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Sample records for semilinear parabolic equation

  1. Asymptotic behaviour of solutions of semilinear parabolic equations

    SciTech Connect

    Egorov, Yu V; Kondratiev, V A

    2008-04-30

    The asymptotic behaviour of solutions of a second-order semilinear parabolic equation is analyzed in a cylindrical domain that is bounded in the space variables. The dominant term of the asymptotic expansion of the solution as t{yields}+{infinity} is found. It is shown that the solution of this problem is asymptotically equivalent to the solution of a certain non-linear ordinary differential equation. Bibliography: 8 titles.

  2. Galerkin/Runge-Kutta discretizations for semilinear parabolic equations

    NASA Technical Reports Server (NTRS)

    Keeling, Stephen L.

    1987-01-01

    A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for semilinear parabolic initial boundary value problems. Unlike any classical counterpart, this class offers arbitrarily high, optimal order convergence. In support of this claim, error estimates are proved, and computational results are presented. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

  3. Generalized Directional Gradients, Backward Stochastic Differential Equations and Mild Solutions of Semilinear Parabolic Equations

    SciTech Connect

    Fuhrman, Marco Tessitore, Gianmario

    2005-05-15

    We study a forward-backward system of stochastic differential equations in an infinite-dimensional framework and its relationships with a semilinear parabolic differential equation on a Hilbert space, in the spirit of the approach of Pardoux-Peng. We prove that the stochastic system allows us to construct a unique solution of the parabolic equation in a suitable class of locally Lipschitz real functions. The parabolic equation is understood in a mild sense which requires the notion of a generalized directional gradient, that we introduce by a probabilistic approach and prove to exist for locally Lipschitz functions.The use of the generalized directional gradient allows us to cover various applications to option pricing problems and to optimal stochastic control problems (including control of delay equations and reaction-diffusion equations),where the lack of differentiability of the coefficients precludes differentiability of solutions to the associated parabolic equations of Black-Scholes or Hamilton-Jacobi-Bellman type.

  4. Stability in terms of two measures for a class of semilinear impulsive parabolic equations

    SciTech Connect

    Dvirnyj, Aleksandr I; Slyn'ko, Vitalij I

    2013-04-30

    The problem of stability in terms of two measures is considered for semilinear impulsive parabolic equations. A new version of the comparison method is proposed, and sufficient conditions for stability in terms of two measures are obtained on this basis. An example of a hybrid impulsive system formed by a system of ordinary differential equations coupled with a partial differential equation of parabolic type is given. The efficiency of the described approaches is demonstrated. Bibliography: 24 titles.

  5. A stability analysis for a semilinear parabolic partial differential equation

    NASA Technical Reports Server (NTRS)

    Chafee, N.

    1973-01-01

    The parabolic partial differential equation considered is u sub t = u sub xx + f(u), where minus infinity x plus infinity and o t plus infinity. Under suitable hypotheses pertaining to f, a class of initial data is exhibited: phi(x), minus infinity x plus infinity, for which the corresponding solutions u(x,t) appraoch zero as t approaches the limit of plus infinity. This convergence is uniform with respect to x on any compact subinterval of the real axis.

  6. Time-dependent singularities in semilinear parabolic equations: Behavior at the singularities

    NASA Astrophysics Data System (ADS)

    Kan, Toru; Takahashi, Jin

    2016-05-01

    Singularities of solutions of semilinear parabolic equations are discussed. A typical equation is ∂t u - Δu =up, x ∈RN ∖ { ξ (t) }, t ∈ I. Here N ≥ 2, p > 1, I ⊂ R is an open interval and ξ ∈Cα (I ;RN) with α > 1 / 2. For this equation it is shown that every nonnegative solution u satisfies ∂t u - Δu =up + Λ in D‧ (RN × I) for some measure Λ whose support is contained in { (ξ (t) , t) ; t ∈ I }. Moreover, if (N - 2) p < N, then u (x , t) = (a (t) + o (1)) Ψ (x - ξ (t)) for almost every t ∈ I as x → ξ (t), where Ψ is the fundamental solution of Laplace's equation in RN and a is some function determined by Λ.

  7. A new parallel solver suited for arbitrary semilinear parabolic partial differential equations based on generalized random trees

    NASA Astrophysics Data System (ADS)

    Acebrón, Juan A.; Rodríguez-Rozas, Ángel

    2011-09-01

    A probabilistic representation for initial value semilinear parabolic problems based on generalized random trees has been derived. Two different strategies have been proposed, both requiring generating suitable random trees combined with a Pade approximant for approximating accurately a given divergent series. Such series are obtained by summing the partial contribution to the solution coming from trees with arbitrary number of branches. The new representation greatly expands the class of problems amenable to be solved probabilistically, and was used successfully to develop a generalized probabilistic domain decomposition method. Such a method has been shown to be suited for massively parallel computers, enjoying full scalability and fault tolerance. Finally, a few numerical examples are given to illustrate the remarkable performance of the algorithm, comparing the results with those obtained with a classical method.

  8. A semilinear parabolic system with a free boundary

    NASA Astrophysics Data System (ADS)

    Wang, Mingxin; Zhao, Yonggang

    2015-12-01

    This paper deals with a semilinear parabolic system with reaction terms {v^p, u^q} and a free boundary {x = s(t)} in one space dimension, where {s(t)} evolves according to the free boundary condition {s'(t) = -μ(u_x + ρ v_x)}. The main aim of this paper was to study the existence, uniqueness, regularity and long-time behavior of positive solution (maximal positive solution). Firstly, we prove that this problem has a unique positive solution when {p, q ≥ 1}, and a (unique) maximal positive solution when {p < 1} or {q < 1}. Then, we study the regularity of {(u,v)} and {s}. At last, we discuss the global existence, finite-time blowup of the unique positive solution (maximal positive solution) and long-time behavior of bounded global solution.

  9. A Semi-linear Backward Parabolic Cauchy Problem with Unbounded Coefficients of Hamilton–Jacobi–Bellman Type and Applications to Optimal Control

    SciTech Connect

    Addona, Davide

    2015-08-15

    We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear backward parabolic Cauchy problem, where the differential equation is the Hamilton–Jacobi–Bellman equation of a suitable optimal control problem. Via backward stochastic differential equations, we show that the mild solution is indeed the value function of the controlled equation and that the feedback law is verified.

  10. Parabolized stability equations

    NASA Astrophysics Data System (ADS)

    Herbert, Thorwald

    1994-04-01

    The parabolized stability equations (PSE) are a new approach to analyze the streamwise evolution of single or interacting Fourier modes in weakly nonparallel flows such as boundary layers. The concept rests on the decomposition of every mode into a slowly varying amplitude function and a wave function with slowly varying wave number. The neglect of the small second derivatives of the slowly varying functions with respect to the streamwise variable leads to an initial boundary-value problem that can be solved by numerical marching procedures. The PSE approach is valid in convectively unstable flows. The equations for a single mode are closely related to those of the traditional eigenvalue problems for linear stability analysis. However, the PSE approach does not exploit the homogeneity of the problem and, therefore, can be utilized to analyze forced modes and the nonlinear growth and interaction of an initial disturbance field. In contrast to the traditional patching of local solutions, the PSE provide the spatial evolution of modes with proper account for their history. The PSE approach allows studies of secondary instabilities without the constraints of the Floquet analysis and reproduces the established experimental, theoretical, and computational benchmark results on transition up to the breakdown stage. The method matches or exceeds the demonstrated capabilities of current spatial Navier-Stokes solvers at a small fraction of their computational cost. Recent applications include studies on localized or distributed receptivity and prediction of transition in model environments for realistic engineering problems. This report describes the basis, intricacies, and some applications of the PSE methodology.

  11. Numerical solution of a semilinear elliptic equation via difference scheme

    NASA Astrophysics Data System (ADS)

    Beigmohammadi, Elif Ozturk; Demirel, Esra

    2016-08-01

    We consider the Bitsadze-Samarskii type nonlocal boundary value problem { -d/2v (t ) d t2 +B v (t ) =h (t ,v (t ) ) ,0 semilinear equation in a Hilbert space H with the self-adjoint positive definite operator B. For the approximate solution of problem (1), we use the first order of accuracy difference scheme. The numerical results are computed by MATLAB.

  12. Existence of anti-periodic (differentiable) mild solutions to semilinear differential equations with nondense domain.

    PubMed

    Liu, Jinghuai; Zhang, Litao

    2016-01-01

    In this paper, we investigate the existence of anti-periodic (or anti-periodic differentiable) mild solutions to the semilinear differential equation [Formula: see text] with nondense domain. Furthermore, an example is given to illustrate our results. PMID:27350933

  13. Evolution of a semilinear parabolic system for migration and selection without dominance

    NASA Astrophysics Data System (ADS)

    Lou, Yuan; Nagylaki, Thomas

    The semilinear parabolic system that describes the evolution of the gene frequencies in the diffusion approximation for migration and selection at a multiallelic locus without dominance is investigated. The population occupies a finite habitat of arbitrary dimensionality and shape (i.e., a bounded, open domain in R). The selection coefficients depend on position; the drift and diffusion coefficients may depend on position. The primary focus of this paper is the dependence of the evolution of the gene frequencies on λ, the strength of selection relative to that of migration. It is proved that if migration is sufficiently strong (i.e., λ is sufficiently small) and the migration operator is in divergence form, then the allele with the greatest spatially averaged selection coefficient is ultimately fixed. The stability of each vertex (i.e., an equilibrium with exactly one allele present) is completely specified. The stability of each edge equilibrium (i.e., one with exactly two alleles present) is fully described when either (i) migration is sufficiently weak (i.e., λ is sufficiently large) or (ii) the equilibrium has just appeared as λ increases. The existence of unexpected, complex phenomena is established: even if there are only three alleles and migration is homogeneous and isotropic (corresponding to the Laplacian), (i) as λ increases, arbitrarily many changes of stability of the edge equilibria and corresponding appearance of an internal equilibrium can occur and (ii) the conditions for protection or loss of an allele can both depend nonmonotonically on λ. Neither of these phenomena can occur in the diallelic case.

  14. L{sup p} Theory for Super-Parabolic Backward Stochastic Partial Differential Equations in the Whole Space

    SciTech Connect

    Du Kai Qiu, Jinniao Tang Shanjian

    2012-04-15

    This paper is concerned with semi-linear backward stochastic partial differential equations (BSPDEs for short) of super-parabolic type. An L{sup p}-theory is given for the Cauchy problem of BSPDEs, separately for the case of p Element-Of (1,2] and for the case of p Element-Of (2,{infinity}). A comparison theorem is also addressed.

  15. Positive or sign-changing solutions for a critical semilinear nonlocal equation

    NASA Astrophysics Data System (ADS)

    Long, Wei; Yang, Jing

    2016-06-01

    We consider the following critical semilinear nonlocal equation involving the fractional Laplacian (-Δ)su = K(|x|)|u|^{2^{*}s-2}u,quad in {R}^N, where {K(|x|)} is a positive radial function, {N > 2 + 2s, 0 < s < 1}, and {2^{*}s = 2N/N-2s}. Under some asymptotic assumptions on K( x) at an extreme point, we show that this problem has infinitely many nonradial positive or sign-changing solutions.

  16. Group-invariant solutions of semilinear Schrödinger equations in multi-dimensions

    SciTech Connect

    Anco, Stephen C.; Feng, Wei

    2013-12-15

    Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schrödinger equations in dimensions n ≠ 1. Both focusing and defocusing cases of a power nonlinearity are considered, including the special case of the pseudo-conformal power p = 4/n relevant for critical dynamics. The methods involve, first, reduction of the Schrödinger equations to group-invariant semilinear complex 2nd order ordinary differential equations (ODEs) with respect to an optimal set of one-dimensional point symmetry groups, and second, use of inherited symmetries, hidden symmetries, and conditional symmetries to solve each ODE by quadratures. Through Noether's theorem, all conservation laws arising from these point symmetry groups are listed. Some group-invariant solutions are found to exist for values of n other than just positive integers, and in such cases an alternative two-dimensional form of the Schrödinger equations involving an extra modulation term with a parameter m = 2−n ≠ 0 is discussed.

  17. Numerical Schemes for Rough Parabolic Equations

    SciTech Connect

    Deya, Aurelien

    2012-04-15

    This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0,1) perturbed by a non-linear rough signal. It is the continuation of Deya (Electron. J. Probab. 16:1489-1518, 2011) and Deya et al. (Probab. Theory Relat. Fields, to appear), where the existence and uniqueness of a solution has been established. The approach combines rough paths methods with standard considerations on discretizing stochastic PDEs. The results apply to a geometric 2-rough path, which covers the case of the multidimensional fractional Brownian motion with Hurst index H>1/3.

  18. Convolutions of Rayleigh functions and their application to semi-linear equations in circular domains

    NASA Astrophysics Data System (ADS)

    Varlamov, Vladimir

    2007-03-01

    Rayleigh functions [sigma]l([nu]) are defined as series in inverse powers of the Bessel function zeros [lambda][nu],n[not equal to]0, where ; [nu] is the index of the Bessel function J[nu](x) and n=1,2,... is the number of the zeros. Convolutions of Rayleigh functions with respect to the Bessel index, are needed for constructing global-in-time solutions of semi-linear evolution equations in circular domains [V. Varlamov, On the spatially two-dimensional Boussinesq equation in a circular domain, Nonlinear Anal. 46 (2001) 699-725; V. Varlamov, Convolution of Rayleigh functions with respect to the Bessel index, J. Math. Anal. Appl. 306 (2005) 413-424]. The study of this new family of special functions was initiated in [V. Varlamov, Convolution of Rayleigh functions with respect to the Bessel index, J. Math. Anal. Appl. 306 (2005) 413-424], where the properties of R1(m) were investigated. In the present work a general representation of Rl(m) in terms of [sigma]l([nu]) is deduced. On the basis of this a representation for the function R2(m) is obtained in terms of the [psi]-function. An asymptotic expansion is computed for R2(m) as m-->[infinity]. Such asymptotics are needed for establishing function spaces for solutions of semi-linear equations in bounded domains with periodicity conditions in one coordinate. As an example of application of Rl(m) a forced Boussinesq equationutt-2b[Delta]ut=-[alpha][Delta]2u+[Delta]u+[beta][Delta](u2)+f with [alpha],b=const>0 and [beta]=const[set membership, variant]R is considered in a unit disc with homogeneous boundary and initial data. Construction of its global-in-time solutions involves the use of the functions R1(m) and R2(m) which are responsible for the nonlinear smoothing effect.

  19. Existence and continuity of bi-spatial random attractors and application to stochastic semilinear Laplacian equations

    NASA Astrophysics Data System (ADS)

    Li, Yangrong; Gu, Anhui; Li, Jia

    2015-01-01

    A concept of a bi-spatial random attractor for a random dynamical system is introduced. A unified result about existence and upper semi-continuity for a family of bi-spatial random attractors is obtained if a family of random systems is convergent, uniformly absorbing in an initial space and uniformly omega-compact in both initial and terminate spaces. The upper semi-continuity result improves all existing results even for single-spatial attractors. As an application of the abstract result, it is shown that every semilinear Laplacian equation on the entire space perturbed by a multiplicative and stochastic noise possesses an (L2, Lq)-random attractor with q > 2. Moreover, it is proved that the family of obtained attractors is upper semi-continuous at any density of noises and the family of attractors for the corresponding compact systems is both upper and lower semi-continuous at infinity under the topology of both spaces.

  20. Normal forms for semilinear equations with non-dense domain with applications to age structured models

    NASA Astrophysics Data System (ADS)

    Liu, Zhihua; Magal, Pierre; Ruan, Shigui

    2014-08-01

    Normal form theory is very important and useful in simplifying the forms of equations restricted on the center manifolds in studying nonlinear dynamical problems. In this paper, using the center manifold theorem associated with the integrated semigroup theory, we develop a normal form theory for semilinear Cauchy problems in which the linear operator is not densely defined and is not a Hille-Yosida operator and present procedures to compute the Taylor expansion and normal form of the reduced system restricted on the center manifold. We then apply the main results and computation procedures to determine the direction of the Hopf bifurcation and stability of the bifurcating periodic solutions in a structured evolutionary epidemiological model of influenza A drift and an age structured population model.

  1. Nonuniform depth grids in parabolic equation solutions.

    PubMed

    Sanders, William M; Collins, Michael D

    2013-04-01

    The parabolic wave equation is solved using a finite-difference solution in depth that involves a nonuniform grid. The depth operator is discretized using Galerkin's method with asymmetric hat functions. Examples are presented to illustrate that this approach can be used to improve efficiency for problems in ocean acoustics and seismo-acoustics. For shallow water problems, accuracy is sensitive to the precise placement of the ocean bottom interface. This issue is often addressed with the inefficient approach of using a fine grid spacing over all depth. Efficiency may be improved by using a relatively coarse grid with nonuniform sampling to precisely position the interface. Efficiency may also be improved by reducing the sampling in the sediment and in an absorbing layer that is used to truncate the computational domain. Nonuniform sampling may also be used to improve the implementation of a single-scattering approximation for sloping fluid-solid interfaces. PMID:23556565

  2. Transparent boundary conditions for iterative high-order parabolic equations

    NASA Astrophysics Data System (ADS)

    Petrov, P. S.; Ehrhardt, M.

    2016-05-01

    Recently a new approach to the construction of high-order parabolic approximations for the Helmholtz equation was developed. These approximations have the form of the system of iterative parabolic equations, where the solution of the n-th equation is used as an input term for the (n + 1)-th equation. In this study the transparent boundary conditions for such systems of coupled parabolic equations are derived. The existence and uniqueness of the solution of the initial boundary value problem for the system of iterative parabolic equations with the derived boundary conditions are proved. The well-posedness of this problem is also established and an unconditionally stable finite difference scheme for its solution is proposed.

  3. The symmetry of least-energy solutions for semilinear elliptic equations

    NASA Astrophysics Data System (ADS)

    Chern, Jann-Long; Lin, Chang-Shou

    In this paper we will apply the method of rotating planes (MRP) to investigate the radial and axial symmetry of the least-energy solutions for semilinear elliptic equations on the Dirichlet and Neumann problems, respectively. MRP is a variant of the famous method of moving planes. One of our main results is to consider the least-energy solutions of the following equation: Δu+K(x)u p=0, x∈B 1, u>0 in B 1, u| ∂B 1=0, where 1

  4. Special functions arising in the study of semi-linear equations in circular domains

    NASA Astrophysics Data System (ADS)

    Varlamov, Vladimir

    2007-05-01

    Rayleigh functions are defined by the formulawhere are zeros of the Bessel function J[nu](x) and n=1,2,3,..., is the number of the zero. These functions appear in the classical problems of vibrating circular membranes, heat conduction in cylinders and diffraction through circular apertures. In the present paper it is shown that a new family of special functions, convolutions of Rayleigh functions with respect to the Bessel index,arises in constructing solutions of semi-linear evolution equations in circular domains (see also [V. Varlamov, Convolution of Rayleigh functions with respect to the Bessel index, J. Math. Anal. Appl. 306 (2005) 413-424]). As an example of its application a forced Cahn-Hilliard equation is considered in a unit disc with homogeneous boundary and initial conditions. Construction of its global-in-time solutions involves the use of R1(m) and R2(m). A general representation of Rl(m) is deduced and on the basis of that a particular result for R2(m) is obtained convenient for computing its asymptotics as m-->[infinity]. The latter issue is important for establishing a function space to which a solution of the corresponding problem belongs.

  5. Spherical harmonics approach to parabolic partial differential equations

    NASA Astrophysics Data System (ADS)

    SenGupta, Indranil; Mariani, Maria C.

    2012-12-01

    This paper is devoted to extend the spherical harmonics technique to the solution of parabolic differential equations and to integro-differential equations. The heat equation and the Black-Scholes equation are solved by using the method of spherical harmonics.

  6. Generalization of the rotated parabolic equation to variable slopes.

    PubMed

    Outing, Donald A; Siegmann, William L; Collins, Michael D; Westwood, Evan K

    2006-12-01

    The rotated parabolic equation [J. Acoust. Soc. Am. 87, 1035-1037 (1990)] is generalized to problems involving ocean-sediment interfaces of variable slope. The approach is based on approximating a variable slope in terms of a series of constant slope regions. The original rotated parabolic equation algorithm is used to march the field through each region. An interpolation-extrapolation approach is used to generate a starting field at the beginning of each region beyond the one containing the source. For the elastic case, a series of operators is applied to rotate the dependent variable vector along with the coordinate system. The variable rotated parabolic equation should provide accurate solutions to a large class of range-dependent seismo-acoustics problems. For the fluid case, the accuracy of the approach is confirmed through comparisons with reference solutions. For the elastic case, variable rotated parabolic equation solutions are compared with energy-conserving and mapping solutions. PMID:17225384

  7. Global and blowup solutions of a mixed problem with nonlinear boundary conditions for a one-dimensional semilinear wave equation

    SciTech Connect

    Kharibegashvili, S. S.; Jokhadze, O. M. E-mail: ojokhadze@yahoo.com

    2014-04-30

    A mixed problem for a one-dimensional semilinear wave equation with nonlinear boundary conditions is considered. Conditions of this type occur, for example, in the description of the longitudinal oscillations of a spring fastened elastically at one end, but not in accordance with Hooke's linear law. Uniqueness and existence questions are investigated for global and blowup solutions to this problem, in particular how they depend on the nature of the nonlinearities involved in the equation and the boundary conditions. Bibliography: 14 titles. (paper)

  8. Finite-difference methods for solving loaded parabolic equations

    NASA Astrophysics Data System (ADS)

    Abdullayev, V. M.; Aida-zade, K. R.

    2016-01-01

    Loaded partial differential equations are solved numerically. For illustrative purposes, a boundary value problem for a parabolic equation with various point loads is considered. By applying difference approximations, the problems are reduced to systems of algebraic equations of special structure, which are solved using a parametric representation involving solutions of auxiliary linear systems with tridiagonal matrices. Numerical results are presented and analyzed.

  9. Extension of Euler’s method to parabolic equations

    NASA Astrophysics Data System (ADS)

    Ibragimov, N. H.

    2009-04-01

    Euler generalized d'Alembert's solution to a wide class of linear hyperbolic equations with two independent variables. He introduced in 1769 the quantities that were rediscovered by Laplace in 1773 and became known as the Laplace invariants. The present paper is devoted to an extension of Euler's method to linear parabolic equations with two independent variables. The new method allows one to derive an explicit formula for the general solution of a wide class of parabolic equations. In particular, the general solution of the Black-Scholes equation is obtained.

  10. On the parallel solution of parabolic equations

    NASA Technical Reports Server (NTRS)

    Gallopoulos, E.; Saad, Youcef

    1989-01-01

    Parallel algorithms for the solution of linear parabolic problems are proposed. The first of these methods is based on using polynomial approximation to the exponential. It does not require solving any linear systems and is highly parallelizable. The two other methods proposed are based on Pade and Chebyshev approximations to the matrix exponential. The parallelization of these methods is achieved by using partial fraction decomposition techniques to solve the resulting systems and thus offers the potential for increased time parallelism in time dependent problems. Experimental results from the Alliant FX/8 and the Cray Y-MP/832 vector multiprocessors are also presented.

  11. Real-time optical laboratory solution of parabolic differential equations

    NASA Technical Reports Server (NTRS)

    Casasent, David; Jackson, James

    1988-01-01

    An optical laboratory matrix-vector processor is used to solve parabolic differential equations (the transient diffusion equation with two space variables and time) by an explicit algorithm. This includes optical matrix-vector nonbase-2 encoded laboratory data, the combination of nonbase-2 and frequency-multiplexed data on such processors, a high-accuracy optical laboratory solution of a partial differential equation, new data partitioning techniques, and a discussion of a multiprocessor optical matrix-vector architecture.

  12. Anisotropic uniqueness classes for a degenerate parabolic equation

    SciTech Connect

    Vil'danova, V F; Mukminov, F Kh

    2013-11-30

    Anisotropic uniqueness classes of Tacklind type are identified for a degenerate linear parabolic equation of the second order in an unbounded domain. The Cauchy problem and mixed problems with boundary conditions of the first and third type are considered. Bibliography: 18 titles.

  13. Accuracy-based time step criteria for solving parabolic equations

    SciTech Connect

    Mohtar, R.; Segerlind, L.

    1995-12-31

    Parabolic equations govern many transient engineering problems. Space integration using finite element or finite difference methods changes the parabolic partial differential equation into an ordinary differential equation. Time integration schemes are needed to solve the later equation. In order to accurately perform the later integration a proper time step must be provided. Time step estimates based on a stability criteria have been prescribed in the literature. The following paper presents time step estimates that satisfy stability as well as accuracy criteria. These estimates were correlated to the Froude and Courant Numbers. The later criteria were found to be overly conservative for some integration schemes. Suggestions as to which time integration scheme is the best to use are also presented.

  14. H-measures and variants applied to parabolic equations

    NASA Astrophysics Data System (ADS)

    Antonic, Nenad; Lazar, Martin

    2008-07-01

    Since their introduction H-measures have been mostly used in problems related to propagation effects for hyperbolic equations and systems. In this study we give an attempt to apply the H-measure theory to other types of equations. Through a number of examples we present how do the differences between parabolic and hyperbolic equations reflect in the properties of H-measures corresponding to the solutions. Secondly, we apply the H-measures to the Schrödinger equation, where we succeed in proving a propagation property. However, our conclusion is that a variant of H-measures should be sought which would be better suited to parabolic problems. We propose such a variant, show some fundamental properties and illustrate its applicability by some examples. In particular, we show that the variant provides new information in a number of situations where the original H-measures did not. Finally, we describe how the new variant can be used in small amplitude homogenisation of parabolic equations.

  15. Complicated dynamics in scalar semilinear parabolic equations in higher space dimension

    NASA Astrophysics Data System (ADS)

    Poláčik, Peter

    We study the dynamics of the boundary value problem ut - Lu = g( x, u, ▽ u), x ɛ Ω, (1) u ¦ ∂Ω = 0 , (2) where L is a second order uniformly elliptic operator and Ω ⊂ R N is diffeomorphic to the ball in R N, N⩾2. The main result asserts that given any C k-vector field V on R N+1 with V(0) = 0 one can adjust coefficients of L and the function g such that the corresponding problem (1), (2) has an N+ 1-dimensional invariant manifold through the equilibrium u ≡ 0 and the Taylor expansion at u ≡ 0 of the vector field representing the flow on this manifold coincides (in appropriate coordinates) with the Taylor expansion of V, up to k-th order terms. This result implies that a hyperbolic invariant N-torus can be found in (1), (2) (if L and g are appropriately chosen). This result also indicates that "chaotic dynamics" is likely to occur for some choices of L and g.

  16. Singular parabolic equations of second order on manifolds with singularities

    NASA Astrophysics Data System (ADS)

    Shao, Yuanzhen

    2016-01-01

    The main aim of this article is to establish an Lp-theory for elliptic operators on manifolds with singularities. The particular class of differential operators discussed herein may exhibit degenerate or singular behavior near the singular ends of the manifolds. Such a theory is of importance for the study of elliptic and parabolic equations on non-compact, or even incomplete manifolds, with or without boundary.

  17. Approximations of optimal control problems for semilinear elliptic equations with discontinuous coefficients and states and with controls in the coefficients multiplying the highest derivatives

    NASA Astrophysics Data System (ADS)

    Lubyshev, F. V.; Fairuzov, M. E.

    2016-07-01

    Mathematical formulations of nonlinear optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions and with controls in the coefficients multiplying the highest derivatives are studied. Finite difference approximations of optimization problems are constructed, and the approximation error is estimated with respect to the state and the cost functional. Weak convergence of the approximations with respect to the control is proved. The approximations are regularized in the sense of Tikhonov.

  18. Cauchy problems of pseudo-parabolic equations with inhomogeneous terms

    NASA Astrophysics Data System (ADS)

    Li, Zhongping; Du, Wanjuan

    2015-12-01

    This paper deals with Cauchy problems of pseudo-parabolic equations with inhomogeneous terms. The aim of the paper is to study the influence of the inhomogeneous term on the asymptotic behavior of solutions. We at first determine the critical Fujita exponent and then give the secondary critical exponent on the decay asymptotic behavior of an initial value at infinity. Furthermore, the precise estimate of life span for the blow-up solution is obtained. Our results show that the asymptotic behavior of solutions is seriously affected by the inhomogeneous term.

  19. 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. PMID:21643384

  20. Nonlocal operators, parabolic-type equations, and ultrametric random walks

    SciTech Connect

    Chacón-Cortes, L. F. Zúñiga-Galindo, W. A.

    2013-11-15

    In this article, we introduce a new type of nonlocal operators and study the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators. Some of these equations are the p-adic master equations of certain models of complex systems introduced by Avetisov, V. A. and Bikulov, A. Kh., “On the ultrametricity of the fluctuation dynamicmobility of protein molecules,” Proc. Steklov Inst. Math. 265(1), 75–81 (2009) [Tr. Mat. Inst. Steklova 265, 82–89 (2009) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Zubarev, A. P., “First passage time distribution and the number of returns for ultrametric random walks,” J. Phys. A 42(8), 085003 (2009); Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic models of ultrametric diffusion in the conformational dynamics of macromolecules,” Proc. Steklov Inst. Math. 245(2), 48–57 (2004) [Tr. Mat. Inst. Steklova 245, 55–64 (2004) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic description of characteristic relaxation in complex systems,” J. Phys. A 36(15), 4239–4246 (2003); Avetisov, V. A., Bikulov, A. H., Kozyrev, S. V., and Osipov, V. A., “p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes,” J. Phys. A 35(2), 177–189 (2002); Avetisov, V. A., Bikulov, A. Kh., and Kozyrev, S. V., “Description of logarithmic relaxation by a model of a hierarchical random walk,” Dokl. Akad. Nauk 368(2), 164–167 (1999) (in Russian). The fundamental solutions of these parabolic-type equations are transition functions of random walks on the n-dimensional vector space over the field of p-adic numbers. We study some properties of these random walks, including the first passage time.

  1. On the complex structures of the Biswas-Milovic equation for power, parabolic and dual parabolic law nonlinearities

    NASA Astrophysics Data System (ADS)

    Manafian, Jalil

    2015-12-01

    We apply the Exp-function method (EFM) to the Biswas-Milovic equation and derive the exact solutions. This paper studies the Biswas-Milovic equation with power law, parabolic law and dual parabolic law nonlinearities by the aid of the Exp-function method. The obtained solutions not only constitute a novel analytical viewpoint in nonlinear complex phenomena, but they also form a new stand alone basis from which physical applications in this arena can be comprehended further, and, moreover, investigated. Furthermore, to concretely enrich this research production, we explain all cases, namely m=1 and m≥ 2. This method is developed for searching exact travelling-wave solutions of nonlinear partial differential equations. It is shown that this methods, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear partial differential equations in mathematical physics.

  2. A Parabolic Equation Approach to Modeling Acousto-Gravity Waves for Local Helioseismology

    NASA Astrophysics Data System (ADS)

    Del Bene, Kevin; Lingevitch, Joseph; Doschek, George

    2016-08-01

    A wide-angle parabolic-wave-equation algorithm is developed and validated for local-helioseismic wave propagation. The parabolic equation is derived from a factorization of the linearized acousto-gravity wave equation. We apply the parabolic-wave equation to modeling acoustic propagation in a plane-parallel waveguide with physical properties derived from helioseismic data. The wavenumber power spectrum and wave-packet arrival-time structure for receivers in the photosphere with separation up to 30° is computed, and good agreement is demonstrated with measured values and a reference spectral model.

  3. A Parabolic Equation Approach to Modeling Acousto-Gravity Waves for Local Helioseismology

    NASA Astrophysics Data System (ADS)

    Del Bene, Kevin; Lingevitch, Joseph; Doschek, George

    2016-07-01

    A wide-angle parabolic-wave-equation algorithm is developed and validated for local-helioseismic wave propagation. The parabolic equation is derived from a factorization of the linearized acousto-gravity wave equation. We apply the parabolic-wave equation to modeling acoustic propagation in a plane-parallel waveguide with physical properties derived from helioseismic data. The wavenumber power spectrum and wave-packet arrival-time structure for receivers in the photosphere with separation up to 30° is computed, and good agreement is demonstrated with measured values and a reference spectral model.

  4. Boundedness for the general semilinear Duffing equations via the twist theorem

    NASA Astrophysics Data System (ADS)

    Jiao, Lei; Piao, Daxiong; Wang, Yiqian

    In this paper, we prove the boundedness of all solutions for the periodic equation x+ωx+ϕ(x)=G(x,t)+p(t), where ω satisfies the Diophantine condition, ϕ(x)∈C is bounded, p(t)∈C and DxiDtjG(x,t) is bounded for 0⩽i+j⩽21.

  5. Three-dimensional parabolic equation modeling of mesoscale eddy deflection.

    PubMed

    Heaney, Kevin D; Campbell, Richard L

    2016-02-01

    The impact of mesoscale oceanography, including ocean fronts and eddies, on global scale low-frequency acoustics is examined using a fully three-dimensional parabolic equation model. The narrowband acoustic signal, for frequencies from 2 to 16 Hz, is simulated from a seismic event on the Kerguellen Plateau in the South Indian Ocean to an array of receivers south of Ascension Island in the South Atlantic, a distance of 9100 km. The path was chosen for its relevance to seismic detections from the HA10 Ascension Island station of the International Monitoring System, for its lack of bathymetric interaction, and for the dynamic oceanography encountered as the sound passes the Cape of Good Hope. The acoustic field was propagated through two years (1992 and 1993) of the eddy-permitting ocean state estimation ECCO2 (Estimating the Circulation and Climate of the Ocean, Phase II) system. The range of deflection of the back-azimuth was 1.8° with a root-mean-square of 0.34°. The refraction due to mesoscale oceanography could therefore have significant impacts upon localization of distant low-frequency sources, such as seismic or nuclear test events. PMID:26936572

  6. Improved algorithm for solving nonlinear parabolized stability equations

    NASA Astrophysics Data System (ADS)

    Zhao, Lei; Zhang, Cun-bo; Liu, Jian-xin; Luo, Ji-sheng

    2016-08-01

    Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. Project supported by the National Natural Science Foundation of China (Grant Nos. 11332007 and 11402167).

  7. Efficient solution of parabolic equations by Krylov approximation methods

    NASA Technical Reports Server (NTRS)

    Gallopoulos, E.; Saad, Y.

    1990-01-01

    Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

  8. Variation of the orbital elements for parabolic trajectories due to a small impulse using Gauss equations

    NASA Astrophysics Data System (ADS)

    Kamel, Osman M.; Ammar, M. K.

    2006-12-01

    Firstly we derive Gauss' perturbation equation for parabolic motion using Murray-Dermott and Kovalevsky procedures. Secondly, we easily deduce the variations of the orbital elements for the parabolic trajectories due to a small impulse at any point along the path and at the vertex of the parabola.

  9. Solutions for semilinear elliptic equations with critical exponents and Hardy potential

    NASA Astrophysics Data System (ADS)

    Cao, Daomin; Han, Pigong

    In this paper, we answer affirmatively an open problem (cf. Theorem 4' in Ferrero and Gazzola (J. Differential Equations 177 (2001) 494): Let Ω∋0 be an open-bounded domain, Ω⊂R N(N⩾5) and assume that 0⩽μ<( {N-2}/{2}) 2-( {N+2}/{N}) 2, then, for all λ>0 there exists a nontrivial solution with critical level in the range (0, {1}/{N}S μ{N}/{2}) for the problem -Δu-μ {u}/{|x| 2}=λu+|u| 2 ∗-2 u in Ω; u=0 on ∂Ω.

  10. Global existence for semilinear wave equations with the critical blow-up term in high dimensions

    NASA Astrophysics Data System (ADS)

    Takamura, Hiroyuki; Wakasa, Kyouhei

    2016-07-01

    We are interested in almost global existence cases in the general theory for nonlinear wave equations, which are caused by critical exponents of nonlinear terms. Such situations can be found in only three cases in the theory, cubic terms in two space dimensions, quadratic terms in three space dimensions and quadratic terms including a square of unknown functions itself in four space dimensions. Except for the last case, criteria to classify nonlinear terms into the almost global, or global existence case, are well-studied and known to be so-called null condition and non-positive condition. Our motivation of this work is to find such a kind of the criterion in four space dimensions. In our previous paper, an example of the non-single term for the almost global existence case is introduced. In this paper, we show an example of the global existence case. These two examples have nonlinear integral terms which are closely related to derivative loss due to high dimensions. But it may help us to describe the final form of the criterion.

  11. On a regular problem for an elliptic-parabolic equation with a potential boundary condition

    NASA Astrophysics Data System (ADS)

    Arepova, Gauhar

    2016-08-01

    In this paper, we construct a lateral boundary condition for an elliptic-parabolic equation in a finite domain. Theorem on existence and uniqueness of a solution of the considered problem is proved by method of theory potential.

  12. Two parabolic equations for propagation in layered poro-elastic media.

    PubMed

    Metzler, Adam M; Siegmann, William L; Collins, Michael D; Collis, Jon M

    2013-07-01

    Parabolic equation methods for fluid and elastic media are extended to layered poro-elastic media, including some shallow-water sediments. A previous parabolic equation solution for one model of range-independent poro-elastic media [Collins et al., J. Acoust. Soc. Am. 98, 1645-1656 (1995)] does not produce accurate solutions for environments with multiple poro-elastic layers. First, a dependent-variable formulation for parabolic equations used with elastic media is generalized to layered poro-elastic media. An improvement in accuracy is obtained using a second dependent-variable formulation that conserves dependent variables across interfaces between horizontally stratified layers. Furthermore, this formulation expresses conditions at interfaces using no depth derivatives higher than first order. This feature should aid in treating range dependence because convenient matching across interfaces is possible with discretized derivatives of first order in contrast to second order. PMID:23862802

  13. Parabolic equation solution of seismo-acoustics problems involving variations in bathymetry and sediment thickness.

    PubMed

    Collis, Jon M; Siegmann, William L; Jensen, Finn B; Zampolli, Mario; Küsel, Elizabeth T; Collins, Michael D

    2008-01-01

    Recent improvements in the parabolic equation method are combined to extend this approach to a larger class of seismo-acoustics problems. The variable rotated parabolic equation [J. Acoust. Soc. Am. 120, 3534-3538 (2006)] handles a sloping fluid-solid interface at the ocean bottom. The single-scattering solution [J. Acoust. Soc. Am. 121, 808-813 (2007)] handles range dependence within elastic sediment layers. When these methods are implemented together, the parabolic equation method can be applied to problems involving variations in bathymetry and the thickness of sediment layers. The accuracy of the approach is demonstrated by comparing with finite-element solutions. The approach is applied to a complex scenario in a realistic environment. PMID:18177137

  14. A method for the spatial discretization of parabolic equations in one space variable

    SciTech Connect

    Skeel, R.D.; Berzins, M.

    1987-02-01

    The aim of this paper is to describe and analyze a new spatial discretization method for parabolic equations in one space variable: Ordinary and parabolic partial differential equations in one space variable x often have a singularity due to the use of polar cylindrical or spherical coordinates. The method we propose is a simple piecewise nonlinear Galerkin/Petrov-Galerkin method which is second order accurate in space. (It supersedes the method proposed by Skeel). The case m = 1 involves the use of the logarithm function, which is probably the only accurate way to model the logarithmic singularity present in the solution. A code based on a variant of the proposed method has already been included as part of the SPRINT package of Berzins, Dew, and Furzeland. The method that we propose here will be distributed in the next release of the D03P (parabolic equations) section of the NAG Library. 18 refs.

  15. The solvability of the first initial-boundary problem for parabolic and degenerate parabolic equations in domains with a conical point

    SciTech Connect

    Degtyarev, Sergey P

    2010-09-02

    The first initial-boundary problem for second-order parabolic and degenerate parabolic equations is investigated in a domain with a conical or angular point. The means of attack is already known and uses weighted classes of smooth or integrable functions. Sufficient conditions for a unique solution to exist and for coercive estimates for the solution to be obtained are formulated in terms of the angular measure of the solid angle and the exponent of the weight. It is also shown that if these conditions fail to hold, then the parabolic problem has elliptic properties, that is, it can have a nonzero kernel or can be nonsolvable, and, in the latter case, it is not even a Fredholm problem. A parabolic equation and an equation with some degeneracy or a singularity at a conical point are considered. Bibliography: 49 titles.

  16. Numerical solution of the stochastic parabolic equation with the dependent operator coefficient

    SciTech Connect

    Ashyralyev, Allaberen; Okur, Ulker

    2015-09-18

    In the present paper, a single step implicit difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is presented. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, this abstract result permits us to obtain the convergence estimates for the solution of difference schemes for the numerical solution of initial boundary value problems for parabolic equations. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments.

  17. About one special boundary value problem for multidimensional parabolic integro-differential equation

    NASA Astrophysics Data System (ADS)

    Khairullin, Ermek

    2016-08-01

    In this paper we consider a special boundary value problem for multidimensional parabolic integro-differential equation with boundary conditions that contains as a boundary condition containing derivatives of order higher than the order of the equation. The solution is sought in the form of a thermal potential of a double layer. Shows lemma of finding the limits of the derivatives of the unknown function in the neighborhood of the hyperplane. Using the boundary condition and lemma obtained integral-differential equation (IDE) of parabolic operators, whĐţre an unknown function under the integral contains higher-order space variables derivatives. IDE is reduced to a singular integral equation (SIE), when an unknown function in the spatial variables satisfies the Holder. The characteristic part is solved in the class of distribution function using method of transformation of Fourier-Laplace. Found an algebraic condition for the transition to the classical generalized solution. Integral equation of the resolvent for the characteristic part of SIE is obtained. Integro-differential equation is reduced to the Volterra-Fredholm type integral equation of the second kind by method of regularization. It is shown that the solution of SIE is a solution of IDE. Obtain a theorem on the solvability of the boundary value problem of multidimensional parabolic integro-differential equation, when a known function of the spatial variables belongs to the Holder class and satisfies the solvability conditions.

  18. Analysis of the linear stability of compressible boundary layers using the PSE. [parabolic stability equations

    NASA Technical Reports Server (NTRS)

    Bertolotti, F. P.; Herbert, TH.

    1991-01-01

    The application of linearized parabolic stability equations (PSE) to compressible flow is considered. The effect of mean-flow nonparallelism is found to be weak on 2D waves and strong on 3D waves. Results for a single choice of free-stream parameters that corresponds to the atmospheric conditions at 15,000 m above sea level are presented.

  19. Role of secondary instability theory and parabolized stability equations in transition modeling

    NASA Technical Reports Server (NTRS)

    El-Hady, Nabil M.; Dinavahi, Surya P.; Chang, Chau-Lyan; Zang, Thomas A.

    1993-01-01

    In modeling the laminar-turbulent transition region, the designer depends largely on benchmark data from experiments and/or direct numerical simulations that are usually extremely expensive. An understanding of the evolution of the Reynolds stresses, turbulent kinetic energy, and quantifies in the transport equations like the dissipation and production is essential in the modeling process. The secondary instability theory and the parabolized stability equations method are used to calculate these quantities, which are then compared with corresponding quantities calculated from available direct numerical simulation data for the incompressible boundary-layer flow of laminar-turbulent transition conditions. The potential of the secondary instability theory and the parabolized stability equations approach in predicting these quantities is discussed; results indicate that inexpensive data that are useful for transition modeling in the early stages of the transition region can be provided by these tools.

  20. Numerical study of finite-rate supersonic combustion using parabolized equations

    NASA Technical Reports Server (NTRS)

    Chitsomboon, T.; Kumar, A.; Tiwari, S. N.

    1987-01-01

    A set of partial differential equations, describing the two-dimensional supersonic chemically-reacting flow of the hydrogen-air system, is formulated such that the equations are parabolic in the streamwise direction. A fully-implicit fully-coupled finite-difference algorithm is used to develop a computer code which solves the governing equations by marching in the streamwise direction. The combustion process is modeled by a two-step finite-rate chemistry whereas turbulence is simulated by an algebraic turbulence model. Results of two calculations of internal supersonic reacting flow show fairly good agreement with the results obtained by the more costly full Navier-Stokes procedure.

  1. A modified dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

    NASA Technical Reports Server (NTRS)

    Cooke, C. H.

    1981-01-01

    A revised version of a split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three-dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard successive overrelaxation iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition.

  2. Oscillations of solutions of vector differential equations of parabolic type with functional arguments

    NASA Astrophysics Data System (ADS)

    Minchev, Emil; Yoshida, Norio

    2003-02-01

    Vector parabolic differential equations with functional arguments are studied and the oscillations of solutions of boundary value problems are investigated. Our approach is to reduce the oscillation problems to the nonexistence of positive solutions of scalar differential inequalities by employing the concept of H-oscillation introduced by Domslak (see: R. Courant, D. Hilbert, Methods of Mathematical Physics, Vol. I, Interscience, New York, 1996), where H denotes a unit vector.

  3. Numerical study of hydrogen-air supersonic combustion by using elliptic and parabolized equations

    NASA Technical Reports Server (NTRS)

    Chitsomboon, T.; Tiwari, S. N.

    1986-01-01

    The two-dimensional Navier-Stokes and species continuity equations are used to investigate supersonic chemically reacting flow problems which are related to scramjet-engine configurations. A global two-step finite-rate chemistry model is employed to represent the hydrogen-air combustion in the flow. An algebraic turbulent model is adopted for turbulent flow calculations. The explicit unsplit MacCormack finite-difference algorithm is used to develop a computer program suitable for a vector processing computer. The computer program developed is then used to integrate the system of the governing equations in time until convergence is attained. The chemistry source terms in the species continuity equations are evaluated implicitly to alleviate stiffness associated with fast chemical reactions. The problems solved by the elliptic code are re-investigated by using a set of two-dimensional parabolized Navier-Stokes and species equations. A linearized fully-coupled fully-implicit finite difference algorithm is used to develop a second computer code which solves the governing equations by marching in spce rather than time, resulting in a considerable saving in computer resources. Results obtained by using the parabolized formulation are compared with the results obtained by using the fully-elliptic equations. The comparisons indicate fairly good agreement of the results of the two formulations.

  4. A nonlinear parabolic equation with discontinuity in the highest order and applications

    NASA Astrophysics Data System (ADS)

    Chen, Robin Ming; Liu, Qing

    2016-01-01

    In this paper we establish a viscosity solution theory for a class of nonlinear parabolic equations with discontinuities of the sign function type in the second derivatives of the unknown function. We modify the definition of classical viscosity solutions and show uniqueness and existence of the solutions. These results are related to the limit behavior for the motion of a curve by a very small power of its curvature, which has applications in image processing. We also discuss the relation between our equation and the total variation flow in one space dimension.

  5. Parabolic orbit determination. Comparison of the Olbers method and algebraic equations

    NASA Astrophysics Data System (ADS)

    Kuznetsov, V. B.

    2016-05-01

    In this paper, the Olbers method for the preliminary parabolic orbit determination (in the Lagrange-Subbotin modification) and the method based on systems of algebraic equations for two or three variables proposed by the author are compared. The maximum number of possible solutions is estimated. The problem of selection of the true solution from the set of solutions obtained both using additional equations and by the problem reduction to finding the objective function minimum is considered. The results of orbit determination of the comets 153P/Ikeya-Zhang and 2007 N3 Lulin are cited as examples.

  6. Galerkin/Runge-Kutta discretizations for parabolic equations with time-dependent coefficients

    NASA Technical Reports Server (NTRS)

    Keeling, Stephen L.

    1989-01-01

    A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients. Unlike any classical counterpart, this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction. In support of this claim, error estimates are proved, and computational results are presented. Additionally, since the time stepping equations involve coefficient matrices changing at each time step, a preconditioned iterative technique is used to solve the linear systems only approximately. Nevertheless, the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

  7. Galerkin/Runge-Kutta discretizations for parabolic equations with time dependent coefficients

    NASA Technical Reports Server (NTRS)

    Keeling, Stephen L.

    1987-01-01

    A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients. Unlike any classical counterpart, this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction. In support of this claim, error estimates are proved, and computational results are presented. Additionally, since the time stepping equations involve coefficient matrices changing at each time step, a preconditioned iterative technique is used to solve the linear systems only approximately. Nevertheless, the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

  8. Parabolic equation formulation via a singular perturbation technique and its application to scattering from irregular surfaces

    NASA Astrophysics Data System (ADS)

    Awadallah, Ra'id S.; Brown, Gary S.

    1998-07-01

    This paper consists of two parts. In the first part, the solution of the Helmholtz equation under forward-scattering or propagation conditions is sought as a uniform asymptotic perturbation expansion using the method of multiple scales. It is then shown that the parabolic wave equation (PWE) solution is the zeroth-order term in this expansion. In the second part, the electric-field integral equation and the magnetic-field integral equation, derived under the PWE approximation, are solved for surface currents induced on a sinusoidal surface. The scattered fields produced by these currents are then calculated using the appropriate radiation integrals. Results are compared to those obtained using the method of ordered multiple interactions developed by Kapp and Brown.

  9. Application of the implicit MacCormack scheme to the parabolized Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Lawrence, J. L.; Tannehill, J. C.; Chaussee, D. S.

    1984-01-01

    MacCormack's implicit finite-difference scheme was used to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method for solving the PNS equations does not require the inversion of block tridiagonal systems of algebraic equations and permits the original explicit MacCormack scheme to be employed in those regions where implicit treatment is not needed. The advantages and disadvantages of the present adaptation are discussed in relation to those of the conventional Beam-Warming scheme for a flat plate boundary layer test case. Comparisons are made for accuracy, stability, computer time, computer storage, and ease of implementation. The present method was also applied to a second test case of hypersonic laminar flow over a 15% compression corner. The computed results compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.

  10. Recovering a coefficient in a parabolic equation using an iterative approach

    NASA Astrophysics Data System (ADS)

    Azhibekova, Aliya S.

    2016-06-01

    In this paper we are concerned with the problem of determining a coefficient in a parabolic equation using an iterative approach. We investigate an inverse coefficient problem in the difference form. To recover the coefficient, we minimize a residual functional between the observed and calculated values. This is done in a constructive way by fitting a finite-difference approximation to the inverse problem. We obtain some theoretical estimates for a direct and adjoint problem. Using these estimates we prove monotonicity of the objective functional and the convergence of iteration sequences.

  11. Stabilization of the solution of a doubly nonlinear parabolic equation

    SciTech Connect

    Andriyanova, È R; Mukminov, F Kh

    2013-09-30

    The method of Galerkin approximations is employed to prove the existence of a strong global (in time) solution of a doubly nonlinear parabolic equation in an unbounded domain. The second integral identity is established for Galerkin approximations, and passing to the limit in it an estimate for the decay rate of the norm of the solution from below is obtained. The estimates characterizing the decay rate of the solution as x→∞ obtained here are used to derive an upper bound for the decay rate of the solution with respect to time; the resulting estimate is pretty close to the lower one. Bibliography: 17 titles.

  12. Solutions to a degenerate system of parabolic equations from marine biology.

    PubMed

    Wörz-Busekros, A

    1976-11-25

    A system of parabolic and ordinary differential equations ut = a2 uxx + F(u,v,w), vt = a2 vxx + G(u,v,w), wx = -k(u) w is studied which has been proposed by Radach and Maier-Reimer for the dynamics of phytoplankton and nutrient in dependence of light intensity. It is shown that there is a unique solution to this system satisfying given initial and boundary conditions. The solution depends continuously on the data. For specific nonlinearities F, G, and k bounds for the solutions are given. PMID:1022838

  13. ON THE PIECEWISE PARABOLIC METHOD FOR COMPRESSIBLE FLOW WITH STELLAR EQUATIONS OF STATE

    SciTech Connect

    Zingale, Michael; Katz, Max P.

    2015-02-01

    The piecewise parabolic method and related schemes are widely used to model stellar flows. Several different methods for extending the validity of these methods to a general equation of state (EOS) have been proposed over time, but direct comparisons among one-another and exact solutions with stellar EOSs are not widely available. We introduce some simple test problems with exact solutions run with a popular stellar EOS and test how two existing codes with different approaches to incorporating general gases perform. The source code for generating the exact solutions is made available.

  14. Noniterative three-dimensional grid generation using parabolic partial differential equations

    NASA Technical Reports Server (NTRS)

    Edwards, T. A.

    1985-01-01

    A new algorithm for generating three-dimensional grids has been developed and implemented which numerically solves a parabolic partial differential equation (PDE). The solution procedure marches outward in two coordinate directions, and requires inversion of a scalar tridiagonal system in the third. Source terms have been introduced to control the spacing and angle of grid lines near the grid boundaries, and to control the outer boundary point distribution. The method has been found to generate grids about 100 times faster than comparable grids generated via solution of elliptic PDEs, and produces smooth grids for finite-difference flow calculations.

  15. A modified Dodge algorithm for the parabolized Navier-Stokes equation and compressible duct flows

    NASA Technical Reports Server (NTRS)

    Cooke, C. H.

    1981-01-01

    A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitive agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions.

  16. A modified Dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

    NASA Technical Reports Server (NTRS)

    Cooke, C. H.; Dwoyer, D. M.

    1983-01-01

    A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitative agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions. Previously announced in STAR as N82-16363

  17. Sound propagation in a turbulent atmosphere near the ground: a parabolic equation approach.

    PubMed

    Ostashev, V E; Salomons, E M; Clifford, S F; Lataitis, R J; Wilson, D K; Blanc-Benon, P; Juvé, D

    2001-05-01

    The interference of the direct wave from the point source to the receiver and the wave reflected from the impedance ground in a turbulent atmosphere is studied. A parabolic equation approach for calculating the sound pressure p at the receiver is formulated. Then, the parabolic equation is solved by the Rytov method yielding expressions for the complex phases of direct and ground-reflected waves. Using these expressions, a formula for the mean squared sound pressure [absolute value(p)2] is derived for the case of anisotropic spectra of temperature and wind velocity fluctuations. This formula contains the "coherence factor," which characterizes the coherence between direct and ground-reflected waves. It is shown that the coherence factor is equal to the normalized coherence function of a spherical sound wave for line-of-sight propagation. For the case of isotropic turbulence, this result allows one to obtain analytical formulas for [absolute value(p)2] for the Kolmogorov, Gaussian, and von Karman spectra of temperature and wind velocity fluctuations. Using these formulas, the effects of temperature and wind velocity fluctuations, and the effects of different spectra of these fluctuations on the mean squared sound pressure, are numerically studied. Also the effect of turbulent anisotropy on the interference of direct and ground reflected waves is numerically studied. Finally, it is shown that the mean squared sound pressure [absolute value(p)2] calculated for the von Karman spectrum of temperature fluctuations agrees well with experimental data obtained in a laboratory experiment. PMID:11386544

  18. Elastic parabolic equation solutions for oceanic T-wave generation and propagation from deep seismic sources.

    PubMed

    Frank, Scott D; Collis, Jon M; Odom, Robert I

    2015-06-01

    Oceanic T-waves are earthquake signals that originate when elastic waves interact with the fluid-elastic interface at the ocean bottom and are converted to acoustic waves in the ocean. These waves propagate long distances in the Sound Fixing and Ranging (SOFAR) channel and tend to be the largest observed arrivals from seismic events. Thus, an understanding of their generation is important for event detection, localization, and source-type discrimination. Recently benchmarked seismic self-starting fields are used to generate elastic parabolic equation solutions that demonstrate generation and propagation of oceanic T-waves in range-dependent underwater acoustic environments. Both downward sloping and abyssal ocean range-dependent environments are considered, and results demonstrate conversion of elastic waves into water-borne oceanic T-waves. Examples demonstrating long-range broadband T-wave propagation in range-dependent environments are shown. These results confirm that elastic parabolic equation solutions are valuable for characterization of the relationships between T-wave propagation and variations in range-dependent bathymetry or elastic material parameters, as well as for modeling T-wave receptions at hydrophone arrays or coastal receiving stations. PMID:26093440

  19. Elastic parabolic equation solutions for underwater acoustic problems using seismic sources.

    PubMed

    Frank, Scott D; Odom, Robert I; Collis, Jon M

    2013-03-01

    Several problems of current interest involve elastic bottom range-dependent ocean environments with buried or earthquake-type sources, specifically oceanic T-wave propagation studies and interface wave related analyses. Additionally, observed deep shadow-zone arrivals are not predicted by ray theoretic methods, and attempts to model them with fluid-bottom parabolic equation solutions suggest that it may be necessary to account for elastic bottom interactions. In order to study energy conversion between elastic and acoustic waves, current elastic parabolic equation solutions must be modified to allow for seismic starting fields for underwater acoustic propagation environments. Two types of elastic self-starter are presented. An explosive-type source is implemented using a compressional self-starter and the resulting acoustic field is consistent with benchmark solutions. A shear wave self-starter is implemented and shown to generate transmission loss levels consistent with the explosive source. Source fields can be combined to generate starting fields for source types such as explosions, earthquakes, or pile driving. Examples demonstrate the use of source fields for shallow sources or deep ocean-bottom earthquake sources, where down slope conversion, a known T-wave generation mechanism, is modeled. Self-starters are interpreted in the context of the seismic moment tensor. PMID:23464007

  20. Uniqueness and Long Time Asymptotic for the Keller-Segel Equation: The Parabolic-Elliptic Case

    NASA Astrophysics Data System (ADS)

    Egaña Fernández, Giani; Mischler, Stéphane

    2016-06-01

    The present paper deals with the parabolic-elliptic Keller-Segel equation in the plane in the general framework of weak (or "free energy") solutions associated to initial datum with finite mass M, finite second moment and finite entropy. The aim of the paper is threefold: (1) We prove the uniqueness of the "free energy" solution on the maximal interval of existence [0, T*) with T* = ∞ in the case when M ≦ 8π and T* < ∞ in the case when M > 8π. The proof uses a DiPerna-Lions renormalizing argument which makes it possible to get the "optimal regularity" as well as an estimate of the difference of two possible solutions in the critical L 4/3 Lebesgue norm similarly to the 2 d vorticity Navier-Stokes equation.

  1. Smoothness of semiflows for parabolic partial differential equations with state-dependent delay

    NASA Astrophysics Data System (ADS)

    Lv, Yunfei; Yuan, Rong; Pei, Yongzhen

    2016-04-01

    In this paper, the smoothness properties of semiflows on C1-solution submanifold of a parabolic partial differential equations with state-dependent delay are investigated. The problem is formulated as an abstract ordinary retarded functional differential equation of the form du (t) / dt = Au (t) + F (ut) with a continuously differentiable map G from an open subset U of the space C1 ([ - h , 0 ] ,L2 (Ω)), where A is the infinitesimal generator of a compact C0-semigroup. The present study is continuation of a previous work [14] that highlights the classical solutions and C1-smoothness of solution manifold. Here, we further prove the continuous differentiability of the semiflow. We finally verify all hypotheses by a biological example which describes a stage structured diffusive model where the delay, which is the time taken from birth to maturity, is assumed as a function of a immature species population.

  2. Study of a family of higher order nonlocal degenerate parabolic equations: From the porous medium equation to the thin film equation

    NASA Astrophysics Data System (ADS)

    Tarhini, Rana

    2015-12-01

    In this paper, we study a nonlocal degenerate parabolic equation of order α + 2 for α ∈ (0, 2). The equation is a generalization of the one arising in the modeling of hydraulic fractures studied by Imbert and Mellet in 2011. Using the same approach, we prove the existence of solutions for this equation for 0 < α < 2 and for nonnegative initial data satisfying appropriate assumptions. The main difference is the compactness results due to different Sobolev embeddings. Furthermore, for α > 1, we construct a nonnegative solution for nonnegative initial data under weaker assumptions.

  3. Hazardous Continuation Backward in Time in Nonlinear Parabolic Equations, and an Experiment in Deblurring Nonlinearly Blurred Imagery

    PubMed Central

    Carasso, Alfred S

    2013-01-01

    Identifying sources of ground water pollution, and deblurring nanoscale imagery as well as astronomical galaxy images, are two important applications involving numerical computation of parabolic equations backward in time. Surprisingly, very little is known about backward continuation in nonlinear parabolic equations. In this paper, an iterative procedure originating in spectroscopy in the 1930’s, is adapted into a useful tool for solving a wide class of 2D nonlinear backward parabolic equations. In addition, previously unsuspected difficulties are uncovered that may preclude useful backward continuation in parabolic equations deviating too strongly from the linear, autonomous, self adjoint, canonical model. This paper explores backward continuation in selected 2D nonlinear equations, by creating fictitious blurred images obtained by using several sharp images as initial data in these equations, and capturing the corresponding solutions at some positive time T. Successful backward continuation from t=T to t = 0, would recover the original sharp image. Visual recognition provides meaningful evaluation of the degree of success or failure in the reconstructed solutions. Instructive examples are developed, illustrating the unexpected influence of certain types of nonlinearities. Visually and statistically indistinguishable blurred images are presented, with vastly different deblurring results. These examples indicate that how an image is nonlinearly blurred is critical, in addition to the amount of blur. The equations studied represent nonlinear generalizations of Brownian motion, and the blurred images may be interpreted as visually expressing the results of novel stochastic processes. PMID:26401430

  4. Unmitigated numerical solution to the diffraction term in the parabolic nonlinear ultrasound wave equation.

    PubMed

    Hasani, Mojtaba H; Gharibzadeh, Shahriar; Farjami, Yaghoub; Tavakkoli, Jahan

    2013-09-01

    Various numerical algorithms have been developed to solve the Khokhlov-Kuznetsov-Zabolotskaya (KZK) parabolic nonlinear wave equation. In this work, a generalized time-domain numerical algorithm is proposed to solve the diffraction term of the KZK equation. This algorithm solves the transverse Laplacian operator of the KZK equation in three-dimensional (3D) Cartesian coordinates using a finite-difference method based on the five-point implicit backward finite difference and the five-point Crank-Nicolson finite difference discretization techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term. In addition, a new empirical algorithm based on the LU decomposition technique is proposed to solve the system of linear equations obtained from this discretization. The proposed empirical algorithm improves the calculation speed and memory usage, while the order of computational complexity remains linear in calculation of the diffraction term in the KZK equation. For evaluating the accuracy of the proposed algorithm, two previously published algorithms are used as comparison references: the conventional 2D Texas code and its generalization for 3D geometries. The results show that the accuracy/efficiency performance of the proposed algorithm is comparable with the established time-domain methods. PMID:23967912

  5. Explicit numerical formulas of improved stability and accuracy for the solution of parabolic equations

    NASA Technical Reports Server (NTRS)

    Olstad, W. B.

    1979-01-01

    A class of explicit numerical formulas which involve next nearest neighbor as well as nearest neighbor points are explored in this paper. These formulas are formal approximations to the linear parabolic partial-differential equation of first order in time and second order in distance. It was found that some of these formulas can employ time steps as much as four times that for the conventional explicit technique without becoming unstable. Others showed improved accuracy for a given time step and spatial grid spacing. One formula achieved a steady-state solution of specified accuracy for an example problem in less than 4 percent of the total computational time required by the conventional explicit technique.

  6. A single-scattering correction for the seismo-acoustic parabolic equation.

    PubMed

    Collins, Michael D

    2012-04-01

    An efficient single-scattering correction that does not require iterations is derived and tested for the seismo-acoustic parabolic equation. The approach is applicable to problems involving gradual range dependence in a waveguide with fluid and solid layers, including the key case of a sloping fluid-solid interface. The single-scattering correction is asymptotically equivalent to a special case of a single-scattering correction for problems that only have solid layers [Küsel et al., J. Acoust. Soc. Am. 121, 808-813 (2007)]. The single-scattering correction has a simple interpretation (conservation of interface conditions in an average sense) that facilitated its generalization to problems involving fluid layers. Promising results are obtained for problems in which the ocean bottom interface has a small slope. PMID:22501044

  7. Radio wave propagation in horizontally inhomogeneous environments by using the parabolic equation method

    NASA Astrophysics Data System (ADS)

    Barrios, A. E.

    1991-05-01

    The validity of a parabolic equation (PE) model for predicting radio field strengths in horizontally inhomogeneous environments was investigated by performing comparisons between the model and experimental data. Excellent agreements were found at VHF and UHF frequencies with good agreement in S- and X-bands. In some cases, the predicted curves for the S-band comparisons under-estimated that of the measured data at large ranges. This may be the result of phenomena such as surface roughness, backscatter, etc., not accounted for in the model. Discrepancies may also result from the presence of evaporation ducts not included in the environmental inputs to the model because of a lack of detailed measurements. This would account for lower predicted signal levels at higher frequencies.

  8. Spectral element method-based parabolic equation for EM-scattering problems

    NASA Astrophysics Data System (ADS)

    He, Zi; Fan, Zhen-Hong; Chen, Ru-Shan

    2016-01-01

    The traditional parabolic equation (PE) method is based on the finite difference (FD) scheme. However, the scattering object cannot be well approximated for complex geometries. As a result, a large number of meshes are needed to discretize the complex scattering objects. In this paper, the spectral element method is introduced to better approximate the complex geometry in each transverse plane, while the FD scheme is used along the paraxial direction. This proposed algorithm begins with expanding the reduced scattered fields with the Gauss-Lobatto-Legendre polynomials and testing them by the Galerkin's method in each transverse plane. Then, the calculation can be taken plane by plane along the paraxial direction. Numerical results demonstrate that the accuracy can be improved by the proposed method with larger meshes when compared with the traditional PE method.

  9. A numerical adjoint parabolic equation (PE) method for tomography and geoacoustic inversion in shallow water

    NASA Astrophysics Data System (ADS)

    Hermand, Jean-Pierre; Berrada, Mohamed; Meyer, Matthias; Asch, Mark

    2005-09-01

    Recently, an analytic adjoint-based method of optimal nonlocal boundary control has been proposed for inversion of a waveguide acoustic field using the wide-angle parabolic equation [Meyer and Hermand, J. Acoust. Soc. Am. 117, 2937-2948 (2005)]. In this paper a numerical extension of this approach is presented that allows the direct inversion for the geoacoustic parameters which are embedded in a spectral integral representation of the nonlocal boundary condition. The adjoint model is generated numerically and the inversion is carried out jointly across multiple frequencies. The paper further discusses the application of the numerical adjoint PE method for ocean acoustic tomography. To show the effectiveness of the implemented numerical adjoint, preliminary inversion results of water sound-speed profile and bottom acoustic properties will be shown for the YELLOW SHARK '94 experimental conditions.

  10. Enhanced propagation modeling of directional aviation noise: A hybrid parabolic equation-fast field program method

    NASA Astrophysics Data System (ADS)

    Rosenbaum, Joyce E.

    2011-12-01

    Commercial air traffic is anticipated to increase rapidly in the coming years. The impact of aviation noise on communities surrounding airports is, therefore, a growing concern. Accurate prediction of noise can help to mitigate the impact on communities and foster smoother integration of aerospace engineering advances. The problem of accurate sound level prediction requires careful inclusion of all mechanisms that affect propagation, in addition to correct source characterization. Terrain, ground type, meteorological effects, and source directivity can have a substantial influence on the noise level. Because they are difficult to model, these effects are often included only by rough approximation. This dissertation presents a model designed for sound propagation over uneven terrain, with mixed ground type and realistic meteorological conditions. The model is a hybrid of two numerical techniques: the parabolic equation (PE) and fast field program (FFP) methods, which allow for physics-based inclusion of propagation effects and ensure the low frequency content, a factor in community impact, is predicted accurately. Extension of the hybrid model to a pseudo-three-dimensional representation allows it to produce aviation noise contour maps in the standard form. In order for the model to correctly characterize aviation noise sources, a method of representing arbitrary source directivity patterns was developed for the unique form of the parabolic equation starting field. With this advancement, the model can represent broadband, directional moving sound sources, traveling along user-specified paths. This work was prepared for possible use in the research version of the sound propagation module in the Federal Aviation Administration's new standard predictive tool.

  11. Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation

    NASA Technical Reports Server (NTRS)

    Baumeister, K. J.; Kreider, K. L.

    1996-01-01

    An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

  12. Eigenfunction approach to the Green's function parabolic equation in outdoor sound: A tutorial.

    PubMed

    Gilbert, Kenneth E

    2016-03-01

    Understanding the physics and mathematics underlying a computational algorithm such as the Green's function parabolic equation (GFPE) is both useful and worthwhile. To this end, the present article aims to give a more widely accessible derivation of the GFPE algorithm than was given originally by Gilbert and Di [(1993). J. Acoust. Soc. Am. 94, 2343-2352]. The present derivation, which uses mathematics familiar to most engineers and physicists, begins with the separation of variables method, a basic and well-known approach for solving partial differential equations. The method leads naturally to eigenvalue-eigenfunction equations. A step-by-step analysis arrives at relatively simple, analytic expressions for the horizontal and vertical eigenfunctions, which are sinusoids plus a surface wave. The eigenfunctions are superposed in an eigenfunction expansion to yield a one-way propagation solution. The one-way solution is generalized to obtain the GFPE algorithm. In addition, and equally important, the eigenfunctions are used to give concrete meaning to abstract operator solutions for one-way acoustic propagation. By using an eigenfunction expansion of the acoustic field, together with an operator solution, one can obtain the GFPE algorithm very directly and concisely. PMID:27036244

  13. 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. PMID:12765364

  14. The stabilization rate of a solution to the Cauchy problem for parabolic equation with lower order coefficients

    NASA Astrophysics Data System (ADS)

    Denisov, Vasilii

    2016-08-01

    In this report, we study sufficient conditions on the lower order coefficients of a parabolic equation guaranteeing the power rate of the uniform stabilization to zero of the solution to the Cauchy problem on every compact K in RN and for any bounded initial function.

  15. Spatiotemporal soliton solution to generalized nonlinear Schrödinger equation with a parabolic potential in Kerr media

    NASA Astrophysics Data System (ADS)

    Kong, Youchao

    2016-07-01

    A class of new spatiotemporal solitary solution to nonlinear Schrödinger equation with a parabolic potential is investigated analytically and numerically using the F-expansion method and homogeneous balance principle. The propagation characteristics of soliton wave solutions are analyzed with/without spatial-temporal chirp. It is noteworthy that, by calculating spatial and temporal second-order intensity moment, several novel features of optical beam propagations are obtained, such as stable, oscillating, decaying and blowing up. Additionally, controllability of these solutions with the modulation depth of the parabolic potential is demonstrated.

  16. Plane waves at or near grazing incidence in the parabolic approximation. [acoustic equations of motion for sound fields

    NASA Technical Reports Server (NTRS)

    Mcaninch, G. L.; Myers, M. K.

    1980-01-01

    The parabolic approximation for the acoustic equations of motion is applied to the study of the sound field generated by a plane wave at or near grazing incidence to a finite impedance boundary. It is shown how this approximation accounts for effects neglected in the usual plane wave reflection analysis which, at grazing incidence, erroneously predicts complete cancellation of the incident field by the reflected field. Examples are presented which illustrate that the solution obtained by the parabolic approximation contains several of the physical phenomena known to occur in wave propagation near an absorbing boundary.

  17. Nonlocal diffusion problems that approximate a parabolic equation with spatial dependence

    NASA Astrophysics Data System (ADS)

    Molino, Alexis; Rossi, Julio D.

    2016-06-01

    In this paper, we show that smooth solutions to the Dirichlet problem for the parabolic equation v_t(x,t)=sum_{i,j=1}N a_{ij}(x)partial2v(x,t)/partial{xipartial{x}j} + sum_{i =1}N bi(x)partial{v}(x,t)/partial{x_i} qquad x in Ω, with v( x, t) = g( x, t), {x in partial Ω,} can be approximated uniformly by solutions of nonlocal problems of the form ut^{\\varepsilon}(x,t)=int_{mathbb{R}n} K_{\\varepsilon}(x,y)(u^{\\varepsilon}(y,t)-u^{\\varepsilon}(x,t))dy, quad x in Ω, with {u^{\\varepsilon}(x,t)=g(x,t)}, {x notin Ω}, as {\\varepsilon to 0}, for an appropriate rescaled kernel {K_{\\varepsilon}}. In this way, we show that the usual local evolution problems with spatial dependence can be approximated by nonlocal ones. In the case of an equation in divergence form, we can obtain an approximation with symmetric kernels, that is, {K_{\\varepsilon}(x,y) = K_{\\varepsilon}(y,x)}.

  18. Modeling Tropospheric Radiowave Propagation Over Rough Sea Surfaces Using the Parabolic Equation Fourier Split-step Method

    NASA Astrophysics Data System (ADS)

    Cadette, Pierre E.

    This thesis develops the theory for solving the parabolic equation (PE) using the Fourier Split-step method for the purpose of modeling tropospheric radiowave propagation over the sea surface. Beginning with Maxwell's equations, the standard parabolic equation (SPE) approximation is derived from a linearly polarized scalar wave equation in Cartesian coordinates. Then, an introduction to the Fourier Split-step method is presented as a solution to the PE equation. Next, we make necessary approximations to the PE formulation to appropriately represented propagation through the troposphere including a conformal transformation of the coordinate system and the inclusion of refractivity profiles to represent evaporation duct conditions. The PE derivation concludes with the incorporation of the effects of finite impedance boundary conditions and sea surface roughness, which has a Split-step solution using the mixed Fourier transform (MFT). Finally, numerical examples are given to compare the field predictions of two well known PE/Split-step propagation models: Tropospheric ElectroMagnetic Parabolic Equation Routine (TEMPER) and Advanced Propagation Model (APM).

  19. The Extended Parabolic Equation Method and Implication of Results for Atmospheric Millimeter-Wave and Optical Propagation

    NASA Technical Reports Server (NTRS)

    Manning, Robert M.

    2004-01-01

    The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the -correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.

  20. Transient Growth Analysis of Compressible Boundary Layers with Parabolized Stability Equations

    NASA Technical Reports Server (NTRS)

    Paredes, Pedro; Choudhari, Meelan M.; Li, Fei; Chang, Chau-Lyan

    2016-01-01

    The linear form of parabolized linear stability equations (PSE) is used in a variational approach to extend the previous body of results for the optimal, non-modal disturbance growth in boundary layer flows. This methodology includes the non-parallel effects associated with the spatial development of boundary layer flows. As noted in literature, the optimal initial disturbances correspond to steady counter-rotating stream-wise vortices, which subsequently lead to the formation of stream-wise-elongated structures, i.e., streaks, via a lift-up effect. The parameter space for optimal growth is extended to the hypersonic Mach number regime without any high enthalpy effects, and the effect of wall cooling is studied with particular emphasis on the role of the initial disturbance location and the value of the span-wise wavenumber that leads to the maximum energy growth up to a specified location. Unlike previous predictions that used a basic state obtained from a self-similar solution to the boundary layer equations, mean flow solutions based on the full Navier-Stokes (NS) equations are used in select cases to help account for the viscous-inviscid interaction near the leading edge of the plate and also for the weak shock wave emanating from that region. These differences in the base flow lead to an increasing reduction with Mach number in the magnitude of optimal growth relative to the predictions based on self-similar mean-flow approximation. Finally, the maximum optimal energy gain for the favorable pressure gradient boundary layer near a planar stagnation point is found to be substantially weaker than that in a zero pressure gradient Blasius boundary layer.

  1. An Explicit Upwind Algorithm for Solving the Parabolized Navier-Stokes Equations

    NASA Technical Reports Server (NTRS)

    Korte, John J.

    1991-01-01

    An explicit, upwind algorithm was developed for the direct (noniterative) integration of the 3-D Parabolized Navier-Stokes (PNS) equations in a generalized coordinate system. The new algorithm uses upwind approximations of the numerical fluxes for the pressure and convection terms obtained by combining flux difference splittings (FDS) formed from the solution of an approximate Riemann (RP). The approximate RP is solved using an extension of the method developed by Roe for steady supersonic flow of an ideal gas. Roe's method is extended for use with the 3-D PNS equations expressed in generalized coordinates and to include Vigneron's technique of splitting the streamwise pressure gradient. The difficulty associated with applying Roe's scheme in the subsonic region is overcome. The second-order upwind differencing of the flux derivatives are obtained by adding FDS to either an original forward or backward differencing of the flux derivative. This approach is used to modify an explicit MacCormack differencing scheme into an upwind differencing scheme. The second order upwind flux approximations, applied with flux limiters, provide a method for numerically capturing shocks without the need for additional artificial damping terms which require adjustment by the user. In addition, a cubic equation is derived for determining Vegneron's pressure splitting coefficient using the updated streamwise flux vector. Decoding the streamwise flux vector with the updated value of Vigneron's pressure splitting improves the stability of the scheme. The new algorithm is applied to 2-D and 3-D supersonic and hypersonic laminar flow test cases. Results are presented for the experimental studies of Holden and of Tracy. In addition, a flow field solution is presented for a generic hypersonic aircraft at a Mach number of 24.5 and angle of attack of 1 degree. The computed results compare well to both experimental data and numerical results from other algorithms. Computational times required

  2. Prediction of far-field wind turbine noise propagation with parabolic equation.

    PubMed

    Lee, Seongkyu; Lee, Dongjai; Honhoff, Saskia

    2016-08-01

    Sound propagation of wind farms is typically simulated by the use of engineering tools that are neglecting some atmospheric conditions and terrain effects. Wind and temperature profiles, however, can affect the propagation of sound and thus the perceived sound in the far field. A better understanding and application of those effects would allow a more optimized farm operation towards meeting noise regulations and optimizing energy yield. This paper presents the parabolic equation (PE) model development for accurate wind turbine noise propagation. The model is validated against analytic solutions for a uniform sound speed profile, benchmark problems for nonuniform sound speed profiles, and field sound test data for real environmental acoustics. It is shown that PE provides good agreement with the measured data, except upwind propagation cases in which turbulence scattering is important. Finally, the PE model uses computational fluid dynamics results as input to accurately predict sound propagation for complex flows such as wake flows. It is demonstrated that wake flows significantly modify the sound propagation characteristics. PMID:27586709

  3. Parabolized Stability Equations analysis of nonlinear interactions with forced eigenmodes to control subsonic jet instabilities

    SciTech Connect

    Itasse, Maxime Brazier, Jean-Philippe Léon, Olivier Casalis, Grégoire

    2015-08-15

    Nonlinear evolution of disturbances in an axisymmetric, high subsonic, high Reynolds number hot jet with forced eigenmodes is studied using the Parabolized Stability Equations (PSE) approach to understand how modes interact with one another. Both frequency and azimuthal harmonic interactions are analyzed by setting up one or two modes at higher initial amplitudes and various phases. While single mode excitation leads to harmonic growth and jet noise amplification, controlling the evolution of a specific mode has been made possible by forcing two modes (m{sub 1}, n{sub 1}), (m{sub 2}, n{sub 2}), such that the difference in azimuth and in frequency matches the desired “target” mode (m{sub 1} − m{sub 2}, n{sub 1} − n{sub 2}). A careful setup of the initial amplitudes and phases of the forced modes, defined as the “killer” modes, has allowed the minimizing of the initially dominant instability in the near pressure field, as well as its estimated radiated noise with a 15 dB loss. Although an increase of the overall sound pressure has been found in the range of azimuth and frequency analyzed, the present paper reveals the possibility to make the initially dominant instability ineffective acoustically using nonlinear interactions with forced eigenmodes.

  4. A numerical method for solving the three-dimensional parabolized Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Dambrosio, Domenic; Marsilio, Robert

    1995-01-01

    A numerical technique that solves the parabolized form of the Navier-Stokes equations is presented. Such a method makes it possible to obtain very detailed descriptions of the flowfield in a relatively modest CPU time. The present approach is based on a space-marching technique, uses a finite volume discretization and an upwind flux-difference splitting scheme for the evaluation of the inviscid fluxes. Second order accuracy is achieved following the guidelines of the the ENO schemes. The methodology is used to investigate three-dimensional supersonic viscous flows over symmetric corners. Primary and secondary streamwise vortical structures embedded in the boundary layer and originated by the interaction with shock waves are detected and studied. For purpose of validation, results are compared with experimental data extracted from literature. The agreement is found to be satisfactory. In conclusion, the numerical method proposed seems to be promising as it permits, at a reasonable computational expense, investigation of complex three-dimensional flowfields in great detail.

  5. Analysis of measured broadband acoustic propagation using a parabolic equation approach

    NASA Astrophysics Data System (ADS)

    Gray, Mason; Knobles, D. P.; Koch, Robert

    2003-10-01

    A broadband parabolic equation (PE) approach is employed to simulate data taken from two Shallow Water Acoustic Measurement Instrument (SWAMI) bottom mounted horizontal line array (HLA) experiments in shallow water environments off the east coast of the U.S. and in the Gulf of Mexico. In both experiments the HLA was deployed along an isobath. Light bulbs were imploded at known depths and ranges in both the range-independent (array end fire) and range-dependent (array broadside) directions. For the east coast experimental data, the PE model is used to infer a seabed geoacoustic description in both the range-dependent and range-independent directions. Also, comparisons of modeled time series were made for the range-independent case with a broadband normal mode model to validate the PE calculations. In the Gulf of Mexico experiment, the sediment geoacoustic profile is well known from previous inversions and geophysical measurements. This known seabed description was used to simulate the range-dependent data. A broadband energy-conserving coupled mode approach is also employed to model the range-dependent propagation. This allows the physical mechanisms associated with range-dependent propagation to be examined in a quantitative manner for this shallow water environment. [Work supported by ONR.

  6. A forecasting system using the parabolic equation: Application to surface-to-air propagation in the presence of elevated layers

    NASA Astrophysics Data System (ADS)

    Craig, K. H.; Levy, M. F.

    1989-09-01

    The parabolic equation approach to clear-air propagation modeling overcomes many of the difficulties associated with ray and mode theory methods. A parabolic equation model was implemented on a PC based system using a transputer to carry out the computationally intensive numerical integrations. The model was used from VHF to millimetric frequencies and applied to evaporation duct and elevated duct problems. The latter are important for surface-to-air propagation and were difficult to solve because of the complicated structure of the layers. A case study of an elevated duct caused by anticyclonic subsidence shows the importance of up-to-date meteorological data from a wide geographical area. A full-wave calculation of the wideband properties of the propagation channel illustrates the possibilities opened up by the new model. The frequency selective effects can be large, and are sensitive to the small-scale structure of the ducting layers.

  7. Semilinear (topological) spaces and applications

    NASA Technical Reports Server (NTRS)

    Prakash, P.; Sertel, M. R.

    1971-01-01

    Semivector spaces are defined and some of their algebraic aspects are developed including some structure theory. These spaces are then topologized to obtain semilinear topological spaces for which a hierarchy of local convexity axioms is identified. A number of fixed point and minmax theorems for spaces with various local convexity properties are established. The spaces of concern arise naturally as various hyperspaces of linear and semilinear (topological) spaces. It is indicated briefly how all this can be applied in socio-economic analysis and optimization.

  8. Fast analysis of wide-band scattering from electrically large targets with time-domain parabolic equation method

    NASA Astrophysics Data System (ADS)

    He, Zi; Chen, Ru-Shan

    2016-03-01

    An efficient three-dimensional time domain parabolic equation (TDPE) method is proposed to fast analyze the narrow-angle wideband EM scattering properties of electrically large targets. The finite difference (FD) of Crank-Nicolson (CN) scheme is used as the traditional tool to solve the time-domain parabolic equation. However, a huge computational resource is required when the meshes become dense. Therefore, the alternating direction implicit (ADI) scheme is introduced to discretize the time-domain parabolic equation. In this way, the reduced transient scattered fields can be calculated line by line in each transverse plane for any time step with unconditional stability. As a result, less computational resources are required for the proposed ADI-based TDPE method when compared with both the traditional CN-based TDPE method and the finite-different time-domain (FDTD) method. By employing the rotating TDPE method, the complete bistatic RCS can be obtained with encouraging accuracy for any observed angle. Numerical examples are given to demonstrate the accuracy and efficiency of the proposed method.

  9. Existence of eigenvalues of problem with shift for an equation of parabolic-hyperbolic type

    NASA Astrophysics Data System (ADS)

    Tengayeva, Aizhan; Dildabek, Gulnar

    2016-08-01

    In the present paper, a spectral problem for an operator of parabolic-hyperbolic type of I kind with non-classical boundary conditions is considered. The problem is considered in a standard domain. The parabolic part of the space is a rectangle. And the hyperbolic part of the space coincides with a characteristic triangle. We consider a problem with the local boundary condition in the domain of parabolicity and with the boundary condition with displacement in the domain of hyperbolicity. We prove the strong solvability of the considered problem. The main aim of the paper is the research of spectral properties of the problem. The existence of eigenvalues of the problem is proved.

  10. Fast Time and Space Parallel Algorithms for Solution of Parabolic Partial Differential Equations

    NASA Technical Reports Server (NTRS)

    Fijany, Amir

    1993-01-01

    In this paper, fast time- and Space -Parallel agorithms for solution of linear parabolic PDEs are developed. It is shown that the seemingly strictly serial iterations of the time-stepping procedure for solution of the problem can be completed decoupled.

  11. Modeling of ultrashort pulsed laser irradiation in the cornea based on parabolic and hyperbolic heat equations using electrical analogy

    NASA Astrophysics Data System (ADS)

    Gheitaghy, A. M.; Takabi, B.; Alizadeh, M.

    2014-03-01

    Hyperbolic and parabolic heat equations are formulated to study a nonperfused homogeneous transparent cornea irradiated by high power and ultrashort pulsed laser in the Laser Thermo Keratoplasty (LTK) surgery. Energy absorption inside the cornea is modeled using the Beer-Lambert law that is incorporated as an exponentially decaying heat source. The hyperbolic and parabolic bioheat models of the tissue were solved by exploiting the mathematical analogy between thermal and electrical systems, by using robust circuit simulation program called Hspice to get the solutions of simultaneous RLC and RC transmission line networks. This method can be used to rapidly calculate the temperature in laser-irradiated tissue at time and space domain. It is found that internal energy gained from the irradiated field results in a rapid rise of temperature in the cornea surface during the early heating period, while the hyperbolic wave model predicts a higher temperature rise than the classical heat diffusion model. In addition, this paper investigates and examines the effect of some critical parameters such as relaxation time, convection coefficient, radiation, tear evaporation and variable thermal conductivity of cornea. Accordingly, it is found that a better accordance between hyperbolic and parabolic models will be achieved by time.

  12. Elastic parabolic equation and normal mode solutions for seismo-acoustic propagation in underwater environments with ice covers.

    PubMed

    Collis, Jon M; Frank, Scott D; Metzler, Adam M; Preston, Kimberly S

    2016-05-01

    Sound propagation predictions for ice-covered ocean acoustic environments do not match observational data: received levels in nature are less than expected, suggesting that the effects of the ice are substantial. Effects due to elasticity in overlying ice can be significant enough that low-shear approximations, such as effective complex density treatments, may not be appropriate. Building on recent elastic seafloor modeling developments, a range-dependent parabolic equation solution that treats the ice as an elastic medium is presented. The solution is benchmarked against a derived elastic normal mode solution for range-independent underwater acoustic propagation. Results from both solutions accurately predict plate flexural modes that propagate in the ice layer, as well as Scholte interface waves that propagate at the boundary between the water and the seafloor. The parabolic equation solution is used to model a scenario with range-dependent ice thickness and a water sound speed profile similar to those observed during the 2009 Ice Exercise (ICEX) in the Beaufort Sea. PMID:27250161

  13. A stabilized Runge–Kutta–Legendre method for explicit super-time-stepping of parabolic and mixed equations

    SciTech Connect

    Meyer, Chad D.; Balsara, Dinshaw S.; Aslam, Tariq D.

    2014-01-15

    Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit solution methods can be unconditionally stable but have the disadvantage of being computationally costly or difficult to implement. Super-time-stepping methods for treating parabolic terms in mixed type partial differential equations occupy an intermediate position. In such methods each superstep takes “s” explicit Runge–Kutta-like time-steps to advance the parabolic terms by a time-step that is s{sup 2} times larger than a single explicit time-step. The expanded stability is usually obtained by mapping the short recursion relation of the explicit Runge–Kutta scheme to the recursion relation of some well-known, stable polynomial. Prior work has built temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Chebyshev polynomials. Since their stability is based on the boundedness of the Chebyshev polynomials, these methods have been called RKC1 and RKC2. In this work we build temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Legendre polynomials. We call these methods RKL1 and RKL2. The RKL1 method is first-order accurate in time; the RKL2 method is second-order accurate in time. We verify that the newly-designed RKL1 and RKL2 schemes have a very desirable monotonicity preserving property for one-dimensional problems – a solution that is monotone at the beginning of a time step retains that property at the end of that time step. It is shown that RKL1 and RKL2 methods are stable for all values of the diffusion coefficient up to the maximum value. We call this a convex monotonicity preserving property and show by examples that it is very

  14. Explicit and implicit ode solvers using Krylov subspace optimization: Application to the diffusion equation and parabolic Maxwell`s system

    SciTech Connect

    Druskin, V.; Knizhnerman, L.

    1994-12-31

    The authors solve the Cauchy problem for an ODE system Au + {partial_derivative}u/{partial_derivative}t = 0, u{vert_bar}{sub t=0} = {var_phi}, where A is a square real nonnegative definite symmetric matrix of the order N, {var_phi} is a vector from R{sup N}. The stiffness matrix A is obtained due to semi-discretization of a parabolic equation or system with time-independent coefficients. The authors are particularly interested in large stiff 3-D problems for the scalar diffusion and vectorial Maxwell`s equations. First they consider an explicit method in which the solution on a whole time interval is projected on a Krylov subspace originated by A. Then they suggest another Krylov subspace with better approximating properties using powers of an implicit transition operator. These Krylov subspace methods generate optimal in a spectral sense polynomial approximations for the solution of the ODE, similar to CG for SLE.

  15. A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

    PubMed

    Motsa, S S; Magagula, V M; Sibanda, P

    2014-01-01

    This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252

  16. A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

    PubMed Central

    Motsa, S. S.; Magagula, V. M.; Sibanda, P.

    2014-01-01

    This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252

  17. A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

    NASA Technical Reports Server (NTRS)

    White, J. A.; Morrison, J. H.

    1999-01-01

    A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.

  18. Computationally efficient parabolic equation solutions to seismo-acoustic problems involving thin or low-shear elastic layers.

    PubMed

    Metzler, Adam M; Collis, Jon M

    2013-04-01

    Shallow-water environments typically include sediments containing thin or low-shear layers. Numerical treatments of these types of layers require finer depth grid spacing than is needed elsewhere in the domain. Thin layers require finer grids to fully sample effects due to elasticity within the layer. As shear wave speeds approach zero, the governing system becomes singular and fine-grid spacing becomes necessary to obtain converged solutions. In this paper, a seismo-acoustic parabolic equation solution is derived utilizing modified difference formulas using Galerkin's method to allow for variable-grid spacing in depth. Propagation results are shown for environments containing thin layers and low-shear layers. PMID:23556690

  19. Numerical solution of supersonic three-dimensional free-mixing flows using the parabolic-elliptic Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Hirsh, R. S.

    1976-01-01

    A numerical method is presented for solving the parabolic-elliptic Navier-Stokes equations. The solution procedure is applied to three-dimensional supersonic laminar jet flow issuing parallel with a supersonic free stream. A coordinate transformation is introduced which maps the boundaries at infinity into a finite computational domain in order to eliminate difficulties associated with the imposition of free-stream boundary conditions. Results are presented for an approximate circular jet, a square jet, varying aspect ratio rectangular jets, and interacting square jets. The solution behavior varies from axisymmetric to nearly two-dimensional in character. For cases where comparisons of the present results with those obtained from shear layer calculations could be made, agreement was good.

  20. Calculation of supersonic three-dimensional free-mixing flows using the parabolic-elliptic Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Hirsh, R. S.

    1975-01-01

    A numerical method is presented which is valid for integration of the parabolic-elliptic Navier-Stokes equations. The solution procedure is applied to the three-dimensional supersonic flow of a jet issuing into a supersonic free stream. Difficulties associated with the imposition of free-stream boundary conditions are noted, and a coordinate transformation, which maps the point at infinity onto a finite value, is introduced to alleviate these difficulties. Results are presented for calculations of a square jet and varying-aspect-ratio rectangular jets. The solution behavior varies from axisymmetry for the square jet to nearly two-dimensional for the high-aspect-ratio rectangle, although the computation always calculates the flow as though it were truly three-dimensional.

  1. A high-order weighted essentially non-oscillatory (WENO) finite difference scheme for nonlinear degenerate parabolic equations

    NASA Astrophysics Data System (ADS)

    Abedian, Rooholah; Adibi, Hojatollah; Dehghan, Mehdi

    2013-08-01

    In this paper, we propose a new WENO finite difference procedure for nonlinear degenerate parabolic equations which may contain discontinuous solutions. Our scheme is based on the method of lines, with a high-order accurate conservative approximation to each of the diffusion terms based on an idea that has been recently presented by Liu et al. [Y. Liu, C.-W. Shu, M. Zhang, High order finite difference WENO schemes for non-linear degenerate parabolic equations, SIAM J. Sci. Comput. 33 (2011) 939-965]. Our scheme tries to circumvent the negative ideal weights that appear when applying the standard WENO idea, as is done in Liu et al. (2011) [13]. In one-dimensional case, first we obtain an optimum polynomial on a six-points stencil. This optimum polynomial is sixth-order accurate in regions of smoothness. Then, we consider this optimum polynomial as a symmetric and convex combination of four polynomials with ideal weights. Following the methodology of the classic WENO procedure, then we calculate the non-oscillatory weights with the ideal weights. Numerical examples are provided to demonstrate the resolution power and accuracy of the scheme. Finally, the new method is extended to multi-dimensional problems by dimension-by-dimension approach. More examples of multi-dimension problems are presented to show that our method remains non-oscillatory while giving good resolution of discontinuities. Finally, we would like to mention that this paper combines and extends the techniques proposed in [13] and Levy et al. (2000) [24].

  2. Recovering the reaction and the diffusion coefficients in a linear parabolic equation

    NASA Astrophysics Data System (ADS)

    Lorenzi, Alfredo; Mola, Gianluca

    2012-07-01

    Let H be a real separable Hilbert space and A: {D}(A) \\rightarrow H be a positive and self-adjoint (unbounded) operator. We consider the identification problem consisting in searching for an H-valued function u and a couple of real numbers λ and μ, the first one being positive, that fulfil the initial-value problem \\begin{eqnarray*} u^{\\prime }(t) + \\lambda Au(t) = \\mu u(t), \\quad t \\in (0,T), \\quad u(0) = u_0, \\end{eqnarray*} and the additional constraints \\begin{eqnarray*} \\Vert A^{r/2}u(T)\\Vert ^{2} = \\varphi \\quad and \\quad \\Vert A^{s/2}u(T)\\Vert ^{2} = \\psi , \\end{eqnarray*} where we denote by As and Ar the powers of A with exponents r < s. Provided that the given data u0 ∈ H, u0 and φ, ψ > 0 satisfy proper a priori limitations, by means of a finite-dimensional approximation scheme, we construct a unique solution (u, λ, μ) on the whole interval [0, T], and exhibit an explicit continuous dependence estimate of Lipschitz type with respect to the data. Also, we provide specific applications to second- and fourth-order parabolic initial-boundary-value problems.

  3. THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

    EPA Science Inventory

    A three-point backward finite-difference method has been derived for a system of mixed hyperbolic¯¯parabolic (convection¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

  4. Application of an Extended Parabolic Equation to the Calculation of the Mean Field and the Transverse and Longitudinal Mutual Coherence Functions Within Atmospheric Turbulence

    NASA Technical Reports Server (NTRS)

    Manning, Robert M.

    2005-01-01

    Solutions are derived for the generalized mutual coherence function (MCF), i.e., the second order moment, of a random wave field propagating through a random medium within the context of the extended parabolic equation. Here, "generalized" connotes the consideration of both the transverse as well as the longitudinal second order moments (with respect to the direction of propagation). Such solutions will afford a comparison between the results of the parabolic equation within the pararaxial approximation and those of the wide-angle extended theory. To this end, a statistical operator method is developed which gives a general equation for an arbitrary spatial statistical moment of the wave field. The generality of the operator method allows one to obtain an expression for the second order field moment in the direction longitudinal to the direction of propagation. Analytical solutions to these equations are derived for the Kolmogorov and Tatarskii spectra of atmospheric permittivity fluctuations within the Markov approximation.

  5. Identifiability for the pointwise source detection in Fisher’s reaction-diffusion equation

    NASA Astrophysics Data System (ADS)

    Ben Belgacem, Faker

    2012-06-01

    We are interested in the detection of a pointwise source in a class of semi-linear advection-diffusion-reaction equations of Fisher type. The source is determined by its location, which may be steady or unsteady, and its time-dependent intensity. Observations recorded at a couple of points are the available data. One observing station is located upstream of the source and the other downstream. This is a severely ill-posed nonlinear inverse problem. In this paper, we pursue an identifiability result. The process we follow has been developed earlier for the linear model and may be sharpened to operate for the semi-linear equation. It is based on the uniqueness for a parabolic (semi-linear) sideways problem, which is obtained by a suitable unique continuation theorem. We state a maximum principle that turns out to be necessary for our proof. The identifiability is finally obtained for a stationary or a moving source. Many applications may be found in biology, chemical physiology or environmental science. The problem we deal with is the detection of pointwise organic pollution sources in rivers and channels. The basic equation to consider is the one-dimensional biochemical oxygen demand equation, with a nonlinear power growth inhibitor and/or the Michaelis-Menten reaction coefficient.

  6. Numerical prediction of three-dimensional juncture region flow using the parabolic Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Baker, A. J.; Manhardt, P. D.; Orzechowski, J. A.

    1979-01-01

    A numerical solution algorithm is established for prediction of subsonic turbulent three-dimensional flows in aerodynamic configuration juncture regions. A turbulence closure model is established using the complete Reynolds stress. Pressure coupling is accomplished using the concepts of complementary and particular solutions to a Poisson equation. Specifications for data input juncture geometry modification are presented.

  7. Global existence and blow-up for weakly coupled degenerate and singular parabolic equations with localized source

    NASA Astrophysics Data System (ADS)

    Zhou, Jun; Mu, Chunlai

    2011-02-01

    This paper deals with the following weakly coupled degenerate and singular parabolic equations with localized source u_t-(x^α u_x)_x=u^m(x_0(t),t)v^n(x_0(t),t),quad v_t-(x^β v_x)_x=v^p(x_0(t),t)u^q(x_0(t),t) in (0, a) × (0, T) with homogeneous Dirichlet boundary conditions, where {x_0(t):{R}^+→(0,a)} is Hölder continuous. T ≤ ∞, a > 0 be constants, m, n, p, q are positive real numbers and {α,βin[0,2)}. The existence of a unique classical non-negative solution is established and the sufficient conditions for the solution that exists globally or blows up in finite time are obtained. Furthermore, under certain conditions, it is proved that the blow-up set of the blowing-up solution is any closed subset of the interval (0, a). Furthermore, we also obtain the blow-up rate under the condition α = β.

  8. Treatment of a sloping fluid-solid interface and sediment layering with the seismo-acoustic parabolic equation.

    PubMed

    Collins, Michael D; Siegmann, William L

    2015-01-01

    The parabolic equation method is extended to handle problems in seismo-acoustics that have multiple fluid and solid layers, continuous depth dependence within layers, and sloping interfaces between layers. The medium is approximated in terms of a series of range-independent regions, and a single-scattering approximation is used to compute transmitted fields across the vertical interfaces between regions. The approach is implemented in terms of a set of dependent variables that is well suited to piecewise continuous depth dependence in the elastic parameters, but one of the fluid-solid interface conditions in that formulation involves a second derivative that complicates the treatment of sloping interfaces. This issue is resolved by using a non-centered, four-point difference formula for the second derivative. The approach is implemented using a matrix decomposition that is efficient when the parameters of the medium have a general dependence within the upper layers of the sediment but only depend on depth in the water column and deep within the sediment. PMID:25618077

  9. Conditioning and stability of finite difference schemes on uniform meshes for a singularly perturbed parabolic convection-diffusion equation

    NASA Astrophysics Data System (ADS)

    Shishkin, G. I.

    2013-04-01

    For a singularly perturbed parabolic convection-diffusion equation, the conditioning and stability of finite difference schemes on uniform meshes are analyzed. It is shown that a convergent standard monotone finite difference scheme on a uniform mesh is not ɛ-uniformly well conditioned or ɛ-uniformly stable to perturbations of the data of the grid problem (here, ɛ is a perturbation parameter, ɛ ∈ (0, 1]). An alternative finite difference scheme is proposed, namely, a scheme in which the discrete solution is decomposed into regular and singular components that solve grid subproblems considered on uniform meshes. It is shown that this solution decomposition scheme converges ɛ-uniformly in the maximum norm at an O( N -1ln N + N {0/-1}) rate, where N + 1 and N 0 + 1 are the numbers of grid nodes in x and t, respectively. This scheme is ɛ-uniformly well conditioned and ɛ-uniformly stable to perturbations of the data of the grid problem. The condition number of the solution decomposition scheme is of order O(δ-2lnδ-1 + δ{0/-1}); i.e., up to a logarithmic factor, it is the same as that of a classical scheme on uniform meshes in the case of a regular problem. Here, δ = N -1ln N and δ0 = N {0/-1} are the accuracies of the discrete solution in x and t, respectively.

  10. Radar coverage predictions through time- and range-dependent refractive atmospheres with planetary boundary layer and electromagnetic parabolic equation models

    NASA Astrophysics Data System (ADS)

    Skura, J. P.; Schemm, C. E.; Ko, H. W.; Manzi, L. P.

    The enhancement of the capability of electromagnetic parabolic equation (EMPE) and other propagation codes by using predictions from an atmospheric forecast model to provide refractivity data for range-dependent and time-varying situations is demonstrated. Starting from measured temperature and humidity data at one location and time, the JHU/APL planetary boundary layer (PBL) model is used to obtained predictions for a 24-h forecast period. Predicted fields of temperature, humidity, and refractivity after 12 and 24 h are compared with measured data to verify the forecast, and vertical profiles of refractivity for each hour are provided, along with appropriate radar parameters, as input to EMPE. The EMPE calculations of expected radiation patterns as functions of height and range at selected times demonstrate the effects of hourly changes in the structure of the lower atmosphere on radar propagation. The radar propagation calculations have been repeated using the IREPS code to illustrate the similarities and differences between the two models when applied to this somewhat idealized, horizontally homogeneous situation.

  11. Built-up terrain wave propagation by Fourier split-step parabolic wave equation-ray optical techniques

    NASA Astrophysics Data System (ADS)

    Eibert, Thomas F.

    2003-04-01

    Fourier split-step (FSS) solutions of the parabolic wave equation (PWE) represent wave fields in terms of plane wave decompositions. However, those field solutions are usually only valid in the air space above built-up terrain, whereas field predictions for modern wireless systems often require knowledge of the fields on a street level. Since FSS PWE solutions with large step sizes are not applicable for field computations between irregular scattering obstacles such as buildings, this problem is overcome by a two-step approach combining the FSS solution of the PWE with ray optical techniques to compute the fields at ground level in wooded and urbanized areas. To account for the great variety of propagation effects in a statistical sense, direct rays, reflected rays, diffracted rays and attenuated rays at typical receiver locations are included into the considerations. Comparisons to a wide variety of measured data show that this two-step approach produces better results than state of the art semiempirical field prediction techniques.

  12. Regularization of a non-characteristic Cauchy problem for a parabolic equation in multiple dimensions

    NASA Astrophysics Data System (ADS)

    Knosowski, Yvonne; von Lieres, Eric; Schneider, Adrian

    1999-06-01

    In this paper we consider the non-characteristic Cauchy problem 0266-5611/15/3/307/img1" ALT="(equation)"/> where 0266-5611/15/3/307/img2" ALT="(equation)"/> with appropriate coefficient functions a, b and c. Assuming that the Cauchy data icons/Journals/Common/varphi" ALT="varphi are given inexactly by a function icons/Journals/Common/varphi" ALT="varphiicons/Journals/Common/varepsilon" ALT="varepsilon" ALIGN="MIDDLE"/> satisfying ||icons/Journals/Common/varphi" ALT="varphi" ALIGN="TOP"/>-icons/Journals/Common/varphi" ALT="varphi" ALIGN="TOP"/>icons/Journals/Common/varepsilon" ALT="varepsilon" ALIGN="MIDDLE"/>||Hricons/Journals/Common/le" ALT="le" ALIGN="TOP"/> icons/Journals/Common/varepsilon" ALT="varepsilon" ALIGN="TOP"/> for some ricons/Journals/Common/le" ALT="le" ALIGN="TOP"/>0 and that f(y,t): = u(l,y,t) exists and belongs to Hs(icons/Journals/Common/BbbR" ALT="BbbR" ALIGN="TOP"/>n-1 × icons/Journals/Common/BbbR" ALT="BbbR" ALIGN="TOP"/>) for some sicons/Journals/Common/in" ALT="in" ALIGN="TOP"/>icons/Journals/Common/BbbR" ALT="BbbR" ALIGN="TOP"/>, it is desired to calculate f from the improper data icons/Journals/Common/varphi" ALT="varphi" ALIGN="TOP"/>icons/Journals/Common/varepsilon" ALT="varepsilon" ALIGN="MIDDLE"/>. This problem is well known to be severely ill-posed: a small perturbation in the Cauchy data may cause a dramatically large error in the solution. In this paper the following mollification method is suggested for this problem: if the Cauchy data are given inexactly then we mollify them by projection on elements of Meyers multiresolution approximation {Vj}jicons/Journals/Common/in" ALT="in" ALIGN="TOP"/>icons/Journals/Common/BbbZ" ALT="BbbZ" ALIGN="TOP"/>. Within every space Vj the solution of the above problem depends continuously on the data, and we can find a mollification parameter J depending on the noise level icons/Journals/Common/varepsilon" ALT="varepsilon" ALIGN="TOP"/> in the Cauchy data such that the error estimation between the

  13. Numerical study of hydrogen-air supersonic combustion by using elliptic and parabolized equations. Progress report, 1 December 1985-31 May 1986

    SciTech Connect

    Chitsomboon, T.; Tiwari, S.N.

    1986-08-01

    The two-dimensional Navier-Stokes and species continuity equations are used to investigate supersonic chemically reacting flow problems which are related to scramjet-engine configurations. A global two-step finite-rate chemistry model is employed to represent the hydrogen-air combustion in the flow. An algebraic turbulent model is adopted for turbulent flow calculations. The explicit unsplit MacCormack finite-difference algorithm is used to develop a computer program suitable for a vector processing computer. The computer program developed is then used to integrate the system of the governing equations in time until convergence is attained. The chemistry source terms in the species continuity equations are evaluated implicitly to alleviate stiffness associated with fast chemical reactions. The problems solved by the elliptic code are re-investigated by using a set of two-dimensional parabolized Navier-Stokes and species equations. A linearized fully-coupled fully-implicit finite difference algorithm is used to develop a second computer code which solves the governing equations by marching in spce rather than time, resulting in a considerable saving in computer resources. Results obtained by using the parabolized formulation are compared with the results obtained by using the fully-elliptic equations. The comparisons indicate fairly good agreement of the results of the two formulations.

  14. High Energy Laser Beam Propagation in the Atmosphere: The Integral Invariants of the Nonlinear Parabolic Equation and the Method of Moments

    NASA Technical Reports Server (NTRS)

    Manning, Robert M.

    2012-01-01

    The method of moments is used to define and derive expressions for laser beam deflection and beam radius broadening for high-energy propagation through the Earth s atmosphere. These expressions are augmented with the integral invariants of the corresponding nonlinear parabolic equation that describes the electric field of high-energy laser beam to propagation to yield universal equations for the aforementioned quantities; the beam deflection is a linear function of the propagation distance whereas the beam broadening is a quadratic function of distance. The coefficients of these expressions are then derived from a thin screen approximation solution of the nonlinear parabolic equation to give corresponding analytical expressions for a target located outside the Earth s atmospheric layer. These equations, which are graphically presented for a host of propagation scenarios, as well as the thin screen model, are easily amenable to the phase expansions of the wave front for the specification and design of adaptive optics algorithms to correct for the inherent phase aberrations. This work finds application in, for example, the analysis of beamed energy propulsion for space-based vehicles.

  15. Trajectory controllability of semilinear systems with multiple variable delays in control

    SciTech Connect

    Klamka, Jerzy E-mail: Michal.Niezabitowski@polsl.pl; Niezabitowski, Michał E-mail: Michal.Niezabitowski@polsl.pl

    2014-12-10

    In this paper, finite-dimensional dynamical control system described by semilinear differential state equation with multiple variable delays in control are considered. The concept of controllability we extend on trajectory controllability for systems with multiple point delays in control. Moreover, remarks and comments on the relationships between different concepts of controllability are presented. Finally, simple numerical example, which illustrates theoretical considerations is also given. The possible extensions are also proposed.

  16. Periodic-parabolic eigenvalue problems with a large parameter and degeneration

    NASA Astrophysics Data System (ADS)

    Daners, Daniel; Thornett, Christopher

    2016-07-01

    We consider a periodic-parabolic eigenvalue problem with a non-negative potential λm vanishing on a non-cylindrical domain Dm satisfying conditions similar to those for the parabolic maximum principle. We show that the limit as λ → ∞ leads to a periodic-parabolic problem on Dm having a periodic-parabolic principal eigenvalue and eigenfunction which are unique in some sense. We substantially improve a result from [Du and Peng, Trans. Amer. Math. Soc. 364 (2012), p. 6039-6070]. At the same time we offer a different approach based on a periodic-parabolic initial boundary value problem. The results are motivated by an analysis of the asymptotic behaviour of positive solutions to semilinear logistic periodic-parabolic problems with temporal and spacial degeneracies.

  17. Weakly nonparallel and curvature effects on stationary crossflow instability: Comparison of results from multiple-scales analysis and parabolized stability equations

    NASA Technical Reports Server (NTRS)

    Singer, Bart A.; Choudhari, Meelan; Li, Fei

    1995-01-01

    A multiple-scales approach is used to approximate the effects of nonparallelism and streamwise surface curvature on the growth of stationary crossflow vortices in incompressible, three-dimesional boundary layers. The results agree with results predicted by solving the parabolized stability equations in regions where the nonparallelism is sufficiently weak. As the nonparallelism increases, the agreement between the two approaches worsens. An attempt has been made to quantify the nonparallelism on flow stability in terms of a nondimensional number that describes the rate of change of the mean flow relative to the disturbance wavelength. We find that the above nondimensional number provides useful information about the adequacy of the multiple-scales approximation for different disturbances for a given flow geometry, but the number does not collapse data for different flow geometries onto a single curve.

  18. Explicit lower bounds for the cost of fast controls for some 1-D parabolic or dispersive equations, and a new lower bound concerning the uniform controllability of the 1-D transport-diffusion equation

    NASA Astrophysics Data System (ADS)

    Lissy, Pierre

    2015-11-01

    In this paper, we prove explicit lower bounds for the cost of fast boundary controls for a class of linear equations of parabolic or dispersive type involving the spectral fractional Laplace operator. We notably deduce the following striking result: in the case of the heat equation controlled on the boundary, Miller's conjecture formulated in Miller (2004) [16] is not verified. Moreover, we also give a new lower bound for the minimal time needed to ensure the uniform controllability of the one-dimensional convection-diffusion equation with negative speed controlled on the left boundary, proving that the conjecture formulated in Coron and Guerrero (2005) [2] concerning this problem is also not verified at least for negative speeds. The proof is based on complex analysis, and more precisely on a representation formula for entire functions of exponential type, and is quite related to the moment method.

  19. On Blowup in Supercritical Wave Equations

    NASA Astrophysics Data System (ADS)

    Donninger, Roland; Schörkhuber, Birgit

    2016-03-01

    We study the blowup behavior for the focusing energy-supercritical semilinear wave equation in 3 space dimensions without symmetry assumptions on the data. We prove the stability in {H^2× H^1} of the ODE blowup profile.

  20. Generation of three-dimensional body-fitted grids by solving hyperbolic and parabolic partial differential equations

    NASA Technical Reports Server (NTRS)

    Steger, Joseph L.

    1989-01-01

    Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.

  1. Scalable implicit methods for reaction-diffusion equations in two and three space dimensions

    SciTech Connect

    Veronese, S.V.; Othmer, H.G.

    1996-12-31

    This paper describes the implementation of a solver for systems of semi-linear parabolic partial differential equations in two and three space dimensions. The solver is based on a parallel implementation of a non-linear Alternating Direction Implicit (ADI) scheme which uses a Cartesian grid in space and an implicit time-stepping algorithm. Various reordering strategies for the linearized equations are used to reduce the stride and improve the overall effectiveness of the parallel implementation. We have successfully used this solver for large-scale reaction-diffusion problems in computational biology and medicine in which the desired solution is a traveling wave that may contain rapid transitions. A number of examples that illustrate the efficiency and accuracy of the method are given here; the theoretical analysis will be presented.

  2. A two-grid method with Richardson extrapolation for a semilinear convection-diffusion problem

    NASA Astrophysics Data System (ADS)

    Tikhovskaya, S. V.; Zadorin, A. I.

    2015-10-01

    A boundary value problem for a second-order semilinear singularly perturbed ordinary differential equation is considered. We use Newton and Picard iterations for a linearization. To solve the problem at each iteration we apply the difference scheme with the property of uniform with respect to the singular perturbation parameter convergence. A modified Samarskii and central difference schemes on Shishkin mesh are considered. It is known that these schemes are almost second order accuracy uniformly with respect to the singular perturbation parameter. To decrease the required number of arithmetical operations for resolving the difference scheme, a two-grid method is proposed. To increase the accuracy of difference scheme, we investigate the possibility to apply Richardson extrapolation using known solutions of the difference scheme on both meshes. The comparison of modified Samarskii and central difference schemes is carried out. The results of some numerical experiments are discussed.

  3. Controllable parabolic-cylinder optical rogue wave

    NASA Astrophysics Data System (ADS)

    Zhong, Wei-Ping; Chen, Lang; Belić, Milivoj; Petrović, Nikola

    2014-10-01

    We demonstrate controllable parabolic-cylinder optical rogue waves in certain inhomogeneous media. An analytical rogue wave solution of the generalized nonlinear Schrödinger equation with spatially modulated coefficients and an external potential in the form of modulated quadratic potential is obtained by the similarity transformation. Numerical simulations are performed for comparison with the analytical solutions and to confirm the stability of the rogue wave solution obtained. These optical rogue waves are built by the products of parabolic-cylinder functions and the basic rogue wave solution of the standard nonlinear Schrödinger equation. Such rogue waves may appear in different forms, as the hump and paw profiles.

  4. Student Parabolic Flight Campaign

    NASA Astrophysics Data System (ADS)

    Sentse, N. S. M.; Ockels, W. J.

    2002-01-01

    After the successful Student Parabolic Flight Campaigns held in 1994 and 1995, the European Space Agency resumed their organisation of parabolic flight campaigns, dedicated to students of all ESA member states on an annual basis. The Student Parabolic Flight Campaigns are in order to promote microgravity research among students, tomorrow's scientists, since students can bring new ideas and initiatives to the space industry. Already four parabolic flight campaigns have flown and the 2002 student parabolic flight campaign has just flown in September. Thirty experiments are selected to fly in each campaign using the criteria of originality, demonstration of zero G, technical complexity and outreach performed by the team. Each experiment team consists of four university students. This is the chance for students to have the real weightlessness experience on board of the A300 ZERO-G aircraft. In addition, for one or two of the very best student experiments from each campaign, there will be the possibility to re-fly themselves and their experiment on ESA's Professional Parabolic Flight Campaigns. Eventually, one student experiment will be flying to the International Space Station. Conclusively, students' experiments can get fundamentally new and exciting results!

  5. Semilinear coherent optical oscillator with frequency shifted feedback.

    PubMed

    Rebhi, Riadh; Mathey, Pierre; Jauslin, Hans Rudolf; Odoulov, Serguey

    2007-12-10

    It is shown that the saw-tooth variation of the cavity length in a photorefractive semilinear coherent oscillator can suppress the instability in the frequency domain and prevent a bifurcation in the oscillation spectrum. To achieve such a suppression the frequency of the cavity length modulation should be chosen appropriately. It depends on the photorefractive crystal parameters (electrooptic properties, photoconductivity, dimensions) and on the experimental conditions (pump intensity ratio, orientation of the pump and oscillation waves with respect to the crystallographic axes, polarization of the pump waves, etc. ). It depends also strongly on a possible misalignment of the two pump waves. On the other hand, within a certain range of the experimental parameters the mirror vibration may lead to a further frequency splitting in the already existing two-mode oscillation spectrum. PMID:19551007

  6. Validation of three-dimensional incompressible spatial direct numerical simulation code: A comparison with linear stability and parabolic stability equation theories for boundary-layer transition on a flat plate

    NASA Technical Reports Server (NTRS)

    Joslin, Ronald D.; Streett, Craig L.; Chang, Chau-Lyan

    1992-01-01

    Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.

  7. Radial symmetry and monotonicity for an integral equation

    NASA Astrophysics Data System (ADS)

    Ma, Li; Chen, Dezhong

    2008-06-01

    In this paper we study radial symmetry and monotonicity of positive solutions of an integral equation arising from some higher-order semilinear elliptic equations in the whole space . Instead of the usual method of moving planes, we use a new Hardy-Littlewood-Sobolev (HLS) type inequality for the Bessel potentials to establish the radial symmetry and monotonicity results.

  8. Parabolic curves in Lie groups

    SciTech Connect

    Pauley, Michael

    2010-05-15

    To interpolate a sequence of points in Euclidean space, parabolic splines can be used. These are curves which are piecewise quadratic. To interpolate between points in a (semi-)Riemannian manifold, we could look for curves such that the second covariant derivative of the velocity is zero. We call such curves Jupp and Kent quadratics or JK-quadratics because they are a special case of the cubic curves advocated by Jupp and Kent. When the manifold is a Lie group with bi-invariant metric, we can relate JK-quadratics to null Lie quadratics which arise from another interpolation problem. We solve JK-quadratics in the Lie groups SO(3) and SO(1,2) and in the sphere and hyperbolic plane, by relating them to the differential equation for a quantum harmonic oscillator00.

  9. Parabolic torus transreflector antenna

    NASA Astrophysics Data System (ADS)

    Diaz, L. M.; Smith, M. S.

    1984-12-01

    The possible scan rate of conventional radar antennas using parabolic dishes is limited to about 60 rev/min. This limitation is related to mechanical rotation requirements. Many radar applications require high data renewal rates, including short-range defense systems and systems for reduction of sea clutter. Faster scan rates can be obtained by using phased arrays and electronic scanning. However, the use of the required equipment introduces considerable complexity and cost. The present investigation is concerned with a novel form of antenna permitting high scan rates, taking into account a parabolic torus transreflector antenna. The feed horn illuminates one side of the radome with polarization parallel to the wires, which therefore reflect the radiation like a dish antenna. In the antenna considered, rotation of the beam is effected by mechanical rotation of the horn feed only, and this provides the potential for high scanning rates.

  10. Session: Parabolic Troughs (Presentation)

    SciTech Connect

    Kutscher, C.

    2008-04-01

    The project description is R and D activities at NREL and Sandia aimed at lowering the delivered energy cost of parabolic trough collector systems and FOA awards to support industry in trought development. The primary objectives are: (1) support development of near-term parabolic trought technology for central station power generation; (2) support development of next-generation trought fields; and (3) support expansion of US trough industry. The major FY08 activities were: (1) improving reflector optics; (2) reducing receiver heat loss (including improved receiver coating and mitigating hydrogen accumulation); (3) measuring collector optical efficiency; (4) optimizing plant performance and reducing cost; (5) reducing plant water consumption; and (6) directly supporting industry needs, including FOA support.

  11. Comparison of Non-Parabolic Hydrodynamic Simulations for Semiconductor Devices

    NASA Technical Reports Server (NTRS)

    Smith, A. W.; Brennan, K. F.

    1996-01-01

    Parabolic drift-diffusion simulators are common engineering level design tools for semiconductor devices. Hydrodynamic simulators, based on the parabolic band approximation, are becoming more prevalent as device dimensions shrink and energy transport effects begin to dominate device characteristic. However, band structure effects present in state-of-the-art devices necessitate relaxing the parabolic band approximation. This paper presents simulations of ballistic diodes, a benchmark device, of Si and GaAs using two different non-parabolic hydrodynamic formulations. The first formulation uses the Kane dispersion relationship in the derivation of the conservation equations. The second model uses a power law dispersion relation {(hk)(exp 2)/2m = xW(exp Y)}. Current-voltage relations show that for the ballistic diodes considered. the non-parabolic formulations predict less current than the parabolic case. Explanations of this will be provided by examination of velocity and energy profiles. At low bias, the simulations based on the Kane formulation predict greater current flow than the power law formulation. As the bias is increased this trend changes and the power law predicts greater current than the Kane formulation. It will be shown that the non-parabolicity and energy range of the hydrodynamic model based on the Kane dispersion relation are limited due to the binomial approximation which was utilized in the derivation.

  12. Parabolic dish module experiment

    NASA Astrophysics Data System (ADS)

    1986-03-01

    A development test model of the 8-meter Solar Brayton Parabolic Dish Module has been designed, fabricated, and tested. The test model consists of five major subsystems: Sanders ceramic honeycomb solar receiver; LaJet LEC460 solar concentrator; AiRsearch SABC MKIIIA engine, Abacus 8 kW ac inverter; and a Sanders designed and built system controller. Goals of the tests were to integrate subsystem components into a working module, demonstrate the concept, and generate 5 kWe (hybrid) and 4.7 kWe (solar only) input. All subsystem integration goals were successfully achieved, but system performance efficiency was lower than expected. Contributing causes of the lower performance efficiencies have been identified. Modifications needed to restore performance to the required levels and improve the system life cycle cost have been addressed and are the subject of this final report.

  13. Localized spin wave modes in parabolic field wells

    NASA Astrophysics Data System (ADS)

    McMichael, Robert; Tartakovskaya, Elena; Pardavi-Horvath, Martha

    We describe spin wave modes trapped in parabolic-profile field wells. Trapped spin waves can be used as local probes of magnetic properties with resolution down to 100 nm in ferromagnetic resonance force microscopy. Localized modes have been shown to form around field minima from a number of sources, including stray fields from magnetic probe tips and inhomogeneous magnetostatic fields near film edges. Here, we address the most basic trap, which is a parabolic minimum in the applied field. The magnetic eigenmodes in this trap are tractable enough to serve as approximations in more realistic situations. For a parabolic field, we select basis mode profiles proportional to Hermite functions because they are eigenfuctions of the applied field and exchange parts of the equations of motion. Additionally, we find that these Hermite modes are approximate eigenfunctions of magnetostatic interactions, showing good agreement with micromagnetic calculations. More precise agreement is achieved by diagonalizing the equations of motion using only a few modes.

  14. Anisotropic electromagnetic wave propagation modeling using parabolic approximations

    NASA Astrophysics Data System (ADS)

    Brent, R. I.; Siegmann, W. L.; Jacobson, M. J.; Jacyna, G. M.

    1990-12-01

    A new method for the investigation of anisotropic electromagnetic wave propagation in the atmosphere is developed using parabolic approximations. Model equations for the electric field components are formulated which include the effects of both the inhomogeneous atmosphere and the static magnetic field of the earth. Application of parabolic-type approximations produces different systems of coupled parabolic equations. Each is valid for different relative magnitudes of components of the electric field. All admissible cases are then synthesized into one system which can be numerically examined, yielding solutions without a priori knowledge of electric field ratios. A specific example is presented and examined to understand static magnetic field effects on electromagnetic wave propagation. The influences of the earth's magnetic field are discussed and displayed in terms of electric components and the Poynting vector. Results demonstrate that the geomagnetic field can significantly influence HF atmospheric propagation.

  15. Numerical simulations for parabolic pulse shaping in non-linear media

    NASA Astrophysics Data System (ADS)

    Nora, R. C.; Durfee, C. G.; Carr, L. D.

    2007-03-01

    Pulses with parabolic temporal profiles have the property that they can propagate through non-linear media in a self similar manner. Parabolic pulses have been generated experimentally in fiber amplifiers. Input pulses develop into parabolic pulses by the combined action of group velocity dispersion, non-linear refractive index, and gain. In this work, we are exploring the feasibility of generating ultrafast parabolic pulses in laser resonators. We have successfully numerically simulated the generation of parabolic pulses in fiber amplifiers using two different algorithms, the Cayley method, and fourth order Runge-Kutta, to solve the Nonlinear Schrodinger equation with gain and periodic boundary conditions. In contrast to fiber amplifiers, pulses in laser resonators must maintain a stable pulse shape on each round trip through the optical cavity. We are exploring the prediction that a time dependent saturable gain will stabilize the pulse in the oscillator and yield parabolic pulses.

  16. Commercialization of parabolic dish systems

    NASA Technical Reports Server (NTRS)

    Washom, B.

    1982-01-01

    The impact of recent federal tax and regulatory legislation on the commercialization of parabolic solar reflector technology is assessed. Specific areas in need of technical or economic improvement are noted.

  17. Commercialization of parabolic dish systems

    NASA Astrophysics Data System (ADS)

    Washom, B.

    1982-07-01

    The impact of recent federal tax and regulatory legislation on the commercialization of parabolic solar reflector technology is assessed. Specific areas in need of technical or economic improvement are noted.

  18. Parabolic solar concentrator

    NASA Astrophysics Data System (ADS)

    Tecpoyotl-Torres, M.; Campos-Alvarez, J.; Tellez-Alanis, F.; Sánchez-Mondragón, J.

    2006-08-01

    In this work we present the basis of the solar concentrator design, which has is located at Temixco, Morelos, Mexico. For this purpose, this place is ideal due to its geographic and climatic conditions, and in addition, because it accounts with the greatest constant illumination in Mexico. For the construction of the concentrator we use a recycled parabolic plate of a telecommunications satellite dish (NEC). This plate was totally covered with Aluminum. The opening diameter is of 332 cm, the focal length is of 83 cm and the opening angle is of 90°. The geometry of the plate guaranties that the incident beams, will be collected at the focus. The mechanical treatment of the plate produces an average reflectance of 75% in the visible region of the solar spectrum, and of 92% for wavelengths up to 3μm in the infrared region. We obtain up to 2000°C of temperature concentration with this setup. The reflectance can be greatly improved, but did not consider it as typical practical use. The energy obtained can be applied to conditions that require of those high calorific energies. In order to optimize the operation of the concentrator we use a control circuit designed to track the apparent sun position.

  19. Parabolic aircraft solidification experiments

    NASA Technical Reports Server (NTRS)

    Workman, Gary L. (Principal Investigator); Smith, Guy A.; OBrien, Susan

    1996-01-01

    A number of solidification experiments have been utilized throughout the Materials Processing in Space Program to provide an experimental environment which minimizes variables in solidification experiments. Two techniques of interest are directional solidification and isothermal casting. Because of the wide-spread use of these experimental techniques in space-based research, several MSAD experiments have been manifested for space flight. In addition to the microstructural analysis for interpretation of the experimental results from previous work with parabolic flights, it has become apparent that a better understanding of the phenomena occurring during solidification can be better understood if direct visualization of the solidification interface were possible. Our university has performed in several experimental studies such as this in recent years. The most recent was in visualizing the effect of convective flow phenomena on the KC-135 and prior to that were several successive contracts to perform directional solidification and isothermal casting experiments on the KC-135. Included in this work was the modification and utilization of the Convective Flow Analyzer (CFA), the Aircraft Isothermal Casting Furnace (ICF), and the Three-Zone Directional Solidification Furnace. These studies have contributed heavily to the mission of the Microgravity Science and Applications' Materials Science Program.

  20. A Parabolic Problem with a Fractional Time Derivative

    NASA Astrophysics Data System (ADS)

    Allen, Mark; Caffarelli, Luis; Vasseur, Alexis

    2016-08-01

    We study regularity for a parabolic problem with fractional diffusion in space and a fractional time derivative. Our main result is a De Giorgi-Nash-Moser Hölder regularity theorem for solutions in a divergence form equation. We also prove results regarding existence, uniqueness, and higher regularity in time.

  1. Linear stability of shock profiles for systems of conservation laws with semi-linear relaxation

    NASA Astrophysics Data System (ADS)

    Godillon, Pauline

    2001-01-01

    The Evans function theory, which has recently been applied to the study of linear stability of viscous shock profiles, is developed below for semi-linear relaxation. We study the linear stability of shock profiles in the Lax, undercompressive and overcompressive cases. The results we obtain are similar to those found for viscous approximations by Gardner and Zumbrun [Commun. Pure Appl. Math. 51 (7) (1998) 797].

  2. Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management

    NASA Astrophysics Data System (ADS)

    Koleva, M. N.

    2011-11-01

    In this work we consider a nonlinear parabolic equation, obtained from Riccati like transformation of the Hamilton-Jacobi-Bellman equation, arising in pension saving management. We discuss two numerical iterative methods for solving the model problem—fully implicit Picard method and mixed Picard-Newton method, which preserves the parabolic characteristics of the differential problem. Numerical experiments for comparison the accuracy and effectiveness of the algorithms are discussed. Finally, observations are given.

  3. Non-parabolic hydrodynamic formulations for the simulation of inhomogeneous semiconductor devices

    NASA Technical Reports Server (NTRS)

    Smith, Arlynn W.; Brennan, Kevin F.

    1995-01-01

    Hydrodynamic models are becoming prevalent design tools for small scale devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band approximation to obtain fairly simple conservation equations. Interest in accounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models can not fully describe the transport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two different non-parabolic formulations of the hydrodynamic model suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship (hk)(exp 2)/2m = W(1 + alpha(W)). The second formulation makes use of a power law ((hk)(exp 2)/2m = xW(sup y)) for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulation readily produces closed form coefficients similar to those obtained using the parabolic band approximation. However, the fitting parameters (x,y) are only valid over a limited energy range. The physical significance of the band non-parabolicity is discussed as well as the advantages/disadvantages and approximations of the two non-parabolic models. A companion paper describes device simulations based on the three dispersion relationships: parabolic, Kane dispersion, and power low dispersion.

  4. Non-Parabolic Hydrodynamic Formulations for the Simulation of Inhomogeneous Semiconductor Devices

    NASA Technical Reports Server (NTRS)

    Smith, A. W.; Brennan, K. F.

    1996-01-01

    Hydrodynamic models are becoming prevalent design tools for small scale devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band approximation to obtain fairly simple conservation equations. Interest in accounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models cannot fully describe the transport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two different non-parabolic formulations or the hydrodynamic model suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship ((hk)(exp 2)/2m = W(1 + alphaW). The second formulation makes use of a power law ((hk)(exp 2)/2m = xW(exp y)) for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulation readily produces closed form coefficients similar to those obtained using the parabolic band approximation. However, the fitting parameters (x,y) are only valid over a limited energy range. The physical significance of the band non-parabolicity is discussed as well as the advantages/disadvantages and approximations of the two non-parabolic models. A companion paper describes device simulations based on the three dispersion relationships; parabolic, Kane dispersion and power law dispersion.

  5. Shenandoah parabolic dish solar collector

    SciTech Connect

    Kinoshita, G.S.

    1985-01-01

    The objectives of the Shenandoah, Georgia, Solar Total Energy System are to design, construct, test, and operate a solar energy system to obtain experience with large-scale hardware systems for future applications. This report describes the initial design and testing activities conducted to select and develop a collector that would serve the need of such a solar total energy system. The parabolic dish was selected as the collector most likely to maximize energy collection as required by this specific site. The fabrication, testing, and installation of the parabolic dish collector incorporating improvements identified during the development testing phase are described.

  6. Composite isogrid structures for parabolic surfaces

    NASA Technical Reports Server (NTRS)

    Silverman, Edward M. (Inventor); Boyd, Jr., William E. (Inventor); Rhodes, Marvin D. (Inventor); Dyer, Jack E. (Inventor)

    2000-01-01

    The invention relates to high stiffness parabolic structures utilizing integral reinforced grids. The parabolic structures implement the use of isogrid structures which incorporate unique and efficient orthotropic patterns for efficient stiffness and structural stability.

  7. JPL's parabolic dish test site

    NASA Technical Reports Server (NTRS)

    Hagen, T. L.

    1980-01-01

    A parabolic dish test site (PDTS) was established in the California Mojave Desert to carry out work in testing solar point focusing concentrator systems and related hardware. The site was chosen because of its high solar insolation level and year around clear sky conditions. The various facilities and equipment at the PDTS, and the concentrator experiments being performed are described.

  8. Parabolic tapers for overmoded waveguides

    DOEpatents

    Doane, J.L.

    1983-11-25

    A waveguide taper with a parabolic profile, in which the distance along the taper axis varies as the square of the tapered dimension, provides less mode conversion than equal length linear tapers and is easier to fabricate than other non-linear tapers.

  9. On two parabolic systems: Convergence and blowup

    NASA Astrophysics Data System (ADS)

    Huang, Yamin

    1998-12-01

    This dissertation studies two parabolic systems. It consists of two parts. In part one (chapter one), we prove a convergence result, namely, the solution (AK,/ BK) of a system of chemical diffusion-reaction equations (with reaction rate K) converges to the solution (A, B) of a diffusion- instantaneous-reaction equation. To prove our main result, we use some L1 and L2 'energy' estimates and a compactness result due to Aubin (1). As a by-product we also prove that as K approaches infinity, the limit solution exhibits phase separation between A and B. In part two (chapter two), we study the blowup rate for a system of heat equations ut=/Delta u,/ vt=/Delta v in a bounded domain Ωtimes(0,T) coupled in the nonlinear Neumann boundary conditions [/partial u/over/partial n]=vp,/ [/partial v/over/partial n]=uq on ∂Omega×[ 0,T), where p>0,/ q>0,/ pq>1 and n is the exterior normal vector on ∂Omega. Under certain assumptions, we establish exact blowup rate which generalizes the corresponding results of some authors' recent work including Deng (2), Deng-Fila-Levine (3) and Hu-Yin (4). ftn (1) J. P. A scUBIN, Un theoreme de compacite, C. R. Acad. Sci., 256(1963), pp. 5042-5044. (2) K. D scENG, Blow-up rates for parabolic systems, Z. Angew. Math. Phys., 47(1996), No. 1, pp. 132-143. (3) K. D scENG, M. F scILA AND H. A. L scEVINE, On critical exponents for a system of heat equations coupled in the boundary conditions, Acta Math. Univ. Comenian. (N.S.), 36(1994), No. 2, pp. 169-192. (4) B. H scU scAND H. M. Y scIN, The profile near blowup time for solutions of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc., 346(1994), pp. 117-135.

  10. Blowup behavior of solutions for a semilinear heat equation with supercritical nonlinearity

    NASA Astrophysics Data System (ADS)

    Mizoguchi, Noriko

    This paper is concerned with blowup phenomena of solutions for the Cauchy and the Cauchy-Dirichlet problem of u t= Δu+u pwith p in the supercritical range in the sense of Sobolev's embedding. We first show that if p>1+7/( N-11) and N⩾12, then there are no radially symmetric bounded positive solutions of Δw- {y}/{2} ∇w- {1}/{p-1} w+w p =0 in RNwhich intersect the radially symmetric singular solution at least twice. Using the above result, the existence of a blowup solution of type II for the Cauchy-Dirichlet problem for (P) in a ball is proved, where a solution u is said to exhibit the type II blowup at t= T if lim sup t↗T (T-t) 1/(p-1)|u(t)| ∞=∞ .

  11. Curvilinear parabolic approximation for surface wave transformation with wave current interaction

    NASA Astrophysics Data System (ADS)

    Shi, Fengyan; Kirby, James T.

    2005-04-01

    The direct coordinate transformation method, which only transforms independent variables and retains Cartesian dependent variables, may not be an appropriate method for the purpose of simplifying the curvilinear parabolic approximation of the vector form of the wave-current equation given by Kirby [Higher-order approximations in the parabolic equation method for water waves, J. Geophys. Res. 91 (1986) 933-952]. In this paper, the covariant-contravariant tensor method is used for the curvilinear parabolic approximation. We use the covariant components of the wave number vector and contravariant components of the current velocity vector so that the derivation of the curvilinear equation closely follows the higher-order approximation in rectangular Cartesian coordinates in Kirby [Higher-order approximations in the parabolic equation method for water waves, J. Geophys. Res. 91 (1986) 933-952]. The resulting curvilinear equation can be easily implemented using the existing model structure and numerical schemes adopted in the Cartesian parabolic wave model [J.T. Kirby, R.A. Dalrymple, F. Shi, Combined Refraction/Diffraction Model REF/DIF 1, Version 2.6. Documentation and User's Manual, Research Report, Center for Applied Coastal Research, Department of Civil and Environmental Engineering, University of Delaware, Newark, 2004]. Several examples of wave simulations in curvilinear coordinate systems, including a case with wave-current interaction, are shown with comparisons to theoretical solutions or measurement data.

  12. Propagation of hypergeometric laser beams in a medium with a parabolic refractive index

    NASA Astrophysics Data System (ADS)

    Kotlyar, V. V.; Kovalev, A. A.; Nalimov, A. G.

    2013-12-01

    An expression to describe the complex amplitude of a family of paraxial hypergeometric laser beams propagating in a parabolic-index fiber is proposed. A particular case of a Gaussian optical vortex propagating in a parabolic-index fiber is studied. Under definite parameters, the Gaussian optical vortices become the modes of the medium. This is a new family of paraxial modes derived for the parabolic-index medium. A wide class of solutions of nonparaxial Helmholtz equations that describe modes in a parabolic refractive index medium is derived in the cylindrical coordinate system. As the solutions derived are proportional to Kummer’s functions, only those of them which are coincident with the nonparaxial Laguerre-Gaussian modes possess a finite energy, meaning that they are physically implementable. A definite length of the graded-index fiber is treated as a parabolic lens, and expressions for the numerical aperture and the focal spot size are deduced. An explicit expression for the radii of the rings of a binary lens approximating a parabolic-index lens is derived. Finite-difference time-domain simulation has shown that using a binary parabolic-index microlens with a refractive index of 1.5, a linearly polarized Gaussian beam can be focused into an elliptic focal spot which is almost devoid of side-lobes and has a smaller full width at half maximum diameter of 0.45 of the incident wavelength.

  13. Parabolic dishes: technology and economics

    SciTech Connect

    Shine, D.J.

    1983-06-01

    The status of parabolic dish technology is described in this paper. The system consists of a dish-shaped concentrator that focuses the sun's rays on a heat transfer fluid. Receivers must be developed to withstand high temperatures. The Brayton engine is recommended by Saunders Associates because it is low cost, has the highest conversion efficiency, uses ordinary atmospheric air, and comes in appropriate sizes. Storage systems can augment periods of solar operation as specified. A true commercial market will not emerge until systems level testing over an extended period has taken place. Federal support of advanced system development is needed.

  14. Shock wave convergence in water with parabolic wall boundaries

    SciTech Connect

    Yanuka, D.; Shafer, D.; Krasik, Ya.

    2015-04-28

    The convergence of shock waves in water, where the cross section of the boundaries between which the shock wave propagates is either straight or parabolic, was studied. The shock wave was generated by underwater electrical explosions of planar Cu wire arrays using a high-current generator with a peak output current of ∼45 kA and rise time of ∼80 ns. The boundaries of the walls between which the shock wave propagates were symmetric along the z axis, which is defined by the direction of the exploding wires. It was shown that with walls having a parabolic cross section, the shock waves converge faster and the pressure in the vicinity of the line of convergence, calculated by two-dimensional hydrodynamic simulations coupled with the equations of state of water and copper, is also larger.

  15. On uniqueness theorem on weak solutions to the parabolic-parabolic Keller-Segel system of degenerate and singular types

    NASA Astrophysics Data System (ADS)

    Miura, Masanari; Sugiyama, Yoshie

    2014-12-01

    The uniqueness of weak solutions to the parabolic-parabolic Keller-Segel systems (KS)m below with m>max⁡{1/2 >-1n,0} is proved in the class of Hölder continuous functions for any space dimension n. Since Hölder continuity is an optimal regularity for weak solutions of the porous medium equation, it seems to be reasonable to investigate its uniqueness in such a class of solutions. Our proof is based on the standard duality argument coupled with vanishing viscosity method which recovers degeneracy for m>1, and which removes singularities for 0

  16. Solar parabolic dish technology evaluation report

    NASA Technical Reports Server (NTRS)

    Lucas, J. W.

    1984-01-01

    The activities of the JPL Solar Thermal Power Systems Parabolic Dish Project for FY 1983 are summarized. Included are discussions on designs of module development including concentrator, receiver, and power conversion subsystems together with a separate discussion of field tests, Small Community Experiment system development, and tests at the Parabolic Dish Test Site.

  17. Solar Parabolic Dish Annual Technology Evaluation Report

    NASA Technical Reports Server (NTRS)

    1983-01-01

    The activities of the JPL Solar Thermal Power Systems Parabolic Dish Project for FY 1982 are summarized. Included are discussions on designs of module development including their concentrator, receiver, and power conversion subsystems. Analyses and test results, along with progress on field tests, Small Community Experiment System development, and tests at the Parabolic Dish Test Site are also included.

  18. Time-harmonic Maxwell equations with asymptotically linear polarization

    NASA Astrophysics Data System (ADS)

    Qin, Dongdong; Tang, Xianhua

    2016-06-01

    This paper is concerned with the following time-harmonic semilinear Maxwell equation: nabla× (nabla× u)+λ u=f(x,u), &in Ω ν × u=0, &on partialΩ, where {Ωsubset {R}3} is a bounded, convex domain and {ν : partial Ωto {R}3} is the exterior normal. Motivated by recent work of Bartsch and Mederski and based on some observations and new techniques, we study above equation by developing the generalized Nehari manifold method. Particularly, existence of ground-state solutions of Nehari-Pankov type for the equation is established with asymptotically linear nonlinearity.

  19. Decay and stability for nonlinear hyperbolic equations

    NASA Astrophysics Data System (ADS)

    Marcati, Pierangelo

    This paper deals with the asymptotic stability of the null solution of a semilinear partial differential equation. The La Salle Invariance Principle has been used to obtain the stability results. The first result is given under quite general hypotheses assuming only the precompactness of the orbits and the local existence. In the second part, under some restrictions, sufficient conditions for precompactness of the orbits and decay of solutions are given. An existence and uniqueness theorem is proved in the Appendix. Some examples are given.

  20. Parabolic dish photovoltaic concentrator development

    NASA Astrophysics Data System (ADS)

    Beninga, K.; Davenport, R.; Featherby, M.; Sandubrae, J.; Walcott, K.

    1991-05-01

    Science Applications International Corporation (SAIC) and Tactical Fabs, Inc. (TFI) have fabricated a prototype parabolic dish photovoltaic (PV) concentrator system to demonstrate the functionality of this approach. A 1.5 m diameter parabolic dish was fabricated of a polyester/fiberglass composite, with a silvered polymer reflective surface. An innovative receiver cooling system used outward radial flow of cooling water in a narrow passage. This configuration matches the heat transfer capability of the cooling system to the flux profile on the PV receiver, minimizing temperature variations across the receiver. The photovoltaic cells used in the system were a new, TFI-proprietary design. Interleaved contacts form a bi-polar, rear-contact cell configuration. Because the electrical contacts are made on the rear of the cells, cells can be close-packed to form receiver arrays of arbitrary shape and size. Optical testing of the dish concentrator was performed by SAIC, SERI, and Sandia National Labs. The dish concentrator, designed for solar thermal applications, had a tight focal spot but exhibited flux non-uniformities away from the focal plane. Thermal testing of the receiver cooling system was performed with excellent success. Single PV cells, 4-cell blocks, and 144-cell receiver modules were built and tested. The cells successfully demonstrated the TFI design concept, but due to cell processing problems their efficiency was very low. Sources of the processing problems were identified and solutions were proposed, but funding limitations precluded further cell production. Operation of the complete PV dish system was conducted, and the functionality of the system was demonstrated. However, low cell efficiencies and receiver plane flux non-uniformities caused the system performance to be very low. These problems are not generic to the concept, and solutions to them proposed.

  1. Converting 10 kW Multi-Mode Fields Into a Single Spatial Mode with a Semilinear Phase Conjugate Mirror

    NASA Astrophysics Data System (ADS)

    Jaatinen, E.; Luther-Davies, B.

    We report on the use of a semilinear phase conjugate mirror to convert 20 % of the power contained in the 10 kW 20 ns pulses emerging from a multi-mode fibre back into a single spatial mode. This use of a phase conjugate mirror to unscramble phase distortions is unusual as only a single pass of the phase aberrating object is required. We also discuss the limitations of the technique that were encountered at high intensities (MW/cm2).

  2. Local density of states in parabolic quantum corrals

    NASA Astrophysics Data System (ADS)

    Trallero-Giner, C.; Ulloa, S. E.; López-Richard, V.

    2004-03-01

    Atomic manipulation and scanning tunnel microscope experiments on metal surfaces have shown that electronic states in a “quantum corral” can be locally monitored and used to analyze the nonlocal effects of perturbations. We study new corral geometries defined by families of confocal parabolas. General solutions of the Schrödinger equation for the interior problem with Dirichlet (hard wall) boundary conditions are found exactly in terms of zeroes of hypergeometric functions. We show that the Hilbert space of solutions is separated in subspaces with odd and even symmetry. We perform numerical evaluation of the zeroes and study the effects of the parabolic curvatures on the eigenvalues and eigenfunctions of the parabolic quantum corral. The evolution of the local density of states with energy as a function of parabolic corral geometry is also analyzed. We find that under suitable conditions, the distribution of state antinodes can be described as directed intensity beams, which could be used as “quantum beacons” in future generations of “quantum mirage” experiments or optical and acoustic analogs of quantum corrals for the state node distribution.

  3. Convergence of shock waves between conical and parabolic boundaries

    NASA Astrophysics Data System (ADS)

    Yanuka, D.; Zinowits, H. E.; Antonov, O.; Efimov, S.; Virozub, A.; Krasik, Ya. E.

    2016-07-01

    Convergence of shock waves, generated by underwater electrical explosions of cylindrical wire arrays, between either parabolic or conical bounding walls is investigated. A high-current pulse with a peak of ˜550 kA and rise time of ˜300 ns was applied for the wire array explosion. Strong self-emission from an optical fiber placed at the origin of the implosion was used for estimating the time of flight of the shock wave. 2D hydrodynamic simulations coupled with the equations of state of water and copper showed that the pressure obtained in the vicinity of the implosion is ˜7 times higher in the case of parabolic walls. However, comparison with a spherical wire array explosion showed that the pressure in the implosion vicinity in that case is higher than the pressure in the current experiment with parabolic bounding walls because of strong shock wave reflections from the walls. It is shown that this drawback of the bounding walls can be significantly minimized by optimization of the wire array geometry.

  4. On the coupling of hyperbolic and parabolic systems: Analytical and numerical approach

    NASA Technical Reports Server (NTRS)

    Gastaldi, Fabio; Quarteroni, Alfio

    1988-01-01

    The coupling of hyperbolic and parabolic systems is discussed in a domain Omega divided into two distinct subdomains omega(+) and omega(-). The main concern is to find the proper interface conditions to be fulfilled at the surface separating the two domains. Next, they are used in the numerical approximation of the problem. The justification of the interface conditions is based on a singular perturbation analysis, i.e., the hyperbolic system is rendered parabolic by adding a small artifical viscosity. As this goes to zero, the coupled parabolic-parabolic problem degenerates into the original one, yielding some conditions at the interface. These are taken as interface conditions for the hyperbolic-parabolic problem. Actually, two alternative sets of interface conditions are discussed according to whether the regularization procedure is variational or nonvariational. It is shown how these conditions can be used in the frame of a numerical approximation to the given problem. Furthermore, a method of resolution is discussed which alternates the resolution of the hyperbolic problem within omega(-) and of the parabolic one within omega(+). The spectral collocation method is proposed, as an example of space discretization (different methods could be used as well); both explicit and implicit time-advancing schemes are considered. The present study is a preliminary step toward the analysis of the coupling between Euler and Navier-Stokes equations for compressible flows.

  5. Analysis of the Quality of Parabolic Flight

    NASA Technical Reports Server (NTRS)

    Lambot, Thomas; Ord, Stephan F.

    2016-01-01

    Parabolic flights allow researchers to conduct several 20 second micro-gravity experiments in the course of a single day. However, the measurement can have large variations over the course of a single parabola, requiring the knowledge of the actual flight environment as a function of time. The NASA Flight Opportunities program (FO) reviewed the acceleration data of over 400 parabolic flights and investigated the quality of micro-gravity for scientific purposes. It was discovered that a parabolic flight can be segmented into multiple parts of different quality and duration, a fact to be aware of when planning an experiment.

  6. Impurity binding energies in quantum dots with parabolic confinement

    NASA Astrophysics Data System (ADS)

    Abramov, Arnold

    2015-03-01

    We present an effective numerical procedure to calculate the binding energies and wave functions of the hydrogen-like impurity states in a quantum dot (QD) with parabolic confinement. The unknown wave function was expressed as an expansion over one-dimensional harmonic oscillator states, which describes the electron's movement along the defined z-axis. Green's function technique used to obtain the solution of Schredinger equation for electronic states in a transverse plane. Binding energy of impurity states is defined as poles of the wave function. The dependences of the binding energy on the position of an impurity, the size of the QD and the magnetic field strength are presented and discussed.

  7. Space–time isogeometric analysis of parabolic evolution problems

    NASA Astrophysics Data System (ADS)

    Langer, Ulrich; Moore, Stephen E.; Neumüller, Martin

    2016-07-01

    We present and analyze a new stable space-time Isogeometric Analysis (IgA) method for the numerical solution of parabolic evolution equations in fixed and moving spatial computational domains. The discrete bilinear form is elliptic on the IgA space with respect to a discrete energy norm. This property together with a corresponding boundedness property, consistency and approximation results for the IgA spaces yields an a priori discretization error estimate with respect to the discrete norm. The theoretical results are confirmed by several numerical experiments with low- and high-order IgA spaces.

  8. Multibump solutions for quasilinear elliptic equations with critical growth

    SciTech Connect

    Liu, Jiaquan; Wang, Zhi-Qiang; Wu, Xian

    2013-12-15

    The current paper is concerned with constructing multibump solutions for a class of quasilinear Schrödinger equations with critical growth. This extends the classical results of Coti Zelati and Rabinowitz [Commun. Pure Appl. Math. 45, 1217–1269 (1992)] for semilinear equations as well as recent work of Liu, Wang, and Guo [J. Funct. Anal. 262, 4040–4102 (2012)] for quasilinear problems with subcritical growth. The periodicity of the potentials is used to glue ground state solutions to construct multibump bound state solutions.

  9. Fast wavelet based algorithms for linear evolution equations

    NASA Technical Reports Server (NTRS)

    Engquist, Bjorn; Osher, Stanley; Zhong, Sifen

    1992-01-01

    A class was devised of fast wavelet based algorithms for linear evolution equations whose coefficients are time independent. The method draws on the work of Beylkin, Coifman, and Rokhlin which they applied to general Calderon-Zygmund type integral operators. A modification of their idea is applied to linear hyperbolic and parabolic equations, with spatially varying coefficients. A significant speedup over standard methods is obtained when applied to hyperbolic equations in one space dimension and parabolic equations in multidimensions.

  10. Test results, Industrial Solar Technology parabolic trough solar collector

    SciTech Connect

    Dudley, V.E.; Evans, L.R.; Matthews, C.W.

    1995-11-01

    Sandia National Laboratories and Industrial Solar Technology are cost-sharing development of advanced parabolic trough technology. As part of this effort, several configurations of an IST solar collector were tested to determine the collector efficiency and thermal losses with black chrome and black nickel receiver selective coatings, combined with aluminized film and silver film reflectors, using standard Pyrex{reg_sign} and anti-reflective coated Pyrex{reg_sign} glass receiver envelopes. The development effort has been successful, producing an advanced collector with 77% optical efficiency, using silver-film reflectors, a black nickel receiver coating, and a solgel anti-reflective glass receiver envelope. For each receiver configuration, performance equations were empirically derived relating collector efficiency and thermal losses to the operating temperature. Finally, equations were derived showing collector performance as a function of input insolation value, incident angle, and operating temperature.

  11. Time-parallel iterative methods for parabolic PDES: Multigrid waveform relaxation and time-parallel multigrid

    SciTech Connect

    Vandewalle, S.

    1994-12-31

    Time-stepping methods for parabolic partial differential equations are essentially sequential. This prohibits the use of massively parallel computers unless the problem on each time-level is very large. This observation has led to the development of algorithms that operate on more than one time-level simultaneously; that is to say, on grids extending in space and in time. The so-called parabolic multigrid methods solve the time-dependent parabolic PDE as if it were a stationary PDE discretized on a space-time grid. The author has investigated the use of multigrid waveform relaxation, an algorithm developed by Lubich and Ostermann. The algorithm is based on a multigrid acceleration of waveform relaxation, a highly concurrent technique for solving large systems of ordinary differential equations. Another method of this class is the time-parallel multigrid method. This method was developed by Hackbusch and was recently subject of further study by Horton. It extends the elliptic multigrid idea to the set of equations that is derived by discretizing a parabolic problem in space and in time.

  12. Tailored dispersion profile in controlling optical solitons in a tapered parabolic index fiber

    NASA Astrophysics Data System (ADS)

    Prakash, S. Arun; Malathi, V.; Mani Rajan, M. S.

    2016-03-01

    We investigate the soliton dynamics in tapered parabolic index fibers via symbolic computation for a variety of dispersion profiles to inspect how a specific dispersion profile controls the optical soliton. By means of AKNS procedure, Lax pair is constructed for nonlinear Schrödinger equation with variable coefficients. Using obtained Lax pair, multi-soliton solutions are generated via Darboux transformation technique. Using multi-soliton solutions, soliton dynamics in tapered parabolic index fiber with the hyperbolic, Gaussian, exponential, and linear profiles are discussed. Results obtained in this study will be of certain potential application on construction of the nonlinear optical devices by soliton control. Results obtained in this study will be of certain value to the studies on the propagation and application of the soliton in the tapered parabolic index fiber and dispersion-managed fiber system.

  13. Piecewise-Planar Parabolic Reflectarray Antenna

    NASA Technical Reports Server (NTRS)

    Hodges, Richard; Zawadzki, Mark

    2009-01-01

    The figure shows a dual-beam, dualpolarization Ku-band antenna, the reflector of which comprises an assembly of small reflectarrays arranged in a piecewise- planar approximation of a parabolic reflector surface. The specific antenna design is intended to satisfy requirements for a wide-swath spaceborne radar altimeter, but the general principle of piecewise-planar reflectarray approximation of a parabolic reflector also offers advantages for other applications in which there are requirements for wideswath antennas that can be stowed compactly and that perform equally in both horizontal and vertical polarizations. The main advantages of using flat (e.g., reflectarray) antenna surfaces instead of paraboloidal or parabolic surfaces is that the flat ones can be fabricated at lower cost and can be stowed and deployed more easily. Heretofore, reflectarray antennas have typically been designed to reside on single planar surfaces and to emulate the focusing properties of, variously, paraboloidal (dish) or parabolic antennas. In the present case, one approximates the nominal parabolic shape by concatenating several flat pieces, while still exploiting the principles of the planar reflectarray for each piece. Prior to the conception of the present design, the use of a single large reflectarray was considered, but then abandoned when it was found that the directional and gain properties of the antenna would be noticeably different for the horizontal and vertical polarizations.

  14. Critical wind effects on parabolic reflectors

    NASA Astrophysics Data System (ADS)

    Campbell, Marvin F.

    2004-09-01

    For decades designers of dish antennas and radio telescopes have known the aerodynamic properties of parabolic reflectors. However, site planners and end users are not necessarily versed in their properties, and so can place them on sites or use them in such a manner that the wind causes a maximum of disruption of the pointing and tracking performance. Parabolic reflectors make excellent airfoils, and as such act like an airplane wing in many respects. Having some knowledge of sensitive wind directions relative to the Line Of Sight (LOS) can lead a user to change his site selection or operating procedures to achieve the optimum pointing and tracking performance for most observations. This knowledge can also contribute information to help specify the necessary performance characteristics. This paper discusses the aerodynamic properties of parabolic reflectors so the reader can get a ready grasp of the issues.

  15. Parabolic flight as a spaceflight analog.

    PubMed

    Shelhamer, Mark

    2016-06-15

    Ground-based analog facilities have had wide use in mimicking some of the features of spaceflight in a more-controlled and less-expensive manner. One such analog is parabolic flight, in which an aircraft flies repeated parabolic trajectories that provide short-duration periods of free fall (0 g) alternating with high-g pullout or recovery phases. Parabolic flight is unique in being able to provide true 0 g in a ground-based facility. Accordingly, it lends itself well to the investigation of specific areas of human spaceflight that can benefit from this capability, which predominantly includes neurovestibular effects, but also others such as human factors, locomotion, and medical procedures. Applications to research in artificial gravity and to effects likely to occur in upcoming commercial suborbital flights are also possible. PMID:26796759

  16. On a Modified Form of Navier-Stokes Equations for Three-Dimensional Flows

    PubMed Central

    Venetis, J.

    2015-01-01

    A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces. PMID:25918743

  17. Holomorphic Parabolic Geometries and Calabi-Yau Manifolds

    NASA Astrophysics Data System (ADS)

    McKay, Benjamin

    2011-09-01

    We prove that the only complex parabolic geometries on Calabi-Yau manifolds are the homogeneous geometries on complex tori. We also classify the complex parabolic geometries on homogeneous compact Kähler manifolds.

  18. Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations

    PubMed Central

    Amirali, I.; Amiraliyev, G. M.; Cakir, M.; Cimen, E.

    2014-01-01

    Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown. PMID:24688392

  19. Explicit finite difference methods for the delay pseudoparabolic equations.

    PubMed

    Amirali, I; Amiraliyev, G M; Cakir, M; Cimen, E

    2014-01-01

    Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown. PMID:24688392

  20. Solar Thermal Power Systems parabolic dish project

    NASA Technical Reports Server (NTRS)

    Truscello, V. C.

    1981-01-01

    The status of the Solar Thermal Power Systems Project for FY 1980 is summarized. Included is: a discussion of the project's goals, program structure, and progress in parabolic dish technology. Analyses and test results of concentrators, receivers, and power converters are discussed. Progress toward the objectives of technology feasibility, technology readiness, system feasibility, and system readiness are covered.

  1. Discontinuous Mixed Covolume Methods for Parabolic Problems

    PubMed Central

    Zhu, Ailing

    2014-01-01

    We present the semidiscrete and the backward Euler fully discrete discontinuous mixed covolume schemes for parabolic problems on triangular meshes. We give the error analysis of the discontinuous mixed covolume schemes and obtain optimal order error estimates in discontinuous H(div) and first-order error estimate in L2. PMID:24983008

  2. Parabolic Dish Concentrator (PDC-2) Development

    NASA Technical Reports Server (NTRS)

    Rafinejad, D.

    1984-01-01

    The design of the Parabolic Dish Concentrator (PDC-2) is described. The following five subsystems of the concentrator are discussed: (1) reflective surface subsystem, (2) support structure subsystem, (3) foundation, (4) drive subsystem, and (5) electrical and control subsystem. The status of the PDC-2 development project is assessed.

  3. Distributed neural signals on parabolic cylindrical shells

    NASA Astrophysics Data System (ADS)

    Hu, S. D.; Li, H.; Tzou, H. S.

    2013-06-01

    Parabolic cylindrical shells are commonly used as key components in communication antennas, space telescopes, solar collectors, etc. This study focuses on distributed modal neural sensing signals on a flexible simply-supported parabolic cylindrical shell panel. The parabolic cylindrical shell is fully laminated with a piezoelectric layer on its outer surface and the piezoelectric layer is segmented into infinitesimal elements (neurons) to investigate the microscopic distributed neural sensing signals. Since the dominant vibration component of the shell is usually the transverse oscillation, a new transverse mode shape function is defined. Two shell cases, i.e., the ratio of the meridian height to the half span distance of a parabola at 1:4 (shallow) and 1:1 (deep), are studied to reveal the curvature effect to the neural sensing signals. Studies suggest that the membrane signal component dominates for lower natural modes and the bending signal component dominates for higher natural modes. The meridional membrane and bending signal components are mostly concentrated on the high-curvature areas, while the longitudinal bending component is mostly concentrated on the relatively flat areas. The concentration behavior becomes more prominent as the parabolic cylindrical shell deepens, primarily resulting from the enhanced membrane effect due to the increased curvature.

  4. The linear regulator problem for parabolic systems

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Kunisch, K.

    1983-01-01

    An approximation framework is presented for computation (in finite imensional spaces) of Riccati operators that can be guaranteed to converge to the Riccati operator in feedback controls for abstract evolution systems in a Hilbert space. It is shown how these results may be used in the linear optimal regulator problem for a large class of parabolic systems.

  5. Manufacture of large, lightweight parabolic antennas

    NASA Technical Reports Server (NTRS)

    Hooper, S. W.

    1973-01-01

    Antenna was produced in segments. Parabole sections were built up as aluminum foil sandwich with core bonded by film adhesive; whole structure was oven-cured after assembly. Structure was assembled with special tool for splice-bonding segments into complete dish, and inflatable bladder to apply pressure at joints during cure.

  6. Close encounters of nearly parabolic comets and planets

    NASA Astrophysics Data System (ADS)

    Tomanov, V. P.

    2016-03-01

    An overview is given of close encounters of nearly parabolic comets (NPCs; with periods of P > 200 years and perihelion distances of q > 0.1 AU; the number of the comets is N = 1041) with planets. The minimum distances Δmin between the cometary and planetary orbits are calculated to select comets whose Δmin are less than the radius of the planet's sphere of influence. Close encounters of these comets with planets are identified by numerical integration of the comets' equations of motion over an interval of ±50 years from the time of passing the perihelion. Close encounters of NPCs with Jupiter in 1663-2011 are reported for seven comets. An encounter with Saturn is reported for comet 2004 F2 (in 2001).

  7. Mechatronic Prototype of Parabolic Solar Tracker.

    PubMed

    Morón, Carlos; Díaz, Jorge Pablo; Ferrández, Daniel; Ramos, Mari Paz

    2016-01-01

    In the last 30 years numerous attempts have been made to improve the efficiency of the parabolic collectors in the electric power production, although most of the studies have focused on the industrial production of thermoelectric power. This research focuses on the application of this concentrating solar thermal power in the unexplored field of building construction. To that end, a mechatronic prototype of a hybrid paraboloidal and cylindrical-parabolic tracker based on the Arduido technology has been designed. The prototype is able to measure meteorological data autonomously in order to quantify the energy potential of any location. In this way, it is possible to reliably model real commercial equipment behavior before its deployment in buildings and single family houses. PMID:27314359

  8. Mechatronic Prototype of Parabolic Solar Tracker

    PubMed Central

    Morón, Carlos; Díaz, Jorge Pablo; Ferrández, Daniel; Ramos, Mari Paz

    2016-01-01

    In the last 30 years numerous attempts have been made to improve the efficiency of the parabolic collectors in the electric power production, although most of the studies have focused on the industrial production of thermoelectric power. This research focuses on the application of this concentrating solar thermal power in the unexplored field of building construction. To that end, a mechatronic prototype of a hybrid paraboloidal and cylindrical-parabolic tracker based on the Arduido technology has been designed. The prototype is able to measure meteorological data autonomously in order to quantify the energy potential of any location. In this way, it is possible to reliably model real commercial equipment behavior before its deployment in buildings and single family houses. PMID:27314359

  9. Prolonging Microgravity on Parabolic Airplane Flights

    NASA Technical Reports Server (NTRS)

    Robinson, David W.

    2003-01-01

    Three techniques have been proposed to prolong the intervals of time available for microgravity experiments aboard airplanes flown along parabolic trajectories. Typically, a pilot strives to keep an airplane on such a trajectory during a nominal time interval as long as 25 seconds, and an experimental apparatus is released to float freely in the airplane cabin to take advantage of the microgravitational environment of the trajectory for as long as possible. It is usually not possible to maintain effective microgravity during the entire nominal time interval because random aerodynamic forces and fluctuations in pilot control inputs cause the airplane to deviate slightly from a perfect parabolic trajectory, such that the freely floating apparatus bumps into the ceiling, floor, or a wall of the airplane before the completion of the parabola.

  10. Nanofocusing Parabolic Refractive X-Ray Lenses

    SciTech Connect

    Schroer, C.G.; Kuhlmann, M.; Hunger, U.T.; Guenzler, T.F.; Kurapova, O.; Feste, S.; Lengeler, B.; Drakopoulos, M.; Somogyi, A.; Simionovici, A. S.; Snigirev, A.; Snigireva, I.

    2004-05-12

    Parabolic refractive x-ray lenses with short focal distance can generate intensive hard x-ray microbeams with lateral extensions in the 100nm range even at short distance from a synchrotron radiation source. We have fabricated planar parabolic lenses made of silicon that have a focal distance in the range of a few millimeters at hard x-ray energies. In a crossed geometry, two lenses were used to generate a microbeam with a lateral size of 330nm by 110nm at 25keV in a distance of 41.8m from the synchrotron radiation source. First microdiffraction and fluorescence microtomography experiments were carried out with these lenses. Using diamond as lens material, microbeams with lateral size down to 20nm and below are conceivable in the energy range from 10 to 100keV.

  11. New Parabolic Flight Platform for Microgravity Experiments

    NASA Astrophysics Data System (ADS)

    Valdatta, M.; Brucas, D.; Tomkus, V.; Ragauskas, U.; Razgunas, M.

    2015-09-01

    Microgravity experiments are important in field of space development; they give the possibility to simulate near-space conditions to test new kind of systems and subsystems for space or to perform biological researches. The existing platforms, to perform reduced gravity experiments, allow achieving the targets of the researches. Otherwise these platforms are either very expensive or of a very short duration. Another important issue is the repeatability of the experiment for some platforms. Fast repeatability platform (ensuring fast turnaround time), can guarantee only few seconds of microgravity time. For these reason there is the need of platforms for microgravity experiments that will cover the needs of all the experiments that cannot fit into required time, cost and repeatability of any other experiment methodology. The paper explains the mission plan and first scientific data of new family of parabolic unmanned planes. Each of these planes can be used to achieve scientific parabolic flight.

  12. Parabolic antennas with a loaded flange

    NASA Astrophysics Data System (ADS)

    Bucci, O. M.; Gennarelli, C.; Palumbo, L.

    1985-07-01

    The radiation characteristics of a parabolic dish with a loaded peripheral flange are examined in detail in order to assess the effectiveness of such a loading in further reducing the backward scattered field. Uniformly valid diffraction coefficients are developed to deal with both isotropic and anisotropic surface impedances. It is shown that substantial improvement of the antenna performance can be obtained in a wide rear angular sector, and the optimal loading conditions are determined.

  13. Building a parabolic solar concentrator prototype

    NASA Astrophysics Data System (ADS)

    Escobar-Romero, J. F. M.; Montiel, S. Vázquez y.; Granados-Agustín, F.; Cruz-Martínez, V. M.; Rodríguez-Rivera, E.; Martínez-Yáñez, L.

    2011-01-01

    In order to not further degrade the environment, people have been seeking to replace non-renewable natural resources such as fossil fuels by developing technologies that are based on renewable resources. An example of these technologies is solar energy. In this paper, we show the building and test of a solar parabolic concentrator as a prototype for the production of steam that can be coupled to a turbine to generate electricity or a steam engine in any particular industrial process.

  14. Stability and attractivity of periodic solutions of parabolic systems with time delays

    NASA Astrophysics Data System (ADS)

    Pao, C. V.

    2005-04-01

    This paper is concerned with the existence, stability, and global attractivity of time-periodic solutions for a class of coupled parabolic equations in a bounded domain. The problem under consideration includes coupled system of parabolic and ordinary differential equations, and time delays may appear in the nonlinear reaction functions. Our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. The existence of time-periodic solutions is for a class of locally Lipschitz continuous reaction functions without any quasimonotone requirement using Schauder fixed point theorem, while the stability and attractivity analysis is for quasimonotone nondecreasing and mixed quasimonotone reaction functions using the monotone iterative scheme. The results for the general system are applied to the standard parabolic equations without time delay and to the corresponding ordinary differential system. Applications are also given to three Lotka-Volterra reaction diffusion model problems, and in each problem a sufficient condition on the reaction rates is obtained to ensure the stability and global attractivity of positive periodic solutions.

  15. Simulation of parabolic reflectors for ultraviolet phototherapy.

    PubMed

    Robert Grimes, David

    2016-08-21

    Ultraviolet (UVR) phototherapy is widely used to treat an array of skin conditions, including psoriasis, eczema and vitiligo. For such interventions, a quantified dose is vital if the treatment is to be both biologically effective and to avoid the detrimental effects of over-dosing. As dose is absorbed at surface level, the orientation of patient site with respect to the UVR lamps modulates effective dose. Previous investigations have modelled this behaviour, and examined the impact of shaped anodized aluminium reflectors typically placed around lamps in phototherapy cabins. These mirrors are effective but tend to yield complex patterns of reflection around the cabin which can result in substantial dose inhomogeneity. There has been some speculation over whether using the reflective property of parabolic mirrors might improve dose delivery or homogeneity through the treatment cabin. In this work, the effects of parabolic mirrors are simulated and compared with standard shaped mirrors. Simulation results strongly suggest that parabolic reflectors reduce total irradiance relative to standard shaped reflectors, and have a negligible impact on dose homogeneity. PMID:27445095

  16. Simulation of parabolic reflectors for ultraviolet phototherapy

    NASA Astrophysics Data System (ADS)

    Grimes, David Robert

    2016-08-01

    Ultraviolet (UVR) phototherapy is widely used to treat an array of skin conditions, including psoriasis, eczema and vitiligo. For such interventions, a quantified dose is vital if the treatment is to be both biologically effective and to avoid the detrimental effects of over-dosing. As dose is absorbed at surface level, the orientation of patient site with respect to the UVR lamps modulates effective dose. Previous investigations have modelled this behaviour, and examined the impact of shaped anodized aluminium reflectors typically placed around lamps in phototherapy cabins. These mirrors are effective but tend to yield complex patterns of reflection around the cabin which can result in substantial dose inhomogeneity. There has been some speculation over whether using the reflective property of parabolic mirrors might improve dose delivery or homogeneity through the treatment cabin. In this work, the effects of parabolic mirrors are simulated and compared with standard shaped mirrors. Simulation results strongly suggest that parabolic reflectors reduce total irradiance relative to standard shaped reflectors, and have a negligible impact on dose homogeneity.

  17. Parabolic Trough Organic Rankine Cycle Power Plant

    SciTech Connect

    Canada, S.; Cohen, G.; Cable, R.; Brosseau, D.; Price, H.

    2005-01-01

    Arizona Public Service (APS) is required to generate a portion of its electricity from solar resources in order to satisfy its obligation under the Arizona Environmental Portfolio Standard (EPS). In recent years, APS has installed and operates over 4.5 MWe of fixed, tracking, and concentrating photovoltaic systems to help meet the solar portion of this obligation and to develop an understanding of which solar technologies provide the best cost and performance to meet utility needs. During FY04, APS began construction of a 1-MWe parabolic trough concentrating solar power plant. This plant represents the first parabolic trough plant to begin construction since 1991. The plant will also be the first commercial deployment of the Solargenix parabolic trough collector technology developed under contract to the National Renewable Energy Laboratory (NREL). The plant will use an organic Rankine cycle (ORC) power plant, provided by Ormat. The ORC power plant is much simpler than a conventional steam Rankine cycle power plant and allows unattended operation of the facility.

  18. A Harnack's inequality for mixed type evolution equations

    NASA Astrophysics Data System (ADS)

    Paronetto, Fabio

    2016-03-01

    We define a homogeneous parabolic De Giorgi classes of order 2 which suits a mixed type class of evolution equations whose simplest example is μ (x)∂ u/∂ t - Δu = 0 where μ can be positive, null and negative, so in particular elliptic-parabolic and forward-backward parabolic equations are included. For functions belonging to this class we prove local boundedness and show a Harnack inequality which, as by-products, gives Hölder-continuity, in particular in the interface I where μ changes sign, and a maximum principle.

  19. Chaotic motion of comets in near-parabolic orbit: Mapping aproaches

    NASA Astrophysics Data System (ADS)

    Liu, Jie; Sun, Yi-Sui

    1994-09-01

    There exist many comets with near-parabolic orbits in the solar system. Among various theories proposed to explain their origin, the Oort cloud hypothesis seems to be the most reasonable. The theory assumes that there is a cometary cloud at a distance 103 to 107 from the sun and that perturbing forces from planets or stars make orbits of some of these comets become the near-parabolic type. Concerning the evolution of these orbits under planetary perturbations, we can raise the question: Will they stay in the solar system forever or will they escape from it? This is an attractive dynamical problem. If we go ahead by directly solving the dynamical differential equations, we may encounter the difficulty of long-time computation. For the orbits of these comets are near-parabolic and their periods are too long to study on their long-term evolution. With mapping approaches the difficulty will be overcome. In another aspect, the study of this model has special meaning for chaotic dynamics. We know that in the neighborhood of any separatrix i.e. the trajectory with zero frequency of the uperturbed motion of a Hamiltonian system, some chaotic motions have to be expected. Actually, the simplest example of separatrix is the parabolic trajectory of the two-body problem which separates the bounded and unbounded motion. From this point of view, the dynamical study of near-parabolic motion is very important. Petrosky's elegant but more abstract deduction gives a Kepler mapping which describes the dynamics of the cometary motion. In this paper we derive a similar mapping directly and discuss its dynamical characters.

  20. Optimal Heat Collection Element Shapes for Parabolic Trough Concentrators

    SciTech Connect

    Bennett, C

    2007-11-15

    For nearly 150 years, the cross section of the heat collection tubes used at the focus of parabolic trough solar concentrators has been circular. This type of tube is obviously simple and easily fabricated, but it is not optimal. It is shown in this article that the optimal shape, assuming a perfect parabolic figure for the concentrating mirror, is instead oblong, and is approximately given by a pair of facing parabolic segments.

  1. Calculation of three-dimensional, viscous flow through turbomachinery blade passages by parabolic marching

    NASA Technical Reports Server (NTRS)

    Katsanis, T.

    1985-01-01

    The three-dimensional compressible Navier-Stokes equations are formulated in a rotating coordinate system, so as to include centrifugal and Coriolis forces. The equations are parabolized by using a previously calculated inviscid static pressure field. The thin layer Navier-Stokes approximation, which neglects streamwise diffusion, is used. A body-fitted coordinate system is used. The streamwise momentum equation is uncoupled from the cross-stream momentum equation by using contravariant momentum components, and then using the contravariant velocity components as primary unknowns. To reduce problems with small separated regions, the Reyhner and Flugge-Lotz approximation is used. The energy equation is included to allow for calculation of heat transfer. The flow may be laminar, or a simple eddy-viscosity turbulence may be used. A number of curved ducts and an axial stator were analyzed, including cases for which experimental data are available.

  2. Thermo-electronic solar power conversion with a parabolic concentrator

    NASA Astrophysics Data System (ADS)

    Olukunle, Olawole C.; De, Dilip K.

    2016-02-01

    We consider the energy dynamics of the power generation from the sun when the solar energy is concentrated on to the emitter of a thermo-electronic converter with the help of a parabolic mirror. We use the modified Richardson-Dushman equation. The emitter cross section is assumed to be exactly equal to the focused area at a height h from the base of the mirror to prevent loss of efficiency. We report the variation of output power with solar insolation, height h, reflectivity of the mirror, and anode temperature, initially assuming that there is no space charge effect. Our methodology allows us to predict the temperature at which the anode must be cooled in order to prevent loss of efficiency of power conversion. Novel ways of tackling the space charge problem have been discussed. The space charge effect is modeled through the introduction of a parameter f (0 < f < 1) in the thermos-electron emission equation. We find that the efficiency of the power conversion depends on solar insolation, height h, apart from radii R of the concentrator aperture and emitter, and the collector material properties. We have also considered solar thermos electronic power conversion by using single atom-layer graphene as an emitter.

  3. Parabolic Trough VSHOT Optical Characterization in 2005-2006 (Presentation)

    SciTech Connect

    Wendelin, T.

    2006-02-01

    This presentation regarding parabolic trough VSHOT optical characterization describes trough deployment and operation phases including: development, manufacture/installation, and maintenance/operation.

  4. Alignment method for parabolic trough solar concentrators

    DOEpatents

    Diver, Richard B.

    2010-02-23

    A Theoretical Overlay Photographic (TOP) alignment method uses the overlay of a theoretical projected image of a perfectly aligned concentrator on a photographic image of the concentrator to align the mirror facets of a parabolic trough solar concentrator. The alignment method is practical and straightforward, and inherently aligns the mirror facets to the receiver. When integrated with clinometer measurements for which gravity and mechanical drag effects have been accounted for and which are made in a manner and location consistent with the alignment method, all of the mirrors on a common drive can be aligned and optimized for any concentrator orientation.

  5. Comments on ``Barut-Girardello Coherent States for the Parabolic Cylinder Functions''

    NASA Astrophysics Data System (ADS)

    Fakhri, H.; Dehghani, A.; Mojaveri, B.

    2009-02-01

    In Chenaghlou and Faizy (Int. J. Theor. Phys. 2008), the authors claim that they have constructed the Barut-Girardello coherent states for the parabolic cylinder functions. However, we point out here that by introducing these coherent states, Schrödinger was able to put forth the idea of “coherent states of the quantum harmonic oscillator” over eighty years ago. These coherent states are derived not only from the Barut-Girardello eigenvalue equation, but also from the Schrödinger and the Klauder-Perelomov approaches. Thus, contrary to their claim, the authors have not introduced new coherent states. In particular, a wide range of the parabolic cylinder functions do not form an orthonormal basis.

  6. Existence and concentration of positive ground states for a Kirchhoff equation involving critical Sobolev exponent

    NASA Astrophysics Data System (ADS)

    Liu, Zhisu; Guo, Shangjiang

    2015-06-01

    In this paper, we consider the following semilinear Kirchhoff type equation where is a small parameter, , a, b are positive constants, μ > 0 is a parameter, and the nonlinear growth of | u|4 u reaches the Sobolev critical exponent since 2* = 6 for three spatial dimensions. We prove the existence of a positive ground state solution with exponential decay at infinity for μ > 0 and sufficiently small under some suitable conditions on the nonnegative functions V, K and Q. Moreover, concentrates around a global minimum point of V as . The methods used here are based on the concentration-compactness principle of Lions.

  7. Parabolic flight - Loss of sense of orientation

    NASA Technical Reports Server (NTRS)

    Lackner, J. R.; Graybiel, A.

    1979-01-01

    On the earth, or in level flight, a blindfolded subject being rotated at constant velocity about his recumbent long body axis experiences illusory orbital motion of his body in the opposite direction. By contrast, during comparable rotation in the free-fall phase of parabolic flight, no body motion is perceived and all sense of external orientation may be lost; when touch and pressure stimulation is applied to the body surface, a sense of orientation is reestablished immediately. The increased gravitoinertial force period of a parabola produces an exaggeration of the orbital motion experienced in level flight. These observations reveal an important influence of touch, pressure, and kinesthetic information on spatial orientation and provide a basis for understanding many of the postural illusions reported by astronauts in space flight.

  8. Steam engine research for solar parabolic dish

    NASA Technical Reports Server (NTRS)

    Demler, R. L.

    1981-01-01

    The parabolic dish solar concentrator provides an opportunity to generate high grade energy in a modular system. Most of the capital is projected to be in the dish and its installation. Assurance of a high production demand of a standard dish could lead to dramatic cost reductions. High production volume in turn depends upon maximum application flexibility by providing energy output options, e.g., heat, electricity, chemicals and combinations thereof. Subsets of these options include energy storage and combustion assist. A steam engine design and experimental program is described which investigate the efficiency potential of a small 25 kW compound reheat cycle piston engine. An engine efficiency of 35 percent is estimated for a 700 C steam temperature from the solar receiver.

  9. Parabolic dish module experiment. Final test report

    SciTech Connect

    Not Available

    1986-03-01

    A development test model of the 8-meter Solar Brayton Parabolic Dish Module has been designed, fabricated, and tested. The test model consists of five major subsystems: Sanders ceramic honeycomb solar receiver; LaJet LEC460 solar concentrator; AiRsearch SABC MKIIIA engine, Abacus 8 kW ac inverter; and a Sanders designed and built system controller. Goals of the tests were to integrate subsystem components into a working module, demonstrate the concept, and generate 5 kWe (hybrid) and 4.7 kWe (solar only) input. All subsystem integration goals were successfully achieved, but system performance efficiency was lower than expected. Contributing causes of the lower performance efficiencies have been identified. Modifications needed to restore performance to the required levels and improve the system life cycle cost have been addressed and are the subject of this final report.

  10. Antireflection Pyrex envelopes for parabolic solar collectors

    NASA Astrophysics Data System (ADS)

    McCollister, H. L.; Pettit, R. B.

    1983-11-01

    Antireflective (AR) coatings, applied to the glass envelopes used in parabolic trough solar collectors around the receiver tube in order to reduce thermal losses, can increase solar transmittance by 7 percent. An AR surface has been formed on Pyrex by first heat treating the glass to cause a compositional phase separation, removing a surface layer after heat treatment through the use of a preetching solution, and finally etching in a solution that contains hydrofluorosilic and ammonium bifluoride acids. AR-coated samples with solar transmittance values of more than 0.97, by comparison to an untreated sample value of 0.91, have been obtained for the 560-630 C range of heat treatment temperatures. Optimum values have also been determined for the other processing parameters.

  11. Analysis of the Quality of Parabolic Flight

    NASA Technical Reports Server (NTRS)

    Lambot, Thomas; Ord, Stephan F.

    2016-01-01

    Parabolic flight allows researchers to conduct several micro-gravity experiments, each with up to 20 seconds of micro-gravity, in the course of a single day. However, the quality of the flight environment can vary greatly over the course of a single parabola, thus affecting the experimental results. Researchers therefore require knowledge of the actual flight environment as a function of time. The NASA Flight Opportunities program (FO) has reviewed the acceleration data for over 400 parabolas and investigated the level of micro-gravity quality. It was discovered that a typical parabola can be segmented into multiple phases with different qualities and durations. The knowledge of the microgravity characteristics within the parabola will prove useful when planning an experiment.

  12. Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type with small data

    NASA Astrophysics Data System (ADS)

    Ishida, Sachiko; Yokota, Tomomi

    This paper deals with the quasilinear degenerate Keller-Segel system (KS) of "parabolic-parabolic" type. The global existence of weak solutions to (KS) with small initial data is established when q⩾m+2/N ( m denotes the intensity of diffusion and q denotes the nonlinearity). In the system of "parabolic-elliptic" type, Sugiyama and Kunii (2006) [13, Theorem 3] and Sugiyama (2007) [12, Theorem 2] state the similar result; note that q=m+2/N corresponds to generalized Fujita's critical exponent. However, the super-critical case where q⩾m+2/N has been unsolved for "parabolic-parabolic" type. Therefore this paper gives an answer to the unsolved problem.

  13. Graviresponses of Paramecium biaurelia during parabolic flights.

    PubMed

    Krause, Martin; Bräucker, Richard; Hemmersbach, Ruth

    2006-12-01

    The thresholds of graviorientation and gravikinesis in Paramecium biaurelia were investigated during the 5th DLR (German Aerospace Center) parabolic-flight campaign at Bordeaux in June 2003. Parabolic flights are a useful tool for the investigation of swimming behaviour in protists at different accelerations. At normal gravity (1 g) and hypergravity (1 g to 1.8 g), precision of orientation and locomotion rates depend linearly on the applied acceleration as seen in earlier centrifuge experiments. After transition from hypergravity to decreased gravity (minimal residual acceleration of <10(-2) g), graviorientation as well as gravikinesis show a full relaxation with different kinetics. The use of twelve independent cell samples per flight guarantees high data numbers and secures the statistical significance of the obtained data. The relatively slow change of acceleration between periods of microgravity and hypergravity (0.4 g/s) enabled us to determine the thresholds of graviorientation at 0.6 g and of gravikinesis at 0.4 g. The gravity-unrelated propulsion rate of the sample was found to be 874 microm/s, exceeding the locomotion rate of horizontally swimming cells (855 microm/s). The measured thresholds of graviresponses were compared with data obtained from earlier centrifuge experiments on the sounding rocket Maxus-2. Measured thresholds of gravireactions indicate that small energies, close to the thermal noise level, are sufficient for the gravitransduction process. Data from earlier hypergravity experiments demonstrate that mechanosensitive ion channels are functioning over a relative wide range of acceleration. From this, we may speculate that gravireceptor channels derive from mechanoreceptor channels. PMID:17180491

  14. The Effect of Boundary Support and Reflector Dimensions on Inflatable Parabolic Antenna Performance

    NASA Technical Reports Server (NTRS)

    Coleman, Michael J.; Baginski, Frank; Romanofsky, Robert R.

    2011-01-01

    For parabolic antennas with sufficient surface accuracy, more power can be radiated with a larger aperture size. This paper explores the performance of antennas of various size and reflector depth. The particular focus is on a large inflatable elastic antenna reflector that is supported about its perimeter by a set of elastic tendons and is subjected to a constant hydrostatic pressure. The surface accuracy of the antenna is measured by an RMS calculation, while the reflector phase error component of the efficiency is determined by computing the power density at boresight. In the analysis, the calculation of antenna efficiency is not based on the Ruze Equation. Hence, no assumption regarding the distribution of the reflector surface distortions is presumed. The reflector surface is modeled as an isotropic elastic membrane using a linear stress-strain constitutive relation. Three types of antenna reflector construction are considered: one molded to an ideal parabolic form and two different flat panel design patterns. The flat panel surfaces are constructed by seaming together panels in a manner that the desired parabolic shape is approximately attained after pressurization. Numerical solutions of the model problem are calculated under a variety of conditions in order to estimate the accuracy and efficiency of these antenna systems. In the case of the flat panel constructions, several different cutting patterns are analyzed in order to determine an optimal cutting strategy.

  15. Experimental Investigation of Pressure-volume-Temperature Mass Gauging Method Under Microgravity Condition by Parabolic Flight

    NASA Astrophysics Data System (ADS)

    Seo, Mansu; Park, Hana; Yoo, DonGyu; Jung, Youngsuk; Jeong, Sangkwon

    Gauging the volume or mass of liquid propellant of a rocket vehicle in space is an important issue for its economic feasibility and optimized design of loading mass. Pressure-volume-temperature (PVT) gauging method is one of the most suitable measuring techniques in space due to its simplicity and reliability. This paper presents unique experimental results and analyses of PVT gauging method using liquid nitrogen under microgravity condition by parabolic flight. A vacuum-insulated and cylindrical-shaped liquid nitrogen storage tank with 9.2 L volume is manufactured by observing regulation of parabolic flight. PVT gauging experiments are conducted under low liquid fraction condition from 26% to 32%. Pressure, temperature, and the injected helium mass into the storage tank are measured to obtain the ullage volume by gas state equation. Liquid volume is finally derived by the measured ullage volume and the known total tank volume. Two sets of parabolic flights are conducted and each set is composed of approximately 10 parabolic flights. In the first set of flights, the short initial waiting time (3 ∼ 5 seconds) cannot achieve sufficient thermal equilibrium condition at the beginning. It causes inaccurate gauging results due to insufficient information of the initial helium partial pressure in the tank. The helium injection after 12 second waiting time at microgravity condition with high mass flow rate in the second set of flights achieves successful initial thermal equilibrium states and accurate measurement results of initial helium partial pressure. Liquid volume measurement errors in the second set are within 11%.

  16. THE PARABOLIC JET STRUCTURE IN M87 AS A MAGNETOHYDRODYNAMIC NOZZLE

    SciTech Connect

    Nakamura, Masanori; Asada, Keiichi E-mail: asada@asiaa.sinica.edu.tw

    2013-10-01

    The structure and dynamics of the M87 jet from sub-milliarcsec to arcsecond scales are continuously examined. We analyzed the Very Long Baseline Array archival data taken at 43 and 86 GHz to measure the size of very long baseline interferometry (VLBI) cores. Millimeter/sub-millimeter VLBI cores are considered as innermost jet emissions, which has been originally suggested by Blandford and Königl. Those components fairly follow an extrapolated parabolic streamline in our previous study so that the jet has a single power-law structure with nearly 5 orders of magnitude in the distance starting from the vicinity of the supermassive black hole (SMBH), less than 10 Schwarzschild radius (r{sub s}). We further inspect the jet parabolic structure as a counterpart of the magnetohydrodynamic (MHD) nozzle in order to identify the property of a bulk acceleration. We interpret that the parabolic jet consists of Poynting-flux dominated flows, powered by large-amplitude, nonlinear torsional Alfvén waves. We examine the non-relativistic MHD nozzle equation in a parabolic shape. The nature of trans-fast magnetosonic flow is similar to the one of transonic solution of Parker's hydrodynamic solar wind; the jet becomes super-escape as well as super-fast magnetosonic at around ∼10{sup 3} r{sub s}, while the upstream trans-Alfvénic flow speed increases linearly as a function of the distance at ∼10{sup 2}-10{sup 3} r{sub s}. We here point out that this is the first evidence to identify these features in astrophysical jets. We propose that the M87 jet is magnetically accelerated, but thermally confined by the stratified interstellar medium inside the sphere of gravitational influence of the SMBH potential, which may be a norm in active galactic nucleus jets.

  17. A study on optical aberrations in parabolic neutron guides

    NASA Astrophysics Data System (ADS)

    Wang, Yu; Wang, Hongli; Liu, Yuntao; Zu, Yong; He, Linfeng; Wei, Guohai; Sun, Kai; Han, Songbai; Chen, Dongfeng

    2015-06-01

    It is widely believed that a neutron beam can be focused to a small spot using a parabolic guide, which will significantly improve the flux. However, researchers have also noted challenges for the neutron inhomogeneous phase space distribution in parabolic focusing guide systems. In this paper, the sources of most prominent optical aberrations, such as an inhomogeneous phase space distribution and irregular divergence distribution, are discussed, and an optimization solution is also proposed. We indicate that optimizing the parabolic guide geometrical configuration removes almost all of the aberrations and yields a considerable intensity gain factor.

  18. Proceedings of the Fifth Parabolic Dish Solar Thermal Power Program

    NASA Technical Reports Server (NTRS)

    Lucas, J. W. (Editor)

    1984-01-01

    The proceedings of the Fifth Parabolic Dish Solar Thermal Power Program Annual Review are presented. The results of activities within the Parabolic Dish Technology and Module/Systems Development element of the Department of Energy's Solar Thermal Energy Systems Program were emphasized. Among the topics discussed were: overall Project and Program aspects, Stirling and Brayton module development, concentrator and engine/receiver development along with associated hardware and test results; distributed systems operating experience; international parabolic dish development activities; and non-DOE-sponsored domestic dish activities. Solar electric generation was also addressed.

  19. Investigation of parabolic computational techniques for internal high-speed viscous flows

    NASA Technical Reports Server (NTRS)

    Anderson, O. L.; Power, G. D.

    1985-01-01

    A feasibility study was conducted to assess the applicability of an existing parabolic analysis (ADD-Axisymmetric Diffuser Duct), developed previously for subsonic viscous internal flows, to mixed supersonic/subsonic flows with heat addition simulating a SCRAMJET combustor. A study was conducted with the ADD code modified to include additional convection effects in the normal momentum equation when supersonic expansion and compression waves were present. It is concluded from the present study that for the class of problems where strong viscous/inviscid interactions are present a global iteration procedure is required.

  20. Entropy solutions for a nonlinear parabolic problems with lower order term in Orlicz spaces

    NASA Astrophysics Data System (ADS)

    Mabdaoui, M.; Moussa, H.; Rhoudaf, M.

    2016-03-01

    We shall give the proof of existence results for the entropy solutions of the following nonlinear parabolic problem [Equation not available: see fulltext.]where A is a Leray-Lions operator having a growth not necessarily of polynomial type. The lower order term Φ :Ω × (0,T)× {R}→ {R}^N is a Carathéodory function, for a.e. (x,t)in Q_T and for all sin R , satisfying only a growth condition and the right hand side f belongs to L^1(Q_T).

  1. Optimal discrete-time LQR problems for parabolic systems with unbounded input: Approximation and convergence

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.

    1988-01-01

    An abstract approximation and convergence theory for the closed-loop solution of discrete-time linear-quadratic regulator problems for parabolic systems with unbounded input is developed. Under relatively mild stabilizability and detectability assumptions, functional analytic, operator techniques are used to demonstrate the norm convergence of Galerkin-based approximations to the optimal feedback control gains. The application of the general theory to a class of abstract boundary control systems is considered. Two examples, one involving the Neumann boundary control of a one-dimensional heat equation, and the other, the vibration control of a cantilevered viscoelastic beam via shear input at the free end, are discussed.

  2. Nearly Interactive Parabolized Navier-Stokes Solver for High Speed Forebody and Inlet Flows

    NASA Technical Reports Server (NTRS)

    Benson, Thomas J.; Liou, May-Fun; Jones, William H.; Trefny, Charles J.

    2009-01-01

    A system of computer programs is being developed for the preliminary design of high speed inlets and forebodies. The system comprises four functions: geometry definition, flow grid generation, flow solver, and graphics post-processor. The system runs on a dedicated personal computer using the Windows operating system and is controlled by graphical user interfaces written in MATLAB (The Mathworks, Inc.). The flow solver uses the Parabolized Navier-Stokes equations to compute millions of mesh points in several minutes. Sample two-dimensional and three-dimensional calculations are demonstrated in the paper.

  3. Development of a semi-parabolic two-fluid model for two-phase ejectors

    SciTech Connect

    Menegay, P.; Kornhauser, A.A.

    1995-12-31

    A semi-parabolic computer code for two-phase flows, currently under development, is presented. When complete, the code will simulate two-phase non-equilibrium flow within an ejector being used as a refrigerant expansion engine. Current two-phase ejector design has been hampered by the inadequacy of available analytical techniques. The code addresses this problem. The applicable two-phase flow conservation equations are presented. Also shown are the interfacial interaction terms, important in modelling the non-equilibrium effects. A stepwise development program has been established where the simplest case is solved first followed by complicating features.

  4. Incomplete iterations in multistep backward difference methods for parabolic problems with smooth and nonsmooth data

    SciTech Connect

    Bramble, J. H.; Pasciak, J. E.; Sammon, P. H.; Thomee, V.

    1989-04-01

    Backward difference methods for the discretization of parabolic boundary value problems are considered in this paper. In particular, we analyze the case when the backward difference equations are only solved 'approximately' by a preconditioned iteration. We provide an analysis which shows that these methods remain stable and accurate if a suitable number of iterations (often independent of the spatial discretization and time step size) are used. Results are provided for the smooth as well as nonsmooth initial data cases. Finally, the results of numerical experiments illustrating the algorithms' performance on model problems are given.

  5. Parabolic Anderson Model in a Dynamic Random Environment: Random Conductances

    NASA Astrophysics Data System (ADS)

    Erhard, D.; den Hollander, F.; Maillard, G.

    2016-06-01

    The parabolic Anderson model is defined as the partial differential equation ∂ u( x, t)/ ∂ t = κ Δ u( x, t) + ξ( x, t) u( x, t), x ∈ ℤ d , t ≥ 0, where κ ∈ [0, ∞) is the diffusion constant, Δ is the discrete Laplacian, and ξ is a dynamic random environment that drives the equation. The initial condition u( x, 0) = u 0( x), x ∈ ℤ d , is typically taken to be non-negative and bounded. The solution of the parabolic Anderson equation describes the evolution of a field of particles performing independent simple random walks with binary branching: particles jump at rate 2 d κ, split into two at rate ξ ∨ 0, and die at rate (- ξ) ∨ 0. In earlier work we looked at the Lyapunov exponents λ p(κ ) = limlimits _{tto ∞} 1/t log {E} ([u(0,t)]p)^{1/p}, quad p in {N} , qquad λ 0(κ ) = limlimits _{tto ∞} 1/2 log u(0,t). For the former we derived quantitative results on the κ-dependence for four choices of ξ : space-time white noise, independent simple random walks, the exclusion process and the voter model. For the latter we obtained qualitative results under certain space-time mixing conditions on ξ. In the present paper we investigate what happens when κΔ is replaced by Δ𝓚, where 𝓚 = {𝓚( x, y) : x, y ∈ ℤ d , x ˜ y} is a collection of random conductances between neighbouring sites replacing the constant conductances κ in the homogeneous model. We show that the associated annealed Lyapunov exponents λ p (𝓚), p ∈ ℕ, are given by the formula λ p({K} ) = {sup} {λ p(κ ) : κ in {Supp} ({K} )}, where, for a fixed realisation of 𝓚, Supp(𝓚) is the set of values taken by the 𝓚-field. We also show that for the associated quenched Lyapunov exponent λ 0(𝓚) this formula only provides a lower bound, and we conjecture that an upper bound holds when Supp(𝓚) is replaced by its convex hull. Our proof is valid for three classes of reversible ξ, and for all 𝓚

  6. Offset semi-parabolic nanoantenna made of a photonic crystal parabolic mirror and a plasmonic bow-tie antenna.

    PubMed

    Hattori, Haroldo T

    2014-10-10

    In a parabolic mirror, light coming parallel to the antenna passes through its focal point. In this work, a waveguide feeds a semi-parabolic photonic crystal mirror and the emerging beam feeds a bow-tie antenna placed at the mirror's focal point-it is shown that the antenna system can not only feed a bow-tie antenna (producing a localized moderately high electric field) but also produces a directional radiation beam. The semi-parabolic mirror is also modified to reduce reflection back to the feeding waveguide. PMID:25322381

  7. The French thermo-helio-electricity-KW parabolic dish program

    NASA Technical Reports Server (NTRS)

    Audibert, M.; Peri, G.

    1982-01-01

    The testing and development of parabolic dish solar thermal power plants to produce, thermal mechanical, or electrical energy are discussed. The design, construction, and experiments of prototype collectors to prove the feasibility of such collectors is described.

  8. FASTRACK (TM): Parabolic and Suborbital Experiment Support Facility

    NASA Technical Reports Server (NTRS)

    Richards, Stephanie E. (Compiler); Levine, Howard G.; Romero, V.

    2016-01-01

    FASTRACK was developed by NASA Kennedy Space Center and Space Florida to provide capabilities to conduct frequent, affordable, and responsive flight opportunities for reduced gravity experiments, technology development, and hardware testing on suborbital vehicles and parabolic flights.

  9. Detail, external parabolic antenna (later addition). Note how waveguide was ...

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

    Detail, external parabolic antenna (later addition). Note how waveguide was cut to remove active portion of antenna. - Western Union Telegraph Company, Jennerstown Relay, Laurel Summit Road off U.S. 30, Laughlintown, Westmoreland County, PA

  10. Antenna cab interior showing waveguide from external parabolic antenna (later ...

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

    Antenna cab interior showing waveguide from external parabolic antenna (later addition), looking north. - Western Union Telegraph Company, Jennerstown Relay, Laurel Summit Road off U.S. 30, Laughlintown, Westmoreland County, PA

  11. 33. July 1958 PARABOLIC BRICK VAULT IN SERVICE MAGAZINE UNDER ...

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

    33. July 1958 PARABOLIC BRICK VAULT IN SERVICE MAGAZINE UNDER RAVELIN (CIVIL WAR PERIOD) - Fort McHenry National Monument & Historic Shrine, East Fort Avenue at Whetstone Point, Baltimore, Independent City, MD

  12. An X-band parabolic antenna based on gradient metasurface

    NASA Astrophysics Data System (ADS)

    Yao, Wang; Yang, Helin; Huang, Xiaojun; Tian, Ying; Guo, Linyan

    2016-07-01

    We present a novel parabolic antenna by employing reflection gradient metasurface which is composed of a series of circle patches on a grounded dielectric substrate. Similar to the traditional parabolic antenna, the proposed antenna take the metasurface as a "parabolic reflector" and a patch antenna was placed at the focal point of the metasurface as a feed source, then the quasi-spherical wave emitted by the source is reflected and transformed to plane wave with high efficiency. Due to the focus effect of reflection, the beam width of the antenna has been decreased from 85.9° to 13° and the gain has been increased from 6.5 dB to 20.8 dB. Simulation and measurement results of both near and far-field plots demonstrate good focusing properties of the proposed parabolic antenna.

  13. Parabolic dish test site: History and operating experience

    NASA Technical Reports Server (NTRS)

    Selcuk, M. K. (Compiler)

    1985-01-01

    The parabolic dish test site (PDTS) was established for testing point-focusing solar concentrator systems operating at temperatures approaching 1650 C. Among tests run were evaluation and performance characterization of parabolic dish concentrators, receivers, power conversion units, and solar/fossil-fuel hybrid systems. The PDTS was fully operational until its closure in June, 1984. The evolution of the test program, a chronological listing of the experiments run, and data summaries for most of the tests conducted are presented.

  14. Solar parabolic dish technology annual evaluation report. Fiscal year 1983

    SciTech Connect

    Not Available

    1984-04-15

    This report summarizes the activities of the JPL Solar Thermal Power Systems Parabolic Dish Project for FY 1983. Included are discussions on designs of module development including their concentrator, receiver, and power conversion subsystem together with a separate discussion of concentrator development. Analyses and test results, along with progress on field tests, Small Community Experiment system development, and tests at the Parabolic Dish Test Site are also included.

  15. The effects of indefinite nonlinear boundary conditions on the structure of the positive solutions set of a logistic equation

    NASA Astrophysics Data System (ADS)

    Ramos Quoirin, Humberto; Umezu, Kenichiro

    2014-12-01

    We investigate a semilinear elliptic equation with a logistic nonlinearity and an indefinite nonlinear boundary condition, both depending on a parameter λ. Overall, we analyze the effect of the indefinite nonlinear boundary condition on the structure of the positive solutions set. Based on variational and bifurcation techniques, our main results establish the existence of three nontrivial non-negative solutions for some values of λ, as well as their asymptotic behavior. These results suggest that the positive solutions set contains an S-shaped component in some case, as well as a combination of a C-shaped and an S-shaped components in another case.

  16. Dynamics of strongly coupled spatially distributed logistic equations with delay

    NASA Astrophysics Data System (ADS)

    Kashchenko, I. S.; Kashchenko, S. A.

    2015-04-01

    The dynamics of a system of two logistic delay equations with spatially distributed coupling is studied. The coupling coefficient is assumed to be sufficiently large. Special nonlinear systems of parabolic equations are constructed such that the behavior of their solutions is determined in the first approximation by the dynamical properties of the original system.

  17. Dynamics of the Kuramoto equation with spatially distributed control

    NASA Astrophysics Data System (ADS)

    Kashchenko, Ilia; Kaschenko, Sergey

    2016-05-01

    We consider the scalar complex equation with spatially distributed control. Its dynamical properties are studied by asymptotic methods when the control coefficient is either sufficiently large or sufficiently small and the function of distribution is either almost symmetric or significantly nonsymmetric relative to zero. In all cases we reduce original equation to quasinormal form - the family of special parabolic equations, which do not contain big and small parameters, which nonlocal dynamics determines the behaviour of solutions of the original equation.

  18. Antireflection pyrex envelopes for parabolic solar collectors

    SciTech Connect

    McCollister, H.L.; Pettit, R.B.

    1983-01-01

    Parabolic trough solar collectors utilize glass envelopes around the receiver tube in order to reduce thermal losses. Antireflective (AR) coatings applied to the envelope can potentially increase the solar transmittance by 0.07. An excellent AR surface can be formed on Pyrex (Corning Code 7740 glass) by first heat treating the glass to cause a compositional phase separation. After heat treating, a surface layer is removed using a pre-etch solution of aqueous ammonium bifluoride. Finally the AR layer is formed by etching in a solution containing hydrofluorosilic and ammonium bifluoride acid. Processing parameters studied included the phase separation temperature and heat treatment time, the pre-etch time, and the etching bath temperature and time. AR-coated samples with solar transmittance values >0.97, as compared to a value of 0.91 in untreated samples, were obtained for a range of heat treatment temperatures from 560 to 630/sup 0/C. The phase separation time and temperature interact so that at 630/sup 0/C short times are required (3 hours) while at 560/sup 0/C longer times are necessary (24 hours). Optimum values for the other processing parameters are 12 to 18 minutes in the pre-etching bath, and 5 to 10 minutes in the film forming bath when maintained between 35 and 45/sup 0/C. Application of this process to full scale 3 m long x 6 cm diameter Pyrex envelopes was successful in producing solar transmittance values greater than or equal to 0.97.

  19. Antireflection Pyrex envelopes for parabolic solar collectors

    SciTech Connect

    McCollister, H.L.; Pettit, R.B.

    1983-11-01

    Parabolic trough solar collectors utilize glass envelopes around the receiver tube in order to reduce thermal losses. Antireflective (AR) coatings applied to the envelope can potentially increase the solar transmittance by 7 percent. An excellent AR surface can be formed on Pyrex (Corning Code 7740 glass) by first heat treating the glass to cause a compositional phase separation. After heat treating, a surface layer is removed using a pre-etch solution of aqueous ammonium bifluoride. Finally, the AR layer is formed by etching in a solution containing hydrofluorosilic and ammonium bifluoride acid. Processing parameters studied included the phase separation temperature and heat treatment time, the pre-etch time, and the etching bath temperature and time. AR-coated samples with solar transmittance values > 0.97, as compared to a value of 0.91 in untreated samples, were obtained for a range of heat treatment temperatures from 560-630/sup 0/C. The phase separation time and temperature interact so that at 630/sup 0/C short times are required (3 hrs) while at 560/sup 0/C longer times are necessary (24 hrs). Optimum values for the other processing parameters are 12-18 min in the pre-etching bath, and 5-10 min in the film forming bath when maintained between 35-45/sup 0/C. Application of this process to full scale 3-m-long X 6-cm dia Pyrex envelopes was successful in producing solar transmittance values greater than or equal to 0.97.

  20. Multigrid methods for a semilinear PDE in the theory of pseudoplastic fluids

    NASA Technical Reports Server (NTRS)

    Henson, Van Emden; Shaker, A. W.

    1993-01-01

    We show that by certain transformations the boundary layer equations for the class of non-Newtonian fluids named pseudoplastic can be generalized in the form the vector differential operator(u) + p(x)u(exp -lambda) = 0, where x is a member of the set Omega and Omega is a subset of R(exp n), n is greater than or equal to 1 under the classical conditions for steady flow over a semi-infinite flat plate. We provide a survey of the existence, uniqueness, and analyticity of the solutions for this problem. We also establish numerical solutions in one- and two-dimensional regions using multigrid methods.

  1. Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation

    SciTech Connect

    Caraballo, Tomas Kloeden, Peter E. Schmalfuss, Bjoern

    2004-10-15

    We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when zero is not a solution for these equations. We prove the existence of anon-trivial stationary solution which is exponentially stable, where the stationary solution is generated by the composition of a random variable and the Wiener shift. We also construct stationary solutions with the stronger property of attracting bounded sets uniformly. The existence of these stationary solutions follows from the theory of random dynamical systems and their attractors. In addition, we prove some perturbation results and formulate conditions for the existence of stationary solutions for semilinear stochastic partial differential equations with Lipschitz continuous non-linearities.

  2. Status of APS 1-Mwe Parabolic Trough Project

    SciTech Connect

    Canada, S.; Brosseau, D.; Kolb, G.; Moore, L.; Cable, R.; Price, H.

    2005-11-01

    Arizona Public Service (APS) is currently installing new power facilities to generate a portion of its electricity from solar resources that will satisfy its obligation under the Arizona Environmental Portfolio Standard (EPS). During FY04, APS began construction on a 1-MWe parabolic trough concentrating solar power plant. This plant represents the first parabolic trough plant to begin construction since 1991. Site preparation and construction activities continued throughout much of FY05, and startup activities are planned for Fall 2005 (with completion early in FY06). The plant will be the first commercial deployment of the Solargenix parabolic trough collector technology developed under contract to the National Renewable Energy Laboratory. The plant will use an organic Rankine cycle (ORC) power plant, provided by Ormat. The ORC power plant is much simpler than the conventional steam Rankine cycle plant and allows unattended operation of the facility.

  3. Stable parabolic Higgs bundles as asymptotically stable decorated swamps

    NASA Astrophysics Data System (ADS)

    Beck, Nikolai

    2016-06-01

    Parabolic Higgs bundles can be described in terms of decorated swamps, which we studied in a recent paper. This description induces a notion of stability of parabolic Higgs bundles depending on a parameter, and we construct their moduli space inside the moduli space of decorated swamps. We then introduce asymptotic stability of decorated swamps in order to study the behaviour of the stability condition as one parameter approaches infinity. The main result is the existence of a constant, such that stability with respect to parameters greater than this constant is equivalent to asymptotic stability. This implies boundedness of all decorated swamps which are semistable with respect to some parameter. Finally, we recover the usual stability condition of parabolic Higgs bundles as asymptotic stability.

  4. Federal technology alert. Parabolic-trough solar water heating

    SciTech Connect

    1998-04-01

    Parabolic-trough solar water heating is a well-proven renewable energy technology with considerable potential for application at Federal facilities. For the US, parabolic-trough water-heating systems are most cost effective in the Southwest where direct solar radiation is high. Jails, hospitals, barracks, and other facilities that consistently use large volumes of hot water are particularly good candidates, as are facilities with central plants for district heating. As with any renewable energy or energy efficiency technology requiring significant initial capital investment, the primary condition that will make a parabolic-trough system economically viable is if it is replacing expensive conventional water heating. In combination with absorption cooling systems, parabolic-trough collectors can also be used for air-conditioning. Industrial Solar Technology (IST) of Golden, Colorado, is the sole current manufacturer of parabolic-trough solar water heating systems. IST has an Indefinite Delivery/Indefinite Quantity (IDIQ) contract with the Federal Energy Management Program (FEMP) of the US Department of Energy (DOE) to finance and install parabolic-trough solar water heating on an Energy Savings Performance Contract (ESPC) basis for any Federal facility that requests it and for which it proves viable. For an ESPC project, the facility does not pay for design, capital equipment, or installation. Instead, it pays only for guaranteed energy savings. Preparing and implementing delivery or task orders against the IDIQ is much simpler than the standard procurement process. This Federal Technology Alert (FTA) of the New Technology Demonstration Program is one of a series of guides to renewable energy and new energy-efficient technologies.

  5. Parabolic approximation method for fast magnetosonic wave propagation in tokamaks

    SciTech Connect

    Phillips, C.K.; Perkins, F.W.; Hwang, D.Q.

    1985-07-01

    Fast magnetosonic wave propagation in a cylindrical tokamak model is studied using a parabolic approximation method in which poloidal variations of the wave field are considered weak in comparison to the radial variations. Diffraction effects, which are ignored by ray tracing mthods, are included self-consistently using the parabolic method since continuous representations for the wave electromagnetic fields are computed directly. Numerical results are presented which illustrate the cylindrical convergence of the launched waves into a diffraction-limited focal spot on the cyclotron absorption layer near the magnetic axis for a wide range of plasma confinement parameters.

  6. Focusing of Intense Laser via Parabolic Plasma Concave Surface

    NASA Astrophysics Data System (ADS)

    Zhou, Weimin; Gu, Yuqiu; Wu, Fengjuan; Zhang, Zhimeng; Shan, Lianqiang; Cao, Leifeng; Zhang, Baohan

    2015-12-01

    Since laser intensity plays an important role in laser plasma interactions, a method of increasing laser intensity - focusing of an intense laser via a parabolic plasma concave surface - is proposed and investigated by three-dimensional particle-in-cell simulations. The geometric focusing via a parabolic concave surface and the temporal compression of high harmonics increased the peak intensity of the laser pulse by about two orders of magnitude. Compared with the improvement via laser optics approaches, this scheme is much more economic and appropriate for most femtosecond laser facilities. supported by National Natural Science Foundation of China (Nos. 11174259, 11175165), and the Dual Hundred Foundation of China Academy of Engineering Physics

  7. Extension of Gauss' method for the solution of Kepler's equation

    NASA Technical Reports Server (NTRS)

    Battin, R. H.; Fill, T. J.

    1978-01-01

    Gauss' method for solving Kepler's equation is extended to arbitrary epochs and orbital eccentricities. Although originally developed for near parabolic orbits in the vicinity of pericenter, a generalization of the method leads to a highly efficient algorithm which compares favorably to other methods in current use. A key virtue of the technique is that convergence is obtained by a method of successive substitutions with an initial approximation that is independent of the orbital parameters. The equations of the algorithm are universal, i.e., independent of the nature of the orbit whether elliptic, hyperbolic, parabolic or rectilinear.

  8. Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type

    NASA Astrophysics Data System (ADS)

    Ishida, Sachiko; Yokota, Tomomi

    This paper deals with the quasilinear degenerate Keller-Segel system (KS) of parabolic-parabolic type. The global existence of weak solutions to (KS) is established when q

  9. A fast algorithm for parabolic PDE-based inverse problems based on Laplace transforms and flexible Krylov solvers

    SciTech Connect

    Bakhos, Tania; Saibaba, Arvind K.; Kitanidis, Peter K.

    2015-10-15

    We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in solving these inverse problems using Newton-type methods is the computational cost associated with solving the forward problem and with repeated construction of the Jacobian, which represents the sensitivity of the measurements to the unknown parameters. Forming the Jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time-dependent parabolic partial differential equations corresponding to multiple sources and receivers. We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently. Our proposed solver speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time. We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests. The algorithms discussed are applied to a synthetic example taken from THT to demonstrate the resulting computational gains of this proposed method.

  10. Orthostatic intolerance and motion sickness after parabolic flight

    NASA Technical Reports Server (NTRS)

    Schlegel, T. T.; Brown, T. E.; Wood, S. J.; Benavides, E. W.; Bondar, R. L.; Stein, F.; Moradshahi, P.; Harm, D. L.; Fritsch-Yelle, J. M.; Low, P. A.

    2001-01-01

    Because it is not clear that the induction of orthostatic intolerance in returning astronauts always requires prolonged exposure to microgravity, we investigated orthostatic tolerance and autonomic cardiovascular function in 16 healthy subjects before and after the brief micro- and hypergravity of parabolic flight. Concomitantly, we investigated the effect of parabolic flight-induced vomiting on orthostatic tolerance, R-wave-R-wave interval and arterial pressure power spectra, and carotid-cardiac baroreflex and Valsalva responses. After parabolic flight 1) 8 of 16 subjects could not tolerate 30 min of upright tilt (compared to 2 of 16 before flight); 2) 6 of 16 subjects vomited; 3) new intolerance to upright tilt was associated with exaggerated falls in total peripheral resistance, whereas vomiting was associated with increased R-wave-R-wave interval variability and carotid-cardiac baroreflex responsiveness; and 4) the proximate mode of new orthostatic failure differed in subjects who did and did not vomit, with vomiters experiencing comparatively isolated upright hypocapnia and cerebral vasoconstriction and nonvomiters experiencing signs and symptoms reminiscent of the clinical postural tachycardia syndrome. Results suggest, first, that syndromes of orthostatic intolerance resembling those developing after space flight can develop after a brief (i.e., 2-h) parabolic flight and, second, that recent vomiting can influence the results of tests of autonomic cardiovascular function commonly utilized in returning astronauts.

  11. The dynamics of parabolic flight: flight characteristics and passenger percepts.

    PubMed

    Karmali, Faisal; Shelhamer, Mark

    2008-09-01

    Flying a parabolic trajectory in an aircraft is one of the few ways to create freefall on Earth, which is important for astronaut training and scientific research. Here we review the physics underlying parabolic flight, explain the resulting flight dynamics, and describe several counterintuitive findings, which we corroborate using experimental data. Typically, the aircraft flies parabolic arcs that produce approximately 25 seconds of freefall (0 g) followed by 40 seconds of enhanced force (1.8 g), repeated 30-60 times. Although passengers perceive gravity to be zero, in actuality acceleration, and not gravity, has changed, and thus we caution against the terms "microgravity" and "zero gravity. " Despite the aircraft trajectory including large (45°) pitch-up and pitch-down attitudes, the occupants experience a net force perpendicular to the floor of the aircraft. This is because the aircraft generates appropriate lift and thrust to produce the desired vertical and longitudinal accelerations, respectively, although we measured moderate (0.2 g) aft-ward accelerations during certain parts of these trajectories. Aircraft pitch rotation (average 3°/s) is barely detectable by the vestibular system, but could influence some physics experiments. Investigators should consider such details in the planning, analysis, and interpretation of parabolic-flight experiments. PMID:19727328

  12. Parabolic Dish Solar Thermal Power Annual Program Review Proceedings

    NASA Technical Reports Server (NTRS)

    Lucas, J. W.

    1982-01-01

    The results of activities of the parabolic dish technology and applications development element of DOE's Solar Thermal Energy System Program are presented. Topics include the development and testing of concentrators, receivers, and power conversion units; system design and development for engineering experiments; economic analysis and marketing assessment; and advanced development activities. A panel discussion concerning industrial support sector requirements is also documented.

  13. The dynamics of parabolic flight: Flight characteristics and passenger percepts

    NASA Astrophysics Data System (ADS)

    Karmali, Faisal; Shelhamer, Mark

    2008-09-01

    Flying a parabolic trajectory in an aircraft is one of the few ways to create freefall on Earth, which is important for astronaut training and scientific research. Here we review the physics underlying parabolic flight, explain the resulting flight dynamics, and describe several counterintuitive findings, which we corroborate using experimental data. Typically, the aircraft flies parabolic arcs that produce approximately 25 s of freefall (0 g) followed by 40 s of enhanced force (1.8 g), repeated 30-60 times. Although passengers perceive gravity to be zero, in actuality acceleration, and not gravity, has changed, and thus we caution against the terms "microgravity" and "zero gravity." Despite the aircraft trajectory including large (45°) pitch-up and pitch-down attitudes, the occupants experience a net force perpendicular to the floor of the aircraft. This is because the aircraft generates appropriate lift and thrust to produce the desired vertical and longitudinal accelerations, respectively, although we measured moderate (0.2 g) aft-ward accelerations during certain parts of these trajectories. Aircraft pitch rotation (average 3°/s) is barely detectable by the vestibular system, but could influence some physics experiments. Investigators should consider such details in the planning, analysis, and interpretation of parabolic-flight experiments.

  14. Lateral migration of a capsule in a parabolic flow.

    PubMed

    Nix, S; Imai, Y; Ishikawa, T

    2016-07-26

    Red blood cells migrate to the center of the blood vessel in a process called axial migration, while other blood cells, such as white blood cells and platelets, are disproportionately found near the blood vessel wall. However, much is still unknown concerning the lateral migration of cells in the blood; the specific effect of hydrodynamic factors such as a wall or a shear gradient is still unclear. In this study, we investigate the lateral migration of a capsule using the boundary integral method, in order to compute exactly an infinite computational domain for an unbounded parabolic flow and a semi-infinite computational domain for a near-wall parabolic flow in the limit of Stokes flow. We show that the capsule lift velocity in an unbounded parabolic flow is linear with respect to the shear gradient, while the lift velocity in a near-wall parabolic flow is dependent on the distance to the wall. Then, using these relations, we give an estimation of the relative effect of the shear gradient as a function of channel width and distance between the capsule and the wall. This estimation can be used to determine cases in which the effect of the shear gradient or wall can be neglected; for example, the formation of the cell-free layer in blood vessels is determined to be unaffected by the magnitude of the shear gradient. PMID:26674473

  15. Orthostatic intolerance and motion sickness after parabolic flight.

    PubMed

    Schlegel, T T; Brown, T E; Wood, S J; Benavides, E W; Bondar, R L; Stein, F; Moradshahi, P; Harm, D L; Fritsch-Yelle, J M; Low, P A

    2001-01-01

    Because it is not clear that the induction of orthostatic intolerance in returning astronauts always requires prolonged exposure to microgravity, we investigated orthostatic tolerance and autonomic cardiovascular function in 16 healthy subjects before and after the brief micro- and hypergravity of parabolic flight. Concomitantly, we investigated the effect of parabolic flight-induced vomiting on orthostatic tolerance, R-wave-R-wave interval and arterial pressure power spectra, and carotid-cardiac baroreflex and Valsalva responses. After parabolic flight 1) 8 of 16 subjects could not tolerate 30 min of upright tilt (compared to 2 of 16 before flight); 2) 6 of 16 subjects vomited; 3) new intolerance to upright tilt was associated with exaggerated falls in total peripheral resistance, whereas vomiting was associated with increased R-wave-R-wave interval variability and carotid-cardiac baroreflex responsiveness; and 4) the proximate mode of new orthostatic failure differed in subjects who did and did not vomit, with vomiters experiencing comparatively isolated upright hypocapnia and cerebral vasoconstriction and nonvomiters experiencing signs and symptoms reminiscent of the clinical postural tachycardia syndrome. Results suggest, first, that syndromes of orthostatic intolerance resembling those developing after space flight can develop after a brief (i.e., 2-h) parabolic flight and, second, that recent vomiting can influence the results of tests of autonomic cardiovascular function commonly utilized in returning astronauts. PMID:11133895

  16. Compound parabolic concentrator with cavity for tubular absorbers

    DOEpatents

    Winston, Roland

    1983-01-01

    A compond parabolic concentrator with a V-shaped cavity is provided in which an optical receiver is emplaced. The cavity redirects all energy entering between the receiver and the cavity structure onto the receiver, if the optical receiver is emplaced a distance from the cavity not greater than 0.27 r (where r is the radius of the receiver).

  17. An Application of Calculus: Optimum Parabolic Path Problem

    ERIC Educational Resources Information Center

    Atasever, Merve; Pakdemirli, Mehmet; Yurtsever, Hasan Ali

    2009-01-01

    A practical and technological application of calculus problem is posed to motivate freshman students or junior high school students. A variable coefficient of friction is used in modelling air friction. The case in which the coefficient of friction is a decreasing function of altitude is considered. The optimum parabolic path for a flying object…

  18. Parabolic trough solar power for competitive U.S. markets

    SciTech Connect

    Price, H.W.; Kistner, R.

    1999-07-01

    Nine parabolic trough power plants located in the California Mojave Desert represent the only commercial development of large-scale solar power plants to date. Although all nine plants continue to operate today, no new solar power plants have been completed since 190. Over the last several years, the parabolic trough industry has focused much of its efforts on international market opportunities. Although the power market in developing countries appears to offer a number of opportunities for parabolic trough technologies due to high growth and the availability of special financial incentives for renewables, these markets are also plagued with many difficulties for developers. In recent years, there has been some renewed interest in the U.S. domestic power market as a results of an emerging green market and green pricing incentives. Unfortunately, many of these market opportunities and incentives focus on smaller, more modular technologies (such as photovoltaics or wind power), and as a result they tend to exclude or are of minimum long-term benefit to large-scale concentrating solar power technologies. This paper looks at what is necessary for large-scale parabolic trough solar power plants to compete with state-of-the-art fossil power technology in a competitive US power market.

  19. Parabolic Trough Solar Power for Competitive U.S. Markets

    SciTech Connect

    Henry W. Price

    1998-11-01

    Nine parabolic trough power plants located in the California Mojave Desert represent the only commercial development of large-scale solar power plants to date. Although all nine plants continue to operate today, no new solar power plants have been completed since 1990. Over the last several years, the parabolic trough industry has focused much of its efforts on international market opportunities. Although the power market in developing countries appears to offer a number of opportunities for parabolic trough technologies due to high growth and the availability of special financial incentives for renewables, these markets are also plagued with many difficulties for developers. In recent years, there has been some renewed interest in the U.S. domestic power market as a result of an emerging green market and green pricing incentives. Unfortunately, many of these market opportunities and incentives focus on smaller, more modular technologies (such as photovoltaics or wind power), and as a result they tend to exclude or are of minimum long-term benefit to large-scale concentrating solar power technologies. This paper looks at what is necessary for large-scale parabolic trough solar power plants to compete with state-of-the-art fossil power technology in a competitive U.S. power market.

  20. The dynamics of parabolic flight: flight characteristics and passenger percepts

    PubMed Central

    Karmali, Faisal; Shelhamer, Mark

    2008-01-01

    Flying a parabolic trajectory in an aircraft is one of the few ways to create freefall on Earth, which is important for astronaut training and scientific research. Here we review the physics underlying parabolic flight, explain the resulting flight dynamics, and describe several counterintuitive findings, which we corroborate using experimental data. Typically, the aircraft flies parabolic arcs that produce approximately 25 seconds of freefall (0 g) followed by 40 seconds of enhanced force (1.8 g), repeated 30–60 times. Although passengers perceive gravity to be zero, in actuality acceleration, and not gravity, has changed, and thus we caution against the terms "microgravity" and "zero gravity. " Despite the aircraft trajectory including large (45°) pitch-up and pitch-down attitudes, the occupants experience a net force perpendicular to the floor of the aircraft. This is because the aircraft generates appropriate lift and thrust to produce the desired vertical and longitudinal accelerations, respectively, although we measured moderate (0.2 g) aft-ward accelerations during certain parts of these trajectories. Aircraft pitch rotation (average 3°/s) is barely detectable by the vestibular system, but could influence some physics experiments. Investigators should consider such details in the planning, analysis, and interpretation of parabolic-flight experiments. PMID:19727328

  1. Boundary control of parabolic systems - Finite-element approximation

    NASA Technical Reports Server (NTRS)

    Lasiecka, I.

    1980-01-01

    The finite element approximation of a Dirichlet type boundary control problem for parabolic systems is considered. An approach based on the direct approximation of an input-output semigroup formula is applied. Error estimates are derived for optimal state and optimal control, and it is noted that these estimates are actually optimal with respect to the approximation theoretic properties.

  2. Orthostatic Intolerance and Motion Sickness After Parabolic Flight

    NASA Technical Reports Server (NTRS)

    Schlegel, Todd T.; Brown, Troy E.; Wood, Scott J.; Benavides, Edgar W.; Bondar, Roberta L.; Stein, Flo; Moradshahi, Peyman; Harm, Deborah L.; Low, Phillip A.

    1999-01-01

    Orthostatic intolerance is common in astronauts after prolonged space flight. However, the "push-pull effect" in military aviators suggests that brief exposures to transitions between hypo- and hypergravity are sufficient to induce untoward autonomic cardiovascular physiology in susceptible individuals. We therefore investigated orthostatic tolerance and autonomic cardiovascular function in 16 healthy test subjects before and after a seated 2-hr parabolic flight. At the same time, we also investigated relationships between parabolic flight-induced vomiting and changes in orthostatic and autonomic cardiovascular function. After parabolic flight, 8 of 16 subjects could not tolerate a 30-min upright tilt test, compared to 2 of 16 before flight. Whereas new intolerance in non-Vomiters resembled the clinical postural tachycardia syndrome (POTS), new intolerance in Vomiters was characterized by comparatively isolated upright hypocapnia and cerebral vasoconstriction. As a group, Vomiters also had evidence for increased postflight fluctuations in efferent vagal-cardiac nerve traffic occurring independently of any superimposed change in respiration. Results suggest that syndromes of orthostatic intolerance resembling those occurring after space flight can occur after a brief (i.e., 2-hr) parabolic flight.

  3. Solar Thermal Power Plants with Parabolic-Trough Collectors

    NASA Astrophysics Data System (ADS)

    Zarza, E.; Valenzuela, L.; León, J.

    2004-12-01

    Parabolic-trough collectors (PTC) are solar concentrating devices suitable to work in the 150°C- 400°C temperature range. Power plants based on this type of solar collectors are a very efficient way to produce electricity with solar energy. At present, there are eight commercial solar plants (called SEGS-II, III,.. IX) producing electricity with parabolic-trough collectors and their total output power is 340 MW. Though all SEGS plants currently in operation use thermal oil as a heat transfer fluid between the solar field and the power block, direct steam generation (DSG) in the receiver tubes is a promising option to reduce the cost of electricity produced with parabolic- trough power plants. Most of technical uncertainties associated to the DSG technology were studied and solved in the DISS project and it is expected that this new technology will be commercially available in a short term. In Spain, the Royal Decree No. 436/204 (March 12th , 2004) has defined a premium of 0,18€/kWh for the electricity produced by solar thermal power plants, thus promoting the installation of solar thermal power plants up to a limit of 200 MW. Due to the current legal and financial framework defined in Spain, several projects to install commercial solar power plants with parabolic-trough collectors are currently underway.

  4. IR Spectrometer Using 90-Degree Off-Axis Parabolic Mirrors

    SciTech Connect

    Robert M. Malone, Ian J. McKenna

    2008-03-01

    A gated spectrometer has been designed for real-time, pulsed infrared (IR) studies at the National Synchrotron Light Source at the Brookhaven National Laboratory. A pair of 90-degree, off-axis parabolic mirrors are used to relay the light from an entrance slit to an output recording camera. With an initial wavelength range of 1500–4500 nm required, gratings could not be used in the spectrometer because grating orders would overlap. A magnesium oxide prism, placed between these parabolic mirrors, serves as the dispersion element. The spectrometer is doubly telecentric. With proper choice of the air spacing between the prism and the second parabolic mirror, any spectral region of interest within the InSb camera array’s sensitivity region can be recorded. The wavelengths leaving the second parabolic mirror are collimated, thereby relaxing the camera positioning tolerance. To set up the instrument, two different wavelength (visible) lasers are introduced at the entrance slit and made collinear with the optical axis via flip mirrors. After dispersion by the prism, these two laser beams are directed to tick marks located on the outside housing of the gated IR camera. This provides first-order wavelength calibration for the instrument. Light that is reflected off the front prism face is coupled into a high-speed detector to verify steady radiance during the gated spectral imaging. Alignment features include tick marks on the prism and parabolic mirrors. This instrument was designed to complement single-point pyrometry, which provides continuous time histories of a small collection of spots from shock-heated targets.

  5. IR Spectrometer Using 90-degree Off-axis Parabolic Mirrors

    SciTech Connect

    Robert M. Malone, Richard, G. Hacking, Ian J. McKenna, and Daniel H. Dolan

    2008-09-02

    A gated spectrometer has been designed for real-time, pulsed infrared (IR) studies at the National Synchrotron Light ource at the Brookhaven National Laboratory. A pair of 90-degree, off-axis parabolic mirrors are used to relay the light from an entrance slit to an output IR recording camera. With an initial wavelength range of 1500–4500 nm required, gratings could not be used in the spectrometer because grating orders would overlap. A magnesium oxide prism, placed between these parabolic mirrors, serves as the dispersion element. The spectrometer is doubly telecentric. With proper choice of the air spacing between the prism and the second parabolic mirror, any spectral region of interest within the InSb camera array’s sensitivity region can be recorded. The wavelengths leaving the second parabolic mirror are collimated, thereby relaxing the camera positioning tolerance. To set up the instrument, two different wavelength (visible) lasers are introduced at the entrance slit and made collinear with the optical axis via flip mirrors. After dispersion by the prism, these two laser beams are directed to tick marks located on the outside housing of the gated IR camera. This provides first-order wavelength calibration for the instrument. Light that is reflected off the front prism face is coupled into a high-speed detector to verify steady radiance during the gated spectral imaging. Alignment features include tick marks on the prism and parabolic mirrors. This instrument was designed to complement singlepoint pyrometry, which provides continuous time histories of a small collection of spots from shock-heated targets.

  6. An efficient numerical method for solving the time-dependent compressible Navier-Stokes equations at high Reynolds number

    NASA Technical Reports Server (NTRS)

    Maccormack, R. W.

    1976-01-01

    A fine-mesh method incorporating two new operators, which drastically reduces the computation time, has been developed for solving the time-dependent Navier-Stokes equations at flight Reynolds numbers. The approach time-splits the equations into a hyperbolic part and a parabolic part, solves the hyperbolic part by a new explicit numerical method based on characteristics theory, and solves the parabolic part by a new efficient implicit parabolic method. The method has reduced the computation time by one and two orders of magnitude from that required previously to solve for the interaction of a shock wave with a boundary layer on a flat plate.

  7. Long-term behavior of reaction-diffusion equations with nonlocal boundary conditions on rough domains

    NASA Astrophysics Data System (ADS)

    Gal, Ciprian G.; Warma, Mahamadi

    2016-08-01

    We investigate the long term behavior in terms of finite dimensional global and exponential attractors, as time goes to infinity, of solutions to a semilinear reaction-diffusion equation on non-smooth domains subject to nonlocal Robin boundary conditions, characterized by the presence of fractional diffusion on the boundary. Our results are of general character and apply to a large class of irregular domains, including domains whose boundary is Hölder continuous and domains which have fractal-like geometry. In addition to recovering most of the existing results on existence, regularity, uniqueness, stability, attractor existence, and dimension, for the well-known reaction-diffusion equation in smooth domains, the framework we develop also makes possible a number of new results for all diffusion models in other non-smooth settings.

  8. Nonuniqueness and multi-bump solutions in parabolic problems with the p-Laplacian

    NASA Astrophysics Data System (ADS)

    Benedikt, Jiří; Girg, Petr; Kotrla, Lukáš; Takáč, Peter

    2016-01-01

    The validity of the weak and strong comparison principles for degenerate parabolic partial differential equations with the p-Laplace operator Δp is investigated for p > 2. This problem is reduced to the comparison of the trivial solution (≡0, by hypothesis) with a nontrivial nonnegative solution u (x, t). The problem is closely related also to the question of uniqueness of a nonnegative solution via the weak comparison principle. In this article, realistic counterexamples to the uniqueness of a nonnegative solution, the weak comparison principle, and the strong maximum principle are constructed with a nonsmooth reaction function that satisfies neither a Lipschitz nor an Osgood standard "uniqueness" condition. Nonnegative multi-bump solutions with spatially disconnected compact supports and zero initial data are constructed between sub- and supersolutions that have supports of the same type.

  9. Parabolized Navier-Stokes solutions of separation and trailing-edge flows

    NASA Technical Reports Server (NTRS)

    Brown, J. L.

    1983-01-01

    A robust, iterative solution procedure is presented for the parabolized Navier-Stokes or higher order boundary layer equations as applied to subsonic viscous-inviscid interaction flows. The robustness of the present procedure is due, in part, to an improved algorithmic formulation. The present formulation is based on a reinterpretation of stability requirements for this class of algorithms and requires only second order accurate backward or central differences for all streamwise derivatives. Upstream influence is provided for through the algorithmic formulation and iterative sweeps in x. The primary contribution to robustness, however, is the boundary condition treatment, which imposes global constraints to control the convergence path. Discussed are successful calculations of subsonic, strong viscous-inviscid interactions, including separation. These results are consistent with Navier-Stokes solutions and triple deck theory.

  10. Extrapolation discontinuous Galerkin method for ultraparabolic equations

    NASA Astrophysics Data System (ADS)

    Marcozzi, Michael D.

    2009-02-01

    Ultraparabolic equations arise from the characterization of the performance index of stochastic optimal control relative to ultradiffusion processes; they evidence multiple temporal variables and may be regarded as parabolic along characteristic directions. We consider theoretical and approximation aspects of a temporally order and step size adaptive extrapolation discontinuous Galerkin method coupled with a spatial Lagrange second-order finite element approximation for a prototype ultraparabolic problem. As an application, we value a so-called Asian option from mathematical finance.

  11. Analysis of band structure, transmission properties, and dispersion behavior of THz wave in one-dimensional parabolic plasma photonic crystal

    SciTech Connect

    Askari, Nasim; Eslami, Esmaeil; Mirzaie, Reza

    2015-11-15

    The photonic band gap of obliquely incident terahertz electromagnetic waves in a one-dimensional plasma photonic crystal is studied. The periodic structure consists of lossless dielectric and inhomogeneous plasma with a parabolic density profile. The dispersion relation and the THz wave transmittance are analyzed based on the electromagnetic equations and transfer matrix method. The dependence of effective plasma frequency and photonic band gap characteristics on dielectric and plasma thickness, plasma density, and incident angle are discussed in detail. A theoretical calculation for effective plasma frequency is presented and compared with numerical results. Results of these two methods are in good agreement.

  12. Two orthogonally polarized optical beams in a family of Kerr-law nonlinear shifted parabolic graded-index rod lenses

    NASA Astrophysics Data System (ADS)

    Li, Y.

    1996-08-01

    The field, the propagation and the imaging characteristics of two Gaussian optical beams with orthogonal polarization passing through a family of Kerr-law nonlinear shifted parabolic graded-index rod lenses are investigated. The coupled differential equations of the dimensionless beam-width parameters of two Gaussian optical beams are derived by using a variational approach and then solved. It is concluded that there are two regimes of propagation and that the power, the incident waist radius and the position of one beam have large effects on the field, the propagation and the imaging characteristics of the other beam.

  13. Electromagnetic Casimir forces of parabolic cylinder and knife-edge geometries

    SciTech Connect

    Graham, Noah; Shpunt, Alexander; Kardar, Mehran; Emig, Thorsten; Rahi, Sahand Jamal; Jaffe, Robert L.

    2011-06-15

    An exact calculation of electromagnetic scattering from a perfectly conducting parabolic cylinder is employed to compute Casimir forces in several configurations. These include interactions between a parabolic cylinder and a plane, two parabolic cylinders, and a parabolic cylinder and an ordinary cylinder. To elucidate the effect of boundaries, special attention is focused on the 'knife-edge' limit in which the parabolic cylinder becomes a half-plane. Geometrical effects are illustrated by considering arbitrary rotations of a parabolic cylinder around its focal axis, and arbitrary translations perpendicular to this axis. A quite different geometrical arrangement is explored for the case of an ordinary cylinder placed in the interior of a parabolic cylinder. All of these results extend simply to nonzero temperatures.

  14. Focusing Light Rays Back to the Vertex of a Reflecting Parabolic Collector: The Equivalent of Dionysius Ear Effect in Optical Systems

    ERIC Educational Resources Information Center

    De Luca, R.; Fedullo, A.

    2009-01-01

    A vertical light ray coming from infinity is reflected by a primary parabolic mirror M[subscript 1] having focus at F[subscript 1]. At a small distance from F[subscript 1] a secondary mirror M[subscript 2], symmetric with respect to the vertical axis, is placed. One would like to find the analytic equation of the mirror M[subscript 2], so that all…

  15. A Review of Psycho-Physiological Responses to Parabolic Flight

    NASA Astrophysics Data System (ADS)

    Brummer, Vera; Schneider, Stefan; Guardiera, Simon; Struder, Heiko K.

    2008-06-01

    This review combines and correlates data of several studies conducted in the recent years where we were able to show an increase in stress hormone concentrations, EEG activity and a decrease in mood during parabolic flights. The aim of these studies was to consider whether previous results showing a decrease in mental and perceptual motor performance during weightlessness were solely due to the changes in gravity itself or were also, at least partly, explainable by an increase of stress and/or arousal during parabolic flights. A correlation between stress hormones and mood but not between EEG activity and mood nor between stress hormones and EEG activity could be found. We propose two different stressors: First an activation of the adrenomedullary system, secondly a general increase of cortical arousal. Whereas the first one is perceived by subjects, this is not the case for the second one.

  16. Parabolic Trouogh Optical Characterization at the National Renewable Energy Laboratory

    SciTech Connect

    Wendelin, T. J.

    2005-01-01

    Solar parabolic trough power plant projects are soon to be implemented in the United States and internationally. In addition to these new projects, parabolic trough power plants totaling approximately 350 MW already exist within the United States and have operated for close to 20 years. As such, the status of the technology exists within several different phases. Theses phases include R&D, manufacturing and installation, and operations and maintenance. One aspect of successful deployment of this technology is achieving and maintaining optical performance. Different optical tools are needed to assist in improving initial designs, provide quality control during manufacture and assembly, and help maintain performance during operation. This paper discusses several such tools developed at SunLab (a joint project of the National Renewable Laboratory and Sandia National Laboratories) for these purposes. Preliminary testing results are presented. Finally, plans for further tool development are discussed.

  17. Irrigation market for solar thermal parabolic dish systems

    NASA Technical Reports Server (NTRS)

    Habib-Agahi, H.; Jones, S. C.

    1981-01-01

    The potential size of the onfarm-pumped irrigation market for solar thermal parabolic dish systems in seven high-insolation states is estimated. The study is restricted to the displacement of three specific fuels: gasoline, diesel and natural gas. The model was developed to estimate the optimal number of parabolic dish modules per farm based on the minimum cost mix of conventional and solar thermal energy required to meet irrigation needs. The study concludes that the potential market size for onfarm-pumped irrigation applications ranges from 101,000 modules when a 14 percent real discount rate is assumed to 220,000 modules when the real discount rate drops to 8 percent. Arizona, Kansas, Nebraska, New Mexico and Texas account for 98 percent of the total demand for this application, with the natural gas replacement market accounting for the largest segment (71 percent) of the total market.

  18. Water Cooled TJ Dense Array Modules for Parabolic Dishes

    NASA Astrophysics Data System (ADS)

    Löckenhoff, Rüdiger; Kubera, Tim; Rasch, Klaus Dieter

    2010-10-01

    AZUR SPACE Solar Power GmbH has developed a novel type of dense array module for use in parabolic dishes. Such dishes never produce a perfectly homogeneous, rectangular light spot but an inhomogeneous light distribution. A regular module would use this light distribution very inefficiently. Therefore AZUR SPACE developed a dense array module concept which can be adapted to inhomogeneous light spots. It is populated with state of the art triple junction solar cells. The modules are designed for light intensities in the range of 50-100 W/cm2 and are actively water cooled. Prototypes are installed in 11 m2 parabolic dishes produced by Zenith Solar. A peak output of 2.3 kW electrical and 5.5 kW thermal power could be demonstrated. The thermal power may be used for solar heating, solar cooling or warm water.

  19. Performance contracting for parabolic trough solar thermal systems

    SciTech Connect

    Brown, H.; Hewett, R.; Walker, A.; Gee, R.; May, K.

    1997-12-31

    Several applications of solar energy have proven viable in the energy marketplace, due to competitive technology and economic performance. One example is the parabolic trough solar collectors, which use focused solar energy to maximize efficiency and reduce material use in construction. Technical improvements are complemented by new business practices to make parabolic trough solar thermal systems technically and economically viable in an ever widening range of applications. Technical developments in materials and fabrication techniques reduce production cost and expand applications from swimming pool heating and service hot water, to higher-temperature applications such as absorption cooling and process steam. Simultaneously, new financing mechanisms such as a recently awarded US Department of Energy (DOE) Federal Energy Management Program (FEMP) indefinite quantity Energy Savings Performance Contract (Super ESPC) facilitate and streamline implementation of the technology in federal facilities such as prisons and military bases.

  20. Development and testing of Parabolic Dish Concentrator No. 1

    NASA Technical Reports Server (NTRS)

    Dennison, E. W.; Thostesen, T. O.

    1984-01-01

    Parabolic Dish Concentrator No. 1 (PDC-1) is a 12-m-diameter prototype concentrator with low life-cycle costs for use with thermal-to-electric energy conversion devices. The concentrator assembly features panels made of a resin transfer molded balsa core/fiberglass sandwich with plastic reflective film as the reflective surface and a ribbed framework to hold the panels in place. The concentrator assembly tracks in azimuth and elevation on a base frame riding on a circular track. It is shown that the panels do not exhibit the proper parabolic contour. However, thermal gradients were discovered in the panels with daily temperature changes. The PDC-1 has sufficient optical quality to operate satisfactorily in a dish-electric system. The PDC-1 development provides the impetus for creating innovative optical testing methods and valuable information for use in designing and fabricating concentrators of future dish-electric systems.

  1. Absorber Alignment Measurement Tool for Solar Parabolic Trough Collectors: Preprint

    SciTech Connect

    Stynes, J. K.; Ihas, B.

    2012-04-01

    As we pursue efforts to lower the capital and installation costs of parabolic trough solar collectors, it is essential to maintain high optical performance. While there are many optical tools available to measure the reflector slope errors of parabolic trough solar collectors, there are few tools to measure the absorber alignment. A new method is presented here to measure the absorber alignment in two dimensions to within 0.5 cm. The absorber alignment is measured using a digital camera and four photogrammetric targets. Physical contact with the receiver absorber or glass is not necessary. The alignment of the absorber is measured along its full length so that sagging of the absorber can be quantified with this technique. The resulting absorber alignment measurement provides critical information required to accurately determine the intercept factor of a collector.

  2. Parabolic discounting of monetary rewards by physical effort.

    PubMed

    Hartmann, Matthias N; Hager, Oliver M; Tobler, Philippe N; Kaiser, Stefan

    2013-11-01

    When humans and other animals make decisions in their natural environments prospective rewards have to be weighed against costs. It is well established that increasing costs lead to devaluation or discounting of reward. While our knowledge about discount functions for time and probability costs is quite advanced, little is known about how physical effort discounts reward. In the present study we compared three different models in a binary choice task in which human participants had to squeeze a handgrip to earn monetary rewards: a linear, a hyperbolic, and a parabolic model. On the group as well as the individual level, the concave parabolic model explained most variance of the choice data, thus contrasting with the typical hyperbolic discounting of reward value by delay. Research on effort discounting is not only important to basic science but also holds the potential to quantify aberrant motivational states in neuropsychiatric disorders. PMID:24140077

  3. Electron trapping and acceleration across a parabolic plasma density profile.

    PubMed

    Kim, J U; Hafz, N; Suk, H

    2004-02-01

    It is known that as a laser wakefield passes through a downward density transition in a plasma some portion of the background electrons are trapped in the laser wakefield and the trapped electrons are accelerated to relativistic high energies over a very short distance. In this study, by using a two-dimensional (2D) particle-in-cell (PIC) simulation, we suggest an experimental scheme that can manipulate electron trapping and acceleration across a parabolic plasma density channel, which is easier to produce and more feasible to apply to the laser wakefield acceleration experiments. In this study, 2D PIC simulation results for the physical characteristics of the electron bunches that are emitted from the parabolic density plasma channel are reported in great detail. PMID:14995568

  4. Configuration selection study for isolated loads using parabolic dish modules

    NASA Technical Reports Server (NTRS)

    Revere, W.; Bowyer, J.; Fujita, T.; Awaya, H.

    1981-01-01

    A configuration tradeoff study has been conducted to determine optimum solar thermal parabolic dish power systems for isolated load applications. The specific application of an essentially constant power demand as required for MX missile shelters is treated. Supplying a continuous level of power with high reliability is shown to require a power system comprising modular parabolic dish power units where the heat engines of the modular power units can be driven by fossil fuels as well as solar-derived heat. Since constraints on reliability result in the provision of a power generating capability that exceeds the constant demand level, efficient utilization of the power system requires battery storage. Tradeoffs regarding the optimum size of storage are investigated as a function of the number of power modules and the cost of the fossil fuel which is used to meet the demand when insolation is unavailable and storage is depleted.

  5. Configuration selection study for isolated loads using parabolic dish modules

    NASA Technical Reports Server (NTRS)

    Revere, W.; Bowyer, J.; Fujita, T.; Awaya, H.

    1982-01-01

    A configuration tradeoff study was conducted to determine optimum solar thermal parabolic dish power systems for isolated load applications. The specific application of an essentially constant power demand as required for MX missile shelters is treated. Supplying a continuous level of power with high reliability is shown to require a power system comprising modular parabolic dish power units where the heat engines of the modular power units can be driven by fossil fuels as well as solar-derived heat. Since constraints on reliability result in the provision of a power generating capability that exceeds the constant demand level, efficient utilization of the power system requires battery storage. Tradeoffs regarding the optimum size of storage are investigated as a function of the number of power modules and the cost of the fossil fuel.

  6. Treatment of motion sickness in parabolic flight with buccal scopolamine

    NASA Technical Reports Server (NTRS)

    Norfleet, William T.; Degioanni, Joseph J.; Reschke, Millard F.; Bungo, Michael W.; Kutyna, Frank A.; Homick, Jerry L.; Calkins, D. S.

    1992-01-01

    Treatment of acute motion sickness induced by parabolic flight with a preparation of scopolamine placed in the buccal pouch was investigated. Twenty-one subjects flew aboard a KC-135 aircraft operated by NASA which performed parabolic maneuvers resulting in periods of 0-g, 1-g, and 1.8-g. Each subject flew once with a tablet containing scopolamine and once with a placebo in a random order, crossover design. Signs and symptoms of motion sickness were systematically recorded during each parabola by an investigator who was blind to the content of the tablet. Compared with flights using placebo, flights with buccal scopolamine resulted in significantly lower scores for nausea (31-35 percent reduction) and vomiting (50 percent reduction in number of parabolas with vomiting). Side effects of the drug during flight were negligible. It is concluded that buccal scopolamine is more effective than a placebo in treating ongoing motion sickness.

  7. Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for Aircraft Acoustic Nacelle Design

    NASA Technical Reports Server (NTRS)

    Baumeister, Kenneth J.; Kreider, Kevin L.

    1996-01-01

    An explicit finite difference iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

  8. Synergies between optical and physical variables in intercepting parabolic targets

    PubMed Central

    Gómez, José; López-Moliner, Joan

    2013-01-01

    Interception requires precise estimation of time-to-contact (TTC) information. A long-standing view posits that all relevant information for extracting TTC is available in the angular variables, which result from the projection of distal objects onto the retina. The different timing models rooted in this tradition have consequently relied on combining visual angle and its rate of expansion in different ways with tau being the most well-known solution for TTC. The generalization of these models to timing parabolic trajectories is not straightforward. For example, these different combinations rely on isotropic expansion and usually assume first-order information only, neglecting acceleration. As a consequence no optical formulations have been put forward so far to specify TTC of parabolic targets with enough accuracy. It is only recently that context-dependent physical variables have been shown to play an important role in TTC estimation. Known physical size and gravity can adequately explain observed data of linear and free-falling trajectories, respectively. Yet, a full timing model for specifying parabolic TTC has remained elusive. We here derive two formulations that specify TTC for parabolic ball trajectories. The first specification extends previous models in which known size is combined with thresholding visual angle or its rate of expansion to the case of fly balls. To efficiently use this model, observers need to recover the 3D radial velocity component of the trajectory which conveys the isotropic expansion. The second one uses knowledge of size and gravity combined with ball visual angle and elevation angle. Taking into account the noise due to sensory measurements, we simulate the expected performance of these models in terms of accuracy and precision. While the model that combines expansion information and size knowledge is more efficient during the late trajectory, the second one is shown to be efficient along all the flight. PMID:23720614

  9. Sea urchin fertilization during a KC-135 parabolic flight.

    PubMed

    Schatten, H; Zoran, S; Levine, H G; Anderson, K; Chakrabarti, A

    1999-07-01

    For long-term exposure to space it is crucial to understand the underlying mechanisms for altered physiological functions. We have chosen the sea urchin system to study the effects of microgravity on various cellular processes visible during fertilization and subsequent development. We report here on experiments performed on NASA's KC-135 during parabolic flight trajectories to validate procedures to be implemented as part of the first Aquatic Research Facility Space Shuttle experiment on STS-77. PMID:11543042

  10. Criteria for evaluation of reflective surface for parabolic dish concentrators

    NASA Technical Reports Server (NTRS)

    Bouquet, F.

    1980-01-01

    Commercial, second surface glass mirror are emphasized, but aluminum and metallized polymeric films are also included. Criteria for sealing solar mirrors in order to prevent environmental degradation and criteria for bonding sagged or bent mirrors to substrate materials are described. An overview of the technical areas involved in evaluating small mirror samples, sections, and entire large gores is presented. A basis for mirror criteria was established that eventually may become part of inspection and evaluation techniques for three dimensional parabolic reflective surfaces.

  11. Radiative Heat Transfer During Atmosphere Entry at Parabolic Velocity

    NASA Technical Reports Server (NTRS)

    Yoshikawa, Kenneth K.; Wick, Bradford H.

    1961-01-01

    Stagnation point radiative heating rates for manned vehicles entering the earth's atmosphere at parabolic velocity are presented and compared with corresponding laminar convective heating rates. The calculations were made for both nonlifting and lifting entry trajectories for vehicles of varying nose radius, weight-to-area ratio, and drag. It is concluded from the results presented that radiative heating will be important for the entry conditions considered.

  12. Discontinuous Galerkin Finite Element Method for Parabolic Problems

    NASA Technical Reports Server (NTRS)

    Kaneko, Hideaki; Bey, Kim S.; Hou, Gene J. W.

    2004-01-01

    In this paper, we develop a time and its corresponding spatial discretization scheme, based upon the assumption of a certain weak singularity of parallel ut(t) parallel Lz(omega) = parallel ut parallel2, for the discontinuous Galerkin finite element method for one-dimensional parabolic problems. Optimal convergence rates in both time and spatial variables are obtained. A discussion of automatic time-step control method is also included.

  13. Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Wang, C.

    1989-01-01

    A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

  14. Proceedings: Fourth Parabolic Dish Solar Thermal Power Program Review

    NASA Technical Reports Server (NTRS)

    1983-01-01

    The results of activities within the parabolic dish technology and applications development program are presented. Stirling, organic Rankine and Brayton module technologies, associated hardware and test results to date; concentrator development and progress; economic analyses; and international dish development activities are covered. Two panel discussions, concerning industry issues affecting solar thermal dish development and dish technology from a utility/user perspective, are also included.

  15. Performance of a blood chemistry analyzer during parabolic flight

    NASA Technical Reports Server (NTRS)

    Spooner, Brian S.; Claassen, Dale E.; Guikema, James A.

    1990-01-01

    The performance of the Vision System Blood Analyzer during parabolic flight on a KC-135 aircraft (NASA 930) has been tested. This fully automated instrument performed flawlessly in these trials, demonstrating its potential for efficient, reliable use in a microgravity environment. In addition to instrument capability, it is demonstrated that investigators could readily fill specially modified test packs with fluid during zero gravity, and that filled test packs could be easily loaded into VISION during an episode of microgravity.

  16. Gas Turbine/Solar Parabolic Trough Hybrid Designs: Preprint

    SciTech Connect

    Turchi, C. S.; Ma, Z.; Erbes, M.

    2011-03-01

    A strength of parabolic trough concentrating solar power (CSP) plants is the ability to provide reliable power by incorporating either thermal energy storage or backup heat from fossil fuels. Yet these benefits have not been fully realized because thermal energy storage remains expensive at trough operating temperatures and gas usage in CSP plants is less efficient than in dedicated combined cycle plants. For example, while a modern combined cycle plant can achieve an overall efficiency in excess of 55%; auxiliary heaters in a parabolic trough plant convert gas to electricity at below 40%. Thus, one can argue the more effective use of natural gas is in a combined cycle plant, not as backup to a CSP plant. Integrated solar combined cycle (ISCC) systems avoid this pitfall by injecting solar steam into the fossil power cycle; however, these designs are limited to about 10% total solar enhancement. Without reliable, cost-effective energy storage or backup power, renewable sources will struggle to achieve a high penetration in the electric grid. This paper describes a novel gas turbine / parabolic trough hybrid design that combines solar contribution of 57% and higher with gas heat rates that rival that for combined cycle natural gas plants. The design integrates proven solar and fossil technologies, thereby offering high reliability and low financial risk while promoting deployment of solar thermal power.

  17. Circulatory filling pressures during transient microgravity induced by parabolic flight

    NASA Technical Reports Server (NTRS)

    Latham, Ricky D.; Fanton, John W.; White, C. D.; Vernalis, Mariana N.; Crisman, R. P.; Koenig, S. C.

    1993-01-01

    Theoretical concepts hold that blood in the gravity dependent portion of the body would relocate to more cephalad compartments under microgravity. The result is an increase in blood volume in the thoraic and cardiac chambers. However, experimental data has been somewhat contradictory and nonconclusive. Early studies of peripheral venous pressure and estimates of central venous pressure (CVP) from these data did not show an increase in CVP under microgravity. However, CVP recorded in human volunteers during a parabolic flight revealed an increase in CVP during the microgravity state. On the STS 40 shuttle mission, a payload specialist wore a fluid line that recorded CVP during the first few hours of orbital insertion. These data revealed decreased CVP. When this CVP catheter was tested during parabolic flight in four subjects, two had increased CVP recordings and two had decreased CVP measurements. In 1991, our laboratory performed parabolic flight studies in several chronic-instrumented baboons. It was again noted that centrally recorded right atrial pressure varied with exposure to microgravity, some animals having an increase, and others a decrease.

  18. Application of parabolic reflector on Raman analysis of gas samples

    NASA Astrophysics Data System (ADS)

    Yu, Anlan; Zuo, Duluo; Gao, Jun; Li, Bin; Wang, Xingbing

    2016-05-01

    Studies on the application of a parabolic reflector in spontaneous Raman scattering for low background Raman analysis of gas samples are reported. As an effective signal enhancing sample cell, photonic bandgap fiber (HC-PBF) or metallined capillary normally result in a strong continuous background in spectra caused by the strong Raman/fluorescence signal from the silica wall and the polymer protective film. In order to obtain enhanced signal with low background, a specially designed sample cell with double-pass and large collecting solid angle constructed by a parabolic reflector and a planar reflector was applied, of which the optical surfaces had been processed by diamond turning and coated by silver film and protective film of high-purity alumina. The influences of optical structure, polarization characteristic, collecting solid-angle and collecting efficiency of the sample cell on light propagation and signal enhancement were studied. A Raman spectrum of ambient air with signal to background ratio of 94 was acquired with an exposure time of 1 sec by an imaging spectrograph. Besides, the 3σ limits of detection (LOD) of 7 ppm for H2, 8 ppm for CO2 and 12 ppm for CO were also obtained. The sample cell mainly based on parabolic reflector will be helpful for compact and high-sensitive Raman system.

  19. Phase retrieval in situ measurement for large aperture parabolic mirror

    NASA Astrophysics Data System (ADS)

    Ding, Lingyan; Wu, Yulie; Li, Shengyi; Liao, Yang; Shu, Yong

    2010-10-01

    Phase retrieval is a promising method for in-situ metrology and has been applied to spherical mirror surface metrology successfully. To meet the requirement of in-situ measurement in manufacturing large aperture parabolic mirror, a new method using phase retrieval technology is developed. In this method, an approximately parallel beam is used to illuminate the large parabolic mirror. The beam is produced by a point light source far away from the tested mirror. Then, intensity of diffraction patterns near the focus is measured by CCD. The experiment of testing a parabolic mirror with aperture 400mm and radius of curvature at vertex 2789.7mm is described. And some advices of improving the setup are presented. Errors brought by the approximately parallel beam are compensated by an algorithm derived from GS iterative algorithm. Phase retrieval result is consistent with that measured by interferometer sub-aperture stitching in error distribution, PV value and RMS value. The experiment shows that this method features simple optical path, good anti-vibration ability and acceptable accuracy.

  20. Parabolic-Trough Technology Roadmap: A Pathway for Sustained Commercial Development and Deployment of Parabolic-Trough Technology

    SciTech Connect

    Price, H.; Kearney, D.

    1999-01-31

    Technology roadmapping is a needs-driven technology planning process to help identify, select, and develop technology alternatives to satisfy a set of market needs. The DOE's Office of Power Technologies' Concentrating Solar Power (CSP) Program recently sponsored a technology roadmapping workshop for parabolic trough technology. The workshop was attended by an impressive cross section of industry and research experts. The goals of the workshop were to evaluate the market potential for trough power projects, develop a better understanding of the current state of the technology, and to develop a conceptual plan for advancing the state of parabolic trough technology. This report documents and extends the roadmap that was conceptually developed during the workshop.

  1. Multilinear Littlewood-Paley estimates with applications to partial differential equations

    PubMed Central

    Fabes, Eugene B.; Jerison, David S.; Kenig, Carlos E.

    1982-01-01

    We obtain a collection of multilinear Littlewood-Paley estimates, which we then apply to two problems in partial differential equations. The first problem is the estimation of the square root of an elliptic operator in divergence form, and the second is the estimation of solutions to the Cauchy problem for nondivergence-form parabolic equations. PMID:16593230

  2. The Minkowski dimension of interior singular points in the incompressible Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Koh, Youngwoo; Yang, Minsuk

    2016-09-01

    We study the possible interior singular points of suitable weak solutions to the three dimensional incompressible Navier-Stokes equations. We present an improved parabolic upper Minkowski dimension of the possible singular set, which is bounded by 95/63. The result also continue to hold for the three dimensional incompressible magnetohydrodynamic equations without any difficulty.

  3. The ABCD matrix for parabolic reflectors and its application to astigmatism free four-mirror cavities

    NASA Astrophysics Data System (ADS)

    Dupraz, K.; Cassou, K.; Martens, A.; Zomer, F.

    2015-10-01

    The ABCD matrix for parabolic reflectors is derived for any incident angles. It is used in numerical studies of four-mirror cavities composed of two flat and two parabolic mirrors. Constraints related to laser beam injection efficiency, optical stability, cavity-mode, beam-waist size and high stacking power are satisfied. A dedicated alignment procedure leading to stigmatic cavity-modes is employed to overcome issues related to the optical alignment of parabolic reflectors.

  4. An implicit upwind parabolized Navier-Stokes code for chemically nonequilibrium flows

    NASA Astrophysics Data System (ADS)

    Chen, Bing; Wang, Li; Xu, Xu

    2013-02-01

    The previously developed single-sweep parabolized Navier-Stokes (SSPNS) space marching code for ideal gas flows has been extended to compute chemically nonequilibrium flows. In the code, the strongly coupled set of gas dynamics, species conservation, and turbulence equations is integrated with the implicit lower-upper symmetric Gauss-Seidel (LU-SGS) method in the streamwise direction in a space marching manner. The AUSMPW+ scheme is used to calculate the inviscid fluxes in the crossflow direction, while the conventional central scheme for the viscous fluxes. The k- g two-equation turbulence model is used. The revised SSPNS code is validated by computing the Burrows-Kurkov non-premixed H2/air supersonic combustion flows, premixed H2/air hypersonic combustion flows in a three-dimensional duct with a 15° compression ramp, as well as the hypersonic laminar chemically nonequilibrium air flows around two 10° half-angle cones. The results of these calculations are in good agreement with those of experiments, NASA UPS or Prabhu's PNS codes. It can be concluded that the SSPNS code is highly efficient for steady supersonic/hypersonic chemically reaction flows when there is no large streamwise separation.

  5. Dexterous Manipulation in Microgravity in Parabolic Flights and on ISS

    NASA Astrophysics Data System (ADS)

    Pletser, V.; Sundblad, P.; Thonnard, J.-L.; Lefevre, P.; McIntyre, J.; Kassel, R.; Derkinderen, W.; Penta, M.; Andre, T.

    It has been shown that during exposure to microgravity in parabolic flights the control of interaction forces when manipulating an object adapts partially to the lack of gravity, yet evidence indicates that anticipation of gravity's effects persists in the short term. The motivation for these experiments to be performed in long-duration space flight is to understand how the central nervous system adapts to an environment without gravity and what will be the consequences of long-term adaptation when an individual returns to a normal (Earth) or partial (Moon or Mars) gravitational field. The experiment “Dexterous Manipulation in Microgravity” (DEX) will target specific questions about the effects of gravity on dexterous manipulation, questions that cannot be addressed in the normal terrestrial environment. Some of the scientific questions have already been studied since nearly ten years and will continue to be addressed in experiments conducted in parabolic flights, during which it will be examined how the nervous system copes with repeated transitions between different gravitational environments. Results from these experiments provide initial data about short-term adaptation to 0g. The experiments proposed for ISS draw from these short-term precursor experiments, but will emphasize long-term adaptation of sensorimotor processes to 0g and re-adaptation to 1g. A first conceptual definition phase of a DEX instrument has been completed under an ESA contract and is now ready to enter into the design and development phase in view of a launch on ISS in the 2013-2014 timeframe. In this paper, the science background will be recalled and several experiments performed during parabolic flights will be presented, showing how these early breadboards testing in microgravity have helped to refine the DEX conceptual design and how it could be used on ISS.

  6. Processing of data from innovative parabolic strip telescope.

    NASA Astrophysics Data System (ADS)

    Kosejk, Vladislav; Novy, J.; Chadzitaskos, Goce

    2015-12-01

    This paper presents an innovative telescope design based on the usage of a parabolic strip fulfilling the function of an objective. Isaac Newton was the first to solve the problem of chromatic aberration, which is caused by a difference in the refractive index of lenses. This problem was solved by a new kind of telescope with a mirror used as an objective. There are many different kinds of telescopes. The most basic one is the lens telescope. This type of a telescope uses a set of lenses. Another type is the mirror telescope, which employs the concave mirror, spherical parabolic mirror or hyperbolically shaped mirror as its objective. The lens speed depends directly on the surface of a mirror. Both types can be combined to form a telescope composed of at least two mirrors and a set of lenses. The light is reflected from the primary mirror to the secondary one and then to the lens system. This type is smaller-sized, with a respectively reduced lens speed. The telescope design presented in this paper uses a parabolic strip fulfilling the function of an objective. Observed objects are projected as lines in a picture plane. Each of the lines of a size equal to the size of the strip corresponds to the sum of intensities of the light coming perpendicular to the objective from an observed object. A series of pictures taken with a different rotation and processed by a special reconstruction algorithm is needed to get 2D pictures. The telescope can also be used for fast detection of objects. In this mode, the rotation and multiple pictures are not needed, just one picture in the focus of a mirror is required to be taken.

  7. The integrated compound parabolic concentrator: From development to demonstration

    SciTech Connect

    Winston, R.; O`Gallagher, J.J.; Duff, W.S.; Cavallaro, A.

    1997-12-31

    The authors describe the fabrication, testing and application of the Integrated Compound Parabolic Concentrator (ICPC) to solar cooling. The cooling technology is a double effect absorption cycle chiller operating at 165 C. The design parameters are optimized for this temperature range. The optical and mechanical design of the solar collector is chosen for compatibility with mass production. A project to employ approximately 350 of these collector tubes to drive a 20 ton commercial double effect chiller on an office building in Sacramento, CA has started. The authors expect the system to be operational this year.

  8. Piecewise-parabolic methods for astrophysical fluid dynamics

    SciTech Connect

    Woodward, P.R.

    1983-11-01

    A general description of some modern numerical techniques for the simulation of astrophysical fluid flow is presented. The methods are introduced with a thorough discussion of the especially simple case of advection. Attention is focused on the piecewise-parabolic method (PPM). A description of the SLIC method for treating multifluid problems is also given. The discussion is illustrated by a number of advection and hydrodynamics test problems. Finally, a study of Kelvin-Helmholtz instability of supersonic jets using PPM with SLIC fluid interfaces is presented.

  9. Overview of software development at the parabolic dish test site

    NASA Technical Reports Server (NTRS)

    Miyazono, C. K.

    1985-01-01

    The development history of the data acquisition and data analysis software is discussed. The software development occurred between 1978 and 1984 in support of solar energy module testing at the Jet Propulsion Laboratory's Parabolic Dish Test Site, located within Edwards Test Station. The development went through incremental stages, starting with a simple single-user BASIC set of programs, and progressing to the relative complex multi-user FORTRAN system that was used until the termination of the project. Additional software in support of testing is discussed including software in support of a meteorological subsystem and the Test Bed Concentrator Control Console interface. Conclusions and recommendations for further development are discussed.

  10. Control system for Parabolic Dish Concentrator No. 1

    SciTech Connect

    Stallkamp, J.A.

    1985-03-15

    This report is a description and discussion of the control system for Parabolic Dish Concentrator No. 1 (PDC-1) as used at the JPL Parabolic Dish Test Site (PDTS). The tracking action is a discontinuous, start/stop motion with sun sensors for primary control and a computed sun ephemeris for a simultaneous check and cloud passage. Project background, functional requirements, and hardware description are presented in brief form. System operation is described in considerable detail and includes the precise message exchange protocol between the module and remote control station, the initialization process, the command list, and the basic control logic used in the local microprocessor. System installation and performance items are given; the unit operated very satisfactorily for the brief period of time before it was moved to Sandia National Laboratories at Albuquerque, New Mexico. It was operated at a 0.05-deg deadband for optical characterization of the reflecting surfaces and mirror geometry. The last section includes significant presentations and discussions of (1) protection against burn by the sun in the case of failure to continue to track and (2) other equipment and personnel safety items. Operation of PDC-1 at the test site was man-attended; for extension to man-unattended operation a number of additional requirements and constraints must be identified and a full implementation of the capabilities of the design performed.

  11. Development effort of sheet molding compound (SMC) parabolic trough panels

    SciTech Connect

    Kirsch, P.A.; Champion, R.L.

    1982-01-01

    The objectives of the development effort are to: investigate the problems of molding parabolic trough solar reflector panels of sheet molding compound (SMC); develop molding techniques and processes by which silvered glass reflector sheets can be integrally molded into SMC trough panels; provide representative prototype panels for evaluation; and provide information regarding the technical feasibility of molding SMC panels in high volume production. The approach taken to meet the objectives was to design the parabolic panel, fabricate a prototype die, choose an SMC formulation and mold the glass and SMC together into a vertex to rim mirrored panel. The main thrust of the program was to successfully co-mold a mirrored glass sheet with the SMC. Results indicate that mirrored glass sheets, if properly strengthened to withstand the temperature and pressure of the molding process, can be successfully molded with SMC in a single press stroke using standard compression molding techniques. The finalized design of the trough panel is given. The SMC formulation chosen is a low shrink, low profile SMC using 40% by weight one inch chopped glass fibers in a uv stabilized polyester resin matrix. A program to test for the adhesion between mirrored glass sheets and the SMC is discussed briefly. (LEW)

  12. Exergetic analysis of parabolic trough solar thermal power plants

    NASA Astrophysics Data System (ADS)

    Petrakopoulou, F.; Ruperez, B.; San Miguel, G.

    2014-12-01

    A very important component to achieve sustainable development in the energy sector is the improvement of energy efficiency of widely applied thermodynamic processes. Evaluation and optimization methods of energy processes play a crucial role in fulfilling this goal. A suitable method for the evaluation and optimization of energy conversion systems has been proven to be the exergetic analysis. In this work, two parabolic trough solar thermal power plants are simulated in detail using commercial software, and they are further analysed and compared using an exergetic analysis. The first plant uses a thermal fluid to produce the steam required in a steam generator, while the second one produces the steam directly in the solar field. The analysis involves the evaluation of the individual components of the power plants, as well as the performance evaluation of the overall structures. The main goal is to detect thermodynamic inefficiencies of the two different configurations and propose measures to minimize those. We find that the two examined plants have similar main sources of exergy destruction: the solar field (parabolic trough solar collectors), followed by the steam generator. This reveals the importance of an optimal design of these particular components, which could reduce inefficiencies present in the system. The differences in the exergy destruction and exergetic efficiencies of individual components of the two plants are analyzed in detail based on comparable operational conditions.

  13. Simulation of point light concentration with parabolic trough collector

    NASA Astrophysics Data System (ADS)

    Danylyuk, Andriy; Zettl, Marcus; Lynass, Mark

    2010-08-01

    As the amount of solar generated energy usage increases worldwide, researches are turning to more advanced methods to increase collection efficiencies and drive down system costs. In this paper, four different optical system designs for solar concentrator applications are discussed. Each of the designs studied utilizes a parabolic trough optical element. The use of the parabolic trough in conjunction with a secondary optical component eliminates the need for expensive complicated 2-axis tracking, whilst still allowing the precise point focus normally only possible with more complex paraboloid systems. The result is an optical system, which offers all the advantages of a linear focus geometry combined with the possibility to utilize point focus concentration. The results were obtained using photometric geometrical ray tracing methods. Ideal surface simulations were initially used to separate surface from geometrical loss contributions. Later, more realistic simulations, including surface and reflectivity data of typical manufacturing methods and materials, were used to compare optical output power densities and system losses. For the systems studied, the minimum and maximum optical efficiencies obtained were 76.73% and 81% respectively. The AM 1.5 solar spectrum power densities in the absorption plane ranged from 50 to 195.8Wm-2.

  14. Thermal storage requirements for parabolic dish solar power plants

    NASA Technical Reports Server (NTRS)

    Wen, L.; Steele, H.

    1980-01-01

    The cost effectiveness of a high temperature thermal storage system is investigated for a representative parabolic dish solar power plant. The plant supplies electrical power in accordance with a specific, seasonally varying demand profile. The solar power received by the plant is supplemented by power from fuel combustion. The cost of electricity generated by the solar power plant is calculated, using the cost of mass-producible subsystems (specifically, parabolic dishes, receivers, and power conversion units) now being designed for this type of solar plant. The trade-off between fuel and thermal storage is derived in terms of storage effectiveness, the cost of storage devices, and the cost of fuel. Thermal storage requirements, such as storage capacity, storage effectiveness, and storage cost are established based on the cost of fuel and the overall objective of minimizing the cost of the electricity produced by the system. As the cost of fuel increases at a rate faster than general inflation, thermal storage systems in the $40 to $70/kWthr range could become cost effective in the near future.

  15. Approximate optimal control design for nonlinear one-dimensional parabolic PDE systems using empirical eigenfunctions and neural network.

    PubMed

    Luo, Biao; Wu, Huai-Ning

    2012-12-01

    This paper addresses the approximate optimal control problem for a class of parabolic partial differential equation (PDE) systems with nonlinear spatial differential operators. An approximate optimal control design method is proposed on the basis of the empirical eigenfunctions (EEFs) and neural network (NN). First, based on the data collected from the PDE system, the Karhunen-Loève decomposition is used to compute the EEFs. With those EEFs, the PDE system is formulated as a high-order ordinary differential equation (ODE) system. To further reduce its dimension, the singular perturbation (SP) technique is employed to derive a reduced-order model (ROM), which can accurately describe the dominant dynamics of the PDE system. Second, the Hamilton-Jacobi-Bellman (HJB) method is applied to synthesize an optimal controller based on the ROM, where the closed-loop asymptotic stability of the high-order ODE system can be guaranteed by the SP theory. By dividing the optimal control law into two parts, the linear part is obtained by solving an algebraic Riccati equation, and a new type of HJB-like equation is derived for designing the nonlinear part. Third, a control update strategy based on successive approximation is proposed to solve the HJB-like equation, and its convergence is proved. Furthermore, an NN approach is used to approximate the cost function. Finally, we apply the developed approximate optimal control method to a diffusion-reaction process with a nonlinear spatial operator, and the simulation results illustrate its effectiveness. PMID:22588610

  16. 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.

  17. Classification of Invariant Differential Operators for Non-Compact Lie Algebras via Parabolic Relations

    NASA Astrophysics Data System (ADS)

    Dobrev, V. K.

    2014-05-01

    In the present paper we review the progress of the project of classification and construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we called earlier 'conformal Lie algebras' (CLA), which have very similar properties to the conformal algebras of Minkowski space-time, though our aim is to go beyond this class in a natural way. For this we introduced recently the new notion of parabolic relation between two non-compact semisimple Lie algebras G and G' that have the same complexification and possess maximal parabolic subalgebras with the same complexification. Thus, we consider the exceptional algebra E7(7) which is parabolically related to the CLA E7(-25). Other interesting examples are the orthogonal algebras so(p, q) all of which are parabolically related to the conformal algebra so(n, 2) with p + q = n + 2, the parabolic subalgebras including the Lorentz subalgebra so(n - 1,1) and its analogs so(p - 1, q - 1). Further we consider the algebras sl(2n, Bbb R) and for n = 2k the algebras su* (4k) which are parabolically related to the CLA su(n,n). Further we consider the algebras sp(r,r) which are parabolically related to the CLA sp(2r, Bbb R). We consider also E6(6) and E6(2) which are parabolically related to the hermitian symmetric case E6(-14),

  18. A fourth-order box method for solving the boundary layer equations

    NASA Technical Reports Server (NTRS)

    Wornom, S. F.

    1977-01-01

    A fourth order box method for calculating high accuracy numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations is presented. The method is the natural extension of the second order Keller Box scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary layer equations. Numerical results for high accuracy test cases show the method to be significantly faster than other higher order and second order methods.

  19. On several aspects and applications of the multigrid method for solving partial differential equations

    NASA Technical Reports Server (NTRS)

    Dinar, N.

    1978-01-01

    Several aspects of multigrid methods are briefly described. The main subjects include the development of very efficient multigrid algorithms for systems of elliptic equations (Cauchy-Riemann, Stokes, Navier-Stokes), as well as the development of control and prediction tools (based on local mode Fourier analysis), used to analyze, check and improve these algorithms. Preliminary research on multigrid algorithms for time dependent parabolic equations is also described. Improvements in existing multigrid processes and algorithms for elliptic equations were studied.

  20. Development status of the PDC-1 Parabolic Dish Concentrator

    NASA Technical Reports Server (NTRS)

    Thostesen, T.; Soczak, I. F.; Pons, R. L.

    1982-01-01

    The status of development of the 12 m diameter parabolic dish concentrator which is planned for use with the Small Community Solar Thermal Power System. The PDC-1 unit features the use of plastic reflector film bonded to structural plastic gores supported by front-bracing steel ribs. An elevation-over-azimuth mount arrangement is employed, with a conventional wheel-and-track arrangement; outboard trunnions permit the dish to be stored in the face down position, with the added advantage of easy access to the power conversion assembly. The control system is comprised of a central computer (LSI 1123), a manual control panel, a concentrator control unit, two motor controllers, a Sun sensor, and two angular position resolvers. The system is designed for the simultaneous control of several concentrators. The optical testing of reflective panels is described.

  1. Optical analysis of point focus parabolic radiation concentrators

    SciTech Connect

    Bendt, P.; Rabl, A.

    1980-04-01

    A simple formalism is developed for analyzing the optical performance of point focus parabolic radiation concentrators. To account for off-axis aberrations of the parabola, an angular acceptance function is defined as that fraction of a beam of parallel radiation incident on the aperture which would reach the receiver if the optics were perfect. The radiation intercepted by the receiver of a real concentrator is obtained as a convolution of angular acceptance function, of optical error distribution, and of angular brightness distribution of the radiation source. Losses resulting from absorption in the reflector or reflection at the receiver are treated by a multiplicative factor rho ..cap alpha.. where rho = reflectance of the reflector and ..cap alpha.. = absorptance of the receiver. For numerical calculations, this method is more accurate and less time-consuming than the ray-tracing method. In many cases, there are acceptable approximations whereby the results can be obtained by reading a graph or evaluating a simple curve fit.

  2. Hypersonic flows generated by parabolic and paraboloidal shock waves

    NASA Technical Reports Server (NTRS)

    Schwartz, L. W.

    1974-01-01

    A computer algorithm has been developed to determine the blunt-body flowfields supporting symmetric parabolic and paraboloidal shock waves at infinite free-stream Mach number. Solutions are expressed in an analytic form as high-order power series, in the coordinate normal to the shock, whose coefficients can be determined exactly. Analytic continuation is provided by the use of Pade approximations. Test cases provide solutions of very high accuracy. In the axisymmetric case for gamma equals 715 the solution has been found far downstream, where it agrees with the modified blast-wave results. For plane flow, on the other hand, a limit line appears within the shock layer, a short distance past the sonic line, suggesting the presence of an imbedded shock. Local solutions in the downstream limit are discussed.

  3. Context-specific adaptation of saccade gain in parabolic flight

    NASA Technical Reports Server (NTRS)

    Shelhamer, Mark; Clendaniel, Richard A.; Roberts, Dale C.

    2002-01-01

    Previous studies established that vestibular reflexes can have two adapted states (e.g., gains) simultaneously, and that a context cue (e.g., vertical eye position) can switch between the two states. Our earlier work demonstrated this phenomenon of context-specific adaptation for saccadic eye movements: we asked for gain decrease in one context state and gain increase in another context state, and then determined if a change in the context state would invoke switching between the adapted states. Horizontal and vertical eye position and head orientation could serve, to varying degrees, as cues for switching between two different saccade gains. In the present study, we asked whether gravity magnitude could serve as a context cue: saccade adaptation was performed during parabolic flight, which provides alternating levels of gravitoinertial force (0 g and 1.8 g). Results were less robust than those from ground experiments, but established that different saccade magnitudes could be associated with different gravity levels.

  4. Two-level parabolic model with phase-jump coupling

    NASA Astrophysics Data System (ADS)

    Lehto, J. M. S.; Suominen, K.-A.

    2016-07-01

    We study the coherent dynamics of a two-level parabolic model and ways to enhance population transfer and even to obtain complete population inversion in such models. Motivated by the complete population inversion effect of zero-area pulses found in [Phys. Rev. A 73, 023416 (2006), 10.1103/PhysRevA.73.023416], we consider a scheme where a given coupling function is transformed to a zero-area coupling by performing a phase jump in the middle of the evolution. With a phase-jump coupling, complete population inversion can be achieved with relatively small coupling. In the case of Zener tunneling, complete population inversion is obtained for strong-enough coupling regardless of the height of the tunneling barrier. We also derive a universal formula for the effect of the phase jump.

  5. Parabolic dish Stirling module development and test results

    SciTech Connect

    Washom, B.

    1984-08-01

    Private industry and the U.S. Department of Energy are presently cost sharing the design, manufacture and test of a 25 Kwe parabolic dish Stirling module, known as Vanguard. The Vanguard module achieved a world's record sunlight to electric conversion efficiency of 31.6% in February 1984 at the Rancho Mirage, California test site. The module is presently operating daily in sunrise to sunset tests to determine the long term performance and O and M requirements of this distributed receiver system. Each module can be easily integrated into a larger field of modules to provide power generation opportunities from a single 25 Kwe unit for isolated loads to 30 Mwe systems for integrated utility power generation.

  6. Large Phased Array Radar Using Networked Small Parabolic Reflectors

    NASA Technical Reports Server (NTRS)

    Amoozegar, Farid

    2006-01-01

    Multifunction phased array systems with radar, telecom, and imaging applications have already been established for flat plate phased arrays of dipoles, or waveguides. In this paper the design trades and candidate options for combining the radar and telecom functions of the Deep Space Network (DSN) into a single large transmit array of small parabolic reflectors will be discussed. In particular the effect of combing the radar and telecom functions on the sizes of individual antenna apertures and the corresponding spacing between the antenna elements of the array will be analyzed. A heterogeneous architecture for the DSN large transmit array is proposed to meet the radar and telecom requirements while considering the budget, scheduling, and strategic planning constrains.

  7. Solar parabolic dish thermal power systems - Technology and applications

    NASA Technical Reports Server (NTRS)

    Lucas, J. W.; Marriott, A. T.

    1979-01-01

    Activities of two projects at JPL in support of DOE's Small Power Systems Program are reported. These two projects are the Point-Focusing Distributed Receiver (PFDR) Technology Project and the Point-Focusing Thermal and Electric Applications (PFTEA) Project. The PFDR Technology Project's major activity is developing the technology of solar concentrators, receivers and power conversion subsystems suitable for parabolic dish or point-focusing distributed receiver power systems. Other PFDR activities include system integration and cost estimation under mass production, as well as the testing of the hardware. The PFTEA Project's first major activity is applications analysis, that is seeking ways to introduce PFDR systems into appropriate user sectors. The second activity is systems engineering and development wherein power plant systems are analyzed for specific applications. The third activity is the installation of a series of engineering experiments in various user environments to obtain actual operating experience

  8. Generic parabolic points are isolated in positive characteristic

    NASA Astrophysics Data System (ADS)

    Lindahl, Karl-Olof; Rivera-Letelier, Juan

    2016-05-01

    We study analytic germs in one variable with a parabolic fixed point at the origin, over an ultrametric ground field of positive characteristic. It is conjectured that for such a germ the origin is isolated as a periodic point. Our main result is an affirmative solution of this conjecture in the case of a generic germ with a prescribed multiplier. The genericity condition is explicit: the power series is minimally ramified, i.e. the degree of the first nonlinear term of each of its iterates is as small as possible. Our main technical result is a computation of the first significant terms of a minimally ramified power series. From this we obtain a lower bound for the norm of nonzero periodic points, from which we deduce our main result. As a by-product we give a new and self-contained proof of a characterization of minimally ramified power series in terms of the iterative residue.

  9. Development of sheet-metal parabolic-trough reflector panels

    SciTech Connect

    Biester, A.W.

    1982-06-01

    Efforts to develop accurate, durable, and mass producible sheet metal parabolic trough solar collectors and the associated support for the collectors are described. The design considered is similar to an automobile hood, a two-piece sheet metal structure consisting of a formed steel frame or stiffening panel and a smooth contoured skin. The two pieces may be bonded or welded to form a rigid structure, and a reflective surface applied such as a film, glass mirror, or any of the presently utilized materials. The work encompassed material selection, adhesive selection and testing, tool design and fabrication, prototype panel production, and design and development of torque tube assemblies on which the trough is inclined. Appended are results of adhesive bonding studies. It is found that high volume technology can be used to produce accurate and structurally sound reflector panels, and one configuration has been selected for fabrication in suitable quantities for performance testing. (LEW)

  10. Generation of entangled matter qubits in two opposing parabolic mirrors

    NASA Astrophysics Data System (ADS)

    Trautmann, N.; Bernád, J. Z.; Sondermann, M.; Alber, G.; Sánchez-Soto, L. L.; Leuchs, G.

    2014-12-01

    We propose a scheme for the remote preparation of entangled matter qubits in free space. For this purpose, a setup of two opposing parabolic mirrors is considered, each one with a single ion trapped at its focus. To get the required entanglement in this extreme multimode scenario, we take advantage of the spontaneous decay, which is usually considered as an apparent nuisance. Using semiclassical methods, we derive an efficient photon-path representation to deal with this problem. We also present a thorough examination of the experimental feasibility of the scheme. The vulnerabilities arising in realistic implementations reduce the success probability, but leave the fidelity of the generated state unaltered. Our proposal thus allows for the generation of high-fidelity entangled matter qubits with high rate.

  11. Fifth parabolic dish solar thermal power program annual review: proceedings

    SciTech Connect

    1984-03-01

    The primary objective of the Review was to present the results of activities within the Parabolic Dish Technology and Module/Systems Development element of the Department of Energy's Solar Thermal Energy Systems Program. The Review consisted of nine technical sessions covering overall Project and Program aspects, Stirling and Brayton module development, concentrator and engine/receiver development, and associated hardware and test results to date; distributed systems operating experience; international dish development activities; and non-DOE-sponsored domestic dish activities. A panel discussion concerning business views of solar electric generation was held. These Proceedings contain the texts of presentations made at the Review, as submitted by their authors at the beginning of the Review; therefore, they may vary slightly from the actual presentations in the technical sessions.

  12. Development status of the PDC-1 Parabolic Dish Concentrator

    NASA Astrophysics Data System (ADS)

    Thostesen, T.; Soczak, I. F.; Pons, R. L.

    1982-07-01

    The status of development of the 12 m diameter parabolic dish concentrator which is planned for use with the Small Community Solar Thermal Power System. The PDC-1 unit features the use of plastic reflector film bonded to structural plastic gores supported by front-bracing steel ribs. An elevation-over-azimuth mount arrangement is employed, with a conventional wheel-and-track arrangement; outboard trunnions permit the dish to be stored in the face down position, with the added advantage of easy access to the power conversion assembly. The control system is comprised of a central computer (LSI 1123), a manual control panel, a concentrator control unit, two motor controllers, a Sun sensor, and two angular position resolvers. The system is designed for the simultaneous control of several concentrators. The optical testing of reflective panels is described.

  13. Cerebral vasoconstriction precedes orthostatic intolerance after parabolic flight

    NASA Technical Reports Server (NTRS)

    Serrador, J. M.; Shoemaker, J. K.; Brown, T. E.; Kassam, M. S.; Bondar, R. L.; Schlegel, T. T.

    2000-01-01

    The effects of brief but repeated bouts of micro- and hypergravity on cerebrovascular responses to head-up tilt (HUT) were examined in 13 individuals after (compared to before) parabolic flight. Middle cerebral artery mean flow velocity (MCA MFV; transcranial Doppler ultrasound), eye level blood pressure (BP) and end tidal CO(2) (P(ET)CO(2)) were measured while supine and during 80 degrees HUT for 30 min or until presyncope. In the postflight tests subjects were classified as being orthostatically tolerant (OT) (n = 7) or intolerant (OI) (n = 6). BP was diminished with HUT in the OT group in both tests (p < 0.05) whereas postflight BP was not different from supine in the OI group. Postflight compared to preflight, the reduction in P(ET)CO(2) with HUT (p < 0.05) increased in both groups, although significantly so only in the OI group (p < 0.05). The OI group also had a significant decrease in supine MCA MFV postflight (p < 0.05) that was unaccompanied by a change in supine P(ET)CO(2). The decrease in MCA MFV that occurred during HUT in both groups preflight (p < 0.05) was accentuated only in the OI group postflight, particularly during the final 30 s of HUT (p < 0.05). However, this accentuated decrease in MCA MFV was not correlated to the greater decrease in P(ET)CO(2) during the same period (R = 0.20, p = 0.42). Although cerebral vascular resistance (CVR) also increased in the OI group during the last 30 s of HUT postflight (p < 0.05), the dynamic autoregulatory gain was not simultaneously changed. Therefore, we conclude that in the OI individuals, parabolic flight was associated with cerebral hypoperfusion following a paradoxical augmentation of CVR by a mechanism that was not related to changes in autoregulation nor strictly to changes in P(ET)CO(2).

  14. Microgravity Active Vibration Isolation System on Parabolic Flights

    NASA Astrophysics Data System (ADS)

    Dong, Wenbo; Pletser, Vladimir; Yang, Yang

    2016-07-01

    The Microgravity Active Vibration Isolation System (MAIS) aims at reducing on-orbit vibrations, providing a better controlled lower gravity environment for microgravity physical science experiments. The MAIS will be launched on Tianzhou-1, the first cargo ship of the China Manned Space Program. The principle of the MAIS is to suspend with electro-magnetic actuators a scientific payload, isolating it from the vibrating stator. The MAIS's vibration isolation capability is frequency-dependent and a decrease of vibration of about 40dB can be attained. The MAIS can accommodate 20kg of scientific payload or sample unit, and provide 30W of power and 1Mbps of data transmission. The MAIS is developed to support microgravity scientific experiments on manned platforms in low earth orbit, in order to meet the scientific requirements for fluid physics, materials science, and fundamental physics investigations, which usually need a very quiet environment, increasing their chances of success and their scientific outcomes. The results of scientific experiments and technology tests obtained with the MAIS will be used to improve future space based research. As the suspension force acting on the payload is very small, the MAIS can only be operative and tested in a weightless environment. The 'Deutsches Zentrum für Luft- und Raumfahrt e.V.' (DLR, German Aerospace Centre) granted a flight opportunity to the MAIS experiment to be tested during its 27th parabolic flight campaign of September 2015 performed on the A310 ZERO-G aircraft managed by the French company Novespace, a subsidiary of the 'Centre National d'Etudes Spatiales' (CNES, French Space Agency). The experiment results confirmed that the 6 degrees of freedom motion control technique was effective, and that the vibration isolation performance fulfilled perfectly the expectations based on theoretical analyses and simulations. This paper will present the design of the MAIS and the experiment results obtained during the

  15. The well-posedness of the Kuramoto-Sivashinsky equation

    NASA Technical Reports Server (NTRS)

    Tadmor, E.

    1984-01-01

    The Kuramoto-Sivashinsky equation arises in a variety of applications, among which are modeling reaction diffusion systems, flame propagation and viscous flow problems. It is considered here, as a prototype to the larger class of generalized Burgers equations: those consist of a quadratic nonlinearity and an arbitrary linear parabolic part. It is shown that such equations are well posed, thus admitting a unique smooth solution, continuously dependent on its initial data. As an attractive alternative to standard energy methods, existence and stability are derived in this case, by patching in the large short time solutions without loss of derivatives.

  16. Asymptotic behavior of degenerate logistic equations

    NASA Astrophysics Data System (ADS)

    Arrieta, José M.; Pardo, Rosa; Rodríguez-Bernal, Aníbal

    2015-12-01

    We analyze the asymptotic behavior of positive solutions of parabolic equations with a class of degenerate logistic nonlinearities of the type λu - n (x)uρ. An important characteristic of this work is that the region where the logistic term n (ṡ) vanishes, that is K0 = { x : n (x) = 0 }, may be non-smooth. We analyze conditions on λ, ρ, n (ṡ) and K0 guaranteeing that the solution starting at a positive initial condition remains bounded or blows up as time goes to infinity. The asymptotic behavior may not be the same in different parts of K0.

  17. Second harmonic generation by relativistic self-focusing of q-Gaussian laser beam in preformed parabolic plasma channel

    SciTech Connect

    Singh, Arvinder E-mail: naveens222@rediffmail.com; Gupta, Naveen E-mail: naveens222@rediffmail.com

    2015-01-15

    This paper presents an investigation of relativistic self-focusing effect of a q-Gaussian laser beam on second harmonic generation in a preformed parabolic plasma channel. An expression has been derived for density perturbation associated with the plasma wave excited by the laser beam. This in turn acts as a source of second harmonic generation. The moment theory approach has been used to derive a differential equation that governs the evolution of spot size of the laser beam with the distance of propagation. The detailed effects of intensity distribution deviation from Gaussian distribution, intensity of laser beam, density, and depth of the channel have been studied on self-focusing as well as on second harmonic generation.

  18. Boundedness and global existence in the higher-dimensional parabolic-parabolic chemotaxis system with/without growth source

    NASA Astrophysics Data System (ADS)

    Xiang, Tian

    2015-06-01

    In this paper, we are concerned with a general class of quasilinear parabolic-parabolic chemotaxis systems with/without growth source, under homogeneous Neumann boundary conditions in a smooth bounded domain Ω ⊂Rn with n ≥ 2. It is recently known that blowup is possible even in the presence of superlinear growth restrictions. Here, we derive new and interesting characterizations on the growth versus the boundedness. We show that the hard task of proving the L∞-boundedness of the cell density can be reduced to proving its Lr-boundedness. In other words, we show that the Lr-boundedness of the cell density can successfully guarantee its L∞-boundedness and hence its global boundedness, where r = n + ɛ or n/2 + ɛ depending on whether the growth restriction is essentially linear (including no growth) or superlinear. Hence, a blowup solution also blows up in Lp-norm for any suitably large p. More detailed information on how the growth source affects the boundedness of the solution is derived. These results reveal deep understandings of blowup mechanism for chemotaxis models. Then we use these criteria to establish uniform boundedness and hence global existence of the underlying models: logistic source in 2-D, cubic source as initially proposed by Mimura and Tsujikawa in 3-D, [ (n - 1) + ɛ ]st source in n-D with n ≥ 4. As a consequence, in a chemotaxis-growth model, blowup is impossible if the growth effect is suitably strong. Finally, we underline that our results remove the commonly assumed convexity on the domain Ω.

  19. Solution Methods for Certain Evolution Equations

    NASA Astrophysics Data System (ADS)

    Vega-Guzman, Jose Manuel

    Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value

  20. Invariant differential operators for non-compact Lie algebras parabolically related to conformal Lie algebras

    NASA Astrophysics Data System (ADS)

    Dobrev, V. K.

    2013-02-01

    In the present paper we continue the project of systematic construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we call 'conformal Lie algebras' (CLA), which have very similar properties to the conformal algebras of Minkowski space-time, though our aim is to go beyond this class in a natural way. For this we introduce the new notion of parabolic relation between two non-compact semisimple Lie algebras G and G ' that have the same complexification and possess maximal parabolic subalgebras with the same complexification. Thus, we consider the exceptional algebra E 7(7) which is parabolically related to the CLA E 7(-25) , the parabolic subalgebras including E 6(6) and E 6(-26). Other interesting examples are the orthogonal algebras so(p, q) all of which are parabolically related to the conformal algebra so( n, 2) with p + q = n + 2, the parabolic subalgebras including the Lorentz subalgebra so( n - 1, 1) and its analogs so( p - 1, q - 1). We consider also E6(6) and E6(2) which are parabolically related to the hermitian symmetric case E6(-14) , the parabolic subalgebras including real forms of sl(6). We also give a formula for the number of representations in the main multiplets valid for CLAs and all algebras that are parabolically related to them. In all considered cases we give the main multiplets of indecomposable elementary representations including the necessary data for all relevant invariant differential operators. In the case of so( p, q) we give also the reduced multiplets. We should stress that the multiplets are given in the most economic way in pairs of shadow fields. Furthermore we should stress that the classification of all invariant differential operators includes as special cases all possible conservation laws and conserved currents, unitary or not.

  1. Mixed finite elements for the Richards' equation: linearization procedure

    NASA Astrophysics Data System (ADS)

    Pop, I. S.; Radu, F.; Knabner, P.

    2004-07-01

    We consider mixed finite element discretization for a class of degenerate parabolic problems including the Richards' equation. After regularization, time discretization is achieved by an Euler implicit scheme, while mixed finite elements are employed for the discretization in space. Based on the results obtained in (Radu et al. RANA Preprint 02-06, Eindhoven University of Technology, 2002), this paper considers a simple iterative scheme to solve the emerging nonlinear elliptic problems.

  2. Biosignal alterations generated by parabolic flights of small aerobatic aircrafts

    NASA Astrophysics Data System (ADS)

    Simon, M. Jose; Perez-Poch, Antoni; Ruiz, Xavier; Gavalda, Fina; Saez, Nuria

    Since the pioneering works of Prof. Strughold in 1948, the aerospace medicine aimed to characterize the modifications induced in the human body by changes in the gravity level. In this respect, it is nowadays well known that one of the most serious problems of these kind of environments is the fluid shift. If this effect is enough severe and persistent, serious changes in the hemodynamic of the brain (cerebral blood flow and blood oxigenation level) appear which could be detected as alterations in the electroencephalogram, EEG [1]. Also, this fluid redistribution, together with the relocation of the heart in the thorax, induces detectable changes in the electrocardiogram, ECG [2]. Other kind of important problems are related with vestibular instability, kinetosis and illusory sensations. In particular since the seventies [3,4] it is known that in parabolic flights and due to eye movements triggered by the changing input from the otholith system, fixed real targets appeared to have moved downward while visual afterimages appeared to have moved upward (oculogravic illusions). In order to cover all the above-mentioned potential alterations, the present work, together with the gravity level, continuously monitors the electroencephalogram, EEG, the electrocardiogram, ECG and the electrooculogram, EOG of a normal subject trying to detect correlations between the different alterations observed in these signals and the changes of gravity during parabolic flights. The small aerobatic aircraft used is a CAP10B and during the flight the subject is located near the pilot. To properly cover all the range of accelerations we have used two sensitive triaxial accelerometers covering the high and low ranges of acceleration. Biosignals have been gathered using a Biopac data unit together with the Acknowledge software package (from BionicÔ). It is important to finally remark that, due to the obvious difference between the power of the different engines, the accelerometric

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

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Kunisch, K.

    1982-01-01

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

  4. Time-Dependent Parabolic Finite Difference Formulation for Harmonic Sound Propagation in a Two-Dimensional Duct with Flow

    NASA Technical Reports Server (NTRS)

    Kreider, Kevin L.; Baumeister, Kenneth J.

    1996-01-01

    An explicit finite difference real time iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for future large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable for a harmonic monochromatic sound field, a parabolic (in time) approximation is introduced to reduce the order of the governing equation. The analysis begins with a harmonic sound source radiating into a quiescent duct. This fully explicit iteration method then calculates stepwise in time to obtain the 'steady state' harmonic solutions of the acoustic field. For stability, applications of conventional impedance boundary conditions requires coupling to explicit hyperbolic difference equations at the boundary. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

  5. Coupling flexible solar cell with parabolic trough solar-concentrator-prototype design and performance

    NASA Astrophysics Data System (ADS)

    Panin, Alexander; Bergquist, Jonathon

    2007-10-01

    Solar cells are still too expensive (5-20/watt) to compete with traditional fossil fuel power generating methods (˜1/watt). Parabolic trough solar concentrator has the advantage of modest concentration ratio (10-100) which is well suited for coupling with solar cell. Thus using small area solar cell placed in the focal line of parabolic trough may be economically viable alternative to flat solar panels. We experiment with flexible solar cell (backed by water cooling pipe) placed in the focus of parabolic trough reflector. Another advantage of parabolic trough concentrator is very relaxed tracking requirement. For example, east-west oriented concentrator (aligned with the ecliptic plane) does not even need any tracking during core 4-6 hours around noon (when maximum illumination is available). The design and the performance of the prototype, as well as possible economical benefits of full scale projects are discussed in the presentation.

  6. A position transducer for studying parabolic motion and rolling down a grooved track

    NASA Astrophysics Data System (ADS)

    Basta, M.; Di Gennaro, M.; Picciarelli, V.

    1994-09-01

    We describe a computerized system based on a position transducer on-line and discuss its applications in two experiments (parabolic motion and rolling down a grooved track) performed in an introductory physics laboratory course.

  7. Hormonal responses of metoclopramide-treated subjects experiencing nausea or emesis during parabolic flight

    NASA Technical Reports Server (NTRS)

    Kohl, Randall L.

    1987-01-01

    The concentrations of adrenocorticotropic hormone (ACTH), vasopressin (AVP), epinephrine (EPI), and norepinephrine (NE) in 22 subjects administered 10 to 20 mg of metoclopramide prior to parabolic flight are measured. The effect of metoclopramide on motion sickness is examined. It is observed that metoclopramide is ineffective in the modulation of motion sickness due to stressful linear and angular acceleration and orbital flight, and it does not affect serum hormones prior to parabolic flight. It is detected that the serum level of AVP declines following emesis induced by parabolic flight and stressful angular acceleration; the serum levels of ACTH and EPI are elevated by parabolic flight and stressful angular acceleration; and serum NE is significantly elevated immediately following emesis. The possible roles of these hormones in the etiology of space motion sickness are discussed.

  8. Wind Tunnel Tests of Parabolic Trough Solar Collectors: March 2001--August 2003

    SciTech Connect

    Hosoya, N.; Peterka, J. A.; Gee, R. C.; Kearney, D.

    2008-05-01

    Conducted extensive wind-tunnel tests on parabolic trough solar collectors to determine practical wind loads applicable to structural design for stress and deformation, and local component design for concentrator reflectors.

  9. High Speed Analysis Of Free Flights With A Parabolic Thruster

    NASA Astrophysics Data System (ADS)

    Scharring, Stefan; Eckel, Hans-Albert; Röser, Hans-Peter

    2010-05-01

    A laser-based rangefinder with high temporal resolution, synchronized with a laser burst, is employed for fast on-site analysis of pulsed free flights. Additional high speed recordings from two different angles of view allow for full 3D-reconstruction of the trajectory and calibration of the rangefinder data. This reveals the whole dynamics of the flyer including the lateral and angular impulse coupling components as well as information on the detonation process. The employment of an ignition pin enhances the reproducibility of the momentum coupling due to a more reliable plasma ignition during the flight. The impact of initial lateral offset is studied and shows beam-riding properties of the parabolic craft within a small range. Back-driving forces are derived and compared with the theoretical model. The flight stability is evaluated with respect to the minimization and compensation of the lateral and angular momentum in a hovering experiment. Stable laser acceleration ranges up to 3 m altitude. Ballistic free flights close to the laboratory ceiling at 7.8 m are reported.

  10. Recent Solar Measurements Results at the Parabolic Dish Test Site

    NASA Technical Reports Server (NTRS)

    Ross, D. L.

    1984-01-01

    After the Mexican volcanic eruptions of March 28, April 3 and 4, 1982, the question of its effect on insolation levels at the Parabolic Dish Test Site (PDTS) naturally arose. Clearly, the answer to the original question is that the Mexican volcanic explosion had a significant impact on energy and insolation levels at the PDTS and, furthermore, it has been quite long lasting. The first really significant decrease in energy and insolation levels occurred in June 1982 when the energy level decreased by 19.7% while the peak insolation levels went down by 4.0%. June of 1982 was also the first month (of 13 consecutive months) when peak insolation levels did not equal or exceed 1,000 W/sq m. Signs of a recovery from the effects of the volcanic explosion began to appear in May of 1983, when the energy level exceeded that of May 1981 as well as May 1982. It would appear that energy and insolation levels are improving at the PDTS, but have not quite reached normal or pre-volcanic levels. At this time the data would seem to suggest a return to normal energy and insolation levels will occur in the very near future.

  11. Piracetam and fish orientation during parabolic aircraft flight

    NASA Technical Reports Server (NTRS)

    Hoffman, R. B.; Salinas, G. A.; Homick, J. L.

    1980-01-01

    Goldfish were flown in parabolic Keplerian trajectories in a KC-135 aircraft to assay both the effectiveness of piracetam as an antimotion sickness drug and the effectiveness of state-dependent training during periods of oscillating gravity levels. Single-frame analyses of infrared films were performed for two classes of responses - role rates in hypogravity or hypogravity orienting responses (LGR) and climbing responses in hypergravity or hypergravity orienting responses (HGR). In Experiment I, preflight training with the vestibular stressor facilitated suppression of LGR by the 10th parabola. An inverse correlation was found between the magnitudes of LGR and HGR. Piracetam was not effective in a state-dependent design, but the drug did significantly increase HGR when injected into trained fish shortly before flight. In Experiment II, injections of saline, piracetam, and modifiers of gamma-aminobutyric acid - aminooxyacetic acid (AOAA) and isonicotinic acid did not modify LGR. AOAA did significantly increase HGR. Thus, the preflight training has a beneficial effect in reducing disorientation in the fish in weightlessness, but the drugs employed were ineffective.

  12. Evaluation of aerosolized medications during parabolic flight maneuvers

    NASA Technical Reports Server (NTRS)

    Lloyd, Charles W.; Martin, William J.; Gosbee, John

    1991-01-01

    The goal was to visually evaluate the effect gravity has on delivery of medications by the use of various aerosol devices. During parabolic flight the same four aerosols were retested as performed in studio ground tests. It appears that the Cetacaine spray and the Ventolin inhaler function without failure during all test. The pump spray (Nostril) appeared to function normally when the container was full, however it appeared to begin to fail to deliver a full mist with larger droplet size when the container was nearly empty. The simple hand spray bottle appeared to work when the container was full and performed progressively worse as the container was emptied. During Apollo flights, it was reported that standard spray bottles did not work well, however, they did not indicate why. It appears that we would also conclude that standard spray bottles do not function as well in zero gravity by failing to produce a normal mist spray. The standard spray bottle allowed the fluid to come out in a narrow fluid stream when held with the nozzle either level or slightly tilted upward.

  13. Slope Error Measurement Tool for Solar Parabolic Trough Collectors: Preprint

    SciTech Connect

    Stynes, J. K.; Ihas, B.

    2012-04-01

    The National Renewable Energy Laboratory (NREL) has developed an optical measurement tool for parabolic solar collectors that measures the combined errors due to absorber misalignment and reflector slope error. The combined absorber alignment and reflector slope errors are measured using a digital camera to photograph the reflected image of the absorber in the collector. Previous work using the image of the reflection of the absorber finds the reflector slope errors from the reflection of the absorber and an independent measurement of the absorber location. The accuracy of the reflector slope error measurement is thus dependent on the accuracy of the absorber location measurement. By measuring the combined reflector-absorber errors, the uncertainty in the absorber location measurement is eliminated. The related performance merit, the intercept factor, depends on the combined effects of the absorber alignment and reflector slope errors. Measuring the combined effect provides a simpler measurement and a more accurate input to the intercept factor estimate. The minimal equipment and setup required for this measurement technique make it ideal for field measurements.

  14. Perception of Egocentric Distance during Gravitational Changes in Parabolic Flight.

    PubMed

    Clément, Gilles; Loureiro, Nuno; Sousa, Duarte; Zandvliet, Andre

    2016-01-01

    We explored the effect of gravity on the perceived representation of the absolute distance of objects to the observers within the range from 1.5-6 m. Experiments were performed on board the CNES Airbus Zero-G during parabolic flights eliciting repeated exposures to short periods of microgravity (0 g), hypergravity (1.8 g), and normal gravity (1 g). Two methods for obtaining estimates of perceived egocentric distance were used: verbal reports and visually directed motion toward a memorized visual target. For the latter method, because normal walking is not possible in 0 g, blindfolded subjects translated toward the visual target by pulling on a rope with their arms. The results showed that distance estimates using both verbal reports and blind pulling were significantly different between normal gravity, microgravity, and hypergravity. Compared to the 1 g measurements, the estimates of perceived distance using blind pulling were shorter for all distances in 1.8 g, whereas in 0 g they were longer for distances up to 4 m and shorter for distances beyond. These findings suggest that gravity plays a role in both the sensorimotor system and the perceptual/cognitive system for estimating egocentric distance. PMID:27463106

  15. Norwich Technologies' Advanced Low-Cost Receivers for Parabolic Troughs

    SciTech Connect

    Stettenheim, Joel; McBride, Troy O.; Brambles, Oliver J.; Cashin, Emil A.

    2013-12-31

    This report summarizes the successful results of our SunShot project, Advanced Low-Cost Receivers for Parabolic Troughs. With a limited budget of $252K and in only 12 months, we have (1) developed validated optical and thermal models and completed rigorous optimization analysis to identify key performance characteristics as part of developing first-generation laboratory prototype designs, (2) built optical and thermal laboratory prototypes and test systems with associated innovative testing protocols, and (3) performed extensive statistically relevant testing. We have produced fully functioning optical and thermal prototypes and accurate, validated models shown to capture important underlying physical mechanisms. The test results from the first-generation prototype establish performance exceeding the FOA requirement of thermal efficiency >90% for a CSP receiver while delivering an exit fluid temperature of > 650 °C and a cost < $150/kWth. Our vacuum-free SunTrap receiver design provides improvements over conventional vacuum-tube collectors, allowing dramatic reductions in thermal losses at high operating temperature.

  16. Parabolic heavy ion flow in the polar magnetosphere

    NASA Technical Reports Server (NTRS)

    Horwitz, J. L.

    1987-01-01

    Recent observations by the Dynamics Explorer 1 satellite over the dayside polar cap magnetosphere have indicated downward flows of heavy ions such as O(+), O(2+), N(+), and N(2+) with flow velocities of the order 1 km/s (Lockwood et al., 1985). These downward flows were interpreted as the result of 'parabolic' flow of these heavy ionospheric ions from a source region associated with the polar cleft topside ionosphere. Here, a two-dimensional kinetic model is utilized to elicit features of the transport of very low energy O(+) ions from the cleft ionosphere. Bulk parameter (density, flux, thermal energies, etc.) distributions in the noon-midnight meridian plane illustrate the effects of varying convection electric fields and source energies. The results illustrate that, particularly under conditions of weak convection electric fields and weak ion heating in the cleft region, much of the intermediate altitude polar cap magnetosphere may be populated by downward flowing heavy ions. It is further shown how two-dimensional transport effects may alter the characteristic vertical profiles of densities and fluxes from ordinary profiles computed in one-dimensional steady-state models.

  17. Mechanism of Hydrogen Formation in Solar Parabolic Trough Receivers

    SciTech Connect

    Moens, L.; Blake, D. M.

    2008-03-01

    Solar parabolic trough systems for electricity production are receiving renewed attention, and new solar plants are under construction to help meet the growing demands of the power market in the Western United States. The growing solar trough industry will rely on operating experience it has gained over the last two decades. Recently, researchers found that trough plants that use organic heat transfer fluids (HTF) such as Therminol VP-1 are experiencing significant heat losses in the receiver tubes. The cause has been traced back to the accumulation of excess hydrogen gas in the vacuum annulus that surrounds the steel receiver tube, thus compromising the thermal insulation of the receiver. The hydrogen gas is formed during the thermal decomposition of the organic HTF that circulates inside the receiver loop, and the installation of hydrogen getters inside the annulus has proven to be insufficient for controlling the hydrogen build-up over the lifetime of the receivers. This paper will provide an overview of the chemical literature dealing with the thermal decomposition of diphenyl oxide and biphenyl, the two constituents of Therminol VP-1.

  18. Perception of Egocentric Distance during Gravitational Changes in Parabolic Flight

    PubMed Central

    Clément, Gilles; Loureiro, Nuno; Sousa, Duarte; Zandvliet, Andre

    2016-01-01

    We explored the effect of gravity on the perceived representation of the absolute distance of objects to the observers within the range from 1.5–6 m. Experiments were performed on board the CNES Airbus Zero-G during parabolic flights eliciting repeated exposures to short periods of microgravity (0 g), hypergravity (1.8 g), and normal gravity (1 g). Two methods for obtaining estimates of perceived egocentric distance were used: verbal reports and visually directed motion toward a memorized visual target. For the latter method, because normal walking is not possible in 0 g, blindfolded subjects translated toward the visual target by pulling on a rope with their arms. The results showed that distance estimates using both verbal reports and blind pulling were significantly different between normal gravity, microgravity, and hypergravity. Compared to the 1 g measurements, the estimates of perceived distance using blind pulling were shorter for all distances in 1.8 g, whereas in 0 g they were longer for distances up to 4 m and shorter for distances beyond. These findings suggest that gravity plays a role in both the sensorimotor system and the perceptual/cognitive system for estimating egocentric distance. PMID:27463106

  19. Teaching Equations.

    ERIC Educational Resources Information Center

    Nibbelink, William H.

    1990-01-01

    Proposed is a gradual transition from arithmetic to the idea of an equation with variables in the elementary grades. Vertical and horizontal formats of open sentences, the instructional sequence, vocabulary, and levels of understanding are discussed in this article. (KR)

  20. Moment equations for a piecewise deterministic PDE

    NASA Astrophysics Data System (ADS)

    Bressloff, Paul C.; Lawley, Sean D.

    2015-03-01

    We analyze a piecewise deterministic PDE consisting of the diffusion equation on a finite interval Ω with randomly switching boundary conditions and diffusion coefficient. We proceed by spatially discretizing the diffusion equation using finite differences and constructing the Chapman-Kolmogorov (CK) equation for the resulting finite-dimensional stochastic hybrid system. We show how the CK equation can be used to generate a hierarchy of equations for the r-th moments of the stochastic field, which take the form of r-dimensional parabolic PDEs on {{Ω }r} that couple to lower order moments at the boundaries. We explicitly solve the first and second order moment equations (r = 2). We then describe how the r-th moment of the stochastic PDE can be interpreted in terms of the splitting probability that r non-interacting Brownian particles all exit at the same boundary; although the particles are non-interacting, statistical correlations arise due to the fact that they all move in the same randomly switching environment. Hence the stochastic diffusion equation describes two levels of randomness: Brownian motion at the individual particle level and a randomly switching environment. Finally, in the limit of fast switching, we use a quasi-steady state approximation to reduce the piecewise deterministic PDE to an SPDE with multiplicative Gaussian noise in the bulk and a stochastically-driven boundary.

  1. Comparison of Fresnel lenses and parabolic mirrors as solar energy concentrators.

    PubMed

    Lorenzo, E; Luque, A

    1982-05-15

    This paper compares the gain that can be achieved with a one- or two-stage concentrator, when the first stage is a Fresnel lens or a parabolic mirror, as a function of the luminosity of the concentrator. The results show that the achievable gain using a parabolic mirror is greater than that obtained using a flat or roof lens but is lower than that obtained using a curved lens. PMID:20389950

  2. Combined optical solitons with parabolic law nonlinearity and spatio-temporal dispersion

    NASA Astrophysics Data System (ADS)

    Zhou, Qin; Zhu, Qiuping

    2015-03-01

    In this work, combined optical solitons are constructed in a weakly nonlocal nonlinear medium. The spatio-temporal dispersion (STD), parabolic law nonlinearity, detuning, nonlinear dispersion as well as inter-modal dispersion are taken into account. The integration tool that is applied is the complex envelope function ansatz. The influences of different parameters on dynamical behavior of combined optical solitons are discussed. The results are useful in describing the propagation of combined optical solitons with STD and parabolic law nonlinearity.

  3. A parabolic function to modify Thornthwaite estimates of potential evapotranspiration for the eastern United States

    USGS Publications Warehouse

    McCabe, G.J., Jr.

    1989-01-01

    Errors of the Thornthwaite model can be analyzed using adjusted pan evaporation as an index of potential evapotranspiration. An examination of ratios of adjusted pan evaporation to Thornthwaite potential evapotranspiration indicates that the ratios are highest in the winter and lowest during summer months. This trend suggests a parabolic pattern. In this study a parabolic function is used to adjust Thornthwaite estimates of potential evapotranspiration. Forty locations east of the Rocky Mountains are analyzed. -from Author

  4. Explicit Nonlinear Finite Element Geometric Analysis of Parabolic Leaf Springs under Various Loads

    PubMed Central

    Kong, Y. S.; Omar, M. Z.; Chua, L. B.; Abdullah, S.

    2013-01-01

    This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability. PMID:24298209

  5. On the accuracy and convergence of implicit numerical integration of finite element generated ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Baker, A. J.; Soliman, M. O.

    1978-01-01

    A study of accuracy and convergence of linear functional finite element solution to linear parabolic and hyperbolic partial differential equations is presented. A variable-implicit integration procedure is employed for the resultant system of ordinary differential equations. Accuracy and convergence is compared for the consistent and two lumped assembly procedures for the identified initial-value matrix structure. Truncation error estimation is accomplished using Richardson extrapolation.

  6. Cluster eye camera using microlenses on parabolic surface

    NASA Astrophysics Data System (ADS)

    Shen, Hui-Kai; Su, Guo-Dung J.

    2013-10-01

    There are two main types of imaging systems that exist in nature: the single aperture eye and the compound eye. Usually, cameras and most of artificial imaging systems are similar to the single aperture eye. But compound lenses can be more compact than single lenses. Our design is based on insect compound eyes, which also have a wide field of view (FOV). With the rise of micro-optical techniques, fabricating compound lenses has become easier. The simplest form of a curved microlens array is a parabolic surface. In this paper, we proposed a multi-channel imaging system, which combines the principles of the insect compound eye and the human eye. The optical system enables the reduction of track length of the imaging optics to achieve miniaturization. With the aid of optical engineering software ZEMAX, the multi-channel structure is simulated by a curved microlens array, and we use a Hypergon lens as the main lens to simulate the human eye, which can achieve the purpose of the wide FOV. With this architecture, each microlens of a microlens array transmits a segment of the overall FOV. The partial images that are separately recorded in different channels are stitched together to form the final image of the whole FOV by software processing. A 2.74 mm thin imaging system with 59 channels and 90° FOV is optimized using ZEMAX sequential ray tracing software on a 6.16 mm × 4.62 mm image plane. Finally, we will discuss the simulation results of this system and compare it with the optical cluster eye system and a mobile phone patent.

  7. Hypocoercivity of linear degenerately dissipative kinetic equations

    NASA Astrophysics Data System (ADS)

    Duan, Renjun

    2011-08-01

    In this paper we develop a general approach of studying the hypocoercivity for a class of linear kinetic equations with both transport and degenerately dissipative terms. As concrete examples, the relaxation operator, Fokker-Planck operator and linearized Boltzmann operator are considered when the spatial domain takes the whole space or torus and when there is a confining force or not. The key part of the developed approach is to construct some equivalent temporal energy functionals for obtaining time rates of the solution trending towards equilibrium in some Hilbert spaces. The result in the case of the linear Boltzmann equation with confining forces is new. The proof mainly makes use of the macro-micro decomposition combined with Kawashima's argument on dissipation of the hyperbolic-parabolic system. At the end, a Korn-type inequality with probability measure is provided to deal with dissipation of momentum components.

  8. Setting boundary conditions on the Khokhlov-Zabolotskaya equation for modeling ultrasound fields generated by strongly focused transducers

    NASA Astrophysics Data System (ADS)

    Rosnitskiy, P. B.; Yuldashev, P. V.; Vysokanov, B. A.; Khokhlova, V. A.

    2016-03-01

    An equivalent source model is developed for setting boundary conditions on the parabolic diffraction equation in order to simulate ultrasound fields radiated by strongly focused medical transducers. The equivalent source is defined in a plane; corresponding boundary conditions for pressure amplitude, aperture, and focal distance are chosen so that the axial solution to the parabolic model in the focal region of the beam matches the solution to the full diffraction model (Rayleigh integral) for a spherically curved uniformly vibrating source. It is shown that the proposed approach to transferring the boundary condition from a spherical surface to a plane makes it possible to match the solutions over an interval of several diffraction maxima around the focus even for focused sources with F-numbers less than unity. This method can be used to accurately simulate nonlinear effects in the fields of strongly focused therapeutic transducers using the parabolic Khokhlov-Zabolotskaya equation.

  9. Beautiful equations

    NASA Astrophysics Data System (ADS)

    Viljamaa, Panu; Jacobs, J. Richard; Chris; JamesHyman; Halma, Matthew; EricNolan; Coxon, Paul

    2014-07-01

    In reply to a Physics World infographic (part of which is given above) about a study showing that Euler's equation was deemed most beautiful by a group of mathematicians who had been hooked up to a functional magnetic-resonance image (fMRI) machine while viewing mathematical expressions (14 May, http://ow.ly/xHUFi).

  10. Interband magneto-spectroscopy in InSb square and parabolic quantum wells

    SciTech Connect

    Kasturiarachchi, T.; Edirisooriya, M.; Mishima, T. D.; Doezema, R. E.; Santos, M. B.; Saha, D.; Pan, X.; Sanders, G. D.; Stanton, C. J.

    2015-06-07

    We measure the magneto-optical absorption due to intersubband optical transitions between conduction and valence subband Landau levels in InSb square and parabolic quantum wells. InSb has the narrowest band gap (0.24 eV at low temperature) of the III–V semiconductors leading to a small effective mass (0.014 m{sub 0}) and a large g–factor (−51). As a result, the Landau level spacing is large at relatively small magnetic fields (<8 T), and one can observe spin-splitting of the Landau levels. We examine two structures: (i) a multiple-square-well structure and (ii) a structure containing multiple parabolic wells. The energies and intensities of the strongest features are well explained by a modified Pidgeon-Brown model based on an 8-band k•p model that explicitly incorporates pseudomorphic strain. The strain is essential for obtaining agreement between theory and experiment. While modeling the square well is relatively straight-forward, the parabolic well consists of 43 different layers of various thickness to approximate a parabolic potential. Agreement between theory and experiment for the parabolic well validates the applicability of the model to complicated structures, which demonstrates the robustness of our model and confirms its relevance for developing electronic and spintronic devices that seek to exploit the properties of the InSb band structure.

  11. Marcus equation

    DOE R&D Accomplishments Database

    1998-09-21

    In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.

  12. Marcus equation

    SciTech Connect

    1998-11-01

    In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.

  13. Parabolic problems with parameters arising in evolution model for phytromediation

    NASA Astrophysics Data System (ADS)

    Sahmurova, Aida; Shakhmurov, Veli

    2012-12-01

    The past few decades, efforts have been made to clean sites polluted by heavy metals as chromium. One of the new innovative methods of eradicating metals from soil is phytoremediation. This uses plants to pull metals from the soil through the roots. This work develops a system of differential equations with parameters to model the plant metal interaction of phytoremediation (see [1]).

  14. Environmental Controls and Eco-geomorphic Interactions of the Barchan-to-parabolic Dune Stabilisation and the Parabolic-to-barchan Dune Reactivation

    NASA Astrophysics Data System (ADS)

    Yan, Na; Baas, Andreas

    2015-04-01

    Parabolic dunes are one of a few common aeolian landforms which are highly controlled by eco-geomorphic interactions. Parabolic dunes, on the one hand, can be developed from highly mobile dune landforms, barchans for instance, in an ameliorated vegetation condition; or on the other hand, they can be reactivated and transformed back into mobile dunes due to vegetation deterioration. The fundamental mechanisms and eco-geomorphic interactions controlling both dune transformations remain poorly understood. To bridge the gap between complex processes involved in dune transformations on a relatively long temporal scale and real world monitoring records on a very limited temporal scale, this research has extended the DECAL model to incorporate 'dynamic' growth functions and the different 'growth' of perennial shrubs between growing and non-growing seasons, informed by field measurements and remote sensing analysis, to explore environmental controls and eco-geomorphic interactions of both types of dune transformation. A non-dimensional 'dune stabilising index' is proposed to capture the interactions between environmental controls (i.e. the capabilities of vegetation to withstand wind erosion and sand burial, the sandy substratum thickness, the height of the initial dune, and the sand transport potential), and establish the linkage between these controls and the geometry of a stabilising dune. An example demonstrates how to use the power-law relationship between the dune stabilising index and the normalised migration distance to assist in extrapolating the historical trajectories of transforming dunes. The modelling results also show that a slight increase in vegetation cover of an initial parabolic dune can significantly increase the reactivation threshold of climatic impact (both drought stress and wind strength) required to reactivate a stabilising parabolic dune into a barchan. Four eco-geomorphic interaction zones that govern a barchan-to-parabolic dune transformation

  15. Applications of the contravariant form of the Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Katsanis, T.

    1983-01-01

    The contravariant Navier-Stokes equations in weak conservation form are well suited to certain fluid flow analysis problems. Three dimensional contravariant momentum equations may be used to obtain Navier-Stokes equations in weak conservation form on a nonplanar two dimensional surface with varying streamsheet thickness. Thus a three dimensional flow can be simulated with two dimensional equations to obtain a quasi-three dimensional solution for viscous flow. When the Navier-Stokes equations on the two dimensional nonplanar surface are transformed to a generalized body fitted mesh coordinate system, the resulting equations are similar to the equations for a body fitted mesh coordinate system on the Euclidean plane. Contravariant momentum components are also useful for analyzing compressible, three dimensional viscous flow through an internal duct by parabolic marching. This type of flow is efficiently analyzed by parabolic marching methods, where the streamwise momentum equation is uncoupled from the two crossflow momentum equations. This can be done, even for ducts with a large amount of turning, if the Navier-Stokes equations are written with contravariant components.

  16. Transition from self tilt to object tilt during maintained lateral tilt in parabolic flight

    NASA Astrophysics Data System (ADS)

    Wetzig, Joachim; Reiser, Michaela; von Baumgarten, Rudolf J.

    19 young healthy subjects were subjected to parabolic rollercoaster flight. A horizontal luminous line was seen by the subjects in a headfixed goggle device. During the hypergravic phases of parabolic flight the luminous line seemed to rotate into and during the hypogravic phase against the direction of static head tilt. Ocular counter rotation and activity of the neck position receptors cannot explain these subjective rotations. We conclude that information from the otolith system, converging with visual information within the brain, dislocated the headfixed visual target line. While the retinal image of the luminous line remains unchanged, loading and unloading the otoliths in parabolic flight changes the sensation of self tilt into object tilt, hereby subjectively rotating visual targets such as the luminous line.

  17. The 3D heat flux density distribution on a novel parabolic trough wavy absorber

    NASA Astrophysics Data System (ADS)

    Demagh, Yassine; Kabar, Yassine; Bordja, Lyes; Noui, Samira

    2016-05-01

    The non-uniform concentrated solar flux distribution on the outer surface of the absorber pipe can lead to large circumferential gradient temperature and high concentrated temperature of the absorber pipe wall, which is one of the primary causes of parabolic trough solar receiver breakdown. In this study, a novel shape of the parabolic trough absorber pipe is proposed as a solution to well homogenize the solar flux distribution, as well as, the temperature in the absorber wall. The conventional straight absorber located along the focal line of the parabola is replaced by wavy one (invention patent by Y. Demagh [1]) for which the heat flux density distribution on the outer surface varies in both axial and azimuthal directions (3D) while it varies only in the azimuthal direction on the former (2D). As far as we know, there is not previous study which has used a longitudinally wavy pipe as an absorber into the parabolic trough collector unit.

  18. A parabolic analogue of the higher-order comparison theorem of De Silva and Savin

    NASA Astrophysics Data System (ADS)

    Banerjee, Agnid; Garofalo, Nicola

    2016-01-01

    We show that the quotient of two caloric functions which vanish on a portion of the lateral boundary of a H k + α domain is H k + α up to the boundary for k ≥ 2. In the case k = 1, we show that the quotient is in H 1 + α if the domain is assumed to be space-time C 1, α regular. This can be thought of as a parabolic analogue of a recent important result in [8], and we closely follow the ideas in that paper. We also give counterexamples to the fact that analogous results are not true at points on the parabolic boundary which are not on the lateral boundary, i.e., points which are at the corner and base of the parabolic boundary.

  19. UPC BarcelonaTech Platform. Innovative aerobatic parabolic flights for life sciences experiments.

    NASA Astrophysics Data System (ADS)

    Perez-Poch, Antoni; Gonzalez, Daniel

    We present an innovative method of performing parabolic flights with aerobatic single-engine planes. A parabolic platform has been established in Sabadell Airport (Barcelona, Spain) to provide an infraestructure ready to allow Life Sciences reduced gravity experiments to be conducted in parabolic flights. Test flights have demonstrated that up to 8 seconds of reduced gravity can be achieved by using a two-seat CAP10B aircraft, with a gravity range between 0.1 and 0.01g in the three axis. A parabolic flight campaign may be implemented with a significant reduction in budget compared to conventional parabolic flight campaigns, and with a very short time-to-access to the platform. Operational skills and proficiency of the pilot controling the aircraft during the maneuvre, sensitivity to wind gusts, and aircraft balance are the key issues that make a parabola successful. Efforts are focused on improving the total “zero-g” time and the quality of reduced gravity achieved, as well as providing more space for experiments. We report results of test flights that have been conducted in order to optimize the quality and total microgravity time. A computer sofware has been developed and implemented to help the pilot optimize his or her performance. Finally, we summarize the life science experiments that have been conducted in this platform. Specific focus is given to the very successful 'Barcelona ZeroG Challenge', this year in its third edition. This educational contest gives undergraduate and graduate students worldwide the opportunity to design their research within our platform and test it on flight, thus becoming real researchers. We conclude that aerobatic parabolic flights have proven to be a safe, unexpensive and reliable way to conduct life sciences reduced gravity experiments.

  20. COMPARING THE FRACTIONAL AND THE CLASSICAL SOLUTE TRANSPORT EQUATIONS WITH DATA ON SOLUTE BREAKTHROUGH IN SOIL COLUMNS

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Solute transport in soils and sediments is commonly simulated with the parabolic advective-dispersive equation, or ADE. In the last decades, it has been reported that this model cannot take in account several important features of solute movement through soil. Recently, a new model base on the assu...

  1. Lipschitz regularity of solutions for mixed integro-differential equations

    NASA Astrophysics Data System (ADS)

    Barles, Guy; Chasseigne, Emmanuel; Ciomaga, Adina; Imbert, Cyril

    We establish new Hölder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method. We thus extend the Hölder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the local and nonlocal term, but their overall behavior is driven by the local-nonlocal interaction, e.g. the fractional diffusion may give the ellipticity in one direction and the classical diffusion in the complementary one.

  2. Parabolic replicator dynamics and the principle of minimum Tsallis information gain

    PubMed Central

    2013-01-01

    Background Non-linear, parabolic (sub-exponential) and hyperbolic (super-exponential) models of prebiological evolution of molecular replicators have been proposed and extensively studied. The parabolic models appear to be the most realistic approximations of real-life replicator systems due primarily to product inhibition. Unlike the more traditional exponential models, the distribution of individual frequencies in an evolving parabolic population is not described by the Maximum Entropy (MaxEnt) Principle in its traditional form, whereby the distribution with the maximum Shannon entropy is chosen among all the distributions that are possible under the given constraints. We sought to identify a more general form of the MaxEnt principle that would be applicable to parabolic growth. Results We consider a model of a population that reproduces according to the parabolic growth law and show that the frequencies of individuals in the population minimize the Tsallis relative entropy (non-additive information gain) at each time moment. Next, we consider a model of a parabolically growing population that maintains a constant total size and provide an “implicit” solution for this system. We show that in this case, the frequencies of the individuals in the population also minimize the Tsallis information gain at each moment of the ‘internal time” of the population. Conclusions The results of this analysis show that the general MaxEnt principle is the underlying law for the evolution of a broad class of replicator systems including not only exponential but also parabolic and hyperbolic systems. The choice of the appropriate entropy (information) function depends on the growth dynamics of a particular class of systems. The Tsallis entropy is non-additive for independent subsystems, i.e. the information on the subsystems is insufficient to describe the system as a whole. In the context of prebiotic evolution, this “non-reductionist” nature of parabolic replicator

  3. Generation and tooth contact analysis of spiral bevel gears with predesigned parabolic functions of transmission errors

    NASA Technical Reports Server (NTRS)

    Litvin, Faydor L.; Lee, Hong-Tao

    1989-01-01

    A new approach for determination of machine-tool settings for spiral bevel gears is proposed. The proposed settings provide a predesigned parabolic function of transmission errors and the desired location and orientation of the bearing contact. The predesigned parabolic function of transmission errors is able to absorb piece-wise linear functions of transmission errors that are caused by the gear misalignment and reduce gear noise. The gears are face-milled by head cutters with conical surfaces or surfaces of revolution. A computer program for simulation of meshing, bearing contact and determination of transmission errors for misaligned gear has been developed.

  4. Transesophageal echocardiographic evaluation of baboons during microgravity induced by parabolic flight

    NASA Technical Reports Server (NTRS)

    Vernalis, Marina N.; Latham, Ricky D.; Fanton, John W.; Geffney, F. Andrew

    1993-01-01

    Transthoracic echocardiography (TTE) is a feasible method to noninvasively examine cardiac anatomy during parabolic flight. However, transducer placement on the chest wall is very difficult to maintain during transition to microgravity. In addition, TTE requires the use of low frequency transponders which limit resolution. Transesophical echocardiography (TEE) is an established imaging technique which obtains echocardiographic information from the esophagus. It is a safe procedure and provides higher quality images of cardiac structure than obtained with TTE. This study is designed to determine whether TEE was feasible to perform during parabolic flight and to determine whether acute central volume responses occur in acute transition to zero gravity by direct visualization of the cardiac chambers.

  5. Two-electron states and state exchange time control in parabolic quantum dot

    NASA Astrophysics Data System (ADS)

    Baghdasaryan, D. A.; Kazaryan, E. M.; Sarkisyan, H. A.

    2014-04-01

    Using the Heisenberg uncertainty relationship and the stationary perturbation theory we consider two-electron states in a spherically symmetric parabolic quantum dot (parabolic helium atom). The dependence of ground-state energy on the QD size is studied. The energy of two-electron system monotonically decreases with QD radius increase. The problem of the state exchange time control in QD is discussed, taking into account the spins of the electrons in the Russell-Saunders approximation. With the increase of the QD radius the state exchange time increases.

  6. A boundary condition to the Khokhlov-Zabolotskaya equation for modeling strongly focused nonlinear ultrasound fields

    SciTech Connect

    Rosnitskiy, P. Yuldashev, P. Khokhlova, V.

    2015-10-28

    An equivalent source model was proposed as a boundary condition to the nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation to simulate high intensity focused ultrasound (HIFU) fields generated by medical ultrasound transducers with the shape of a spherical shell. The boundary condition was set in the initial plane; the aperture, the focal distance, and the initial pressure of the source were chosen based on the best match of the axial pressure amplitude and phase distributions in the Rayleigh integral analytic solution for a spherical transducer and the linear parabolic approximation solution for the equivalent source. Analytic expressions for the equivalent source parameters were derived. It was shown that the proposed approach allowed us to transfer the boundary condition from the spherical surface to the plane and to achieve a very good match between the linear field solutions of the parabolic and full diffraction models even for highly focused sources with F-number less than unity. The proposed method can be further used to expand the capabilities of the KZ nonlinear parabolic equation for efficient modeling of HIFU fields generated by strongly focused sources.

  7. A boundary condition to the Khokhlov-Zabolotskaya equation for modeling strongly focused nonlinear ultrasound fields

    NASA Astrophysics Data System (ADS)

    Rosnitskiy, P.; Yuldashev, P.; Khokhlova, V.

    2015-10-01

    An equivalent source model was proposed as a boundary condition to the nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation to simulate high intensity focused ultrasound (HIFU) fields generated by medical ultrasound transducers with the shape of a spherical shell. The boundary condition was set in the initial plane; the aperture, the focal distance, and the initial pressure of the source were chosen based on the best match of the axial pressure amplitude and phase distributions in the Rayleigh integral analytic solution for a spherical transducer and the linear parabolic approximation solution for the equivalent source. Analytic expressions for the equivalent source parameters were derived. It was shown that the proposed approach allowed us to transfer the boundary condition from the spherical surface to the plane and to achieve a very good match between the linear field solutions of the parabolic and full diffraction models even for highly focused sources with F-number less than unity. The proposed method can be further used to expand the capabilities of the KZ nonlinear parabolic equation for efficient modeling of HIFU fields generated by strongly focused sources.

  8. An efficient iteration strategy for upwind/relaxation solutions to the thin-layer Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Newsome, Richard W.; Walters, Robert W.; Thomas, James L.

    1987-01-01

    A previously developed upwind/relaxation algorithm for solving the unsteady, compressible, thin-layer Navier-Stokes equations is presently modified so that the downstream influence of the subsonic part of the boundary layer in an otherwise supersonic flow is suppressed by restricting the streamwise pressure gradient. A 'parabolized' solution is then efficiently obtained by marching downstream and iterating locally in each crossflow plane until achieving convergence. This parabolized solution is an excellent final one for problems without large adverse streamwise pressure gradients.

  9. Optimal trajectories based on linear equations

    NASA Technical Reports Server (NTRS)

    Carter, Thomas E.

    1990-01-01

    The Principal results of a recent theory of fuel optimal space trajectories for linear differential equations are presented. Both impulsive and bounded-thrust problems are treated. A new form of the Lawden Primer vector is found that is identical for both problems. For this reason, starting iteratives from the solution of the impulsive problem are highly effective in the solution of the two-point boundary-value problem associated with bounded thrust. These results were applied to the problem of fuel optimal maneuvers of a spacecraft near a satellite in circular orbit using the Clohessy-Wiltshire equations. For this case two-point boundary-value problems were solved using a microcomputer, and optimal trajectory shapes displayed. The results of this theory can also be applied if the satellite is in an arbitrary Keplerian orbit through the use of the Tschauner-Hempel equations. A new form of the solution of these equations has been found that is identical for elliptical, parabolic, and hyperbolic orbits except in the way that a certain integral is evaluated. For elliptical orbits this integral is evaluated through the use of the eccentric anomaly. An analogous evaluation is performed for hyperbolic orbits.

  10. Parabolic flight experience is related to increased release of stress hormones.

    PubMed

    Schneider, Stefan; Brümmer, Vera; Göbel, Simon; Carnahan, Heather; Dubrowski, Adam; Strüder, Heiko K

    2007-06-01

    Numerous studies have shown significant effects of weightlessness on adaptational processes of the CNS, cardiovascular and/or muscular system. Most of these studies have been carried out during parabolic flights, using the recurring 20 s of weightlessness at each parabola. Although some of these studies reported on potential influences not only of weightlessness but also of the stressful situation within a parabolic flight, especially provoked by the ongoing changes between 1.8, 1 and 0 G, so far there seems to be only marginal information about objective parameters of stress evoked by parabolic flights. By collecting blood samples from a permanent venous catheter several times during parabolic flights, we were able to show an increase of prolactin, cortisol and ACTH in the course of a 120 min flight. We conclude, therefore, that previous reported effects of weightlessness on adaptational processes may be affected not only by weightlessness but also by the exposure to other stressors experienced within the environment of a Zero-G airbus. PMID:17351784

  11. Quasilinear parabolic variational inequalities with multi-valued lower-order terms

    NASA Astrophysics Data System (ADS)

    Carl, Siegfried; Le, Vy K.

    2014-10-01

    In this paper, we provide an analytical frame work for the following multi-valued parabolic variational inequality in a cylindrical domain : Find and an such that where is some closed and convex subset, A is a time-dependent quasilinear elliptic operator, and the multi-valued function is assumed to be upper semicontinuous only, so that Clarke's generalized gradient is included as a special case. Thus, parabolic variational-hemivariational inequalities are special cases of the problem considered here. The extension of parabolic variational-hemivariational inequalities to the general class of multi-valued problems considered in this paper is not only of disciplinary interest, but is motivated by the need in applications. The main goals are as follows. First, we provide an existence theory for the above-stated problem under coercivity assumptions. Second, in the noncoercive case, we establish an appropriate sub-supersolution method that allows us to get existence, comparison, and enclosure results. Third, the order structure of the solution set enclosed by sub-supersolutions is revealed. In particular, it is shown that the solution set within the sector of sub-supersolutions is a directed set. As an application, a multi-valued parabolic obstacle problem is treated.

  12. Estimation of discontinuous coefficients in parabolic systems: Applications to reservoir simulation

    NASA Technical Reports Server (NTRS)

    Lamm, P. D.

    1984-01-01

    Spline based techniques for estimating spatially varying parameters that appear in parabolic distributed systems (typical of those found in reservoir simulation problems) are presented. The problem of determining discontinuous coefficients, estimating both the functional shape and points of discontinuity for such parameters is discussed. Convergence results and a summary of numerical performance of the resulting algorithms are given.

  13. Simple Verification of the Parabolic Shape of a Rotating Liquid and a Boat on Its Surface

    ERIC Educational Resources Information Center

    Sabatka, Z.; Dvorak, L.

    2010-01-01

    This article describes a simple and inexpensive way to create and to verify the parabolic surface of a rotating liquid. The liquid is water. The second part of the article deals with the problem of a boat on the surface of a rotating liquid. (Contains 1 table, 10 figures and 5 footnotes.)

  14. Stability of shock waves for multi-dimensional hyperbolic-parabolic conservation laws

    NASA Astrophysics Data System (ADS)

    Li, Dening

    1988-01-01

    The uniform linear stability of shock waves is considerd for quasilinear hyperbolic-parabolic coupled conservation laws in multi-dimensional space. As an example, the stability condition and its dynamic meaning for isothermal shock wave in radiative hydrodynamics are analyzed.

  15. Ex Vivo Assessment of a Parabolic-Tip Inflow Cannula for Pediatric Continuous-Flow VADs.

    PubMed

    Griffin, Michael T; Grzywinski, Matthew F; Voorhees, Hannah J; Kameneva, Marina V; Olia, Salim E

    2016-01-01

    To address the challenge of unloading the left ventricle during pediatric mechanical circulatory support using next-generation rotary blood pumps, a novel inflow cannula was developed. This unique inflow cannula for pediatric, continuous-flow, left ventricular assist devices (VADs) with a parabolic-shaped inlet entrance was evaluated alongside a bevel-tip and fenestrated-tip cannula via an ex vivo, isolated-heart experimental setup. Performance was characterized using two clinical scenarios of over-pumping and hypovolemia, created by varying pump speed and filling preload pressure, respectively, at ideal and off-axis cannula placement to assess ventricular unloading and positional sensitivity. Quantitative and qualitative assessments were performed on the resultant hemodynamics and intra-ventricular boroscopic images to classify conditions of nonsuction, partial, gradual or severe entrainment, and ventricular collapse. The parabolic-tip cannula was found to be significantly less sensitive to placement position (p < 0.001) than the bevel-tip cannula under all conditions, while not statistically different from the fenestrated cannula. Visual analysis of the parabolic-tip cannula showed complete resistance to entrainment, whereas the fenestrated-tip had partial entrainment in 90% and 87% of the over-pumping and hypovolemic studies, respectively. We conclude that future pediatric VAD designs may benefit from incorporating the parabolic-tip inflow cannula design to maximize unloading of the left ventricle in ideal and nonoptimal conditions. PMID:27442862

  16. Spike-adding in parabolic bursters: The role of folded-saddle canards

    NASA Astrophysics Data System (ADS)

    Desroches, Mathieu; Krupa, Martin; Rodrigues, Serafim

    2016-09-01

    The present work develops a new approach to studying parabolic bursting, and also proposes a novel four-dimensional canonical and polynomial-based parabolic burster. In addition to this new polynomial system, we also consider the conductance-based model of the Aplysia R15 neuron known as the Plant model, and a reduction of this prototypical biophysical parabolic burster to three variables, including one phase variable, namely the Baer-Rinzel-Carillo (BRC) phase model. Revisiting these models from the perspective of slow-fast dynamics reveals that the number of spikes per burst may vary upon parameter changes, however the spike-adding process occurs in an explosive fashion that involves special solutions called canards. This spike-adding canard explosion phenomenon is analysed by using tools from geometric singular perturbation theory in tandem with numerical bifurcation techniques. We find that the bifurcation structure persists across all considered systems, that is, spikes within the burst are incremented via the crossing of an excitability threshold given by a particular type of canard orbit, namely the true canard of a folded-saddle singularity. However there can be a difference in the spike-adding transitions in parameter space from one case to another, according to whether the process is continuous or discontinuous, which depends upon the geometry of the folded-saddle canard. Using these findings, we construct a new polynomial approximation of the Plant model, which retains all the key elements for parabolic bursting, including the spike-adding transitions mediated by folded-saddle canards. Finally, we briefly investigate the presence of spike-adding via canards in planar phase models of parabolic bursting, namely the theta model by Ermentrout and Kopell.

  17. Design of a Thermal Imaging Diagnostic Using 90-Degree, Off-Axis, Parabolic Mirrors

    SciTech Connect

    Malone, Robert M.; Becker, Steven A.; Dolan, Daniel H.; Hacking, Richard G.; Hickman, Randy J.; Kaufman, Morris I.; Stevens, Gerald D.; Turley, William D.

    2006-09-01

    Thermal imaging is an important, though challenging, diagnostic for shockwave experiments. Shock-compressed materials undergo transient temperature changes that cannot be recorded with standard (greater than ms response time) infrared detectors. A further complication arises when optical elements near the experiment are destroyed. We have designed a thermal-imaging system for studying shock temperatures produced inside a gas gun at Sandia National Laboratories. Inexpensive, diamond-turned, parabolic mirrors relay an image of the shocked target to the exterior of the gas gun chamber through a sapphire vacuum port. The 3000–5000-nm portion of this image is directed to an infrared camera which acquires a snapshot of the target with a minimum exposure time of 150 ns. A special mask is inserted at the last intermediate image plane, to provide dynamic thermal background recording during the event. Other wavelength bands of this image are split into high-speed detectors operating at 900–1700 nm, and at 1700–3000 nm for timeresolved pyrometry measurements. This system incorporates 90-degree, off-axis parabolic mirrors, which can collect low f/# light over a broad spectral range, for high-speed imaging. Matched mirror pairs must be used so that aberrations cancel. To eliminate image plane tilt, proper tip-to-tip orientation of the parabolic mirrors is required. If one parabolic mirror is rotated 180 degrees about the optical axis connecting the pair of parabolic mirrors, the resulting image is tilted by 60 degrees. Different focal-length mirrors cannot be used to magnify the image without substantially sacrificing image quality. This paper analyzes performance and aberrations of this imaging diagnostic.

  18. Activation of vegetated parabolic dunes into mobile barchans under potential environmental change scenarios

    NASA Astrophysics Data System (ADS)

    Yan, Na; Baas, Andreas C. W.

    2016-04-01

    Parabolic dunes are a quintessential example of the co-evolution of soil, landform, and vegetation, and they are found around the world, on coasts, river valleys, lake shores, and margins of deserts and steppes. These areas are often sensitive to changes in natural and anthropogenic forcings and socio-economic activities. Some studies have indicated parabolic dunes can lose vegetation and transform into barchan and transverse dunes by environmental change such as decreased precipitation or lowered water table, as well as anthropogenic stress such as increased burning and grazing. These transformations and shifts between states of eco-geomorphic systems may have significant implications on land management and social-economic development. This study utilises the Extended-DECAL - parameterised by field measurements of dune topography and vegetation characteristics combined with remote sensing - to explore how increases in drought stress, wind strength, and grazing stress may lead to the activation of stabilised parabolic dunes into highly mobile barchans. The modelling results show that the mobility of an initial parabolic dune at the outset of perturbations determines to a large extent the capacity of a system to absorb the environmental change, and a slight increase in vegetation cover of an initial parabolic dune can increase the activation threshold significantly. Plants with a higher deposition tolerance increase the activation threshold for the climatic impact and sand transport rate, whereas the erosion tolerance of plants influences the patterns of resulting barchans. The change in the characteristics of eco-geomorphic interaction zones may indirectly reflect the dune stability and predict an ongoing transformation, whilst the activation angle may be potentially used as a proxy of environmental stresses. In contrast to the natural environmental changes which tend to affect relatively weak and young plants, grazing stress can exert a broader impact on all

  19. A note on the regularity of solutions of infinite dimensional Riccati equations

    NASA Technical Reports Server (NTRS)

    Burns, John A.; King, Belinda B.

    1994-01-01

    This note is concerned with the regularity of solutions of algebraic Riccati equations arising from infinite dimensional LQR and LQG control problems. We show that distributed parameter systems described by certain parabolic partial differential equations often have a special structure that smoothes solutions of the corresponding Riccati equation. This analysis is motivated by the need to find specific representations for Riccati operators that can be used in the development of computational schemes for problems where the input and output operators are not Hilbert-Schmidt. This situation occurs in many boundary control problems and in certain distributed control problems associated with optimal sensor/actuator placement.

  20. Efficient numerical method for solving Cauchy problem for the Gamma equation

    NASA Astrophysics Data System (ADS)

    Koleva, Miglena N.

    2011-12-01

    In this work we consider Cauchy problem for the so called Gamma equation, derived by transforming the fully nonlinear Black-Scholes equation for option price into a quasilinear parabolic equation for the second derivative (Greek) Γ = VSS of the option price V. We develop an efficient numerical method for solving the model problem concerning different volatility terms. Using suitable change of variables the problem is transformed on finite interval, keeping original behavior of the solution at the infinity. Then we construct Picard-Newton algorithm with adaptive mesh step in time, which can be applied also in the case of non-differentiable functions. Results of numerical simulations are given.

  1. Iterative methods for distributed parameter estimation in parabolic PDE

    SciTech Connect

    Vogel, C.R.; Wade, J.G.

    1994-12-31

    The goal of the work presented is the development of effective iterative techniques for large-scale inverse or parameter estimation problems. In this extended abstract, a detailed description of the mathematical framework in which the authors view these problem is presented, followed by an outline of the ideas and algorithms developed. Distributed parameter estimation problems often arise in mathematical modeling with partial differential equations. They can be viewed as inverse problems; the `forward problem` is that of using the fully specified model to predict the behavior of the system. The inverse or parameter estimation problem is: given the form of the model and some observed data from the system being modeled, determine the unknown parameters of the model. These problems are of great practical and mathematical interest, and the development of efficient computational algorithms is an active area of study.

  2. MHD flow past a parabolic flow past an infinite isothermal vertical plate in the presence of thermal radiation and chemical reaction

    NASA Astrophysics Data System (ADS)

    Muthucumaraswamy, R.; Sivakumar, P.

    2016-02-01

    The problem of MHD free convection flow with a parabolic starting motion of an infinite isothermal vertical plate in the presence of thermal radiation and chemical reaction has been examined in detail in this paper. The fluid considered here is a gray, absorbing emitting radiation but a non-scattering medium. The dimensionless governing coupled linear partial differential equations are solved using the Laplace transform technique. A parametric study is performed to illustrate the influence of the radiation parameter, magnetic parameter, chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number and time on the velocity, temperature, concentration. The results are discussed graphically and qualitatively. The numerical results reveal that the radiation induces a rise in both the velocity and temperature, and a decrease in the concentration. The model finds applications in solar energy collection systems, geophysics and astrophysics, aerospace and also in the design of high temperature chemical process systems.

  3. Neumann domination for the Yang-Mills heat equation

    NASA Astrophysics Data System (ADS)

    Charalambous, Nelia; Gross, Leonard

    2015-07-01

    Long time existence and uniqueness of solutions to the Yang-Mills heat equation have been proven over a compact 3-manifold with boundary for initial data of finite energy. In the present paper, we improve on previous estimates by using a Neumann domination technique that allows us to get much better pointwise bounds on the magnetic field. As in the earlier work, we focus on Dirichlet, Neumann, and Marini boundary conditions. In addition, we show that the Wilson Loop functions, gauge invariantly regularized, converge as the parabolic time goes to infinity.

  4. Parallelizing across time when solving time-dependent partial differential equations

    SciTech Connect

    Worley, P.H.

    1991-09-01

    The standard numerical algorithms for solving time-dependent partial differential equations (PDEs) are inherently sequential in the time direction. This paper describes algorithms for the time-accurate solution of certain classes of linear hyperbolic and parabolic PDEs that can be parallelized in both time and space and have serial complexities that are proportional to the serial complexities of the best known algorithms. The algorithms for parabolic PDEs are variants of the waveform relaxation multigrid method (WFMG) of Lubich and Ostermann where the scalar ordinary differential equations (ODEs) that make up the kernel of WFMG are solved using a cyclic reduction type algorithm. The algorithms for hyperbolic PDEs use the cyclic reduction algorithm to solve ODEs along characteristics. 43 refs.

  5. Application of locally one-dimensional semi-implicit scheme in phase-field equations

    NASA Astrophysics Data System (ADS)

    Cai, Dan; Zhang, Lijun; Du, Yong

    2015-07-01

    A locally one-dimensional (LOD) semi-implicit scheme is proposed for improving the numerical efficiency in the solving of parabolic partial differential equations in phase-field simulations. With LOD splitting, multi-dimensional parabolic problems can be numerically approximated by treating each of the spatial variables individually in single cycles. Additionally, each spatial variable can be treated in either real or Fourier space, allowing equations to be solved across a range of boundary conditions, including periodic, non-periodic, and even partial periodic. The proposed LOD semi-implicit scheme exhibits noticeable advantages over both explicit and implicit traditional schemes in terms of computational efficiency and accuracy, as demonstrated by two standard numerical tests. It is anticipated that future large-scale phase-field simulations will benefit greatly from the use of this LOD scheme.

  6. Spatial complexity of solutions of higher order partial differential equations

    NASA Astrophysics Data System (ADS)

    Kukavica, Igor

    2004-03-01

    We address spatial oscillation properties of solutions of higher order parabolic partial differential equations. In the case of the Kuramoto-Sivashinsky equation ut + uxxxx + uxx + u ux = 0, we prove that for solutions u on the global attractor, the quantity card {x epsi [0, L]:u(x, t) = lgr}, where L > 0 is the spatial period, can be bounded by a polynomial function of L for all \\lambda\\in{\\Bbb R} . A similar property is proven for a general higher order partial differential equation u_t+(-1)^{s}\\partial_x^{2s}u+ \\sum_{k=0}^{2s-1}v_k(x,t)\\partial_x^k u =0 .

  7. On the Homogenization of a Damped Wave Equation

    SciTech Connect

    Timofte, C.

    2010-11-25

    The goal of this paper is to analyze the effective behavior of the solution of a wave equation with interior and boundary damping, defined in a periodically perforated medium. We deal, at the microscale, with an {epsilon}-periodic structure obtained by removing from a bounded connected open set {Omega} in R{sup n} a number of closed subsets of characteristic size {epsilon}. As a result, we obtain a perforated domain {Omega}{sup {epsilon}}, in which we consider a wave equation, with interior sources and damping and with dynamic boundary conditions imposed on the boundaries of the perforations. Assuming suitable initial conditions, we prove that the asymptotic behavior, as the small parameter e which characterizes the size of the perforations tends to zero, of the solution of such a problem is governed by a parabolic equation, defined on the entire domain {Omega}.

  8. Extended rate equations

    SciTech Connect

    Shore, B.W.

    1981-01-30

    The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence.

  9. Non linear shock wave propagation in heterogeneous fluids: a numerical approach beyond the parabolic approximation with application to sonic boom.

    NASA Astrophysics Data System (ADS)

    Dagrau, Franck; Coulouvrat, François; Marchiano, Régis; Héron, Nicolas

    2008-06-01

    Dassault Aviation as a civil aircraft manufacturer is studying the feasibility of a supersonic business jet with the target of an "acceptable" sonic boom at the ground level, and in particular in case of focusing. A sonic boom computational process has been performed, that takes into account meteorological effects and aircraft manoeuvres. Turn manoeuvres and aircraft acceleration create zones of convergence of rays (caustics) which are the place of sound amplification. Therefore two elements have to be evaluated: firstly the geometrical position of the caustics, and secondly the noise level in the neighbourhood of the caustics. The modelling of the sonic boom propagation is based essentially on the assumptions of geometrical acoustics. Ray tracing is obtained according to Fermat's principle as paths that minimise the propagation time between the source (the aircraft) and the receiver. Wave amplitude and time waveform result from the solution of the inviscid Burgers' equation written along each individual ray. The "age variable" measuring the cumulative nonlinear effects is linked to the ray tube area. Caustics are located as the place where the ray tube area vanishes. Since geometrical acoustics does not take into account diffraction effects, it breaks down in the neighbourhood of caustics where it would predict unphysical infinite pressure amplitude. The aim of this study is to describe an original method for computing the focused noise level. The approach involves three main steps that can be summarised as follows. The propagation equation is solved by a forward marching procedure split into three successive steps: linear propagation in a homogeneous medium, linear perturbation due to the weak heterogeneity of the medium, and non-linear effects. The first step is solved using an "exact" angular spectrum algorithm. Parabolic approximation is applied only for the weak perturbation due to the heterogeneities. Finally, non linear effects are performed by solving the

  10. A parabolic model of drag coefficient for storm surge simulation in the South China Sea

    NASA Astrophysics Data System (ADS)

    Peng, Shiqiu; Li, Yineng

    2015-10-01

    Drag coefficient (Cd) is an essential metric in the calculation of momentum exchange over the air-sea interface and thus has large impacts on the simulation or forecast of the upper ocean state associated with sea surface winds such as storm surges. Generally, Cd is a function of wind speed. However, the exact relationship between Cd and wind speed is still in dispute, and the widely-used formula that is a linear function of wind speed in an ocean model could lead to large bias at high wind speed. Here we establish a parabolic model of Cd based on storm surge observations and simulation in the South China Sea (SCS) through a number of tropical cyclone cases. Simulation of storm surges for independent Tropical cyclones (TCs) cases indicates that the new parabolic model of Cd outperforms traditional linear models.

  11. Evaluation of the three-dimensional parabolic flow computer program SHIP

    NASA Technical Reports Server (NTRS)

    Pan, Y. S.

    1978-01-01

    The three-dimensional parabolic flow program SHIP designed for predicting supersonic combustor flow fields is evaluated to determine its capabilities. The mathematical foundation and numerical procedure are reviewed; simplifications are pointed out and commented upon. The program is then evaluated numerically by applying it to several subsonic and supersonic, turbulent, reacting and nonreacting flow problems. Computational results are compared with available experimental or other analytical data. Good agreements are obtained when the simplifications on which the program is based are justified. Limitations of the program and the needs for improvement and extension are pointed out. The present three dimensional parabolic flow program appears to be potentially useful for the development of supersonic combustors.

  12. Cost/performance of solar reflective surfaces for parabolic dish concentrators

    NASA Technical Reports Server (NTRS)

    Bouquet, F.

    1980-01-01

    Materials for highly reflective surfaces for use in parabolic dish solar concentrators are discussed. Some important factors concerning performance of the mirrors are summarized, and typical costs are treated briefly. Capital investment cost/performance ratios for various materials are computed specifically for the double curvature parabolic concentrators using a mathematical model. The results are given in terms of initial investment cost for reflective surfaces per thermal kilowatt delivered to the receiver cavity for various operating temperatures from 400 to 1400 C. Although second surface glass mirrors are emphasized, first surface, chemically brightened and anodized aluminum surfaces as well as second surface, metallized polymeric films are treated. Conventional glass mirrors have the lowest cost/performance ratios, followed closely by aluminum reflectors. Ranges in the data due to uncertainties in cost and mirror reflectance factors are given.

  13. Low-frequency sound propagation modeling over a locally-reacting boundary using the parabolic approximation

    NASA Technical Reports Server (NTRS)

    Robertson, J. S.; Siegman, W. L.; Jacobson, M. J.

    1989-01-01

    There is substantial interest in the analytical and numerical modeling of low-frequency, long-range atmospheric acoustic propagation. Ray-based models, because of frequency limitations, do not always give an adequate prediction of quantities such as sound pressure or intensity levels. However, the parabolic approximation method, widely used in ocean acoustics, and often more accurate than ray models for lower frequencies of interest, can be applied to acoustic propagation in the atmosphere. Modifications of an existing implicit finite-difference implementation for computing solutions to the parabolic approximation are discussed. A locally-reacting boundary is used together with a one-parameter impedance model. Intensity calculations are performed for a number of flow resistivity values in both quiescent and windy atmospheres. Variations in the value of this parameter are shown to have substantial effects on the spatial variation of the acoustic signal.

  14. Parabolic single-crystal diamond lenses for coherent x-ray imaging

    NASA Astrophysics Data System (ADS)

    Terentyev, Sergey; Blank, Vladimir; Polyakov, Sergey; Zholudev, Sergey; Snigirev, Anatoly; Polikarpov, Maxim; Kolodziej, Tomasz; Qian, Jun; Zhou, Hua; Shvyd'ko, Yuri

    2015-09-01

    We demonstrate parabolic single-crystal diamond compound refractive lenses designed for coherent x-ray imaging resilient to extreme thermal and radiation loading expected from next generation light sources. To ensure the preservation of coherence and resilience, the lenses are manufactured from the highest-quality single-crystalline synthetic diamond material grown by a high-pressure high-temperature technique. Picosecond laser milling is applied to machine lenses to parabolic shapes with a ≃ 1 μ m precision and surface roughness. A compound refractive lens comprised of six lenses with a radius of curvature R = 200 μ m at the vertex of the parabola and a geometrical aperture A = 900 μ m focuses 10 keV x-ray photons from an undulator source at the Advanced Photon Source facility to a focal spot size of ≃ 20 × 90 μ m 2 with a gain factor of ≃ 50 - 100 .

  15. Inverse parabolic quantum dot: The transition energy under magnetic field effect

    NASA Astrophysics Data System (ADS)

    Safwan, S. A.; El Meshed, Nagwa

    2016-08-01

    We present here, the evolution of the transition energy with a static magnetic field, when the electron and the hole are confined in inverse parabolic quantum dot (IPQD). The unexpected behavior is found, at the weak confinement regime the conduction band minimum and the top of valance band change from s-state to p-state or d-state for confined electron and hole inside IPQD, respectively. The strength of the inverse parabolic potential (potential hump) inside a quantum dot has the upper hand in tuning the ground state momentum for both electron and hole, and consequently their interband transition energy is changed. Knowing that this is not the case for the other types of potentials. The quantum size, the magnetic field and inverse potential hump effects on electron and hole ground and excited states are discussed.

  16. Oscillation of electron mobility in parabolic double quantum well structure due to applied electric field

    SciTech Connect

    Sahoo, Narayan; Sahu, Trinath

    2014-12-15

    We show that oscillation of low temperature electron mobility μ can be obtained by applying an electric field F along the growth direction of the asymmetrically barrier delta doped Al{sub x}Ga{sub 1-x}As parabolic double quantum well structure. The drastic changes in the subband Fermi energies and distributions of subband wave functions as a function of F yield nonmonotonic intra- and intersubband scattering rate matrix elements mediated by intersubband effects. The oscillatory enhancement of μ, which is attributed to the subband mobilities governed by the ionized impurity scattering, magnifies with increase in well width and decrease in height of the parabolic structure potential. The results can be utilized for nanoscale low temperature device applications.

  17. Gas Turbine/Solar Parabolic Trough Hybrid Design Using Molten Salt Heat Transfer Fluid: Preprint

    SciTech Connect

    Turchi, C. S.; Ma, Z.

    2011-08-01

    Parabolic trough power plants can provide reliable power by incorporating either thermal energy storage (TES) or backup heat from fossil fuels. This paper describes a gas turbine / parabolic trough hybrid design that combines a solar contribution greater than 50% with gas heat rates that rival those of natural gas combined-cycle plants. Previous work illustrated benefits of integrating gas turbines with conventional oil heat-transfer-fluid (HTF) troughs running at 390?C. This work extends that analysis to examine the integration of gas turbines with salt-HTF troughs running at 450 degrees C and including TES. Using gas turbine waste heat to supplement the TES system provides greater operating flexibility while enhancing the efficiency of gas utilization. The analysis indicates that the hybrid plant design produces solar-derived electricity and gas-derived electricity at lower cost than either system operating alone.

  18. Strong coupling and stimulated emission in single parabolic quantum well microcavity for terahertz cascade

    SciTech Connect

    Tzimis, A.; Savvidis, P. G.; Trifonov, A. V.; Ignatiev, I. V.; Christmann, G.; Tsintzos, S. I.; Hatzopoulos, Z.; Kavokin, A. V.

    2015-09-07

    We report observation of strong light-matter coupling in an AlGaAs microcavity (MC) with an embedded single parabolic quantum well. The parabolic potential is achieved by varying aluminum concentration along the growth direction providing equally spaced energy levels, as confirmed by Brewster angle reflectivity from a reference sample without MC. It acts as an active region of the structure which potentially allows cascaded emission of terahertz (THz) light. Spectrally and time resolved pump-probe spectroscopy reveals characteristic quantum beats whose frequencies range from 0.9 to 4.5 THz, corresponding to energy separation between relevant excitonic levels. The structure exhibits strong stimulated nonlinear emission with simultaneous transition to weak coupling regime. The present study highlights the potential of such devices for creating cascaded relaxation of bosons, which could be utilized for THz emission.

  19. A parabolic model of drag coefficient for storm surge simulation in the South China Sea.

    PubMed

    Peng, Shiqiu; Li, Yineng

    2015-01-01

    Drag coefficient (Cd) is an essential metric in the calculation of momentum exchange over the air-sea interface and thus has large impacts on the simulation or forecast of the upper ocean state associated with sea surface winds such as storm surges. Generally, Cd is a function of wind speed. However, the exact relationship between Cd and wind speed is still in dispute, and the widely-used formula that is a linear function of wind speed in an ocean model could lead to large bias at high wind speed. Here we establish a parabolic model of Cd based on storm surge observations and simulation in the South China Sea (SCS) through a number of tropical cyclone cases. Simulation of storm surges for independent Tropical cyclones (TCs) cases indicates that the new parabolic model of Cd outperforms traditional linear models. PMID:26499262

  20. Reduction of effective terahertz focal spot size by means of nested concentric parabolic reflectors

    SciTech Connect

    Neumann, V. A.; Laurita, N. J.; Pan, LiDong; Armitage, N. P.

    2015-09-15

    An ongoing limitation of terahertz spectroscopy is that the technique is generally limited to the study of relatively large samples of order 4 mm across due to the generally large size of the focal beam spot. We present a nested concentric parabolic reflector design which can reduce the terahertz focal spot size. This parabolic reflector design takes advantage of the feature that reflected rays experience a relative time delay which is the same for all paths. The increase in effective optical path for reflected light is equivalent to the aperture diameter itself. We have shown that the light throughput of an aperture of 2 mm can be increased by a factor 15 as compared to a regular aperture of the same size at low frequencies. This technique can potentially be used to reduce the focal spot size in terahertz spectroscopy and enable the study of smaller samples.

  1. Reducing the Cost of Energy from Parabolic Trough Solar Power Plants: Preprint

    SciTech Connect

    Price, H.; Kearney, D.

    2003-01-01

    Parabolic trough solar technology is the most proven and lowest cost large-scale solar power technology available today, primarily because of the nine large commercial-scale solar power plants that are operating in the California Mojave Desert. However, no new plants have been built during the past ten years because the cost of power from these plants is more expensive than power from conventional fossil fuel power plants. This paper reviews the current cost of energy and the potential for reducing the cost of energy from parabolic trough solar power plant technology based on the latest technological advancements and projected improvements from industry and sponsored R&D. The paper also looks at the impact of project financing and incentives on the cost of energy.

  2. A parabolic model of drag coefficient for storm surge simulation in the South China Sea

    PubMed Central

    Peng, Shiqiu; Li, Yineng

    2015-01-01

    Drag coefficient (Cd) is an essential metric in the calculation of momentum exchange over the air-sea interface and thus has large impacts on the simulation or forecast of the upper ocean state associated with sea surface winds such as storm surges. Generally, Cd is a function of wind speed. However, the exact relationship between Cd and wind speed is still in dispute, and the widely-used formula that is a linear function of wind speed in an ocean model could lead to large bias at high wind speed. Here we establish a parabolic model of Cd based on storm surge observations and simulation in the South China Sea (SCS) through a number of tropical cyclone cases. Simulation of storm surges for independent Tropical cyclones (TCs) cases indicates that the new parabolic model of Cd outperforms traditional linear models. PMID:26499262

  3. Towards standardization of in-site parabolic trough collector testing in solar thermal power plants

    NASA Astrophysics Data System (ADS)

    Sallaberry, Fabienne; Valenzuela, Loreto; de Jalón, Alberto García; Leon, Javier; Bernad, Ignacio David

    2016-05-01

    This paper presents a summary of the testing procedure and a validation of the methodology of parabolic trough collector in solar thermal power plants. The applied testing methodology is the one proposed within the Spanish standardization sub-committee AEN/CTN 206/SC117 working group WG2 related to the components for solar thermal power plants. This methodology is also proposed within the international committee IEC TC 117 (Standard draft IEC 62862-3-2 Ed. 1.0). This study is done at Plataforma Solar de Almería (PSA) in Almeria within the European project STAGE-STE. This paper presents the results of the optical and thermal efficiency of a large-size parabolic trough collector. The obtained values are similar to the previous analysis on this collector by PSA. The results of the tracking system have a good accuracy compared to the acceptance angle of the concentrator.

  4. Near-term improvements in parabolic troughs: an economic and performance assessment

    SciTech Connect

    Gee, R.; Murphy, L.M.

    1981-08-01

    Improved parabolic-trough concentrating collectors will result from better design, improved fabrication techniques, and the development and utilization of improved materials. This analysis qualifies the performance potential of various parabolic-trough component improvements from a systems viewpoint and uses these performance data to determine the worth of each improvement on an economic basis. The improvements considered are evacuated receivers, silvered-glass reflectors, improved receiver, selective coatings, higher optical accuracy concentrations, and higher transmittance receiver glazings. Upper-bound costs for each improvement are provided as well as estimates of the increased solar system rates of return that are made possible by these improvements. The performance and economic potential of some of these improvements are shown to be substantial, especially at higher collector operating temperatures.

  5. Quantum damped oscillator II: Bateman's Hamiltonian vs. 2D parabolic potential barrier

    SciTech Connect

    Chruscinski, Dariusz . E-mail: darch@phys.uni.torun.pl

    2006-04-15

    We show that quantum Bateman's system which arises in the quantization of a damped harmonic oscillator is equivalent to a quantum problem with 2D parabolic potential barrier known also as 2D inverted isotropic oscillator. It turns out that this system displays the family of complex eigenvalues corresponding to the poles of analytical continuation of the resolvent operator to the complex energy plane. It is shown that this representation is more suitable than the hyperbolic one used recently by Blasone and Jizba.

  6. Design and fabrication of a low-specific-weight parabolic dish solar concentrator

    NASA Technical Reports Server (NTRS)

    Richter, C. W.; Birchenough, A. G.; Marquis, G. A.; Mroz, T. S.

    1978-01-01

    A segmented design and fabrication and assembly techniques were developed for a 1.8 m (6 ft) diameter parabolic concentrator for space application. This design and these techniques were adaptable to a low cost, mass-produced concentrator. Minimal machining was required. Concentrator segments of formed magnesium were used. The concentrator weighed only 1.6 kg sq m (0.32 lbm/sq ft).

  7. Quadratic spline collocation and parareal deferred correction method for parabolic PDEs

    NASA Astrophysics Data System (ADS)

    Liu, Jun; Wang, Yan; Li, Rongjian

    2016-06-01

    In this paper, we consider a linear parabolic PDE, and use optimal quadratic spline collocation (QSC) methods for the space discretization, proceed the parareal technique on the time domain. Meanwhile, deferred correction technique is used to improve the accuracy during the iterations. The error estimation is presented and the stability is analyzed. Numerical experiments, which is carried out on a parallel computer with 40 CPUs, are attached to exhibit the effectiveness of the hybrid algorithm.

  8. Life science experiments during parabolic flight: The McGill experience

    NASA Technical Reports Server (NTRS)

    Watt, D. G. D.

    1988-01-01

    Over the past twelve years, members of the Aerospace Medical Research Unit of McGill University have carried out a wide variety of tests and experiments in the weightless condition created by parabolic flight. This paper discusses the pros and cons of that environment for the life scientist, and uses examples from the McGill program of the types of activities which can be carried out in a transport aircraft such as the NASA KC-135.

  9. Electron transport in electrically biased inverse parabolic double-barrier structure

    NASA Astrophysics Data System (ADS)

    M, Bati; S, Sakiroglu; I, Sokmen

    2016-05-01

    A theoretical study of resonant tunneling is carried out for an inverse parabolic double-barrier structure subjected to an external electric field. Tunneling transmission coefficient and density of states are analyzed by using the non-equilibrium Green’s function approach based on the finite difference method. It is found that the resonant peak of the transmission coefficient, being unity for a symmetrical case, reduces under the applied electric field and depends strongly on the variation of the structure parameters.

  10. Laser-written parabolic micro-antennas for efficient photon collection

    SciTech Connect

    Schell, Andreas W. Neumer, Tanja; Benson, Oliver; Shi, Qiang; Kaschke, Johannes; Fischer, Joachim; Wegener, Martin

    2014-12-08

    Efficient collection of photons from solid-state single-photon emitters, like quantum dots, molecules, or defect centers in diamond, is a very demanding task. Here, we introduce parabolic micro-antennas fabricated by two-photon direct laser-writing to enhance the collection efficiency by directing emitted light into a small solid angle. The antennas can be fabricated on-site at the position of a pre-selected single-photon emitter.

  11. Peculiarities of parabolic-barrier penetrability and thermal decay rate with the quantum diffusion approach

    SciTech Connect

    Kuzyakin, R. A.; Sargsyan, V. V.; Adamian, G. G.; Antonenko, N. V.

    2011-06-15

    With the quantum diffusion approach, the passing probability through the parabolic barrier is examined in the limit of linear coupling in the momentum between the collective subsystem and environment. The dependencies of the penetrability on time, energy, and the coupling strength between the interacting subsystems are studied. The quasistationary thermal decay rate from a metastable state is considered in the cases of linear couplings both in the momentum and in the coordinate.

  12. The relative isoperimetric inequality on a conformally parabolic manifold with boundary

    SciTech Connect

    Kesel'man, Vladimir M

    2011-07-31

    For an arbitrary noncompact n-dimensional Riemannian manifold with a boundary of conformally parabolic type it is proved that there exists a conformal change of metric such that a relative isoperimetric inequality of the same form as in the closed n-dimensional Euclidean half-space holds on the manifold with the new metric. This isoperimetric inequality is asymptotically sharp. Bibliography: 6 titles.

  13. LCOE reduction for parabolic trough CSP: Innovative solar receiver with improved performance at medium temperature

    NASA Astrophysics Data System (ADS)

    Stollo, A.; Chiarappa, T.; D'Angelo, A.; Maccari, A.; Matino, F.

    2016-05-01

    Concentrated Solar Power (CSP) applications represent an effective possibility to gain energy from the Sun; however, the lasting CSP market crisis compels continuous improvements in terms of cost reduction and performance increase. Focused on parabolic trough technology, this paper describes the innovation studied and realized on solar receivers to gain optimized optical performance while increasing the production versatility, hence boosting the solar plant efficiency and finally reducing the estimated LCOE.

  14. Blow-up properties in the parabolic problems with anisotropic nonstandard growth conditions

    NASA Astrophysics Data System (ADS)

    Liu, Bingchen; Yang, Jie

    2016-03-01

    In this paper, we study the parabolic problems with anisotropic nonstandard growth nonlinearities. We first give the existence and uniqueness of weak solutions in variable Sobolev spaces. Second, we use the energy methods to show the existence of blow-up solutions with negative or positive initial energy, respectively. Both the variable exponents and the coefficients make important roles in Fujita blow-up phenomena. Moreover, asymptotic properties of the blow-up solutions are determined.

  15. Asymptotic profile of a parabolic-hyperbolic system with boundary effect arising from tumor angiogenesis

    NASA Astrophysics Data System (ADS)

    Mei, Ming; Peng, Hongyun; Wang, Zhi-An

    2015-11-01

    This paper concerns a parabolic-hyperbolic system on the half space R+ with boundary effect. The system is derived from a singular chemotaxis model describing the initiation of tumor angiogenesis. We show that the solution of the system subject to appropriate boundary conditions converges to a traveling wave profile as time tends to infinity if the initial data is a small perturbation around the wave which is shifted far away from the boundary but its amplitude can be arbitrarily large.

  16. Tuning of a high magnification compact parabolic telescope for centimeter-scale laser beams.

    PubMed

    Tacca, Matteo; Sorrentino, Fiodor; Buy, Christelle; Laporte, Matthieu; Pillant, Gabriel; Genin, Eric; La Penna, Paolo; Barsuglia, Matteo

    2016-02-20

    Off-axis parabolic telescopes, widely used in astronomy and laser optics, if perfectly tuned, are virtually free from aberrations along the parabola's axis direction, but their alignment is very critical. We present a detailed method to align a high magnification off-axis afocal parabolic telescope. The method is composed of two steps: an initial pre-alignment using autocollimators, followed by a fine tuning with a collimated laser beam. Due to the large telescope magnification, the outcoming beam cannot be measured without being refocused. The beam is therefore reflected on a flat mirror and sent back through the telescope. This double-pass configuration allows the measurement of the beam quality without the need for large additional optics. In the fine-tuning step, a numerical simulation is also used to identify the degrees of freedom to be adjusted. The experimental results presented are obtained with one of the mode-matching parabolic telescopes of the gravitational wave interferometric detector Advanced Virgo. PMID:26906579

  17. Aerial projection of three-dimensional motion pictures by electro-holography and parabolic mirrors

    PubMed Central

    Kakue, Takashi; Nishitsuji, Takashi; Kawashima, Tetsuya; Suzuki, Keisuke; Shimobaba, Tomoyoshi; Ito, Tomoyoshi

    2015-01-01

    We demonstrate an aerial projection system for reconstructing 3D motion pictures based on holography. The system consists of an optical source, a spatial light modulator corresponding to a display and two parabolic mirrors. The spatial light modulator displays holograms calculated by computer and can reconstruct holographic motion pictures near the surface of the modulator. The two parabolic mirrors can project floating 3D images of the motion pictures formed by the spatial light modulator without mechanical scanning or rotating. In this demonstration, we used a phase-modulation-type spatial light modulator. The number of pixels and the pixel pitch of the modulator were 1,080 × 1,920 and 8.0 μm × 8.0 μm, respectively. The diameter, the height and the focal length of each parabolic mirror were 288 mm, 55 mm and 100 mm, respectively. We succeeded in aerially projecting 3D motion pictures of size ~2.5 mm3 by this system constructed by the modulator and mirrors. In addition, by applying a fast computational algorithm for holograms, we achieved hologram calculations at ~12 ms per hologram with 4 CPU cores. PMID:26152453

  18. A parabolic model to control quantum interference in T-shaped molecular junctions.

    PubMed

    Nozaki, Daijiro; Sevinçli, Hâldun; Avdoshenko, Stanislav M; Gutierrez, Rafael; Cuniberti, Gianaurelio

    2013-09-01

    Quantum interference (QI) effects in molecular devices have drawn increasing attention over the past years due to their unique features observed in the conductance spectrum. For the further development of single molecular devices exploiting QI effects, it is of great theoretical and practical interest to develop simple methods controlling the emergence and the positions of QI effects like anti-resonances or Fano line shapes in conductance spectra. In this work, starting from a well-known generic molecular junction with a side group (T-shaped molecule), we propose a simple graphical method to visualize the conditions for the appearance of quantum interference, Fano resonances or anti-resonances, in the conductance spectrum. By introducing a simple graphical representation (parabolic diagram), we can easily visualize the relation between the electronic parameters and the positions of normal resonant peaks and anti-resonant peaks induced by quantum interference in the conductance spectrum. This parabolic model not only can predict the emergence and energetic position of quantum interference from a few electronic parameters but also can enable one to know the coupling between the side group and the main conduction channel from measurements in the case of orthogonal basis. The results obtained within the parabolic model are validated using density-functional based quantum transport calculations in realistic T-shaped molecular junctions. PMID:23558406

  19. Energetic protons from an ultraintense laser interacting with a symmetric parabolic concave target

    SciTech Connect

    Ali Bake, Muhammad; Xie Baisong; Shan Zhang; Wang Hongyu

    2013-03-15

    A scheme of a symmetric parabolic concave target irradiated by an ultraintense laser for efficient proton acceleration is proposed and involved problem is studied by using two-dimensional particle-in-cell (PIC) simulations. Results indicate that on one hand, the laser field is focused by the front parabolic concave surface of target and, on the other hand, more energetic hot electrons will traverse to the rear surface of target due to concave shape. The space-charge-separation field, induced by those hot electrons escaping form parabolic concave rear surface of target, can accelerate protons to relatively high energy with narrow energy spread. The dependence of the efficiency of proton acceleration on the target parameters is examined, and the optimal target parameters are obtained. Particle-in-cell simulations show that the proton peak energy and energy spread are greatly enhanced when the target parameters are chosen optimal, for example, a proton bunch with the maximum energy {approx}27.5 MeV and energy spread {approx}7% can be generated. Some implications of our results to experiments and comparisons with the other works are also discussed briefly.

  20. Aerial projection of three-dimensional motion pictures by electro-holography and parabolic mirrors

    NASA Astrophysics Data System (ADS)

    Kakue, Takashi; Nishitsuji, Takashi; Kawashima, Tetsuya; Suzuki, Keisuke; Shimobaba, Tomoyoshi; Ito, Tomoyoshi

    2015-07-01

    We demonstrate an aerial projection system for reconstructing 3D motion pictures based on holography. The system consists of an optical source, a spatial light modulator corresponding to a display and two parabolic mirrors. The spatial light modulator displays holograms calculated by computer and can reconstruct holographic motion pictures near the surface of the modulator. The two parabolic mirrors can project floating 3D images of the motion pictures formed by the spatial light modulator without mechanical scanning or rotating. In this demonstration, we used a phase-modulation-type spatial light modulator. The number of pixels and the pixel pitch of the modulator were 1,080 × 1,920 and 8.0 μm × 8.0 μm, respectively. The diameter, the height and the focal length of each parabolic mirror were 288 mm, 55 mm and 100 mm, respectively. We succeeded in aerially projecting 3D motion pictures of size ~2.5 mm3 by this system constructed by the modulator and mirrors. In addition, by applying a fast computational algorithm for holograms, we achieved hologram calculations at ~12 ms per hologram with 4 CPU cores.

  1. A novel ROM compression architecture for DDFS utilizing the parabolic approximation of equi-section division.

    PubMed

    Jeng, Shiann-Shiun; Lin, Hsing-Chen; Lin, Chi-Huei

    2012-12-01

    In this paper, we propose the parabolic approximation of equi-section division (PAESD) utilizing the symmetry property and amplitude approximation of a sinusoidal waveform to design a direct digital frequency synthesizer (DDFS). The sinusoidal phase of a one-quarter period is divided into equi-sections. The proposed method utilizes the curvature equivalence to derive each parabolic curve function, and then the value of the error function between each parabolic curve function and the sinusoidal function is stored in an error-compensation ROM to reconstruct the real sinusoidal waveform. The upper/lower bound of the maximum error value stored in the error-compensation ROM is derived to determine the minimum required memory word length relative to the number of bits of the equi-sections. Thus, the minimum size of the total ROMs of the DDFS using the PAESD without error-compensation ROM is compressed to 544 bits; the total compression ratio, compared with the minimum size of the total ROMs of the DDFS using the basic look-up table (LUT), is approximately 843:1, achieved by consuming additional circuits [71 adaptive look-up tables (ALUTs), 3 digital signal processor (DSP) block 9-bit elements]. Consequently, the results show that the proposed ROM compression method can effectively achieve a better compression ratio than the state-of-the-art solutions without affecting the spectrum performance of an average spurious-free dynamic range (SFDR) of -85 dBc. PMID:23221209

  2. Thermal buffering of receivers for parabolic dish solar thermal power plants

    NASA Technical Reports Server (NTRS)

    Manvi, R.; Fujita, T.; Gajanana, B. C.; Marcus, C. J.

    1980-01-01

    A parabolic dish solar thermal power plant comprises a field of parabolic dish power modules where each module is composed of a two-axis tracking parabolic dish concentrator which reflects sunlight (insolation) into the aperture of a cavity receiver at the focal point of the dish. The heat generated by the solar flux entering the receiver is removed by a heat transfer fluid. In the dish power module, this heat is used to drive a small heat engine/generator assembly which is directly connected to the cavity receiver at the focal point. A computer analysis is performed to assess the thermal buffering characteristics of receivers containing sensible and latent heat thermal energy storage. Parametric variations of the thermal inertia of the integrated receiver-buffer storage systems coupled with different fluid flow rate control strategies are carried out to delineate the effect of buffer storage, the transient response of the receiver-storage systems and corresponding fluid outlet temperature. It is concluded that addition of phase change buffer storage will substantially improve system operational characteristics during periods of rapidly fluctuating insolation due to cloud passage.

  3. The controllability and observability analysis of the one-dimensional heat flow

    NASA Astrophysics Data System (ADS)

    Sutrima; Muslich; Wibowo, S.

    2016-02-01

    In this paper controllability and observability analysis are performed for the heat flow on the state-space of one dimension. The process is described by a semilinear parabolic partial differential equation. We report that the associated linear infinite-dimensional operator is a Riesz-spectral operator and generates a C 0-semigroup of bounded linear operators. Then we construct a sufficient and necessary condition for the approximate controllability and observability of the system. In particular, a finite number of dominant modes of the system are approximately observable when the input is measured at the heat output by an appropriate sensor.

  4. Backward uniqueness of the s.c. semigroup arising in parabolic-hyperbolic fluid-structure interaction

    NASA Astrophysics Data System (ADS)

    Avalos, George; Triggiani, Roberto

    A 2-d or 3-d fluid-structure interaction model in its linear form is considered, for which semigroup well-posedness (with explicit generator) was recently established in [G. Avalos, R. Triggiani, The coupled PDE-system arising in fluid-structure interaction. Part I: Explicit semigroup generator and its spectral properties, in: Fluids and Waves, in: Contemp. Math., vol. 440, Amer. Math. Soc., 2007, pp. 15-55; G. Avalos, R. Triggiani, The coupled PDE-system arising in fluid-structure interaction. Part II: Uniform stabilization with boundary dissipation at the interface, Discrete Contin. Dyn. Syst., in press]. This is a system which couples at the interface the linear version of the Navier-Stokes equations with the equations of linear elasticity (wave-like). In this paper, we establish a backward uniqueness theorem for such a parabolic-hyperbolic coupled PDE system. If { is the (contraction) s.c. semigroup describing its evolution on the finite energy space H, then ey=0 for some T>0 and y∈H, implies y=0. This property has implications in establishing unique continuation and controllability properties, as in the case of thermoelastic equations [M. Eller, I. Lasiecka, R. Triggiani, Simultaneous exact/approximate boundary controllability of thermoelastic plates with variable coefficient, in: Marcel Dekker Lect. Notes Pure Appl. Math., vol. 216, February 2001, pp. 109-230, invited paper for the special volume entitled Shape Optimization and Optimal Designs, J. Cagnol, J.P. Zolesio (Eds). (Preliminary version is in invited paper in: A.V. Balakrishnan (Ed.), Semigroup of Operators and Applications, Birkhäuser, 2000, pp. 335-351.); M. Eller, I. Lasiecka, R. Triggiani, Simultaneous exact/approximate boundary controllability of thermoelastic plates with variable thermal coefficient and moment control, J. Math. Anal. Appl. 251 (2000) 452-478; M. Eller, I. Lasiecka, R. Triggiani, Simultaneous exact/approximate boundary controllability of thermoelastic plates with variable

  5. Solving the cardiac bidomain equations for discontinuous conductivities.

    PubMed

    Austin, Travis M; Trew, Mark L; Pullan, Andrew J

    2006-07-01

    Fast simulations of cardiac electrical phenomena demand fast matrix solvers for both the elliptic and parabolic parts of the bidomain equations. It is well known that fast matrix solvers for the elliptic part must address multiple physical scales in order to show robust behavior. Recent research on finding the proper solution method for the bidomain equations has addressed this issue whereby multigrid preconditioned conjugate gradients has been used as a solver. In this paper, a more robust multigrid method, called Black Box Multigrid, is presented as an alternative to conventional geometric multigrid, and the effect of discontinuities on solver performance for the elliptic and parabolic part is investigated. Test problems with discontinuities arising from inserted plunge electrodes and naturally occurring myocardial discontinuities are considered. For these problems, we explore the advantages to using a more advanced multigrid method like Black Box Multigrid over conventional geometric multigrid. Results will indicate that for certain discontinuous bidomain problems Black Box Multigrid provides 60% faster simulations than using conventional geometric multigrid. Also, for the problems examined, it will be shown that a direct usage of conventional multigrid leads to faster simulations than an indirect usage of conventional multigrid as a preconditioner unless there are sharp discontinuities. PMID:16830931

  6. Spin field equations and Heun's equations

    NASA Astrophysics Data System (ADS)

    Jiang, Min; Wang, Xuejing; Li, Zhongheng

    2015-06-01

    The Kerr-Newman-(anti) de Sitter metric is the most general stationary black hole solution to the Einstein-Maxwell equation with a cosmological constant. We study the separability of the equations of the massless scalar (spin s=0), neutrino ( s=1/2), electromagnetic ( s=1), Rarita-Schwinger ( s=3/2), and gravitational ( s=2) fields propagating on this background. We obtain the angular and radial master equations, and show that the master equations are transformed to Heun's equation. Meanwhile, we give the condition of existence of event horizons for Kerr-Newman-(anti) de Sitter spacetime by using Sturm theorem.

  7. Blow-up behavior of positive solutions for a chemical fuel ignition device model

    SciTech Connect

    Jia, Yunfeng; Wu, Jianhua; Xu, Hong-Kun

    2014-04-15

    Blow-up behavior of positive solutions of a semi-linear parabolic system arising from thermal explosion, which subject to the homogenous Dirichlet boundary conditions, is investigated. In particular, sufficient conditions for the solutions to blow up are obtained.

  8. Basic lubrication equations

    NASA Technical Reports Server (NTRS)

    Hamrock, B. J.; Dowson, D.

    1981-01-01

    Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.

  9. Survey of the status of finite element methods for partial differential equations

    NASA Technical Reports Server (NTRS)

    Temam, Roger

    1986-01-01

    The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.

  10. Finite volume method for the Black-Scholes equation transformed on finite interval

    NASA Astrophysics Data System (ADS)

    Valkov, R.

    2012-11-01

    In this paper, we present a fitted FVM for the degenerate at the two ends parabolic equation, derived from the Black-Scholes equation after a transformation to a finite interval. For the case of European options we describe a fully discretization of the vertical method of lines, where the spatial discretization is formulated as a Petrov-Galerkin FEM. We show that the method is O(h) convergent and monotone. Numerical experiments are presented to verify the theoretical results. Experiments on a power-graded mesh demonstrate higher accuracy.

  11. Optimal Regularity and Long-Time Behavior of Solutions for the Westervelt Equation

    SciTech Connect

    Meyer, Stefan Wilke, Mathias

    2011-10-15

    We investigate an initial-boundary value problem for the quasilinear Westervelt equation which models the propagation of sound in fluidic media. We prove that, if the initial data are sufficiently small and regular, then there exists a unique global solution with optimal L{sub p}-regularity. We show furthermore that the solution converges to zero at an exponential rate as time tends to infinity. Our techniques are based on maximal L{sub p}-regularity for abstract quasilinear parabolic equations.

  12. The Navier-Stokes Equations in Nonendpoint Borderline Lorentz Spaces

    NASA Astrophysics Data System (ADS)

    Phuc, Nguyen Cong

    2015-12-01

    It is shown both locally and globally that {L_t^{∞}(L_x^{3,q})} solutions to the three-dimensional Navier-Stokes equations are regular provided {q≠∞}. Here {L_x^{3,q}}, {0 < q ≤∞}, is an increasing scale of Lorentz spaces containing {L^3_x}. Thus the result provides an improvement of a result by Escauriaza et al. (Uspekhi Mat Nauk 58:3-44, 2003; translation in Russ Math Surv 58, 211-250, 2003), which treated the case q = 3. A new local energy bound and a new {ɛ}-regularity criterion are combined with the backward uniqueness theory of parabolic equations to obtain the result. A weak-strong uniqueness of Leray-Hopf weak solutions in {L_t^{∞}(L_x^{3,q})}, {q≠∞}, is also obtained as a consequence.

  13. Nonlinear Solver Approaches for the Diffusive Wave Approximation to the Shallow Water Equations

    NASA Astrophysics Data System (ADS)

    Collier, N.; Knepley, M.

    2015-12-01

    The diffusive wave approximation to the shallow water equations (DSW) is a doubly-degenerate, nonlinear, parabolic partial differential equation used to model overland flows. Despite its challenges, the DSW equation has been extensively used to model the overland flow component of various integrated surface/subsurface models. The equation's complications become increasingly problematic when ponding occurs, a feature which becomes pervasive when solving on large domains with realistic terrain. In this talk I discuss the various forms and regularizations of the DSW equation and highlight their effect on the solvability of the nonlinear system. In addition to this analysis, I present results of a numerical study which tests the applicability of a class of composable nonlinear algebraic solvers recently added to the Portable, Extensible, Toolkit for Scientific Computation (PETSc).

  14. Chemical Equation Balancing.

    ERIC Educational Resources Information Center

    Blakley, G. R.

    1982-01-01

    Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

  15. Equations and closure methods

    NASA Technical Reports Server (NTRS)

    1977-01-01

    Basic differential equations governing compressible turbulent boundary layer flow are reviewed, including conservation of mass and energy, momentum equations derived from Navier-Stokes equations, and equations of state. Closure procedures were broken down into: (1) simple or zeroth-order methods, (2) first-order or mean field closure methods, and (3) second-order or mean turbulence field methods.

  16. Modeling of a Parabolic Trough Solar Field for Acceptance Testing: A Case Study

    SciTech Connect

    Wagner, M. J.; Mehos, M. S.; Kearney, D. W.; McMahan, A. C.

    2011-01-01

    As deployment of parabolic trough concentrating solar power (CSP) systems ramps up, the need for reliable and robust performance acceptance test guidelines for the solar field is also amplified. Project owners and/or EPC contractors often require extensive solar field performance testing as part of the plant commissioning process in order to ensure that actual solar field performance satisfies both technical specifications and performance guaranties between the involved parties. Performance test code work is currently underway at the National Renewable Energy Laboratory (NREL) in collaboration with the SolarPACES Task-I activity, and within the ASME PTC-52 committee. One important aspect of acceptance testing is the selection of a robust technology performance model. NREL1 has developed a detailed parabolic trough performance model within the SAM software tool. This model is capable of predicting solar field, sub-system, and component performance. It has further been modified for this work to support calculation at subhourly time steps. This paper presents the methodology and results of a case study comparing actual performance data for a parabolic trough solar field to the predicted results using the modified SAM trough model. Due to data limitations, the methodology is applied to a single collector loop, though it applies to larger subfields and entire solar fields. Special consideration is provided for the model formulation, improvements to the model formulation based on comparison with the collected data, and uncertainty associated with the measured data. Additionally, this paper identifies modeling considerations that are of particular importance in the solar field acceptance testing process and uses the model to provide preliminary recommendations regarding acceptable steady-state testing conditions at the single-loop level.

  17. Well-Posedness for a Class of Thin-Film Equations with General Mobility in the Regime of Partial Wetting

    NASA Astrophysics Data System (ADS)

    Knüpfer, Hans

    2015-11-01

    We establish well-posedness for the family of thin-film equations with . The model (1) with has been used to describe the evolution of a capillary driven thin liquid droplet on a solid substrate in terms of its height profile . The family of thin-film equations (1) provides a model problem to investigate contact line propagation in fluid dynamics under relaxed slip conditions. The parabolicity of the fourth order parabolic problem degenerates at the free boundary, which leads to a loss of regularity at the moving contact point. Our solutions are regular in terms of the two variables d( x) and d( x)3- n , where d( x) is the distance to the free boundary. The main technical difficulty in the analysis of (1) is related to the loss of regularity at the contact points.

  18. Operation and performance of the Ciba-Corning 512 coagulation monitor during parabolic flight

    NASA Technical Reports Server (NTRS)

    Gocke, Robyn; Lloyd, Charles W.; Greenthaner, Nancy K.

    1991-01-01

    The goal was to assess the functionality and evaluate the procedures and operations required to operate the Ciba-Corning 512 Coagulation Monitor during parabolic flight. This monitor determines the clotting characteristics of blood. The analyzer operates by laser detection of the cessation of blood flow in a capillary channel within a test cartridge. Test simulator results were excellent for both pre-and post-flight. In-flight results were not obtained due to the warm-up time required for the simulator. Since this is an electronic function only, the expected results on the simulator would be the same in zero-g.

  19. Beam overlapping in a multipass Ti:sapphire amplifier based on a parabolic mirror

    NASA Astrophysics Data System (ADS)

    Yang, Shengyi

    2005-06-01

    According to laser beam transporting in a multipass Ti:sapphire amplifier based on a parabolic mirror, the influential factors to induce astigmatism are analyzed. The beam waists of the laser beam transporting in the multipass amplifier are calculated by ABCD law in sagittal and tangential planes, respectively, and are compared with each other. Our analyses of these influential factors provide valuable data to optimize this design of multipass Ti:sapphire amplifier, and our experimental results of getting Gaussian beam from such a kind of amplifier confirmed our theoretical analyses.

  20. Elastic analysis of heterogeneous thick-walled spherical pressure vessels with parabolic varying properties

    NASA Astrophysics Data System (ADS)

    Karami, Keyhan; Abedi, Majid; Zamani Nejad, Mohammad; Lotfian, Mohammad Hassan

    2012-12-01

    On the basis of plane elasticity theory (PET), the displacement and stress components in a thick-walled spherical pressure vessels made of heterogeneous materials subjected to internal and external pressure is developed. The mechanical properties except the Poisson's ratio are assumed to obey the parabolic variations throughout the thickness. Effect of material inhomogeneity on the elastic deformations and stresses is investigated. The analytical solutions and the solutions carried out through the FEM have a good agreement. The values used in this study are arbitrary chosen to demonstrate the effect of inhomogeneity on displacements, and stresses distributions.

  1. Preparation for Containerless Processing on ISS: Parabolic Flights with the TEMPUS Facility

    NASA Astrophysics Data System (ADS)

    Diefenbach, A.; Dreier, W.; Lohöfer, G.; Piller, J.

    2002-01-01

    The concept of electro-magnetic levitation as a means for measuring material parameters of liquid metals over a wide temperature range under microgravity conditions has been successfully applied in the Spacelab facility TEMPUS. This German payload was flown on the international missions IML- 2, MSL-1 and MSL-1R as well as on six parabolic flight campaigns yielding new results on thermo- physical properties and solidification behavior of undercooled metals and alloys. It is planned to further enhance the established electro-magnetic levitation technique and to develop a new ISS facility, the Electromagnetic Levitator (EML), which shall be a contribution to the ESA payload Materials Sciences Laboratory (MSL). The EML features a highly modular facility concept, with respect to subsystem components and diagnostics features. The sample positioning and heating shall be achieved by use of one single RF coil where the positioning and heating currents are superpositioned. A milestone in this development line has been the performance of a parabolic flight campaign performed with the Airbus A300 as part of the 3rd DLR campaign with an advanced (1) TEMPUS breadboard. During two flight days, a thorough facility test program proved that the newly implemented superpositioning principle concept in combination with two new coil designs stably positions and heats a variety of test samples. The third flight day was dedicated to scientific experiments. For viscosity measurements, sample surface oscillations were induced by applying short heater pulses during sample cooling. During undercooling experiments, the recalescence events were captured with an acquisition rate of 100kHz. In parallel to the envisaged hardware development of the MSL-EML facility, further parabolic flight campaigns both for facility testing and scientific research are planned, with the next campaign planned for November 2002. The paper will provide a brief overview of the MSL-EML features (2) , focus on the

  2. Physical optics model of side lobe nulling by discs on a parabolic reflector

    NASA Astrophysics Data System (ADS)

    Trapp, D. A.

    1985-12-01

    By mounting small disc reflectors that are moveable relative to the inner reflector surface of a parabolic dish antenna, nulls can be generated in the side lobe region of the power radiation pattern with minimal distortion effects to the main beam. A physical optics model of this antenna system is developed to investigate in a simplified direct manner the phenomena of phase nulling caused by disc movement. Array theory using isotropic radiators is used to sample the aperture distribution to approximate the far field electric field of the dish. A physical optics approximation for scattering off a flat metal disc is used for discs and feed blockage effects.

  3. Heat and electricity from the sun using parabolic dish collector systems

    NASA Technical Reports Server (NTRS)

    Truscello, V. C.; Williams, A. N.

    1979-01-01

    The paper investigates point focus distributed receiver (PFDR) solar thermal technology for the production of electric power and of industrial process heat. Attention is given to a thermal systems project conducted by JPL under DOE sponsorship. It is reported that project emphasis is on the development of cost-effective systems which will accelerate the commercialization and industrialization of plants up to 10 MWe, using parabolic dish collectors. Also discussed are the characteristics of PFDR systems, the cost targets for major systems hardware, and markets for this technology. Finally, the present system status of the technology development effort is discussed.

  4. A remarkable focusing property of a parabolic mirror for neutrons in the gravitational field: Geometric proof

    NASA Astrophysics Data System (ADS)

    Masalovich, S.

    2014-11-01

    An extraordinary focusing property of a parabolic mirror for ultracold neutrons in the presence of the gravitational field was first reported by Steyerl and co-authors. It was shown that all neutrons emitted from the focus of the mirror will be reflected back upon the same focus passing a point of return in the gravitational field in between. The present note offers a complementary geometric proof of this feature and discusses its application to many-mirror systems. The results can also be applied to electrons and ions in an electric field.

  5. Diffraction-resistant scalar beams generated by a parabolic reflector and a source of spherical waves.

    PubMed

    Zamboni-Rached, Michel; de Assis, Mariana Carolina; Ambrosio, Leonardo A

    2015-07-01

    In this work, we propose the generation of diffraction-resistant beams by using a parabolic reflector and a source of spherical waves positioned at a point slightly displaced from its focus (away from the reflector). In our analysis, considering the reflector dimensions much greater than the wavelength, we describe the main characteristics of the resulting beams, showing their properties of resistance to the diffraction effects. Due to its simplicity, this method may be an interesting alternative for the generation of long-range diffraction-resistant waves. PMID:26193137

  6. Compound parabolic concentrator design for red, green, blue, and white LED light mixing

    NASA Astrophysics Data System (ADS)

    Wei, An-Chi; Lo, Shih-Chieh; Hung, Pei-Fang; Lee, Ju-Yi; Yeh, Hong-Yih; Huang, Hong-Cheng; Li, Chia-Ming

    2016-08-01

    A light-mixing module consisting of a compound parabolic concentrator (CPC) and a fiber for mixing light from red, green, blue, and white (RGBW) LEDs was proposed. The design principle was investigated and a design prototype was demonstrated in a simulation. The simulated results showed that the chromatic nonuniformity was reduced to 1/10 when the fiber length was 40 times the core width, and the module efficiencies were more than 80% and more than 60% when the fiber lengths were 350 mm and 5 m, respectively. The proposed module is suitable for solar lighting compensation or indoor lighting, such as plant-factory lighting.

  7. Analysis of the incidence angle of the beam radiation on CPC. [Compound Parabolic Concentrator

    SciTech Connect

    Pinazo, J.M.; Canada, J.; Arago, F. )

    1992-09-01

    Analytic expressions have been derived for the projected incidence angles {var theta}{sub 1} and {var theta}{sub 2} from a two-dimensional compound parabolic concentrator solar collector. For a CPC the fraction of the incident rays on the aperture at angle {var theta}, which reaches the absorber, depends only on the {var theta}{sub 1} angle. In this paper, a mathematical expression for {var theta}{sub 1} and {var theta}{sub t} has been calculated to determine the times at which acceptance of the sun's beam radiation begins and ceases for a CPC consisting of arbitrary orientation.

  8. Analytical Approach Treating Three-Dimensional Geometrical Effects of Parabolic Trough Collectors: Preprint

    SciTech Connect

    Binotti, M.; Zhu, G.; Gray, A.; Manzollini, G.

    2012-04-01

    An analytical approach, as an extension of one newly developed method -- First-principle OPTical Intercept Calculation (FirstOPTIC) -- is proposed to treat the geometrical impact of three-dimensional (3-D) effects on parabolic trough optical performance. The mathematical steps of this analytical approach are presented and implemented numerically as part of the suite of FirstOPTIC code. In addition, the new code has been carefully validated against ray-tracing simulation results and available numerical solutions. This new analytical approach to treating 3-D effects will facilitate further understanding and analysis of the optical performance of trough collectors as a function of incidence angle.

  9. Improving the convergence rate to steady state of parabolic ADI methods. [Alternating Direction Implicit

    NASA Technical Reports Server (NTRS)

    Abarbanel, Saul S.; Dwoyer, Douglas L.; Gottlieb, David

    1986-01-01

    The present, residuals' L(2)-norms analysis of the rate of convergence to steady state for parabolic ADI solvers allows the prediction of the number of iterations required for convergence, as a function of the Courant number alpha. A modification of current ADI codes is presented which significantly improves the convergence rate and is insensitive to the Courant number over a large range of alpha. This corrected algorithm is tested for the cases of Dirichlet problems for uniform grids of many mesh sizes, mixed Dirichlet-Neumann problems, and problems defined on stretched grids and/or problems with variable coefficients.

  10. Dynamic loading of spur gears with linear or parabolic tooth profile modifications

    NASA Technical Reports Server (NTRS)

    Lin, H. H.; Oswald, F. B.; Townsend, D. P.

    1989-01-01

    A computer simulation was conducted to investigate the effects of both linear and parabolic tooth profile modification on the dynamic response of low-contact-ratio spur gears. The effect of the total amount of modification and the length of the modification zone were studied at various loads and speeds to find the optimal profile modification for minimal dynamic loading. Design charts consisting of normalized maximum dynamic load curves were generated for gear systems operated at various loads and with different tooth profile modification. An optimum profile modification can be determined from these design charts to minimize the dynamic loads of spur gear systems.

  11. Dynamic loading of spur gears with linear or parabolic tooth profile modification

    NASA Technical Reports Server (NTRS)

    Lin, Hsiang Hsi; Oswald, Fred B.; Townsend, Dennis P.

    1989-01-01

    A computer simulation was conducted to investigate the effects of both linear and parabolic tooth profile modification on the dynamic response of low-contact-ratio spur gears. The effect of the total amount of modification and the length of the modification zone were studied at various loads and speeds to find the optimal profile modification for minimal dynamic loading. Design charts consisting of normalized maximum dynamic load curves were generated for gear systems operated at various loads and with different tooth profile modification. An optimum profile modification can be determined from these design charts to minimize the dynamic loads of spur gear systems.

  12. Global and nonglobal existence for a strongly coupled parabolic system on a general domain

    NASA Astrophysics Data System (ADS)

    Castillo, Ricardo; Loayza, Miguel; Paixão, Crislene S.

    2016-09-01

    We consider the parabolic system ut - Δu = f (t)urvs ,vt - Δv = g (t)uqvs, in Ω × (0 , T), where Ω ⊂RN is either an unbounded or bounded domain and f , g ∈ C [ 0 , ∞). We find conditions for the global existence or nonglobal existence, which are expressed in terms of the behavior of ‖ S (t)u0 ‖ ∞ as t → ∞, where u (t) = S (t)u0 is the solution of the linear problem ut - Δu = 0 , u (0) =u0.

  13. Test results on parabolic dish concentrators for solar thermal power systems

    NASA Technical Reports Server (NTRS)

    Jaffe, Leonard D.

    1989-01-01

    This paper presents results of development testing of various solar thermal parabolic dish concentrators. The concentrators were mostly designed for the production of electric power using dish-mounted Rankine, Brayton or Stirling cycle engines, intended to be produced at low cost. Measured performance for various dishes included optical efficiencies ranging from 0.32 to 0.86 at a geometric concentration ratio of 500, and from about 0.09 to 0.85 at a geometric concentration ratio of 3000. Some malfunctions were observed. The tests should provide operating information of value in developing concentrators with improved performance and reduced maintenance.

  14. Visualization of Shock Wave Driven by Millimeter Wave Plasma in a Parabolic Thruster

    SciTech Connect

    Yamaguchi, Toshikazu; Shimada, Yutaka; Shiraishi, Yuya; Shibata, Teppei; Komurasaki, Kimiya; Oda, Yasuhisa; Kajiwara, Ken; Takahashi, Koji; Kasugai, Atsushi; Sakamoto, Keishi; Arakawa, Yoshihiro

    2010-05-06

    By focusing a high-power millimeter wave beam generated by a 170 GHz gyrotron, a breakdown occurred and a shock wave was driven by plasma heated by following microwave energy. The shock wave and the plasma around a focal point of a parabolic thruster were visualized by a shadowgraph method, and a transition of structures between the shock wave and the plasma was observed. There was a threshold local power density to make the transition, and the propagation velocity at the transition was around 800 m/s.

  15. Interferometric null test of a deep parabolic reflector generating a Hertzian dipole field

    SciTech Connect

    Leuchs, Gerd; Mantel, Klaus; Berger, Andreas; Konermann, Hildegard; Sondermann, Markus; Peschel, Ulf; Lindlein, Norbert; Schwider, Johannes

    2008-10-20

    We report on interferometric characterization of a deep parabolic mirror with a depth of more than five times its focal length. The interferometer is of Fizeau type; its core consists of the mirror itself, a spherical null element, and a reference flat. Because of the extreme solid angle produced by the paraboloid, the alignment of the setup appears to be very critical and needs auxiliary systems for control. Aberrations caused by misalignments are removed via fitting of suitable functionals provided by means of ray tracing simulations. It turns out that the usual misalignment approximations fail under these extreme conditions.

  16. Enhancement of multisubband electron mobility in parabolic AlxGa1-xAs-GaAs double quantum well structures

    NASA Astrophysics Data System (ADS)

    Sahu, Trinath; Palo, Sangeeta; Panda, A. K.

    2013-02-01

    We analyze the low temperature multisubband electron mobility in AlxGa1-xAs-GaAs parabolic double quantum well structures in which the outer barriers are delta doped with Si. The structural parabolic potential, obtained from gradual variation of the alloy fraction x (from 0 to xp), partly compensates the triangular like potential profile near the outer interfaces inducing the electrons to move towards the centre of the wells. We study the effect of interplay of ionized impurity (II) scattering and alloy disorder (AD) scattering on the subband mobility. We show that when single subband is occupied both II- and AD-scatterings govern the mobility. However, once second subband is occupied, the mobility is influenced by II-scattering mediated by intersubband effects. It is gratifying to show that the mobility is considerably enhanced in parabolic double quantum wells (0.3 ≥ xp > 0) compared to the square double quantum well structures (xp = 0) at large well widths where double subband is occupied. By increasing the electron density (Ns), the enhancement increases further. We also show that in case of a parabolic single quantum well structure large enhancement in mobility is obtained compared to that of square single quantum well structure as long as single subband is occupied, unlike the double quantum well systems. Our results of mobility in parabolic double quantum wells can be utilized for low temperature device applications.

  17. Parabolic dunes and their transformations under environmental and climatic changes: Towards a conceptual framework for understanding and prediction

    NASA Astrophysics Data System (ADS)

    Yan, Na; Baas, Andreas C. W.

    2015-01-01

    The formation and evolution of parabolic aeolian dunes depend on vegetation, and as such are particularly sensitive to changes in environmental controls (e.g., temperature, precipitation, and wind regime) as well as to human disturbances (e.g., grazing, agriculture, and recreation). Parabolic dunes can develop from the stabilisation of highly mobile barchan dunes and transverse dunes as well as from blowouts, as a consequence of colonisation and establishment of vegetation when aeolian sand transport is reduced and/or when water stress is relieved (by increasing precipitation, for instance). Conversely, existing parabolic dunes can be activated and may be transformed into barchan dunes and/or transverse dunes when vegetation suffers environmental or anthropogenic stresses. Predicted increases in temperature and drought severity in various regions raise concerns that dune activation and transformations may intensify, and this intensification would have far-reaching implications for environmental, social, and economic sustainability. To date, a broad examination of the development of parabolic dunes and their related transformations across a variety of climate gradients has been absent. This paper reviews existing literature, compares data on the morphology and development of parabolic dunes in a comprehensive global inventory, and scrutinises the mechanisms of different dune transformations and the eco-geomorphic interactions involved. This knowledge is then integrated into a conceptual framework to facilitate understanding and prediction of potential aeolian dune transformations induced by changes in environmental controls and human activities. This conceptual framework can aid judicious land management policies for better adaptations to climatic changes.

  18. Algebraic and numerical analysis of imaging properties of thin tunable-focus fluidic membrane lenses with parabolic surfaces.

    PubMed

    Miks, Antonin; Novak, Jiri; Novak, Pavel

    2013-04-01

    The theory of third-order aberrations for a system of rotationally symmetric thin tunable-focus fluidic membrane lenses with parabolic surfaces is described. A complex analysis of the third-order design of tunable fluidic lenses is performed considering all types of primary aberrations. Moreover, formulas are derived for the calculation of the change of aberration coefficients of the parabolic tunable fluidic membrane lens with respect to the wavelength. It is shown that spherical aberration of a simple tunable-focus fluidic membrane lens with parabolic surfaces can be corrected, which is not possible with a classical spherical lens. The presented analysis is explained on examples. Derived formulas make possible to calculate parameters of optical systems with fluidic membrane lenses with small residual aberrations. PMID:23545969

  19. Performance of light sources and radiation sensors under low gravity realized by parabolic airplane flights

    NASA Astrophysics Data System (ADS)

    Hirai, Hiroaki; Kitaya, Yoshiaki; Hirai, Takehiro

    A fundamental study was conducted to establish an experimental system for space farming. Since to ensure optimal light for plant cultivation in space is of grave importance, this study examined the performance of light sources and radiation sensors under microgravity conditions created during the parabolic airplane flight. Three kinds of light sources, a halogen bulb, a fluorescent tube, and blue and red LEDs, and ten models of radiation sensors available in the market were used for the experiment. Surface temperature of the light sources, output signals from the radiation sensors, spectroscopic characteristics were measured at the gravity levels of 0.01, 1.0 and 1.8 G for 20 seconds each during parabolic airplane flights. As a result, the performance of the halogen lamp was affected the most by the gravity level among the three light sources. Under the microgravity conditions which do not raise heat convection, the temperature of the halogen lamp rose and the output of the radiation sensors increased. Spectral distributions of the halogen lamp indicated that peak wavelength appeared the highest at the level of 0.01G, which contributed to the increase in light intensity. In the case of red and blue LEDs, which are promising light sources in space farming, the temperature of both LED chips rose but irradiance from red LED increased and that from blue LED decreased under microgravity conditions due to the different thermal characteristics.

  20. Responses of blind fish to gravitational changes as achieved in parabolic flight

    NASA Technical Reports Server (NTRS)

    Vonbaumgarten, R. J.; Shillinger, G. L., Jr.; Baldright, G.

    1972-01-01

    Blind fish, during parabolic flight, display a measurable and consistent behavior. The most spectacular new behavioral response is the forward looping of blind fish in or near weightlessness. This response shows no measurable adaptation during the entire period of weightlessness of about 30 sec. During the entrance and exit of weightless parabolas (pushover and pullout) respectively, the fish assumes a forward tilted diving position. Parabolic flight with negative g in the range between 0g and -1g causes similar diving responses of the fish with the only difference being that the dive is directed toward the top of the fish tank. When the response to a g value less than 1g is compared to the response to increased g load on the ground (escape of darting response) an essential difference is seen: higher horizontal acceleration or jerk on the ground causes fish to swim, or even dart, against the direction of inertial force; fish during weightless parabolas move into the direction of the inertial or gravitational force. Since the vestibular system of fish is homologous to that of man, the observed behavior of fish in weightless flight could help to better understand human performance and sensations in comparable situations.