The core idea is a generic and component-based approach, enabling the implementation of specific experiment requirements with low effort. This so called DTS-platform will support standards like MTCA.4 in hard- and software to ensure compatibility with commercial components. Its capability to deploy on other crate standards or FPGA-boards with PCI express or Ethernet interfaces remains an essential feature. Competences of the participating centres are coordinated in order to provide a solid technological basis for both research topics in the Helmholtz Programme ``Matter and Technology'': ``Detector Technology and Systems'' and ``Accelerator Research and Development''. The DTS-platform aims at reducing costs and development time and will ensure access to latest technologies for the collaboration. Due to its flexible approach, it has the potential to be applied in other scientific programs.

  3. Helmholtz and Goethe -- controversies at the birth of modern neuroscience.

    PubMed

    Kesselring, Jürg

    2013-01-01

    Hermann von Helmholtz (1821-1894), a great German scientist and philosopher, made his mark during the exciting twilight period from the Enlightenment and Romanticism to the beginnings of modern neuroscience and offered new perspectives through his work. His early inclination was for physics, which he found more attractive than purely geometric and algebraic studies, but his father was not able to make it possible for him to study physics, and so he studied medicine in order to earn a living. His lecture before the Physical Society in Berlin on July 23, 1847, 'about the conservation of the force' marked an epochal turn, even though his intention had been to deliver 'merely, some critical investigations and arrangement of facts in favor of the physiologists' as well as good arguments for the refusal of the theory of 'vitality'. Even though these new concepts were at first dismissed as fantastic speculation by some of the authorities in physics and philosophy of the day, they were enthusiastically welcomed by younger students of philosophy and the older men soon had to allow themselves to be persuaded that the effectiveness of vitality, though great and beautiful, is actually always dependent on some source of energy. Helmholtz critically assessed Goethe as a physical scientist but he did not dispute his great importance as a poet.

  4. A multiple degree of freedom electromechanical Helmholtz resonator.

    PubMed

    Liu, Fei; Horowitz, Stephen; Nishida, Toshikazu; Cattafesta, Louis; Sheplak, Mark

    2007-07-01

    The development of a tunable, multiple degree of freedom (MDOF) electromechanical Helmholtz resonator (EMHR) is presented. An EMHR consists of an orifice, backing cavity, and a compliant piezoelectric composite diaphragm. Electromechanical tuning of the acoustic impedance is achieved via passive electrical networks shunted across the piezoceramic. For resistive and capacitive loads, the EMHR is a 2DOF system possessing one acoustic and one mechanical DOF. When inductive ladder networks are employed, multiple electrical DOF are added. The dynamics of the multi-energy domain system are modeled using lumped elements and are represented in an equivalent electrical circuit, which is used to analyze the tunable acoustic input impedance of the EMHR. The two-microphone method is used to measure the acoustic impedance of two EMHR designs with a variety of resistive, capacitive, and inductive shunts. For the first design, the data demonstrate that the tuning range of the second resonant frequency for an EMHR with non-inductive shunts is limited by short- and open-circuit conditions, while an inductive shunt results in a 3DOF system possessing an enhanced tuning range. The second design achieves stronger coupling between the Helmholtz resonator and the piezoelectric backplate, and both resonant frequencies can be tuned with different non-inductive loads.

  5. Another Look at Helmholtz's Model for the Gravitational Contraction of the Sun

    ERIC Educational Resources Information Center

    Tort, A. C.; Nogarol, F.

    2011-01-01

    We take another look at the Helmholtz model for the gravitational contraction of the Sun. We show that there are two other pedagogically useful ways of rederiving Helmholtz's main results that make use of Gauss's law, the concept of gravitational field energy and the work-kinetic energy theorem. An account of the energy balance involved in the…

  6. Another Look at Helmholtz's Model for the Gravitational Contraction of the Sun

    ERIC Educational Resources Information Center

    Tort, A. C.; Nogarol, F.

    2011-01-01

    We take another look at the Helmholtz model for the gravitational contraction of the Sun. We show that there are two other pedagogically useful ways of rederiving Helmholtz's main results that make use of Gauss's law, the concept of gravitational field energy and the work-kinetic energy theorem. An account of the energy balance involved in the…

  7. Erratum: SDO-AIA Observation of Kelvin-helmholtz Instability in the Solar Corona

    NASA Technical Reports Server (NTRS)

    Ofman, Leon; Thompson, Barbara J.

    2012-01-01

    The first SDOAIA observation of the KelvinHelmholtz instability in the solar corona in the 2010 April 8 event was reported by Ofman Thompson (2010, 2011). Foullon et al. (2011), which was published prior to Ofman Thompson (2011), claimed the detection of the KelvinHelmholtz instability in a later event (2010 November 3), and should have been cited in Ofman Thompson (2011).

  8. Local energy decay for linear wave equations with variable coefficients

    NASA Astrophysics Data System (ADS)

    Ikehata, Ryo

    2005-06-01

    A uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients. We deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data, and its proof is quite simple. This generalizes a previous famous result due to Morawetz [The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961) 561-568]. In order to prove local energy decay, we mainly apply two types of ideas due to Ikehata-Matsuyama [L2-behaviour of solutions to the linear heat and wave equations in exterior domains, Sci. Math. Japon. 55 (2002) 33-42] and Todorova-Yordanov [Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489].

  9. Electron-helium scattering in the S-wave model using exterior complex scaling

    SciTech Connect

    Horner, Daniel A.; McCurdy, C. William; Rescigno, Thomas N.

    2004-06-16

    Electron-impact excitation and ionization of helium is studied in the S-wave model. The problem is treated in full dimensionality using a time-dependent formulation of the exterior complex scaling method that does not involve the solution of large linear systems of equations. We discuss the steps that must be taken to compute stable ionization amplitudes. We present total excitation, total ionization and single differential cross sections from the ground and n=2 excited states and compare our results with those obtained by others using a frozen-core model.

  10. Infinite-range exterior complex scaling as a perfect absorber in time-dependent problems

    SciTech Connect

    Scrinzi, Armin

    2010-05-15

    We introduce infinite range exterior complex scaling (irECS) which provides for complete absorption of outgoing flux in numerical solutions of the time-dependent Schroedinger equation with strong infrared fields. This is demonstrated by computing high harmonic spectra and wave-function overlaps with the exact solution for a one-dimensional model system and by three-dimensional calculations for the H atom and an Ne atom model. We lay out the key ingredients for correct implementation and identify criteria for efficient discretization.

  11. On Stability of Steady Circular Flows in a Two-Dimensional Exterior Disk

    NASA Astrophysics Data System (ADS)

    Maekawa, Yasunori

    2017-07-01

    We study the stability of some exact stationary solutions to the two-dimensional Navier-Stokes equations in an exterior domain to the unit disk. These stationary solutions are known as a simple model of the flow around a rotating obstacle, while their stability has been open due to the difficulty arising from their spatial decay in a scale-critical order. In this paper we affirmatively settle this problem for small solutions. That is, we will show that if these exact solutions are small enough then they are asymptotically stable with respect to small L 2 perturbations.

  12. Experimental study of liquid level gauge for liquid hydrogen using Helmholtz resonance technique

    NASA Astrophysics Data System (ADS)

    Nakano, Akihiro; Nishizu, Takahisa

    2016-07-01

    The Helmholtz resonance technique was applied to a liquid level gauge for liquid hydrogen to confirm the applicability of the technique in the cryogenic industrial field. A specially designed liquid level gauge that has a Helmholtz resonator with a small loudspeaker was installed in a glass cryostat. A swept frequency signal was supplied to the loudspeaker, and the acoustic response was detected by measuring the electrical impedance of the loudspeaker's voice coil. The penetration depth obtained from the Helmholtz resonance frequency was compared with the true value, which was read from a scale. In principle, the Helmholtz resonance technique is available for use with liquid hydrogen, however there are certain problems as regards practical applications. The applicability of the Helmholtz resonance technique to liquid hydrogen is discussed in this study.

  13. Exterior doorway detail south side of building (first floor) east ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Exterior doorway detail south side of building (first floor) east inset porch; interior staircase visible in background - Fitzsimons General Hospital, Open Air Tuberculosis Ward, West Pennington Avenue & North Hickey Street Southwest Corner, Aurora, Adams County, CO

  14. 32. Credit JTL. Exterior transformer bank; note lightning arrestors removed ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    32. Credit JTL. Exterior transformer bank; note lightning arrestors removed from pad and smaller arrestors installed on transformers and in area near air switches. - Dam No. 4 Hydroelectric Plant, Potomac River, Martinsburg, Berkeley County, WV

  15. View of exterior detail; bay on north side of front ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    View of exterior detail; bay on north side of front gable element. - Mare Island Naval Shipyard, Quarters P, Walnut Avenue, northwest corner of Walnut Avenue & Fifth Street, Vallejo, Solano County, CA

  16. EXTERIOR VIEW, LOOKING EAST, FRONT FACADE AND ENTRANCE TO COMPANY ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW, LOOKING EAST, FRONT FACADE AND ENTRANCE TO COMPANY SCHOOL FOR CHILDREN OF BLACK TCI-US STEEL RED ORE MINE WORKERS - Company School for Blacks, 413 Morgan Road, Bessemer, Jefferson County, AL

  17. 2. REAR VIEW SHOWING SPLIT SHAKE EXTERIOR AND HEXAHEDRAL PLAN ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    2. REAR VIEW SHOWING SPLIT SHAKE EXTERIOR AND HEXAHEDRAL PLAN AND DENSE LANDSCAPE - Camp Cleawox, Adirondack Sleeping Shelter, Oregon Dunes National Recreation Area, Siuslaw National Forest, Florence, Lane County, OR

  18. EXTERIOR VIEW, BLAST FURNACE NO. 3 (JANE FURNACE) CENTER, NO. ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW, BLAST FURNACE NO. 3 (JANE FURNACE) CENTER, NO. 3 CAST HOUSE TO THE LEFT, WEST ORE BRIDGE TO THE RIGHT. - Pittsburgh Steel Company, Monessen Works, Blast Furnace No. 3, Donner Avenue, Monessen, Westmoreland County, PA

  19. 1. EXTERIOR VIEW, FRONT (EAST) FACADE WITH FIVE POINTS FOUNTAIN ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. EXTERIOR VIEW, FRONT (EAST) FACADE WITH FIVE POINTS FOUNTAIN (CENTER), DULION APARTMENTS AND ELEVENTH AVENUE SOUTH (RIGHT). VIEW TAKEN JUST AFTER BIRMINGHAM BLIZZARD OF 1993. - Highlands United Methodist Church, 1045 Twentieth Street South, Birmingham, Jefferson County, AL

  20. 13. CO'S STATEROOM (CABIN'S QUARTERS), PORT EXTERIOR. NOTE PORTHOLE AND ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    13. CO'S STATEROOM (CABIN'S QUARTERS), PORT EXTERIOR. NOTE PORTHOLE AND WOODEN FRAME WINDOWS. - U.S. Coast Guard Cutter WHITE LUPINE, U.S. Coast Guard Station Rockland, east end of Tillson Avenue, Rockland, Knox County, ME

  1. 8. UPPER STORY (EXTERIOR), FROM SOUTHWEST CORNER OF BUILDING ROOFTOP, ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    8. UPPER STORY (EXTERIOR), FROM SOUTHWEST CORNER OF BUILDING ROOFTOP, LOOKING EAST-NORTHEAST. - Oakland Naval Supply Center, Coffee Roasting Plant, East of Fourth Street, between J & K, Oakland, Alameda County, CA

  2. 3. BUILDING 901, EXTERIOR DETAILING ON NORTH SIDE SHOWING CONCRETE ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    3. BUILDING 901, EXTERIOR DETAILING ON NORTH SIDE SHOWING CONCRETE FOUNDATION AND METAL TERMITE SHIELD. - Presidio of San Francisco, Warehouse, West End of Crissy Field, Livingston Street, San Francisco, San Francisco County, CA

  3. 7. Photocopy of painting (Source unknown, Date unknown) EXTERIOR SOUTH ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    7. Photocopy of painting (Source unknown, Date unknown) EXTERIOR SOUTH FRONT VIEW OF MISSION AND CONVENTO AFTER 1913 - Mission San Francisco Solano de Sonoma, First & Spain Streets, Sonoma, Sonoma County, CA

  4. 25. Photocopy of photograph (Source unknown, c. 19231925) EXTERIOR, CLOSEUP ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    25. Photocopy of photograph (Source unknown, c. 1923-1925) EXTERIOR, CLOSE-UP OF SOUTH FRONT OF MISSION AFTER RESTORATION, C. 1923-1925 - Mission San Francisco Solano de Sonoma, First & Spain Streets, Sonoma, Sonoma County, CA

  5. 1. EXTERIOR VIEW, LOOKING EAST, WITH ENTRANCES AND SIDE ELEVATIONS ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. EXTERIOR VIEW, LOOKING EAST, WITH ENTRANCES AND SIDE ELEVATIONS ALONG THE OLD BANKHEAD HIGHWAY (NOW 20TH STREET) AND ELLIOTT BOULEVARD - G. W. Posey Store, Twentieth Street & Elliot Boulevard, Jasper, Walker County, AL

  6. 2. EXTERIOR VIEW LOOKING SOUTHEAST AT ELECTRIC FURNACE BUILDING AND ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    2. EXTERIOR VIEW LOOKING SOUTHEAST AT ELECTRIC FURNACE BUILDING AND ELECTRIC FURNACE OFFICE & CHEMICAL LABORATORY BUILDING. INGOT MOLDS IN RIGHT FOREGROUND. - U.S. Steel Duquesne Works, Electric Furnace Steelmaking Plant, Along Monongahela River, Duquesne, Allegheny County, PA

  7. EXTERIOR NORTHEAST VIEW OF BUILDING 21B, AIRCRAFT FIRE PROTECTION ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR NORTHEAST VIEW OF BUILDING 21B, AIRCRAFT FIRE PROTECTION - Wright-Patterson Air Force Base, Area B, Building 21, Old Armament Building, Southwest corner of Seventh & E Streets, Dayton, Montgomery County, OH

  8. 1. EXTERIOR VIEW TO THE NORTHWEST OF ANCILLARY STRUCTURES ASSOCIATED ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. EXTERIOR VIEW TO THE NORTHWEST OF ANCILLARY STRUCTURES ASSOCIATED WITH AND SURROUNDING BUILDING 3210. - Nevada Test Site, Test Cell C Facility, Elevated Water Tower, Area 25, Jackass Flats, Road J, Mercury, Nye County, NV

  9. 8. Interior view, basement, west addition, looking northeast towards (exterior) ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    8. Interior view, basement, west addition, looking northeast towards (exterior) west wall of original section, bottom corbel of chimney base visible along wall - Latham House, 1200 North Quaker Lane, Alexandria, Independent City, VA

  10. Duplicate of the historic view showing the exterior of the ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Duplicate of the historic view showing the exterior of the library from approximately the same vantage point as MD-1109-Q-16 - National Park Seminary, Miller Library, 2801 Woodstock Avenue, Silver Spring, Montgomery County, MD

  11. Exterior, looking north at south elevation with closeup of building ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Exterior, looking north at south elevation with close-up of building entrance - Over-the-Horizon Backscatter Radar Network, Bangor Air National Guard Base Operations Building, At the end of Maine Road, Bangor, Penobscot County, ME

  12. Exterior, looking northnorthwest at south elevation with entrance to facility ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Exterior, looking north-northwest at south elevation with entrance to facility - Over-the-Horizon Backscatter Radar Network, Bangor Air National Guard Base Operations Building, At the end of Maine Road, Bangor, Penobscot County, ME

  13. 25. GENERAL EXTERIOR VIEW LOOKING WEST, SHOWING FISH LADDER DOWNSTREAM ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    25. GENERAL EXTERIOR VIEW LOOKING WEST, SHOWING FISH LADDER DOWNSTREAM FROM THE DAM/SPILLWAY ON THE WASHINGTON SHORE. - Bonneville Project, Bonneville Dam, Columbia River, Bonneville, Multnomah County, OR

  14. 22. DETAIL EXTERIOR VIEW LOOKING NORTHWEST, SHOWING FISH LADDER AT ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    22. DETAIL EXTERIOR VIEW LOOKING NORTHWEST, SHOWING FISH LADDER AT NORTH END OF DAM/SPILLWAY; VIEW SHOWS SECTION OF FISH LADDER NEAR WHERE IT ENTERS THE COLUMBIA RIVER. - Bonneville Project, Bonneville Dam, Columbia River, Bonneville, Multnomah County, OR

  15. 17. GENERAL EXTERIOR VIEW LOOKING NORTHEAST, SHOWING FISH LADDER ON ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    17. GENERAL EXTERIOR VIEW LOOKING NORTHEAST, SHOWING FISH LADDER ON BRADFORD ISLAND; VIEW IS TAKEN FROM ROOF OF POWERHOUSE #1; THE DAM/SPILLWAY IS IN RIGHT BACKGROUND. - Bonneville Project, Bonneville Dam, Columbia River, Bonneville, Multnomah County, OR

  16. 24. DETAIL EXTERIOR VIEW LOOKING EAST, SHOWING FISH LADDER AT ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    24. DETAIL EXTERIOR VIEW LOOKING EAST, SHOWING FISH LADDER AT NORTH END OF DAM/SPILLWAY; WATER FLOWING THROUGH FISH LADDER IS VISIBLE AT BOTTOM. - Bonneville Project, Bonneville Dam, Columbia River, Bonneville, Multnomah County, OR

  17. 12. DETAIL EXTERIOR VIEW LOOKING SOUTHWEST, SHOWING CONTROL TOWER AT ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    12. DETAIL EXTERIOR VIEW LOOKING SOUTHWEST, SHOWING CONTROL TOWER AT SOUTH END OF DAM/SPILLWAY; ENTRANCE TO BRADFORD ISLAND FISH LADDER IS VISIBLE IN FOREGROUND. - Bonneville Project, Bonneville Dam, Columbia River, Bonneville, Multnomah County, OR

  18. 18. GENERAL EXTERIOR VIEW LOOKING NORTHEAST, SHOWING FISH LADDER ON ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    18. GENERAL EXTERIOR VIEW LOOKING NORTHEAST, SHOWING FISH LADDER ON BRADFORD ISLAND; DAM/SPILLWAY IS VISIBLE IN CENTER BACKGROUND. - Bonneville Project, Bonneville Dam, Columbia River, Bonneville, Multnomah County, OR

  19. Detail exterior view looking northwest showing field gas cleaner in ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Detail exterior view looking northwest showing field gas cleaner in the center. - Burnsville Natural Gas Pumping Station, Saratoga Avenue between Little Kanawha River & C&O Railroad line, Burnsville, Braxton County, WV

  20. Detail exterior view looking southwest of gas cooling system. Engine ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Detail exterior view looking southwest of gas cooling system. Engine house is shown in right background. - Burnsville Natural Gas Pumping Station, Saratoga Avenue between Little Kanawha River & C&O Railroad line, Burnsville, Braxton County, WV

  1. Exterior view looking northwest with construction facilities of "new" pumping ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Exterior view looking northwest with construction facilities of "new" pumping station in foreground. Doug Hine is man in picture. - Burnsville Natural Gas Pumping Station, Saratoga Avenue between Little Kanawha River & C&O Railroad line, Burnsville, Braxton County, WV

  2. Detail exterior view looking north showing piping system adjacent to ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Detail exterior view looking north showing piping system adjacent to engine house. Gas cooling system is on far right. - Burnsville Natural Gas Pumping Station, Saratoga Avenue between Little Kanawha River & C&O Railroad line, Burnsville, Braxton County, WV

  3. Exterior view of boiler house looking southwest with steam exhaust ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Exterior view of boiler house looking southwest with steam exhaust vents in foreground. Engine house is on left. - Burnsville Natural Gas Pumping Station, Saratoga Avenue between Little Kanawha River & C&O Railroad line, Burnsville, Braxton County, WV

  4. Facility No. 175, exterior oblique view of northeast and northwest ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Facility No. 175, exterior oblique view of northeast and northwest sides, corner of Facility No. 176 is in background - U.S. Naval Base, Pearl Harbor, Landplane Hangar Type, Wasp Boulevard and Gambier Bay Street, Pearl City, Honolulu County, HI

  5. 6. EXTERIOR ELEVATION OF SOUTH END OF EAST FACADE OF ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    6. EXTERIOR ELEVATION OF SOUTH END OF EAST FACADE OF STEAM PLANT, BUILDING 740, LOOKING WEST. - Oakland Naval Supply Center, Steam Plant, Sixth Street south of East K Street, Oakland, Alameda County, CA

  6. 5. EXTERIOR ELEVATION OF NORTH END OF EAST FACADE OF ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    5. EXTERIOR ELEVATION OF NORTH END OF EAST FACADE OF STEAM PLANT, BUILDING 740, LOOKING WEST. - Oakland Naval Supply Center, Steam Plant, Sixth Street south of East K Street, Oakland, Alameda County, CA

  7. 4. DETAIL EXTERIOR VIEW LOOKING NORTHEAST, SHOWING PIERS AND MOVABLE ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    4. DETAIL EXTERIOR VIEW LOOKING NORTHEAST, SHOWING PIERS AND MOVABLE STONEY GATES ON DOWNSTREAM FACE OF DAM/SPILLWAY. - Bonneville Project, Bonneville Dam, Columbia River, Bonneville, Multnomah County, OR

  8. 2. GENERAL EXTERIOR VIEW LOOKING SOUTH, SHOWING DOWNSTREAM FACE OF ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    2. GENERAL EXTERIOR VIEW LOOKING SOUTH, SHOWING DOWNSTREAM FACE OF DAM/SPILLWAY; PARKING LOT/WORK AREA ON WASHINGTON SHORE IS VISIBLE IN FOREGROUND. - Bonneville Project, Bonneville Dam, Columbia River, Bonneville, Multnomah County, OR

  9. 16. GENERAL EXTERIOR VIEW LOOKING NORTHWEST, SHOWING TRANSMISSION TOWERS ON ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    16. GENERAL EXTERIOR VIEW LOOKING NORTHWEST, SHOWING TRANSMISSION TOWERS ON WEST END OF BRADFORD ISLAND; BRADFORD SLOUGH DOWNSTREAM FROM POWERHOUSE #1 IS IN FOREGROUND. - Bonneville Project, Bonneville Dam, Columbia River, Bonneville, Multnomah County, OR

  10. 6. GENERAL EXTERIOR VIEW LOOKING SOUTHWEST, SHOWING UPSTREAM FACE OF ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    6. GENERAL EXTERIOR VIEW LOOKING SOUTHWEST, SHOWING UPSTREAM FACE OF DAM/SPILLWAY; FOLIAGE IN FOREGROUND IS ON WASHINGTON SHORELINE. - Bonneville Project, Bonneville Dam, Columbia River, Bonneville, Multnomah County, OR

  11. 10. GENERAL EXTERIOR VIEW LOOKING SOUTH, SHOWING UPSTREAM FACE OF ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    10. GENERAL EXTERIOR VIEW LOOKING SOUTH, SHOWING UPSTREAM FACE OF DAM/SPILLWAY; ELECTRICALLY-OPERATED GATE MECHANISMS ARE ON RIGHT; GANTRY CRANES ARE VISIBLE IN CENTER/LEFT. - Bonneville Project, Bonneville Dam, Columbia River, Bonneville, Multnomah County, OR

  12. 8. GENERAL EXTERIOR VIEW LOOKING SOUTH, SHOWING UPSTREAM FACE OF ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    8. GENERAL EXTERIOR VIEW LOOKING SOUTH, SHOWING UPSTREAM FACE OF DAM/SPILLWAY; THE VIEW HIGHLIGHTS THE UPSTREAM APPEARANCE OF THE PIERS SUPPORTING THE MOVABLE STONEY GATES. - Bonneville Project, Bonneville Dam, Columbia River, Bonneville, Multnomah County, OR

  13. 13. DETAIL EXTERIOR VIEW LOOKING NORTHEAST, SHOWING CONTROL TOWER AT ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    13. DETAIL EXTERIOR VIEW LOOKING NORTHEAST, SHOWING CONTROL TOWER AT UPSTREAM FACE OF DAM/SPILLWAY ON BRADFORD ISLAND. - Bonneville Project, Bonneville Dam, Columbia River, Bonneville, Multnomah County, OR

  14. Low-cost exterior insulation process and structure

    DOEpatents

    Vohra, A.

    1999-03-02

    A low-cost exterior insulation process of stacking bags of insulating material against a wall and covering them with wire mesh and stucco provides a durable structure with good insulating value. 2 figs.

  15. 14. EXTERIOR VIEW OF GEAROPERATED WINDOWS ON SOUTH ELEVATION OF ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    14. EXTERIOR VIEW OF GEAR-OPERATED WINDOWS ON SOUTH ELEVATION OF STAIRS TAKEN FROM ROOF ABOVE SOUTH ENTRANCE - Kodiak Naval Operating Base, Gymnasium, U.S. Coast Guard Station, Kodiak, Kodiak Island Borough, AK

  16. EXTERIOR VIEW OF AIRLOCK FOR ALTITUDE CHAMBER R, FACING SOUTHEAST ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW OF AIRLOCK FOR ALTITUDE CHAMBER R, FACING SOUTHEAST - Cape Canaveral Air Force Station, Launch Complex 39, Altitude Chambers, First Street, between Avenue D and Avenue E, Cape Canaveral, Brevard County, FL

  17. EXTERIOR OF ALTITUDE CHAMBERS R (TO LEFT) AND L (TO ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR OF ALTITUDE CHAMBERS R (TO LEFT) AND L (TO RIGHT), FACING NORTHEAST - Cape Canaveral Air Force Station, Launch Complex 39, Altitude Chambers, First Street, between Avenue D and Avenue E, Cape Canaveral, Brevard County, FL

  18. EXTERIOR AND INTERIOR VIEW OF AIRLOCK FOR ALTITUDE CHAMBER R, ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR AND INTERIOR VIEW OF AIRLOCK FOR ALTITUDE CHAMBER R, FACING SOUTH - Cape Canaveral Air Force Station, Launch Complex 39, Altitude Chambers, First Street, between Avenue D and Avenue E, Cape Canaveral, Brevard County, FL

  19. EXTERIOR OF ALTITUDE CHAMBERS R (TO LEFT) AND L (TO ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR OF ALTITUDE CHAMBERS R (TO LEFT) AND L (TO RIGHT), FACING NORTHWEST - Cape Canaveral Air Force Station, Launch Complex 39, Altitude Chambers, First Street, between Avenue D and Avenue E, Cape Canaveral, Brevard County, FL

  20. 1. VIEW OF BUILDING 883 EXTERIOR, LOOKING SOUTHEAST. VENTILATION EQUIPMENT ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. VIEW OF BUILDING 883 EXTERIOR, LOOKING SOUTHEAST. VENTILATION EQUIPMENT IS VISIBLE. (11/27/56) - Rocky Flats Plant, Uranium Rolling & Forming Operations, Southeast section of plant, southeast quadrant of intersection of Central Avenue & Eighth Street, Golden, Jefferson County, CO

  1. 3. EXTERIOR NORTHEAST CORNER VIEW, FACING SOUTHWEST. BUILDING NO 42 ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    3. EXTERIOR NORTHEAST CORNER VIEW, FACING SOUTHWEST. BUILDING NO 42 GARAGE & TRANSPORTATION MAINTENANCE FACILITY - NASA Industrial Plant, Garage & Transportation Maintenance Facility, 12214 Lakewood Boulevard, Downey, Los Angeles County, CA

  2. 2. EXTERIOR SOUTHEAST CORNER VIEW, FACING NORTHWEST. BUILDING NO 42 ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    2. EXTERIOR SOUTHEAST CORNER VIEW, FACING NORTHWEST. BUILDING NO 42 GARAGE & TRANSPORTATION MAINTENANCE FACILITY - NASA Industrial Plant, Garage & Transportation Maintenance Facility, 12214 Lakewood Boulevard, Downey, Los Angeles County, CA

  3. 4. EXTERIOR NORTHWEST CORNER VIEW, FACING SOUTHEAST. BUILDING NO 42 ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    4. EXTERIOR NORTHWEST CORNER VIEW, FACING SOUTHEAST. BUILDING NO 42 GARAGE & TRANSPORTATION MAINTENANCE FACILITY - NASA Industrial Plant, Garage & Transportation Maintenance Facility, 12214 Lakewood Boulevard, Downey, Los Angeles County, CA

  4. 1. EXTERIOR SOUTHWEST CORNER VIEW, FACING NORTHEAST. BUILDING NO. 42 ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. EXTERIOR SOUTHWEST CORNER VIEW, FACING NORTHEAST. BUILDING NO. 42 GARAGE & TRANSPORTATION MAINTENANCE FACILITY - NASA Industrial Plant, Garage & Transportation Maintenance Facility, 12214 Lakewood Boulevard, Downey, Los Angeles County, CA

  5. 10. DETAIL EXTERIOR VIEW OF SWITCHING EQUIPMENT AND METAL FRAME ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    10. DETAIL EXTERIOR VIEW OF SWITCHING EQUIPMENT AND METAL FRAME SUPPORT STRUCTURE ON ROOF OF POWERHOUSE #1. - Bonneville Project, Powerhouse No.1, Spanning Bradford Slough, from Bradford Island, Bonneville, Multnomah County, OR

  6. Transverse electromagnetic horn antenna with resistively-loaded exterior surfaces

    DOEpatents

    Aurand, John F.

    1999-01-01

    An improved transverse electromagnetic (TEM) horn antenna comprises a resistive loading material on the exterior surfaces of the antenna plates. The resistive loading material attenuates or inhibits currents on the exterior surfaces of the TEM horn antenna. The exterior electromagnetic fields are of opposite polarity in comparison to the primary and desired interior electromagnetic field, thus inherently cause partial cancellation of the interior wave upon radiation or upon reception. Reducing the exterior fields increases the radiation efficiency of the antenna by reducing the cancellation of the primary interior field (supported by the interior surface currents). This increases the transmit gain and receive sensitivity of the TEM horn antenna, as well as improving the transient (time-domain) response.

  7. 52. DETAIL VIEW OF FRONT DOOR (EXTERIOR), FLUTED BUTTRESSES, AND ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    52. DETAIL VIEW OF FRONT DOOR (EXTERIOR), FLUTED BUTTRESSES, AND PARAPETED GABLE, NORTHWEST SIDE OF CAPTAIN'S GALLEY, LOOKING EAST - Huntington Beach Municipal Pier, Pacific Coast Highway at Main Street, Huntington Beach, Orange County, CA

  8. EXTERIOR VIEW WITH HEART OF DIXIE MUSEUM'S HISTORIC LOCOMOTIVE IN ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW WITH HEART OF DIXIE MUSEUM'S HISTORIC LOCOMOTIVE IN MUSEUM'S POWELL AVENUE YARD (BOTTOM) AND SOUTHERN RAILWAY BOXCAR ON ACTIVE TRACKAGE (ABOVE). - Heart of Dixie Railroad, Rolling Stock, 1800 Block Powell Avenue, Birmingham, Jefferson County, AL

  9. 12. Exterior detail view of roof structure at eave, showing ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    12. Exterior detail view of roof structure at eave, showing exposed rafter tails, skip sheathing and gutter - American Railway Express Company Freight Building, 1060 Northeast Division Street, Bend, Deschutes County, OR

  10. 4. EXTERIOR VIEW LOOKING EAST. WATER IN THE AQUEDUCT CAN ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    4. EXTERIOR VIEW LOOKING EAST. WATER IN THE AQUEDUCT CAN CAN BE DIVERTED AT THE WASTE WEIR TO BE DISCHARGED INTO THE CULVERT IN FOREGROUND. - Old Croton Aqueduct, Northern Waste Weir, Snowden Avenue & Van Wick Street, Ossining, Westchester County, NY

  11. 5. DETAIL EXTERIOR VIEW OF CUPOLA AND WEATHER VANE ON ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    5. DETAIL EXTERIOR VIEW OF CUPOLA AND WEATHER VANE ON TOP OF THE FISH HATCHERY BUILDING. - Bonneville Project, Fish Hatchery, On Columbia River bordered on South by Union Pacific, Bonneville, Multnomah County, OR

  12. EXTERIOR, A view looking northwest from far hill toward the ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR, A view looking northwest from far hill toward the Mounds complex and the HH Building - Department of Energy, Mound Facility, Hydrolysis House Building (HH Building), One Mound Road, Miamisburg, Montgomery County, OH

  13. EXTERIOR, A view looking northeast toward the south elevation and ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR, A view looking northeast toward the south elevation and stacks of HH Building - Department of Energy, Mound Facility, Hydrolysis House Building (HH Building), One Mound Road, Miamisburg, Montgomery County, OH

  14. EXTERIOR, A view looking southeast toward the north elevation of ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR, A view looking southeast toward the north elevation of the building including the dock and overhead piping and stacks - Department of Energy, Mound Facility, Hydrolysis House Building (HH Building), One Mound Road, Miamisburg, Montgomery County, OH

  15. EXTERIOR, A view looking west that captures the east elevation ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR, A view looking west that captures the east elevation of the building with parking lot to the right - Department of Energy, Mound Facility, Hydrolysis House Building (HH Building), One Mound Road, Miamisburg, Montgomery County, OH

  16. EXTERIOR, A close up view, looking southeast at the dock ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR, A close up view, looking southeast at the dock and overhead piping - Department of Energy, Mound Facility, Hydrolysis House Building (HH Building), One Mound Road, Miamisburg, Montgomery County, OH

  17. EXTERIOR, A view looking northeast at the south and west ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR, A view looking northeast at the south and west facades of the building and staircase - Department of Energy, Mound Facility, Hydrolysis House Building (HH Building), One Mound Road, Miamisburg, Montgomery County, OH

  18. 1. EXTERIOR VIEW SHOWING THE SOUTHWEST & SOUTHEAST SIDES OF ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. EXTERIOR VIEW SHOWING THE SOUTHWEST & SOUTHEAST SIDES OF THE AUDITORIUM, LOOKING NORTHEAST - Fort McCoy, Building No. T-1056, Southwest of intersection of South Tenth Avenue & South "X" Street, Block 10, Sparta, Monroe County, WI

  19. 37. EXTERIOR, DETAIL VIEW OF GUTTERS AND DRAINAGE PIPES ON ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    37. EXTERIOR, DETAIL VIEW OF GUTTERS AND DRAINAGE PIPES ON EAST ELEVATION FROM SOUTHEAST - Mark Twain House, 351 Farmington Avenue (corrected from original address of 531 Farmington Avenue), Hartford, Hartford County, CT

  20. Exterior overall oblique view of the northeast and southeast sides ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Exterior overall oblique view of the northeast and southeast sides - U.S. Naval Base, Pearl Harbor, Scrap Metal Packaging Facility, Seventh Street between Facility Nos. 6 & 247, Pearl City, Honolulu County, HI

  1. Exterior view of the southwest side, taken from Facility No. ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Exterior view of the southwest side, taken from Facility No. 247 with Facility No. 6 beyond - U.S. Naval Base, Pearl Harbor, Scrap Metal Packaging Facility, Seventh Street between Facility Nos. 6 & 247, Pearl City, Honolulu County, HI

  2. 5. EXTERIOR OF NORTH SIDE SHOWING ENCLOSED FRONT PORCH AREA, ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    5. EXTERIOR OF NORTH SIDE SHOWING ENCLOSED FRONT PORCH AREA, ALUMINUM SLIDING GLASS WINDOW GLAZING REPLACEMENTS, AND RAILING FOR STAIRS TO BASEMENT. VIEW TO SOUTHWEST. - Bishop Creek Hydroelectric System, Plant 4, Worker Cottage, Bishop Creek, Bishop, Inyo County, CA

  3. 5. VIEW OF EXTERIOR FACINGS, SOUTH ELEVATION, ILLUSTRATING RANDOM COURSING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    5. VIEW OF EXTERIOR FACINGS, SOUTH ELEVATION, ILLUSTRATING RANDOM COURSING THAT USES UNSQUARED, IRREGULAR BASALT STONE WITH SMALLER FRAGMENTS SNECKED INTO THE JOINTING, LOOKING NORTH - Rock Wall, North side of Battle Creek Canyon, Shingletown, Shasta County, CA

  4. EXTERIOR VIEW LOOKING NORTH TO SMOKESTACK, ALONG WITH POWER PLANT ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW LOOKING NORTH TO SMOKESTACK, ALONG WITH POWER PLANT (BUILDING 45) - National Home for Disabled Volunteer Soldiers, Northwestern Branch, Smoke Stack, 5000 West National Avenue, Milwaukee, Milwaukee County, WI

  5. WEST BACK EXTERIOR OF SMOKESTACK, ALONG WITH POWER PLANT (BUILDING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    WEST BACK EXTERIOR OF SMOKESTACK, ALONG WITH POWER PLANT (BUILDING 45) - National Home for Disabled Volunteer Soldiers, Northwestern Branch, Smoke Stack, 5000 West National Avenue, Milwaukee, Milwaukee County, WI

  6. SOUTH SIDE EXTERIOR OF SMOKESTACK, ALONG WITH POWER PLANT (BUILDING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    SOUTH SIDE EXTERIOR OF SMOKESTACK, ALONG WITH POWER PLANT (BUILDING 45) - National Home for Disabled Volunteer Soldiers, Northwestern Branch, Smoke Stack, 5000 West National Avenue, Milwaukee, Milwaukee County, WI

  7. 4. EXTERIOR VIEW TO THE NORTH OF THE WATER TOWER ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    4. EXTERIOR VIEW TO THE NORTH OF THE WATER TOWER AND MISCELLANEOUS EQUIPMENT ALONG THE EAST SIDE OF THE COMPOUND. - Nevada Test Site, Pluto Facility, Area 26, Wahmonie Flats, Cane Spring Road, Mercury, Nye County, NV

  8. 3. EXTERIOR VIEW TO THE NORTHEAST OF A RAILROAD CAR ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    3. EXTERIOR VIEW TO THE NORTHEAST OF A RAILROAD CAR ON THE TRACKS AND THE PARTS OF AN ENGINE STAND. - Nevada Test Site, Pluto Facility, Area 26, Wahmonie Flats, Cane Spring Road, Mercury, Nye County, NV

  9. View of exterior circumferential path at northwest side of building, ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    View of exterior circumferential path at northwest side of building, looking east toward building entrance - National Zoological Park, Bird House, 3001 Connecticut Avenue NW, Washington, District of Columbia, DC

  10. 2. VAL CONTROL STATION, VIEW OF INTERIOR SHOWING EXTERIOR DOOR, ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    2. VAL CONTROL STATION, VIEW OF INTERIOR SHOWING EXTERIOR DOOR, WINDOWS AND CONTROL PANELS, LOOKING SOUTHEAST. - Variable Angle Launcher Complex, Control Station, CA State Highway 39 at Morris Reservior, Azusa, Los Angeles County, CA

  11. 1. GENERAL EXTERIOR VIEW OF THE ELECTRIC FURNACE STEELMAKING PLANT ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. GENERAL EXTERIOR VIEW OF THE ELECTRIC FURNACE STEELMAKING PLANT LOOKING NORTHEAST. - U.S. Steel Duquesne Works, Electric Furnace Steelmaking Plant, Along Monongahela River, Duquesne, Allegheny County, PA

  12. 3. EXTERIOR OF SOUTH SIDE SHOWING DOOR TO ENCLOSED FRONT ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    3. EXTERIOR OF SOUTH SIDE SHOWING DOOR TO ENCLOSED FRONT PORCH ON PHOTO RIGHT AND DOOR TO KITCHEN AT PHOTO LEFT. VIEW TO NORTH. - Bishop Creek Hydroelectric System, Control Station, Worker Cottage, Bishop Creek, Bishop, Inyo County, CA

  13. 2. EXTERIOR OF ENGINE ROOM, CONTAINING MESTACORLISS CROSSCOMPOUND ENGINE, FOR ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    2. EXTERIOR OF ENGINE ROOM, CONTAINING MESTA-CORLISS CROSS-COMPOUND ENGINE, FOR 40" BLOOMING MILL - Republic Iron & Steel Company, Youngstown Works, Blooming Mill & Blooming Mill Engines, North of Poland Avenue, Youngstown, Mahoning County, OH

  14. 1. EXTERIOR OF ENGINE ROOM, CONTAINING UNITEDTOD TWINTANDEM ENGINE, FOR ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. EXTERIOR OF ENGINE ROOM, CONTAINING UNITED-TOD TWIN-TANDEM ENGINE, FOR 40" BLOOMING MILL - Republic Iron & Steel Company, Youngstown Works, Blooming Mill & Blooming Mill Engines, North of Poland Avenue, Youngstown, Mahoning County, OH

  15. 10. Historic exterior view of Building 100. August 22, 1957. ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    10. Historic exterior view of Building 100. August 22, 1957. On file at NASA Plumbrook Research Center, Sandusky, Ohio. NASA photo number C-45766. - Rocket Engine Testing Facility, GRC Building No. 100, NASA Glenn Research Center, Cleveland, Cuyahoga County, OH

  16. 9. TROJAN MILL, EXTERIOR FROM NORTHWEST, c. 191828. WINTER SNOW ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    9. TROJAN MILL, EXTERIOR FROM NORTHWEST, c. 1918-28. WINTER SNOW SHOWS LINE OF CRUDE ORE BIN STAIR. CREDIT JW. - Bald Mountain Gold Mill, Nevada Gulch at head of False Bottom Creek, Lead, Lawrence County, SD

  17. Exterior oblique view of south end of Building 7 from ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Exterior oblique view of south end of Building 7 from across Francisco Street, looking north-northwest - North Beach Place, 431 Bay Street, 530 Francisco Street, 431 Bay Street, 530 Francisco Street, San Francisco, San Francisco County, CA

  18. 7. EXTERIOR SOUTHEAST SIDE DETAIL VIEW, FACING SOUTHWEST. BUILDINGS 101, ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    7. EXTERIOR SOUTHEAST SIDE DETAIL VIEW, FACING SOUTHWEST. BUILDINGS 101, 278 AND CANOPY 685 DETAILED. - NASA Industrial Plant, Missile Research Laboratory, 12214 Lakewood Boulevard, Downey, Los Angeles County, CA

  19. 3. EXTERIOR NORTH SIDE DETAIL VIEW, FACING SOUTHWEST. THE ROOFLINE ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    3. EXTERIOR NORTH SIDE DETAIL VIEW, FACING SOUTHWEST. THE ROOFLINE CLEARLY SHOWS THE ATTACHMENTS TO THE NORTH (FORMERLY CANOPY 764) AND EAST (FORMERLY BUILDING 13). - NASA Industrial Plant, Maintenance Facility, 12214 Lakewood Boulevard, Downey, Los Angeles County, CA

  20. 6. EXTERIOR NORTHEAST CORNER VIEW, FACING SOUTHWEST. CLEAR SHOP OF ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    6. EXTERIOR NORTHEAST CORNER VIEW, FACING SOUTHWEST. CLEAR SHOP OF CANOPY 723 AS WELL NORTH FACADES OF ADDITIONS TO BUILDING 10. - NASA Industrial Plant, Maintenance Facility, 12214 Lakewood Boulevard, Downey, Los Angeles County, CA

  1. 2. EXTERIOR VIEW TO THE NORTH OF THE SOUTH ELEVATION ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    2. EXTERIOR VIEW TO THE NORTH OF THE SOUTH ELEVATION OF THE HOT DISASSEMBLY AREA. - Nevada Test Site, Reactor Maintenance Assembly & Dissassembly Facility, Area 25, Jackass Flats, Junction of Roads F & G, Mercury, Nye County, NV

  2. 8. EXTERIOR VIEW TO THE WEST OF THE EAST ELEVATION ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    8. EXTERIOR VIEW TO THE WEST OF THE EAST ELEVATION OF THE HOT DISASSEMBLY AREA. - Nevada Test Site, Reactor Maintenance Assembly & Dissassembly Facility, Area 25, Jackass Flats, Junction of Roads F & G, Mercury, Nye County, NV

  3. 4. EXTERIOR VIEW TO THE EAST OF THE WEST ELEVATION ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    4. EXTERIOR VIEW TO THE EAST OF THE WEST ELEVATION OF THE COLD ASSEMBLY AREA. - Nevada Test Site, Reactor Maintenance Assembly & Dissassembly Facility, Area 25, Jackass Flats, Junction of Roads F & G, Mercury, Nye County, NV

  4. 7. EXTERIOR VIEW TO THE SOUTHWEST OF THE NORTH AND ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    7. EXTERIOR VIEW TO THE SOUTHWEST OF THE NORTH AND EAST ELEVATIONS. - Nevada Test Site, Reactor Maintenance Assembly & Dissassembly Facility, Area 25, Jackass Flats, Junction of Roads F & G, Mercury, Nye County, NV

  5. 6. EXTERIOR VIEW TO THE SOUTH OF THE NORTH ELEVATION ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    6. EXTERIOR VIEW TO THE SOUTH OF THE NORTH ELEVATION OF THE HOT DISASSEMBLY AREA. - Nevada Test Site, Reactor Maintenance Assembly & Dissassembly Facility, Area 25, Jackass Flats, Junction of Roads F & G, Mercury, Nye County, NV

  6. 9. EXTERIOR VIEW TO THE NORTHWEST OF THE SOUTH AND ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    9. EXTERIOR VIEW TO THE NORTHWEST OF THE SOUTH AND EAST ELEVATIONS. - Nevada Test Site, Reactor Maintenance Assembly & Dissassembly Facility, Area 25, Jackass Flats, Junction of Roads F & G, Mercury, Nye County, NV

  7. Exterior detail, west elevation showing identical window bays set into ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Exterior detail, west elevation showing identical window bays set into brick wall which tapers from thick at grade to thin at the higher stories; view to east. - Lawrence Machine Shop, Building No. 4, 70 General Street, Lawrence, Essex County, MA

  8. Exterior view through the western bay door of the interior ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Exterior view through the western bay door of the interior of the Descanso Station garage, building no. 2304. View is toward the south. - Descanso Ranger Station, Engine Garage, 24321 Viejas Grade Road, Descanso, San Diego County, CA

  9. 3. EXTERIOR VIEW INTO PART OF OPEN HEARTH NO. 5 ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    3. EXTERIOR VIEW INTO PART OF OPEN HEARTH NO. 5 WITH RAILROAD TRESTLE IN FOREGROUND. (Jet Lowe) - U.S. Steel Homestead Works, Open Hearth Steelmaking Plant, Along Monongahela River, Homestead, Allegheny County, PA

  10. 4. FRONT PORCH EXTERIOR DETAIL SHOWING PLANK CEILING, LIGHT FIXTURE, ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    4. FRONT PORCH EXTERIOR DETAIL SHOWING PLANK CEILING, LIGHT FIXTURE, AND DORIC COLUMNS. VIEW TO SOUTH. - Big Creek Hydroelectric System, Big Creek Town, Operator House, Orchard Avenue south of Huntington Lake Road, Big Creek, Fresno County, CA

  11. 20. EXTERIOR OBLIQUE CONTEXT VIEW OF WEST FACADE OF BUILDINGS ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    20. EXTERIOR OBLIQUE CONTEXT VIEW OF WEST FACADE OF BUILDINGS 711 FOREGROUND AND 741 IN THE DISTANCE, LOOKING SOUTH. - Oakland Naval Supply Center, Warehouse Type D, Maritime Street at Seventh Avenue, Oakland, Alameda County, CA

  12. 8. Exterior view of Blacksmith Shop window. Central of ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    8. Exterior view of Blacksmith Shop window. - Central of Georgia Railway, Savannah Repair Shops & Terminal Facilities, Blacksmith Shop, Bounded by West Broad, Jones, West Boundary & Hull Streets, Savannah, Chatham County, GA

  13. Exterior view of southwest front looking from Bank Street to ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Exterior view of southwest front looking from Bank Street to show excavation for the underground facility (to be under the lawn when complete) - Virginia State Capitol, Bank and 10th Streets, Capitol Square, Richmond, Independent City, VA

  14. Exterior view to the southeast of the west camera bunker ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Exterior view to the southeast of the west camera bunker outside the fenced facility area - Nevada Test Site, Test Cell C Facility, West Camera Bunker, Area 25, Jackass Flats, Road J, Mercury, Nye County, NV

  15. FACILITY 712, EXTERIOR DETAIL OF FIREPLACE AND LEADEDGLASS WINDOWS, VIEW ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    FACILITY 712, EXTERIOR DETAIL OF FIREPLACE AND LEADED-GLASS WINDOWS, VIEW FACING WEST. - Schofield Barracks Military Reservation, Central-Entry Single-Family Housing Type, Between Bragg & Grime Streets near Ayres Avenue, Wahiawa, Honolulu County, HI

  16. Detail, exterior side of doubleplanked north end, Burton Park Club ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Detail, exterior side of double-planked north end, Burton Park Club House, view to south-southwest (135mm lens). - Burton Park, Club House & Amphitheater, Adjacent ot south end of Chestnut Avenue, San Carlos, San Mateo County, CA

  17. 53. Exterior view of marine railway complex with railway #3 ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    53. Exterior view of marine railway complex with railway #3 in foreground, #2 middle, #1 back. Note rail/roller type (steel railway/steel wheels) - Barbour Boat Works, Tryon Palace Drive, New Bern, Craven County, NC

  18. 57. Exterior view of marine railway #4. BBW work Tun ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    57. Exterior view of marine railway #4. BBW work Tun Sam on the ways seen from Starboard Bow. Note rail/roller type (steel railway/steel wheels). - Barbour Boat Works, Tryon Palace Drive, New Bern, Craven County, NC

  19. 55. Exterior view of marine railway #4. BBW work Tug ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    55. Exterior view of marine railway #4. BBW work Tug Sam on the ways seen from Port Bow. This was first railway built by BBW on site (Ca.1936). - Barbour Boat Works, Tryon Palace Drive, New Bern, Craven County, NC

  20. 40. Exterior view of dockage, marine railway #4, and assembly ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    40. Exterior view of dockage, marine railway #4, and assembly building. Note BBW Tug Sam on railway and BBW-Built Stardust (#1) at end of dock. - Barbour Boat Works, Tryon Palace Drive, New Bern, Craven County, NC

  1. 8. EXTERIOR DETAIL OF FRONT ENTRY PORCH SHOWING ORIGINAL ARTS ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    8. EXTERIOR DETAIL OF FRONT ENTRY PORCH SHOWING ORIGINAL ARTS AND CRAFTS STYLE ELECTRICAL LANTERN. VIEW TO SOUTH. - Rush Creek Hydroelectric System, Clubhouse Cottage, Rush Creek, June Lake, Mono County, CA

  2. 1. EXTERIORS OF PAINT LOCKER, BUILDING 101, ON RIGHT, AND ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. EXTERIORS OF PAINT LOCKER, BUILDING 101, ON RIGHT, AND CIVIL ENGINEERING STORAGE, BUILDING 105 ON LEFT, LOOKING NORTH. - Mill Valley Air Force Station, Storage Building Types, East Ridgecrest Boulevard, Mount Tamalpais, Mill Valley, Marin County, CA

  3. 1. Mill exterior, high grade chute partially restored on the ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. Mill exterior, high grade chute partially restored on the outside of mill building center of picture. Looking northeast from below bridge. - Kennecott Copper Corporation, Concentration Mill, On Copper River & Northwestern Railroad, Kennicott, Valdez-Cordova Census Area, AK

  4. EXTERIOR VIEW OF THE REAR AND SOUTHEAST SIDE OF BUILDING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW OF THE REAR AND SOUTHEAST SIDE OF BUILDING 471 FACING NORTHEAST - U.S. Naval Base, Pearl Harbor, Waterfront Transit Shed, Corner of Northampton Avenue & Simms Street, Pearl City, Honolulu County, HI

  5. EXTERIOR VIEW OF THE FRONT AND NORTH SIDE OF BUILDING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW OF THE FRONT AND NORTH SIDE OF BUILDING 477 FACING SOUTH - U.S. Naval Base, Pearl Harbor, Waterfront Transit Shed, Corner of Astoria Avenue & Gaffney Street, Pearl City, Honolulu County, HI

  6. EXTERIOR VIEW OF THE REAR AND SOUTH SIDE OF BUILDING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW OF THE REAR AND SOUTH SIDE OF BUILDING 477 FACING NORTH - U.S. Naval Base, Pearl Harbor, Waterfront Transit Shed, Corner of Astoria Avenue & Gaffney Street, Pearl City, Honolulu County, HI

  7. EXTERIOR VIEW OF THE FRONT AND NORTH SIDE OF BUILDING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW OF THE FRONT AND NORTH SIDE OF BUILDING 447 FACING SOUTHWEST - U.S. Naval Base, Pearl Harbor, Waterfront Transit Shed, Between Northampton Avenue & Wharf K3, Pearl City, Honolulu County, HI

  8. EXTERIOR VIEW OF THE FRONT AND NORTHWEST SIDE OF BUILDING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW OF THE FRONT AND NORTHWEST SIDE OF BUILDING 471 FACING SOUTH - U.S. Naval Base, Pearl Harbor, Waterfront Transit Shed, Corner of Northampton Avenue & Simms Street, Pearl City, Honolulu County, HI

  9. EXTERIOR VIEW OF THE FRONT AND SOUTH SIDE OF BUILDING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW OF THE FRONT AND SOUTH SIDE OF BUILDING 447 FACING NORTHWEST - U.S. Naval Base, Pearl Harbor, Waterfront Transit Shed, Between Northampton Avenue & Wharf K3, Pearl City, Honolulu County, HI

  10. General exterior view to northeast (Building 203 in background right) ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    General exterior view to northeast (Building 203 in background right) - Charlestown Navy Yard, Oxygen Plant, Midway along northern boundary of Charlestown Navy Yard, on Little Mystic Channel, near junction of Eighteenth Street & Fourth Avenue, Boston, Suffolk County, MA

  11. Looking Southwest to Dry and Wet Exterior Scrubbers at Rear ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Looking Southwest to Dry and Wet Exterior Scrubbers at Rear of Oxide Building - Hematite Fuel Fabrication Facility, Oxide Building & Oxide Loading Dock, 3300 State Road P, Festus, Jefferson County, MO

  12. OBLIQUE VIEW. NOTE THE ROUGHSURFACED EXTERIOR OF THE CONCRETE WALLS. ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    OBLIQUE VIEW. NOTE THE ROUGH-SURFACED EXTERIOR OF THE CONCRETE WALLS. VIEW FACING NORTHEAST - U.S. Naval Base, Pearl Harbor, Ford Island 5-Inch Antiaircraft Battery, Battery Command Center, Ford Island, Pearl City, Honolulu County, HI

  13. 46. Exterior view at the corner of Seventh Avenue and ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    46. Exterior view at the corner of Seventh Avenue and Olive Way, looking NE. Opening night film, 'The Broadway Melody,' displayed on the canopy marquee. - Fox Theater, Seventh Avenue & Olive Way, Seattle, King County, WA

  14. Exterior view of hipped roof with coffee processing structure in ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Exterior view of hipped roof with coffee processing structure in background, view towards the southwest - Pou Coffee Processing Structure, Casa No. 2, Highway 139, Kilometer 12, Maraguez, Ponce Municipio, PR

  15. 1. EXTERIOR FROM THE SOUTHEAST (view taken 1887; from Title ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. EXTERIOR FROM THE SOUTHEAST (view taken 1887; from Title Insurance Company Collection, San Diego Historical Society. Photocopy by Bert Shankland, San Diego, August 20, 1976). - Grand Hotel, 332 F Street, San Diego, San Diego County, CA

  16. Exteriors with Hull Damage as of 2008, Port Profile, Stern ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Exteriors with Hull Damage as of 2008, Port Profile, Stern Profile, Bow Profile, Loose Plate - Sub Marine Explorer, Located along the beach of Isla San Telmo, Pearl Islands, Isla San Telmo, Former Panama Canal Zone, CZ

  17. EXTERIOR OF LOCKER ROOM PROJECTION, FACING SOUTHEAST Cape Canaveral ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR OF LOCKER ROOM PROJECTION, FACING SOUTHEAST - Cape Canaveral Air Force Station, Launch Complex 34, Operations Support Building, Freedom Road, Southwest of Launch Stand CX-34, Cape Canaveral, Brevard County, FL

  18. EXTERIOR DOOR DETAIL, CORRIDOR 137, FACING EAST Cape Canaveral ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR DOOR DETAIL, CORRIDOR 137, FACING EAST - Cape Canaveral Air Force Station, Launch Complex 34, Operations Support Building, Freedom Road, Southwest of Launch Stand CX-34, Cape Canaveral, Brevard County, FL

  19. 4. DETAIL ALONG WEST SIDE, SHOWING EXTERIOR STAIRWAY, BUILDING NO. ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    4. DETAIL ALONG WEST SIDE, SHOWING EXTERIOR STAIRWAY, BUILDING NO. 1 IN THE CENTER DISTANCE, AND ONE OF THE BENDING SHOPS AT RIGHT. - United Engineering Company Shipyard, Engineering Building, 2900 Main Street, Alameda, Alameda County, CA

  20. 1. EXTERIOR VIEW, OBLIQUE PERSPECTIVE, LOOKING NORTHEAST, WITH SIDE AND ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. EXTERIOR VIEW, OBLIQUE PERSPECTIVE, LOOKING NORTHEAST, WITH SIDE AND FRONT ELEVATIONS OF THE CHURCH AND THE GAZEBO BAND STAND (LEFT) - St. Mark's Catholic Church, 1040 Tenth Avenue West, Thomas, Jefferson County, AL

  1. 42. Exterior view of dockage and barracks on piers used ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    42. Exterior view of dockage and barracks on piers used during construction of minesweepers. Now used for storage. Sunken barge crane in foreground. - Barbour Boat Works, Tryon Palace Drive, New Bern, Craven County, NC

  2. EXTERIOR ELEVATION, LOOKING SOUTH, ALSO SHOWING THE NORFOLK SOUTHERN STEAM ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR ELEVATION, LOOKING SOUTH, ALSO SHOWING THE NORFOLK SOUTHERN STEAM RESTORATION FLOOR INTERIOR WITH A DRILL PRESS (LEFT) AND BORING MILL (RIGHT). - Norfolk & Southern Steam Locomotive No. 1218, Norris Yards, East of Ruffner Road, Irondale, Jefferson County, AL

  3. 1. T12, exterior overall view, looking north. Thallheimer Whiteman ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. T-12, exterior overall view, looking north. Thallheimer - Whiteman Air Force Base, Minuteman Missile Launch Facility Trainer T-12, Northeast of Oscar-01 Missile Alert Facility, Knob Noster, Johnson County, MO

  4. Exterior view of southern half of east porch, showing entrance ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Exterior view of southern half of east porch, showing entrance to second story of la casa, view towards the west - Pou Coffee Processing Structure, Casa No. 2, Highway 139, Kilometer 12, Maraguez, Ponce Municipio, PR

  5. 1. EXTERIOR OF CIVIL ENGINEERING MAINTENANCE SHOP, BUILDING 103, LOOKING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. EXTERIOR OF CIVIL ENGINEERING MAINTENANCE SHOP, BUILDING 103, LOOKING NORTH. - Mill Valley Air Force Station, Civil Engineering Maintenance Shop, East Ridgecrest Boulevard, Mount Tamalpais, Mill Valley, Marin County, CA

  6. 6. EXTERIOR OF REAR (EAST END) AND NORTH SIDE SHOWING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    6. EXTERIOR OF REAR (EAST END) AND NORTH SIDE SHOWING ASBESTOS SIDING, BACKYARD LAWN, AND CLOTHESLINE. VIEW TO SOUTHWEST. - Bishop Creek Hydroelectric System, Plant 4, Worker Cottage, Bishop Creek, Bishop, Inyo County, CA

  7. EXTERIOR VIEW OF THE FRONT AND WEST SIDE OF BUILDING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW OF THE FRONT AND WEST SIDE OF BUILDING T65, FACING NORTH. - U.S. Naval Base, Pearl Harbor, Technical Materials Assembly Shed, North Road between Astoria & Quincey Avenues, Pearl City, Honolulu County, HI

  8. EXTERIOR VIEW OF THE REAR AND EAST SIDE OF BUILDING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW OF THE REAR AND EAST SIDE OF BUILDING T65, FACING SOUTH. - U.S. Naval Base, Pearl Harbor, Technical Materials Assembly Shed, North Road between Astoria & Quincey Avenues, Pearl City, Honolulu County, HI

  9. EXTERIOR VIEW OF THE FRONT AND EAST SIDE OF BUILDING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW OF THE FRONT AND EAST SIDE OF BUILDING T65, FACING WEST. - U.S. Naval Base, Pearl Harbor, Technical Materials Assembly Shed, North Road between Astoria & Quincey Avenues, Pearl City, Honolulu County, HI

  10. Exterior, looking west Beale Air Force Base, Perimeter Acquisition ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Exterior, looking west - Beale Air Force Base, Perimeter Acquisition Vehicle Entry Phased-Array Warning System, Civil Engineering Storage Building, End of Spencer Paul Road, north of Warren Shingle Road (14th Street), Marysville, Yuba County, CA

  11. 1. EXTERIOR VIEW LOOKING NORTHWEST AT BATCH FURNACE BUILDING, 22' ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. EXTERIOR VIEW LOOKING NORTHWEST AT BATCH FURNACE BUILDING, 22' BAR MILL BUILDING, AND 22 BAR MILL MOTOR ROOM. - U.S. Steel Duquesne Works, 22-Inch Bar Mill, Along Monongahela River, Duquesne, Allegheny County, PA

  12. DETAIL ELEVATION VIEW OF EXTERIOR STAIRS ON THE EAST END ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    DETAIL ELEVATION VIEW OF EXTERIOR STAIRS ON THE EAST END OF BUILDING 63, FACING SOUTH. - Naval Computer & Telecommunications Area Station, Enlisted Men's Barracks, West corner of Central Street & Midway Drive, Wahiawa, Honolulu County, HI

  13. 1. GENERAL EXTERIOR VIEW LOOKING SOUTH, SHOWING FACADE OF FISH ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. GENERAL EXTERIOR VIEW LOOKING SOUTH, SHOWING FACADE OF FISH HATCHERY BUILDING. - Bonneville Project, Fish Hatchery, On Columbia River bordered on South by Union Pacific, Bonneville, Multnomah County, OR

  14. 6. DETAIL EXTERIOR VIEW OF WINDOW SHUTTERS ON OUTSIDE OF ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    6. DETAIL EXTERIOR VIEW OF WINDOW SHUTTERS ON OUTSIDE OF FISH HATCHERY BUILDING. - Bonneville Project, Fish Hatchery, On Columbia River bordered on South by Union Pacific, Bonneville, Multnomah County, OR

  15. 3. DETAIL EXTERIOR VIEW LOOKING SOUTHEAST SHOWING CENTER GABLE SECTION ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    3. DETAIL EXTERIOR VIEW LOOKING SOUTHEAST SHOWING CENTER GABLE SECTION OF THE FISH HATCHERY BUILDING. - Bonneville Project, Fish Hatchery, On Columbia River bordered on South by Union Pacific, Bonneville, Multnomah County, OR

  16. 4. DETAIL EXTERIOR VIEW OF FISH HATCHERY BUILDING'S CENTRAL GABLE; ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    4. DETAIL EXTERIOR VIEW OF FISH HATCHERY BUILDING'S CENTRAL GABLE; MASONRY WALL AND FLOWERBED IN FOREGROUND. - Bonneville Project, Fish Hatchery, On Columbia River bordered on South by Union Pacific, Bonneville, Multnomah County, OR

  17. 9. GENERAL EXTERIOR VIEW LOOKING NORTH, SHOWING FORMER FISH HATCHERY ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    9. GENERAL EXTERIOR VIEW LOOKING NORTH, SHOWING FORMER FISH HATCHERY OFFICE BUILDING (PRESENTLY USED AS GARDENER'S OFFICE). - Bonneville Project, Fish Hatchery, On Columbia River bordered on South by Union Pacific, Bonneville, Multnomah County, OR

  18. 2. GENERAL EXTERIOR VIEW OF FISH HATCHERY BUILDING LOOKING NORTH; ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    2. GENERAL EXTERIOR VIEW OF FISH HATCHERY BUILDING LOOKING NORTH; REINFORCED CONCRETE FISH PONDS IN FOREGROUND. - Bonneville Project, Fish Hatchery, On Columbia River bordered on South by Union Pacific, Bonneville, Multnomah County, OR

  19. Interior view of bedroom 2 showing louvers in former exterior ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Interior view of bedroom 2 showing louvers in former exterior window opening, facing northwest. - Albrook Air Force Station, Field Officer's Quarters, West side of Dargue Avenue Circle, Balboa, Former Panama Canal Zone, CZ

  20. 4. DETAIL VIEW OF CROSS SECTION OF STRUCTURE, SHOWING EXTERIOR ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    4. DETAIL VIEW OF CROSS SECTION OF STRUCTURE, SHOWING EXTERIOR FACINGS LINED WITH RUBBLE BACKING AND EARTH INFILL, LOOKING EAST - Rock Wall, North side of Battle Creek Canyon, Shingletown, Shasta County, CA

  1. 1. BLOWER (EXTERIOR CONFIGURATION). Hot Springs National Park Bathhouse ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. BLOWER (EXTERIOR CONFIGURATION). - Hot Springs National Park Bathhouse Row, Maurice Bathhouse: Mechanical & Piping Systems, State Highway 7, 1 mile north of U.S. Highway 70, Hot Springs, Garland County, AR

  2. 7. EXTERIOR, SIDE VIEW FROM GARDEN SHOWING GRAPE ARBOR undated ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    7. EXTERIOR, SIDE VIEW FROM GARDEN SHOWING GRAPE ARBOR undated - Jean Baptiste Valle House, 99 South Main Street (Northwest corner of Main & Market Streets), Sainte Genevieve, Ste. Genevieve County, MO

  3. 14. EXTERIOR STAIRS AT NORTH AND SOUTH ELEVATIONS SUBSISTENCE BUILDING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    14. EXTERIOR STAIRS AT NORTH AND SOUTH ELEVATIONS SUBSISTENCE BUILDING FROM GRADE TO ROOF OF COVERED WALK, SHEET 38 - U.S. Naval Hospital, North Ward, Park Boulevard, Balboa Park, San Diego, San Diego County, CA

  4. 2. EXTERIOR VIEW TO THE SOUTH OF THE PIPING ON ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    2. EXTERIOR VIEW TO THE SOUTH OF THE PIPING ON THE ROOF OF AND NEXT TO THE BUILDING. - Nevada Test Site, Test Cell A Facility, Test Cell A Building & Addition, Area 25, Jackass Flats, Road F, Mercury, Nye County, NV

  5. 5. EXTERIOR VIEW TO THE WEST OF THE EAST ELEVATION ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    5. EXTERIOR VIEW TO THE WEST OF THE EAST ELEVATION OF THE TEST CELL, WITH DEWARS IN THE BACKGROUND. - Nevada Test Site, Test Cell C Facility, Building No. 3210, Area 25, Jackass Flats, Road J, Mercury, Nye County, NV

  6. 3. EXTERIOR VIEW TO THE SOUTHEAST OF THE NORTH AND ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    3. EXTERIOR VIEW TO THE SOUTHEAST OF THE NORTH AND WEST ELEVATIONS OF THE TEST CELL. - Nevada Test Site, Test Cell C Facility, Building No. 3210, Area 25, Jackass Flats, Road J, Mercury, Nye County, NV

  7. 6. EXTERIOR VIEW TO THE NORTHWEST OF THE SOUTHEAST CORNER ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    6. EXTERIOR VIEW TO THE NORTHWEST OF THE SOUTHEAST CORNER OF THE EAST ELEVATION OF THE TEST CELL. - Nevada Test Site, Test Cell C Facility, Building No. 3210, Area 25, Jackass Flats, Road J, Mercury, Nye County, NV

  8. 4. EXTERIOR VIEW TO THE NORTH OF THE WESTERN PORTION ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    4. EXTERIOR VIEW TO THE NORTH OF THE WESTERN PORTION OF THE SOUTH ELEVATION OF THE TEST CELL. - Nevada Test Site, Test Cell C Facility, Building No. 3210, Area 25, Jackass Flats, Road J, Mercury, Nye County, NV

  9. 16. Exterior of assembly building (mold loft #2) used for ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    16. Exterior of assembly building (mold loft #2) used for runabout production, constructed CA. 1932. Most of the production run boats were assembled here. - Barbour Boat Works, Tryon Palace Drive, New Bern, Craven County, NC

  10. EXTERIOR VIEW, SOUTH ELEVATION WITH THOMAS COKE BYPRODUCTS PLANT AND ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW, SOUTH ELEVATION WITH THOMAS COKE BYPRODUCTS PLANT AND THOMAS INDUSTRIAL COMMUNITY (NOT PICTURED AT FAR LEFT). - Birmingham Southern Railroad Bridge, U.S. Highway 78, Birmingham, Jefferson County, AL

  11. 40. EXTERIOR VIEW, BERK SWITCH TOWER, SOUTH NORWALK, SHOWING FRONT ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    40. EXTERIOR VIEW, BERK SWITCH TOWER, SOUTH NORWALK, SHOWING FRONT ELEVATION AND PIPES LEADING TO SWITCHES - New York, New Haven & Hartford Railroad, Automatic Signalization System, Long Island Sound shoreline between Stamford & New Haven, Stamford, Fairfield County, CT

  12. 45. EXTERIOR VIEW, GREEN SWITCH TOLWER, COS COB, SHOWING BARS ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    45. EXTERIOR VIEW, GREEN SWITCH TOLWER, COS COB, SHOWING BARS AND PIPES LEADING TO SWITCHES - New York, New Haven & Hartford Railroad, Automatic Signalization System, Long Island Sound shoreline between Stamford & New Haven, Stamford, Fairfield County, CT

  13. 22. FANTAIL DECK, SHOWING DETAIL OF DECK EXTENSION AND EXTERIOR ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    22. FANTAIL DECK, SHOWING DETAIL OF DECK EXTENSION AND EXTERIOR LOCKING MECHANISM ON HATCH DOOR TO CREW'S BERTHING. - U.S. Coast Guard Cutter WHITE HEATH, USGS Integrated Support Command Boston, 427 Commercial Street, Boston, Suffolk County, MA

  14. EXTERIOR VIEW, BEE HIVE COKE OVEN DOOR. Pratt Coal ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW, BEE HIVE COKE OVEN DOOR. - Pratt Coal & Coke Company, Pratt Mines, Coke Ovens & Railroad, Bounded by First Street, Avenue G, Third Place, Birmingham Southern Railroad, Birmingham, Jefferson County, AL

  15. 9. EXTERIOR PERSPECTIVE OF POWER PLANT BUILDING LOOKING NORTHEAST. DRY ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    9. EXTERIOR PERSPECTIVE OF POWER PLANT BUILDING LOOKING NORTHEAST. DRY CANAL BED IN FOREGROUND. - Potomac Power Plant, On West Virginia Shore of Potomac River, about 1 mile upriver from confluence with Shenandoah River, Harpers Ferry, Jefferson County, WV

  16. 7. EXTERIOR OF POWER PLANT BUILDING LOOKING NORTHWEST. DETAIL OF ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    7. EXTERIOR OF POWER PLANT BUILDING LOOKING NORTHWEST. DETAIL OF TRASH RACK IN FOREGROUND. - Potomac Power Plant, On West Virginia Shore of Potomac River, about 1 mile upriver from confluence with Shenandoah River, Harpers Ferry, Jefferson County, WV

  17. 29. View of exterior of bathroom located in southwest corner ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    29. View of exterior of bathroom located in southwest corner of central section. Photo was taken on Oct 22, 2002, looking southwest. - College Heights Lemon Packing House, 519-532 West First Street, Claremont, Los Angeles County, CA

  18. EXTERIOR, A view looking west between the south side of ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR, A view looking west between the south side of the building and a stack which is located in the courtyard - Department of Energy, Mound Facility, B Building, One Mound Road, Miamisburg, Montgomery County, OH

  19. EXTERIOR, A view looking east that captures the southwest corner ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR, A view looking east that captures the southwest corner of the building with surveyor's rod to indicate scale - Department of Energy, Mound Facility, B Building, One Mound Road, Miamisburg, Montgomery County, OH

  20. EXTERIOR, A view from above looking southwest toward the roof ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR, A view from above looking southwest toward the roof and stacks of B Building with I Building in the background - Department of Energy, Mound Facility, B Building, One Mound Road, Miamisburg, Montgomery County, OH

  1. EXTERIOR, A view looking northeast toward the south side of ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR, A view looking northeast toward the south side of the building including the diesel fuel tank and bottom portion of a stack - Department of Energy, Mound Facility, B Building, One Mound Road, Miamisburg, Montgomery County, OH

  2. 3. GROUND VIEW OF EXTERIOR STAIRWAY ENTRANCE FACING SOUTHEAST. ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    3. GROUND VIEW OF EXTERIOR STAIRWAY ENTRANCE FACING SOUTHEAST. - U.S. Naval Base, Pearl Harbor, Signal Tower, Corner of Seventh Street & Avenue D east of Drydock No. 1, Pearl City, Honolulu County, HI

  3. EXTERIOR VIEW OF THE FRONT AND SOUTHWEST SIDE OF BUILDING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW OF THE FRONT AND SOUTHWEST SIDE OF BUILDING 190 FACING NORTH. - U.S. Naval Base, Pearl Harbor, Warehouse & Cold Storage Building, North corner of Pokomoke Street & Hornet Avenue, Pearl City, Honolulu County, HI

  4. EXTERIOR VIEW OF THE FRONT AND NORTHEAST SIDE OF BUILDING ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW OF THE FRONT AND NORTHEAST SIDE OF BUILDING 190 FACING WEST. - U.S. Naval Base, Pearl Harbor, Warehouse & Cold Storage Building, North corner of Pokomoke Street & Hornet Avenue, Pearl City, Honolulu County, HI

  5. 12. Detail view, north wall of porch containing the exterior ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    12. Detail view, north wall of porch containing the exterior pantry door (note the lintel stone with the abstracted wave motif). - John Bartram House & Garden, House, 54th Street & Lindbergh Boulevard, Philadelphia, Philadelphia County, PA

  6. 1. EXTERIOR VIEW TO THE NORTHEAST OF A BROCK HOUSE ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. EXTERIOR VIEW TO THE NORTHEAST OF A BROCK HOUSE USED FOR THE WATER FILTERING SYSTEM. - Nevada Test Site, Pluto Facility, Water Filtering System Brock House, Area 26, Wahmonie Flats, Cane Spring Road, Mercury, Nye County, NV

  7. 2. EXTERIOR VIEW TO THE NORTH OF WATER FILTERING EQUIPMENT ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    2. EXTERIOR VIEW TO THE NORTH OF WATER FILTERING EQUIPMENT AND BROCK HOUSES ALONG THE EAST SIDE OF THE COMPOUND. - Nevada Test Site, Pluto Facility, Area 26, Wahmonie Flats, Cane Spring Road, Mercury, Nye County, NV

  8. 8. EXTERIOR VIEW OF THE BARNES BUILDING FROM POPLAR STREET, ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    8. EXTERIOR VIEW OF THE BARNES BUILDING FROM POPLAR STREET, FACING NORTHEAST. CITY AUDITORIUM (BACKGROUND RIGHT) AND THE SHRINE TEMPLE (BACKGROUND LEFT). - Barnes Building, 477 Cotton Avenue, Macon, Bibb County, GA

  9. 37. Exterior view of main yard. Stock room building (left), ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    37. Exterior view of main yard. Stock room building (left), old machine shop (center), steel fabrication building (right), and traveling yard crane (middle fore). - Barbour Boat Works, Tryon Palace Drive, New Bern, Craven County, NC

  10. 1. Exterior, corner, wall, and barrel of cannon used to ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. Exterior, corner, wall, and barrel of cannon used to protect corner of building from cart wheels. 1960. - Jefferson Barracks, Brick & Stone Powder Magazine, Jefferson Barracks, St. Louis County, MO

  11. 1. EXTERIOR VIEW OF THE EXPLOSIVE STORAGE SHED, BUILDING 306, ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. EXTERIOR VIEW OF THE EXPLOSIVE STORAGE SHED, BUILDING 306, LOOKING NORTHWEST. - Mill Valley Air Force Station, Explosive Storage, East Ridgecrest Boulevard, Mount Tamalpais, Mill Valley, Marin County, CA

  12. 6. EXTERIOR 1961 NORTHEAST ADDITION VIEW, FACING NORTHWEST. BUILDING 276 ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    6. EXTERIOR 1961 NORTHEAST ADDITION VIEW, FACING NORTHWEST. BUILDING 276 VISIBLE TO RIGHT OF FRAME. - NASA Industrial Plant, Missile Research Laboratory, 12214 Lakewood Boulevard, Downey, Los Angeles County, CA

  13. 8. EXTERIOR DETAIL, BUILDING 18 (POWER PLANT RESEARCH LABORATORY) (1991). ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    8. EXTERIOR DETAIL, BUILDING 18 (POWER PLANT RESEARCH LABORATORY) (1991). - Wright-Patterson Air Force Base, Area B, Building 18, Power Plant Laboratory Complex, Northeast corner of C & Fifth Streets, Dayton, Montgomery County, OH

  14. 5. EXTERIOR 1961 NORTHEAST ADDITION VIEW, FACING NORTHWEST. BUILDING 276 ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    5. EXTERIOR 1961 NORTHEAST ADDITION VIEW, FACING NORTHWEST. BUILDING 276 VISIBLE TO RIGHT OF FRAME. - NASA Industrial Plant, Missile Research Laboratory, 12214 Lakewood Boulevard, Downey, Los Angeles County, CA

  15. 7. EXTERIOR NORTHWEST VIEW, BUILDING 18 (POWER PLANT RESEARCH LABORATORY) ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    7. EXTERIOR NORTHWEST VIEW, BUILDING 18 (POWER PLANT RESEARCH LABORATORY) (1991). - Wright-Patterson Air Force Base, Area B, Building 18, Power Plant Laboratory Complex, Northeast corner of C & Fifth Streets, Dayton, Montgomery County, OH

  16. 12. Exterior of main offices, stock room and payroll offices ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    12. Exterior of main offices, stock room and payroll offices view from yard (middle building formerly mold loft #1). Building at left is stock room desk and offices. - Barbour Boat Works, Tryon Palace Drive, New Bern, Craven County, NC

  17. 13. Exterior of main offices and stock room from yard. ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    13. Exterior of main offices and stock room from yard. Middle Building formerly mold loft #1. Building at left is stock room desk and offices. - Barbour Boat Works, Tryon Palace Drive, New Bern, Craven County, NC

  18. 1. EXTERIOR VIEW OF COTTAGE 231 TAKEN FROM ROOF OF ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    1. EXTERIOR VIEW OF COTTAGE 231 TAKEN FROM ROOF OF PUMP HOUSE. CAMERA FACING NORTH. NOTE ROCK RETAINING WALL BUILD WITH NATIVE LAVA ROCK FROM CANYON. - Swan Falls Village, Superintendent's Cottage, Snake River, Kuna, Ada County, ID

  19. North exterior elevation of Pope Quadrangle. Note the bas relief ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    North exterior elevation of Pope Quadrangle. Note the bas relief sculpture over the doorway, which includes the school motto, Aspirando et Perseverando. - Avon Old Farms School, 500 Avon Old Farms Road, Avon, Hartford County, CT

  20. EXTERIOR VIEW, LOOKING SOUTH, NEW AVENUE WITH A FORMER TCIUS ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    EXTERIOR VIEW, LOOKING SOUTH, NEW AVENUE WITH A FORMER TCI-US STEEL "DOUBLE THREE ROOM" COMPANY HOUSE BUILT FOR BLACK ORE MINERS AND THEIR FAMILIES DURING WORLD WAR I - New Village Worker Houses, New Avenue, Bessemer, Jefferson County, AL