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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. 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.

  4. 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

  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. 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

  13. 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

  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. 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.

  1. 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.

  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. 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

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  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. 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.

  8. 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.

  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. 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

  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. 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.

  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. 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.

  3. 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.

  4. 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

  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. 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

  18. 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.

  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. 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

  8. 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.

  9. 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.

  10. 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.

  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. 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.

  10. 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.

  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. 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.

  14. 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.

  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. 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.

  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. 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.

  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, 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.

  4. 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.

  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. 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.

  17. 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.

  18. 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.

  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. 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.

  3. 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.

  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. 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.

  6. 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.

  7. 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.

  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. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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

  5. 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.

  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. 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.

  8. 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.

  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. 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

  11. 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

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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

  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. 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.

  11. 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.

  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. 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).

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  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. 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.

  10. 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