NASA Astrophysics Data System (ADS)
Ji, Shanming; Yin, Jingxue; Cao, Yang
2016-11-01
In this paper, we consider the periodic problem for semilinear heat equation and pseudo-parabolic equation with logarithmic source. After establishing the existence of positive periodic solutions, we discuss the instability of such solutions.
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.
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.
Stability in terms of two measures for a class of semilinear impulsive parabolic equations
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.
NASA Astrophysics Data System (ADS)
Pan, Hongjing; Xing, Ruixiang
2008-03-01
In this paper, we derive blow-up rates for higher-order semilinear parabolic equations and systems. Our proof is by contradiction and uses a scaling argument. This procedure reduces the problems of blow-up rate to Fujita-type theorems. In addition, we also give some new Fujita-type theorems for higher-order semilinear parabolic equations and systems with the time variable on . These results are not restricted to positive solutions.
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.
Semilinear Kolmogorov Equations and Applications to Stochastic Optimal Control
Masiero, Federica
2005-03-15
Semilinear parabolic differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. Applications to stochastic optimal control problems are studied by solving the associated Hamilton-Jacobi-Bellman equation. These results are applied to some controlled stochastic partial differential equations.
The Hartman-Grobman theorem for semilinear hyperbolic evolution equations
NASA Astrophysics Data System (ADS)
Hein, Marie-Luise; Prüss, Jan
2016-10-01
The famous Hartman-Grobman theorem for ordinary differential equations is extended to abstract semilinear hyperbolic evolution equations in Banach spaces by means of simple direct proof. It is also shown that the linearising map is Hölder continuous. Several applications to abstract and specific damped wave equations are given, to demonstrate the strength of our results.
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.
Optimality Conditions for Semilinear Hyperbolic Equations with Controls in Coefficients
Li Bo; Lou Hongwei
2012-06-15
An optimal control problem for semilinear hyperbolic partial differential equations is considered. The control variable appears in coefficients. Necessary conditions for optimal controls are established by method of two-scale convergence and homogenized spike variation. Results for problems with state constraints are also stated.
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
Dynamics of parabolic equations via the finite element method I. Continuity of the set of equilibria
NASA Astrophysics Data System (ADS)
Figueroa-López, R. N.; Lozada-Cruz, G.
2016-11-01
In this paper we study the dynamics of parabolic semilinear differential equations with homogeneous Dirichlet boundary conditions via the discretization of finite element method. We provide an appropriate functional setting to treat this problem and, as a first step, we show the continuity of the set of equilibria and of its linear unstable manifolds.
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
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.
Long time existence for the semi-linear beam equation on irrational tori of dimension two
NASA Astrophysics Data System (ADS)
Imekraz, Rafik
2016-10-01
We prove a long time existence result for the semi-linear beam equation with small and smooth initial data. We use a regularizing effect of the structure of beam equations and a very weak separation property of the spectrum of an irrational torus under a Diophantine assumption on the radius. Our approach is inspired from a paper by Zhang about the Klein-Gordon equation with a quadratic potential.
Stepanova, Ekaterina V; Shishkov, Andrey E
2013-03-31
The propagation of supports of solutions of second-order quasilinear parabolic equations is studied; the equations are of the type of nonstationary diffusion, having semilinear absorption with an absorption potential which degenerates on the initial plane. We find sufficient conditions, which are sharp in a certain sense, on the relationship between the boundary regime and the type of degeneration of the potential to ensure the strong localization of solutions. We also establish a weak localization of solutions for an arbitrary potential which degenerates only on the initial plane. Bibliography: 12 titles.
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.
Group-invariant solutions of semilinear Schrödinger equations in multi-dimensions
NASA Astrophysics Data System (ADS)
Anco, Stephen C.; Feng, Wei
2013-12-01
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.
Group-invariant solutions of semilinear Schrödinger equations in multi-dimensions
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.
Elliptic and parabolic equations for measures
NASA Astrophysics Data System (ADS)
Bogachev, Vladimir I.; Krylov, Nikolai V.; Röckner, Michael
2009-12-01
This article gives a detailed account of recent investigations of weak elliptic and parabolic equations for measures with unbounded and possibly singular coefficients. The existence and differentiability of densities are studied, and lower and upper bounds for them are discussed. Semigroups associated with second-order elliptic operators acting in L^p-spaces with respect to infinitesimally invariant measures are investigated. Bibliography: 181 titles.
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.
Nonlinear collapse in the semilinear wave equation in AdS space
NASA Astrophysics Data System (ADS)
Liebling, Steven L.
2013-04-01
Previous studies of the semilinear wave equation in Minkowski space have shown a type of critical behavior in which large initial data collapse to singularity formation due to nonlinearities while small initial data does not. Numerical solutions in spherically symmetric anti-de Sitter space are presented here which suggest that, in contrast, even small initial data collapse eventually. Such behavior appears analogous to the recent result of Bizoń and Rostworowski [Phys. Rev. Lett. 107, 031102, 2011] that found that even weak, scalar initial data collapse gravitationally to black hole formation via a weakly turbulent instability. Furthermore, the imposition of a reflecting boundary condition in the bulk introduces a cutoff, below which initial data fails to collapse. This threshold appears to arise because of the dispersion introduced by the boundary condition.
Numerical Schemes for Rough Parabolic Equations
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.
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.
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)
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.
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.
Asymptotic analysis of a semilinear elliptic equation in highly oscillating thin domains
NASA Astrophysics Data System (ADS)
Pereira, Marcone Corrêa
2016-10-01
In this work we are interested in the asymptotic behavior of a family of solutions of a semilinear elliptic problem with homogeneous Neumann boundary condition defined in a two-dimensional bounded set which degenerates to the unit interval as a positive parameter {ɛ} goes to zero. Here we also allow that upper and lower boundaries from this singular region present highly oscillatory behavior with different orders and variable profile. Combining results from linear homogenization theory and nonlinear analyzes we get the limit problem showing upper and lower semicontinuity of the solutions at {ɛ=0}.
Propagation equation for tight-focusing by a parabolic mirror.
Couairon, A; Kosareva, O G; Panov, N A; Shipilo, D E; Andreeva, V A; Jukna, V; Nesa, F
2015-11-30
Part of the chain in petawatt laser systems may involve extreme focusing conditions for which nonparaxial and vectorial effects have high impact on the propagation of radiation. We investigate the possibility of using propagation equations to simulate numerically the focal spot under these conditions. We derive a unidirectional propagation equation for the Hertz vector, describing linear and nonlinear propagation under situations where nonparaxial diffraction and vectorial effects become significant. By comparing our simulations to the results of vector diffraction integrals in the case of linear tight-focusing by a parabolic mirror, we establish a practical criterion for the critical f -number below which initializing a propagation equation with a parabolic input phase becomes inaccurate. We propose a method to find suitable input conditions for propagation equations beyond this limit. Extreme focusing conditions are shown to be modeled accurately by means of numerical simulations of the unidirectional Hertz-vector propagation equation initialized with suitable input conditions.
Propagation equation for tight-focusing by a parabolic mirror.
Couairon, A; Kosareva, O G; Panov, N A; Shipilo, D E; Andreeva, V A; Jukna, V; Nesa, F
2015-11-30
Part of the chain in petawatt laser systems may involve extreme focusing conditions for which nonparaxial and vectorial effects have high impact on the propagation of radiation. We investigate the possibility of using propagation equations to simulate numerically the focal spot under these conditions. We derive a unidirectional propagation equation for the Hertz vector, describing linear and nonlinear propagation under situations where nonparaxial diffraction and vectorial effects become significant. By comparing our simulations to the results of vector diffraction integrals in the case of linear tight-focusing by a parabolic mirror, we establish a practical criterion for the critical f -number below which initializing a propagation equation with a parabolic input phase becomes inaccurate. We propose a method to find suitable input conditions for propagation equations beyond this limit. Extreme focusing conditions are shown to be modeled accurately by means of numerical simulations of the unidirectional Hertz-vector propagation equation initialized with suitable input conditions. PMID:26698752
Anisotropic uniqueness classes for a degenerate parabolic equation
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.
Quenching phenomena for fourth-order nonlinear parabolic equations
NASA Astrophysics Data System (ADS)
Yi, Niu; Xiaotong, Qiu; Runzhang, Xu
2012-09-01
In this paper, we investigate the quenching phenomena of the initial boundary value problem for the fourth-order nonlinear parabolic equation in bounded domain. By some assumptions on the exponents and initial data for a class of equations with the general source term, we not only obtain the quenching phenomena in finite time but also estimate the quenching time. Our main tools are maximum principle, comparison principle and eigenfunction method.
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.
Parabolic approximation method for the mode conversion-tunneling equation
Phillips, C.K.; Colestock, P.L.; Hwang, D.Q.; Swanson, D.G.
1987-07-01
The derivation of the wave equation which governs ICRF wave propagation, absorption, and mode conversion within the kinetic layer in tokamaks has been extended to include diffraction and focussing effects associated with the finite transverse dimensions of the incident wavefronts. The kinetic layer considered consists of a uniform density, uniform temperature slab model in which the equilibrium magnetic field is oriented in the z-direction and varies linearly in the x-direction. An equivalent dielectric tensor as well as a two-dimensional energy conservation equation are derived from the linearized Vlasov-Maxwell system of equations. The generalized form of the mode conversion-tunneling equation is then extracted from the Maxwell equations, using the parabolic approximation method in which transverse variations of the wave fields are assumed to be weak in comparison to the variations in the primary direction of propagation. Methods of solving the generalized wave equation are discussed. 16 refs.
Multiple positive solutions for semilinear Schrödinger equations with critical growth in ℝN
NASA Astrophysics Data System (ADS)
Wang, Jun; Lu, Dianchen; Xu, Junxiang; Zhang, Fubao
2015-04-01
In this paper, we study the existence, multiplicity, and concentration of positive solutions for the semilinear Schrödinger equation - ɛ 2 Δ u + K ( x ) u = Q ( x ) |u| p - 2 u + f ( u ) , u ∈ H 1 ( R N ) , where ɛ > 0 is a small parameter, N ≥ 3 and 2 < p < 2 ∗ = /2 N N - 2 , K and Q are positive continuous functions, f is a continuous superlinear nonlinearity with critical growth. First of all, we prove that there are two families of semiclassical positive solutions for ɛ > 0 small, one is concentrating on the set of minimal points of K, another is concentrating on the sets of maximal points of Q. Second of all, we investigate the relation between the number of solutions and the topology of the set of the global minima (or maxima) of the potentials (K and Q) by the Ljusternik-Schnirelmann and theory minimax theorems. Finally, we obtain some sufficient conditions for the nonexistence of positive ground state solution.
Optimal Control of a Parabolic Equation with Dynamic Boundary Condition
Hoemberg, D. Krumbiegel, K.; Rehberg, J.
2013-02-15
We investigate a control problem for the heat equation. The goal is to find an optimal heat transfer coefficient in the dynamic boundary condition such that a desired temperature distribution at the boundary is adhered. To this end we consider a function space setting in which the heat flux across the boundary is forced to be an L{sup p} function with respect to the surface measure, which in turn implies higher regularity for the time derivative of temperature. We show that the corresponding elliptic operator generates a strongly continuous semigroup of contractions and apply the concept of maximal parabolic regularity. This allows to show the existence of an optimal control and the derivation of necessary and sufficient optimality conditions.
Asymptotic behavior on a kind of parabolic Monge-Ampère equation
NASA Astrophysics Data System (ADS)
Wang, Bo; Bao, Jiguang
2015-07-01
In this paper, we apply level set and nonlinear perturbation methods to obtain the asymptotic behavior of the solution to a kind of parabolic Monge-Ampère equation at infinity. The Jörgens-Calabi-Pogorelov theorem for parabolic and elliptic Monge-Ampère equation can be regarded as special cases of our result.
Stabilization of semilinear heat equations, with fading memory, by boundary feedbacks
NASA Astrophysics Data System (ADS)
Munteanu, Ionuţ
2015-07-01
In this paper, we design stabilizing Dirichlet boundary feedback laws for heat equations with fading memory. The linear finite-dimensional controllers are easily manageable from the computational point of view, because of their simple feedback form, involving only the first N ∈ N eigenfunctions of the Laplace operator. Two examples are provided at the end of the paper, in order to illustrate the acquired results.
Nonlocal operators, parabolic-type equations, and ultrametric random walks
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.
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.
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.
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.
Lateral boundary differentiability of solutions of parabolic equations in nondivergence form
NASA Astrophysics Data System (ADS)
Huang, Yongpan; Li, Dongsheng; Wang, Lihe
The lateral boundary differentiability is shown for solutions of parabolic differential equations in nondivergence form under the assumptions that the parabolic boundary satisfies the exterior Dini condition and is punctually C1 differentiable one-sided in t-direction. The classical barrier technique, the maximum principle, the interior Harnack inequality and an iteration procedure are the main analytical tools.
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).
Three-dimensional parabolic equation modeling of mesoscale eddy deflection.
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.
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.
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).
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.
NASA Astrophysics Data System (ADS)
Budd, C. J.; Humphries, A. R.
2003-02-01
We use a variety of careful numerical and semi-analytical methods to investigate two outstanding conjectures on the solutions of the parametrised semi-linear elliptic equation [Delta]u+[lambda]u+u5=0, u>0, where u is defined to be zero on the boundary of a three dimensional domain. This equation is important in analysis and in studies of combustion and polytropic gases. It is known that there is a value [lambda]0>0 such that no solutions exist for [lambda]<[lambda]0. McLeod and Schoen, and Bandle and Flucher have given different estimates for [lambda]0; both of which have been conjectured to be exact. We perform a semi-analytic study of solutions on cylindrical domains and construct numerical approximations on cuboid domains using the finite element method combined with a careful post-processing step to reduce the otherwise significant errors. We compute these estimates for cylindrical and cuboid domains, and show that on these domains the estimates do not agree. We conclude that the conjecture of Bandle and Flucher is false. Our numerical computations on cuboid domains are consistent with McLeod's conjecture being true.
A method for the spatial discretization of parabolic equations in one space variable
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.
Two parabolic equations for propagation in layered poro-elastic media.
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.
Numerical solution of the stochastic parabolic equation with the dependent operator coefficient
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.
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.
Solution blow-up for a class of parabolic equations with double nonlinearity
Korpusov, Maxim O
2013-03-31
We consider a class of parabolic-type equations with double nonlinearity and derive sufficient conditions for finite time blow-up of its solutions in a bounded domain under the homogeneous Dirichlet condition. To prove the solution blow-up we use a modification of Levine's method. Bibliography: 13 titles.
Solution blow-up for a class of parabolic equations with double nonlinearity
NASA Astrophysics Data System (ADS)
Korpusov, Maxim O.
2013-03-01
We consider a class of parabolic-type equations with double nonlinearity and derive sufficient conditions for finite time blow-up of its solutions in a bounded domain under the homogeneous Dirichlet condition. To prove the solution blow-up we use a modification of Levine's method. Bibliography: 13 titles.
The asymptotics of a solution of a parabolic equation as time increases without bound
Degtyarev, Denis O; Il'in, Arlen M
2012-11-30
A boundary-value problem for a second order parabolic equation on a half-line is considered. A uniform asymptotic approximation to a solution to within any power of t{sup -1} is constructed and substantiated. Bibliography: 8 titles.
Quenching phenomena for second-order nonlinear parabolic equation with nonlinear source
NASA Astrophysics Data System (ADS)
Mingyou, Zhang; Huichao, Xu; Runzhang, Xu
2012-09-01
In this paper, we investigate the quenching phenomena of the Cauchy problem for the second-order nonlinear parabolic equation on unbounded domain. It is shown that the solution quenches in finite time under some assumptions on the exponents and the initial data. Our main tools are comparison principle and maximum principle. We extend the result to the case of more generally nonlinear absorption.
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.
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.
On some general properties of parabolic conservation equations
Dresner, L.
1993-10-01
This report deals with certain general properties of partial differential equations of the form S(c)c{sub t} + q{sub z} = Q(c), where t may thought of as time, z as distance, c as an intensive quantity (e.g., temperature), and q its flux (e.g., heat flux), and where q depends on both c and c{sub z}. Six topics are studied, namely: Maximum and minimum principles; ordering of solutions; invariance to stretching (affine) groups; stability of steady states; comparability of solutions; and traveling wave solutions. Illustrative examples are given from the field of nonlinear diffusion, applied superconductivity, and helium cryogenics.
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.
Solutions to higher-order anisotropic parabolic equations in unbounded domains
Kozhevnikova, L M; Leont'ev, A A
2014-01-31
The paper is devoted to a certain class of doubly nonlinear higher-order anisotropic parabolic equations. Using Galerkin approximations it is proved that the first mixed problem with homogeneous Dirichlet boundary condition has a strong solution in the cylinder D=(0,∞)×Ω, where Ω⊂R{sup n}, n≥3, is an unbounded domain. When the initial function has compact support the highest possible rate of decay of this solution as t→∞ is found. An upper estimate characterizing the decay of the solution is established, which is close to the lower estimate if the domain is sufficiently 'narrow'. The same authors have previously obtained results of this type for second order anisotropic parabolic equations. Bibliography: 29 titles.
Treatment of ice cover and other thin elastic layers with the parabolic equation method.
Collins, Michael D
2015-03-01
The parabolic equation method is extended to handle problems involving ice cover and other thin elastic layers. Parabolic equation solutions are based on rational approximations that are designed using accuracy constraints to ensure that the propagating modes are handled properly and stability constrains to ensure that the non-propagating modes are annihilated. The non-propagating modes are especially problematic for problems involving thin elastic layers. It is demonstrated that stable results may be obtained for such problems by using rotated rational approximations [Milinazzo, Zala, and Brooke, J. Acoust. Soc. Am. 101, 760-766 (1997)] and generalizations of these approximations. The approach is applied to problems involving ice cover with variable thickness and sediment layers that taper to zero thickness.
Time regularity and long-time behavior of parabolic p-Laplace equations on infinite graphs
NASA Astrophysics Data System (ADS)
Hua, Bobo; Mugnolo, Delio
2015-12-01
We consider the so-called discrete p-Laplacian, a nonlinear difference operator that acts on functions defined on the nodes of a possibly infinite graph. We study the corresponding Cauchy problem and identify the generator of the associated nonlinear semigroups. We prove higher order time regularity of the solutions. We investigate the long-time behavior of the solutions and discuss in particular finite extinction time and conservation of mass. Namely, on one hand, for small p if an infinite graph satisfies some isoperimetric inequality, then the solution to the parabolic p-Laplace equation vanishes in finite time; on the other hand, for large p, these parabolic p-Laplace equations always enjoy conservation of mass.
A higher-order tangent linear parabolic-equation solution of three-dimensional sound propagation.
Lin, Ying-Tsong
2013-08-01
A higher-order square-root operator splitting algorithm is employed to derive a tangent linear solution for the three-dimensional parabolic wave equation due to small variations of the sound speed in the medium. The solution shown in this paper unifies other solutions obtained from less accurate approximations. Examples of three-dimensional acoustic ducts are presented to demonstrate the accuracy of the solution. Future work on the applications of associated adjoint models for acoustic inversions is proposed and discussed.
Obstacle problem for a class of parabolic equations of generalized p-Laplacian type
NASA Astrophysics Data System (ADS)
Lindfors, Casimir
2016-11-01
We study nonlinear parabolic PDEs with Orlicz-type growth conditions. The main result gives the existence of a unique solution to the obstacle problem related to these equations. To achieve this we show the boundedness of weak solutions and that a uniformly bounded sequence of weak supersolutions converges to a weak supersolution. Moreover, we prove that if the obstacle is continuous, so is the solution.
Parakkal, Santosh; Gilbert, Kenneth E; Di, Xiao
2012-02-01
The Beilis-Tappert (1979) parabolic equation method is attractive for irregular terrain because it treats surface variations in terms of a simple multiplicative factor ("phase screen"). However, implementing the exact sloping-surface impedance condition is problematic if one wants the computational efficiency of a Fourier parabolic equation algorithm. This article investigates an approximate flat-ground impedance condition that allows the Beilis-Tappert phase screen method to be used with a Fourier algorithm without any added complications. The exact sloping-surface impedance condition is derived and applied to propagation predictions over hills with maximum slopes from 5° to 22°. The predictions with the exact impedance condition are compared to predictions using the approximate flat-ground impedance condition. It is found that for slopes less than 15°-20°, the flat-ground impedance condition is sufficiently accurate. For slopes greater than approximately 20°, the limiting factor on numerical accuracy is not the flat-ground impedance approximation, but rather the narrow-angle approximation required by the Beilis-Tappert method. Thus, within the 20° limitation and using the flat-ground impedance condition with a Fourier parabolic equation, sound propagation over irregular terrain can be computed simply, efficiently, and accurately.
Dong Hongjie Krylov, Nicolai V.
2007-06-15
We consider degenerate parabolic and elliptic fully nonlinear Bellman equations with Lipschitz coefficients in domains. Error bounds of order h{sup 1/2} in the sup norm for certain types of finite-difference schemes are obtained.
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.
Alkhutov, Yu A; Zhikov, V V
2014-03-31
The paper is concerned with the solvability of the initial-boundary value problem for second-order parabolic equations with variable nonlinearity exponents. In the model case, this equation contains the p-Laplacian with a variable exponent p(x,t). The problem is shown to be uniquely solvable, provided the exponent p is bounded away from both 1 and ∞ and is log-Hölder continuous, and its solution satisfies the energy equality. Bibliography: 18 titles.
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.
Efficient parallel solution of parabolic equations - Implicit methods on the Cedar multicluster
NASA Technical Reports Server (NTRS)
Gallopoulos, E.; Saad, Y.
1990-01-01
A class of implicit methods for the parallel solution of linear parabolic differential equations based on Pade and Chebyshev rational approximations to the matrix exponential are presented. It is pointed out that this approach incorporates both natural hierarchical parallelism, improved intrinsic efficiency, and fewer timesteps. These advantages lead to an extremely fast family of methods for the solution of certain time-dependent problems. These techniques are illustrated with numerical experiments on the University of Illinois Cedar multicluster architecture. The experiments indicate that implicit methods of very high degree offer great promise for the solution of certain parabolic problems when in computational environment with parallel resources. Hierarchically organized parallel computers, such as the Cedar multicluster, are found to be especially attractive for these schemes.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Ali, Z. I.; Sango, M.
2016-07-01
In this paper, we investigate a class of stochastic quasilinear parabolic initial boundary value problems with nonstandard growth in the functional setting of generalized Sobolev spaces. The deterministic version of the equation was first introduced and studied by Samokhin in [45] as a generalized model for polytropic filtration. We establish an existence result of weak probabilistic solutions when the forcing terms do not satisfy Lipschitz conditions. Under the Lipschitz property of the forcing terms, we obtain the uniqueness of weak probabilistic solutions. Combining the uniqueness and the famous Yamada-Watanabe result, we prove the existence of a unique strong probabilistic solution of the problem.
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.
Gilbert, Kenneth E
2015-01-01
The original formulation of the Green's function parabolic equation (GFPE) can have numerical accuracy problems for large normalized surface impedances. To solve the accuracy problem, an improved form of the GFPE has been developed. The improved GFPE formulation is similar to the original formulation, but it has the surface-wave pole "subtracted." The improved GFPE is shown to be accurate for surface impedances varying over 2 orders of magnitude, with the largest having a magnitude exceeding 1000. Also, the improved formulation is slightly faster than the original formulation because the surface-wave component does not have to be computed separately.
ON THE PIECEWISE PARABOLIC METHOD FOR COMPRESSIBLE FLOW WITH STELLAR EQUATIONS OF STATE
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.
A higher-order split-step Fourier parabolic-equation sound propagation solution scheme.
Lin, Ying-Tsong; Duda, Timothy F
2012-08-01
A three-dimensional Cartesian parabolic-equation model with a higher-order approximation to the square-root Helmholtz operator is presented for simulating underwater sound propagation in ocean waveguides. The higher-order approximation includes cross terms with the free-space square-root Helmholtz operator and the medium phase speed anomaly. It can be implemented with a split-step Fourier algorithm to solve for sound pressure in the model. Two idealized ocean waveguide examples are presented to demonstrate the performance of this numerical technique.
Stabilization of the solution of a doubly nonlinear parabolic equation
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.
Parabolic equation modeling of high frequency acoustic transmission with an evolving sea surface.
Senne, J; Song, A; Badiey, M; Smith, K B
2012-09-01
The present paper examines the temporal evolution of acoustic fields by modeling forward propagation subject to sea surface dynamics with time scales of less than a second to tens of seconds. A time-evolving rough sea surface model is combined with a rough surface formulation of a parabolic equation model for predicting time-varying acoustic fields. Surface waves are generated from surface wave spectra, and stepped in time using a Runge-Kutta integration technique applied to linear evolution equations. This evolving, range-dependent surface information is combined with other environmental parameters and input to the acoustic model, giving an approximation of the time-varying acoustic field. The wide-angle parabolic equation model manages the rough sea surfaces by molding them into the boundary conditions for calculations of the near-surface acoustic field. This merged acoustic model is validated using concurrently-collected acoustic and environmental information, including surface wave spectra. Data to model comparisons demonstrate that the model is able to approximate the ensemble-averaged acoustic intensity at ranges of about a kilometer for acoustic signals of around 15 kHz. Furthermore, the model is shown to capture variations due to surface fluctuations occurring over time scales of less than a second to tens of seconds.
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.
The behavior of hyperbolic heat equations' solutions near their parabolic limits
NASA Astrophysics Data System (ADS)
Nagy, Gabriel B.; Ortiz, Omar E.; Reula, Oscar A.
1994-08-01
Standard energy methods are used to study the relation between the solutions of one parameter families of hyperbolic systems of equations describing heat propagation near their parabolic limits, which for these cases are the usual diffusive heat equation. In the linear case it is proven that given any solution to the hyperbolic equations there is always a solution to the diffusion equation which after a short time stays very close to it for all times. The separation between these solutions depends on the square of the ratio between the assumed very short decay time appearing in Cattaneo's relation and the usual characteristic smoothing time (initial data dependent) of the limiting diffusive equation. The techniques used in the linear case can be readily used for nonlinear equations. As an example we consider the theories of heat propagation introduced by Coleman, Fabrizio, and Owen, and prove that near a solution to the limiting diffusive equation there is always a solution to the nonlinear hyperbolic equations for a time which usually is much longer than the decay time of the corresponding Cattaneo relation. An alternative derivation of the heat theories of divergence type, which are consistent with thermodynamic principles, is given as an appendix.
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
Elastic parabolic equation solutions for underwater acoustic problems using seismic sources.
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
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.
Elastic parabolic equation solutions for underwater acoustic problems using seismic sources.
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.
The numerical solution of the boundary inverse problem for a parabolic equation
NASA Astrophysics Data System (ADS)
Vasil'ev, V. V.; Vasilyeva, M. V.; Kardashevsky, A. M.
2016-10-01
Boundary inverse problems occupy an important place among the inverse problems of mathematical physics. They are connected with the problems of diagnosis, when additional measurements on one of the borders or inside the computational domain are necessary to restore the boundary regime in the other border, inaccessible to direct measurements. The boundary inverse problems belong to a class of conditionally correct problems, and therefore, their numerical solution requires the development of special computational algorithms. The paper deals with the solution of the boundary inverse problem for one-dimensional second-order parabolic equations, consisting in the restoration of boundary regime according to measurements inside the computational domain. For the numerical solution of the inverse problem it is proposed to use an analogue of a computational algorithm, proposed and developed to meet the challenges of identification of the right side of the parabolic equations in the works P.N.Vabishchevich and his students based on a special decomposition of solving the problem at each temporal layer. We present and discuss the results of a computational experiment conducted on model problems with quasi-solutions, including with random errors in the input data.
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.
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.
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
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.
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.
Simultaneous determination of time and space-dependent coefficients in a parabolic equation
NASA Astrophysics Data System (ADS)
Hussein, M. S.; Lesnic, D.
2016-04-01
This paper investigates a couple of inverse problems of simultaneously determining time and space dependent coefficients in the parabolic heat equation using initial and boundary conditions of the direct problem and overdetermination conditions. The measurement data represented by these overdetermination conditions ensure that these inverse problems have unique solutions. However, the problems are still ill-posed since small errors in the input data cause large errors in the output solution. To overcome this instability we employ the Tikhonov regularization method. The finite-difference method (FDM) is employed as a direct solver which is fed iteratively in a nonlinear minimization routine. Both exact and noisy data are inverted. Numerical results for a few benchmark test examples are presented, discussed and assessed with respect to the FDM mesh size discretization, the level of noise with which the input data is contaminated, and the chosen regularization parameters.
Limiting Motion for the Parabolic Ginzburg-Landau Equation with Infinite Energy Data
NASA Astrophysics Data System (ADS)
Côte, Delphine; Côte, Raphaël
2016-08-01
We study a class of solutions to the parabolic Ginzburg-Landau equation in dimension 2 or higher, with ill-prepared infinite energy initial data. We show that, asymptotically, the vorticity evolves according to motion by mean curvature in Brakke's weak formulation. Then, we prove that in the plane, point vortices do not move in the original time scale. These results extend the works of Bethuel, Orlandi and Smets (Ann Math (2) 163(1):37-163, 2006; Duke Math J 130(3):523-614, 2005) to infinite energy data; they allow us to consider point vortices on a lattice (in dimension 2), or filament vortices of infinite length (in dimension 3).
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.
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.
ON BOUNDARY AND INITIAL CONDITIONS IN \\mathscr{L}_p, p>1, OF SOLUTIONS OF PARABOLIC EQUATIONS
NASA Astrophysics Data System (ADS)
Petrushko, I. M.
1986-02-01
Necessary and sufficient conditions on the solutions of parabolic equations in a cylinder are established for the existence of limits in \\mathscr{L}_p on the lateral surface of the cylinder and in \\mathscr{L}_p with a weight on its lower base.Bibliography: 9 titles.
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.
Eigenfunction approach to the Green's function parabolic equation in outdoor sound: A tutorial.
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.
Eigenfunction approach to the Green's function parabolic equation in outdoor sound: A tutorial.
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
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.
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.
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.
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)}.
On a problem of the Frankl type for an equation of the mixed parabolic-hyperbolic type
NASA Astrophysics Data System (ADS)
Kalmenov, Tynysbek Sh.; Sadybekov, Makhmud
2016-08-01
In the paper a new non-local boundary value problem for an equation of the parabolic-hyperbolic type is formulated. This equation is of the first kind, that is, the line of type change is not a characteristic of the equation. The suggested new nonlocal condition binds points on boundaries of the parabolic and hyperbolic parts of the domain with each other. This problem is generalization of the well-known problems of Frankl type. Unlike the existing publications of the other authors related to the theme, in the suggested formulation of the problem the hyperbolic part of the domain coincides with a characteristic triangle. Unique solvability of the formulated problem is proved in the sense of classical and strong solutions.
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.
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
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.
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.
Prediction of far-field wind turbine noise propagation with parabolic equation.
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.
Leading-order cross term correction of three-dimensional parabolic equation models.
Sturm, Frédéric
2016-01-01
The issue of handling a leading-order cross-multiplied term in three-dimensional (3D) parabolic equation (PE) based models is addressed. In particular, numerical results obtained incorporating a leading-order cross-term correction in an existing 3D PE model, written in cylindrical coordinates, based on higher-order Padé approximations in both depth and azimuth, and a splitting operator technique are reported. Note that the numerical algorithm proposed in this paper could be used in the future to update any 3D PE codes that neglect cross terms and use a splitting numerical technique. The 3D penetrable wedge benchmark problem is chosen to illustrate the accuracy of the now-fully wide-angle enhanced 3D PE model. The comparisons with a 3D reference solution based on the image source clearly show that handling the leading-order cross term in the 3D PE computation is sufficient to remove the phase errors inherent to any 3D PE models that neglect cross terms in their formulations.
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.
Prediction of far-field wind turbine noise propagation with parabolic equation.
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
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.
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.
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.
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.
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.
Simulation of large turbulent structures with the parabolic Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Rakich, J. V.; Davis, R. T.; Barnett, M.
1982-01-01
The theoretical basis for well posed marching of a Parabolic Navier-Stokes (PNS) computational technique for supersonic flow is discussed and examples given to verify the analysis. It is demonstrated that stable computations can be made even with very small steps in the marching direction. The method is applied to cones at large angle of attack in high Reynolds number, supersonic flow. Streamline trajectories generated from the numerical solutions demonstrate the development of vortex structures on the lee side of the cone.
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
Sturm, Frédéric; Korakas, Alexios
2013-01-01
In this paper, laboratory scale measurements of long range across-slope acoustic propagation in a three-dimensional (3-D) wedge-like environment are compared to numerical solutions. In a previous work, it was shown that the experimental data contain strong 3-D effects like mode shadow zones and multiple mode arrivals, in qualitative agreement with theoretical and numerical predictions. In the present work, the experimental data are compared with numerical solutions obtained using a fully 3-D parabolic equation based model. A subspace inversion approach is used for the refinement of some of the parameters describing the model experiment. The inversion procedure is implemented in a Bayesian framework based on the exhaustive search over the parameter space. The comparisons are performed both in the time and in the frequency domain using the maximum a posteriori estimates of the refined parameters as input in the 3-D model. A very good quantitative agreement is achieved between the numerical predictions provided by the 3-D parabolic equation model and the experimental data.
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.
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.
Lin, Ying-Tsong; Collis, Jon M; Duda, Timothy F
2012-11-01
An alternating direction implicit (ADI) three-dimensional fluid parabolic equation solution method with enhanced accuracy is presented. The method uses a square-root Helmholtz operator splitting algorithm that retains cross-multiplied operator terms that have been previously neglected. With these higher-order cross terms, the valid angular range of the parabolic equation solution is improved. The method is tested for accuracy against an image solution in an idealized wedge problem. Computational efficiency improvements resulting from the ADI discretization are also discussed.
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
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.
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
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.
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.
A Pseubo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Morrison, J. H.; White, J. A.
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.
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.
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...
Malcolm, A E; Reitich, F; Yang, J; Greenleaf, J F; Fatemi, M
2008-11-01
This paper aims to model ultrasound vibro-acoustography to improve our understanding of the underlying physics of the technique thus facilitating the collection of better images. Ultrasound vibro-acoustography is a novel imaging technique combining the resolution of high-frequency imaging with the clean (speckle-free) images obtained with lower frequency techniques. The challenge in modeling such an experiment is in the variety of scales important to the final image. In contrast to other approaches for modeling such problems, we break the experiment into three parts: high-frequency propagation, non-linear interaction and the propagation of the low-frequency acoustic emission. We then apply different modeling strategies to each part. For the high-frequency propagation we choose a parabolic approximation as the field has a strong preferred direction and small propagation angles. The non-linear interaction is calculated directly with Fourier methods for computing derivatives. Because of the low-frequency omnidirectional nature of the acoustic emission field and the piecewise constant medium we model the low-frequency field with a surface integral approach. We use our model to compare with experimental data and to visualize the relevant fields at points in the experiment where laboratory data is difficult to collect, in particular the source of the low-frequency field. To simulate experimental conditions we perform the simulations with the two frequencies 3 and 3.05 MHz with an inclusion of varying velocity submerged in water.
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.
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.
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.
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 delta-correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The comprehensive operator solution also allows one to obtain expressions for the longitudinal (generalized) second order moment. This is also considered and the solution for the atmospheric case is obtained and discussed. 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.
Miles, David A; Hewitt, Robin N; Donnelly, Marcus K; Clarke, Timothy
2003-09-01
A variable depth step implementation of the range-dependent acoustic model (RAM) is applied to the modeling of forward scattering from a rough sea surface. The sea surface is treated within RAM simply as an internal interface between a water layer and an air upper halfspace. A comparison with a numerically exact integral equation is undertaken for the scattering of single frequencies from Pierson-Moskowitz sea surfaces. The method is extended to model the variability of linear frequency modulated pulses from a series of frozen sea surfaces in a shallow water waveguide. The subsequent effect of rough boundary scattering on the replica correlation process is investigated. PMID:14514180
Spectral methods in time for a class of parabolic partial differential equations
Ierley, G. ); Spencer, B. ); Worthing, R. )
1992-09-01
In this paper, we introduce a fully spectral solution for the partial differential equation u[sub t] + uu[sub x] + vu[sub xx] + [mu]u[sub xxx] + [lambda]u[sub xxxx] = O. For periodic boundary conditions in space, the use of a Fourier expansion in x admits of a particularly efficient algorithm with respect to expansion of the time dependence in a Chebyshev series. Boundary conditions other than periodic may still be treated with reasonable, though lesser, efficiency. for all cases, very high accuracy is attainable at moderate computational cost relative to the expense of variable order finite difference methods in time. 14 refs., 9 figs.
Domínguez, Jorge Bouza; Bérubé-Lauzière, Yves
2011-01-01
We introduce a system of coupled time-dependent parabolic simplified spherical harmonic equations to model the propagation of both excitation and fluorescence light in biological tissues. We resort to a finite element approach to obtain the time-dependent profile of the excitation and the fluorescence light fields in the medium. We present results for cases involving two geometries in three-dimensions: a homogeneous cylinder with an embedded fluorescent inclusion and a realistically-shaped rodent with an embedded inclusion alike an organ filled with a fluorescent probe. For the cylindrical geometry, we show the differences in the time-dependent fluorescence response for a point-like, a spherical, and a spherically Gaussian distributed fluorescent inclusion. From our results, we conclude that the model is able to describe the time-dependent excitation and fluorescent light transfer in small geometries with high absorption coefficients and in nondiffusive domains, as may be found in small animal diffuse optical tomography (DOT) and fluorescence DOT imaging. PMID:21483606
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.
Kostin, A B
2013-10-31
We study the inverse problem for a parabolic equation of recovering the source, that is, the right-hand side F(x,t)=h(x,t)f(x), where the function f(x) is unknown. To find f(x), along with the initial and boundary conditions, we also introduce an additional condition of nonlocal observation of the form ∫{sub 0}{sup T}u(x,t) dμ(t)=χ(x). We prove the Fredholm property for the problem stated in this way, and obtain sufficient conditions for the existence and uniqueness of a solution. These conditions are of the form of readily verifiable inequalities and put no restrictions on the value of T>0 or the diameter of the domain Ω under consideration. The proof uses a priori estimates and the qualitative properties of solutions of initial-boundary value problems for parabolic equations. Bibliography: 40 titles.
Numerical study of a parametric parabolic equation and a related inverse boundary value problem
NASA Astrophysics Data System (ADS)
Mustonen, Lauri
2016-10-01
We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the nonhomogeneous diffusion coefficient in the interior of an object. The method in this paper relies on solving the forward problem for a whole family of diffusivities by using a spectral Galerkin method in the high-dimensional parameter domain. The evaluation of the parametric solution and its derivatives is then completely independent of spatial and temporal discretizations. In the case of a quadratic approximation for the parameter dependence and a direct solver for linear least squares problems, we show that the evaluation of the parametric solution does not increase the complexity of any linearized subproblem arising from a Gauss-Newtonian method that is used to minimize a Tikhonov functional. The feasibility of the proposed algorithm is demonstrated by diffusivity reconstructions in two and three spatial dimensions.
Trajectory controllability of semilinear systems with multiple variable delays in control
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.
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.
Apushkinskaya, D.E.; Nazarov, A.I.
1995-12-05
A linear parabolic equation with special singularities is studied. A priori boundary estimates are established for the maximum of the modulus of the gradient of a solution and for the Holder constants as well. These estimates depend linearly on the functions appearing on the right-hand side of the equation.
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.
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.
Poisson problems for semilinear Brinkman systems on Lipschitz domains in
NASA Astrophysics Data System (ADS)
Kohr, Mirela; Lanza de Cristoforis, Massimo; Wendland, Wolfgang L.
2015-06-01
The purpose of this paper is to combine a layer potential analysis with the Schauder fixed point theorem to show the existence of solutions of the Poisson problem for a semilinear Brinkman system on bounded Lipschitz domains in with Dirichlet or Robin boundary conditions and data in L 2-based Sobolev spaces. We also obtain an existence and uniqueness result for the Dirichlet problem for a special semilinear elliptic system, called the Darcy-Forchheimer-Brinkman system.
Scalable implicit methods for reaction-diffusion equations in two and three space dimensions
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.
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.
A new global Carleman estimate for Cahn-Hilliard type equation and its applications
NASA Astrophysics Data System (ADS)
Gao, Peng
2016-01-01
We establish a new Carleman inequality for linear Cahn-Hilliard type equation when the norms of right hand sides are in Sobolev spaces of negative orders, and apply it to obtain the Unique Continuation Property (UCP) for Cahn-Hilliard type equation with the coefficients of terms of lower order that are not regular and null controllability for semilinear Cahn-Hilliard type equation whose semilinear term contains derivatives of first and second order of solutions.
Gao, Nan; Xie, Changqing
2014-06-15
We generalize the concept of diffraction free beams to parabolic scaling beams (PSBs), whose normalized intensity scales parabolically during propagation. These beams are nondiffracting in the circular parabolic coordinate systems, and all the diffraction free beams of Durnin's type have counterparts as PSBs. Parabolic scaling Bessel beams with Gaussian apodization are investigated in detail, their nonparaxial extrapolations are derived, and experimental results agree well with theoretical predictions.
Focusing the parabolic antenna
NASA Technical Reports Server (NTRS)
Wu, L. K.; Moore, R. K.; Ulaby, F. T.
1983-01-01
The focused parabolic antenna has far field pattern characteristics in the radiating near field region. Therefore, it can provide fine resolutions in the across range dimensions. The technique of focusing the parabolic antenna is discussed and applied to a 2-1/2 foot parabolic antenna at X-band. The results of the pattern measurements at various ranges from 2.8 m to 5 m are provided.
Controllable parabolic-cylinder optical rogue wave.
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.
Measurement of Liquid Viscosities in Tapered or Parabolic Capillaries.
Ershov; Zorin; Starov
1999-08-01
The possibility of using tapered or parabolic capillaries for measurement of liquid viscosities is investigated both experimentally and theoretically. It is demonstrated that even small deviations in capillary radius from a constant value may substantially affect measurement results. Equations are derived which allow correct analysis of the measurement results in tapered or parabolic capillaries. The following cases are analyzed: a water imbibition into a tapered or parabolic capillary and displacement of one liquid by another immiscible liquid in tapered or parabolic capillaries. Two possibilities are considered: (a) the narrow end of the capillary as capillary inlet and (b) the wide end of the capillary as capillary inlet. Copyright 1999 Academic Press.
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.
Parabolic curves in Lie groups
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.
Three-dimensional nonparaxial beams in parabolic rotational coordinates.
Deng, Dongmei; Gao, Yuanmei; Zhao, Juanying; Zhang, Peng; Chen, Zhigang
2013-10-01
We introduce a class of three-dimensional nonparaxial optical beams found in a parabolic rotational coordinate system. These beams, representing exact solutions of the nonparaxial Helmholtz equation, have inherent parabolic symmetries. Assisted with a computer-generated holography, we experimentally demonstrate the generation of different modes of these beams. The observed transverse beam patterns along the propagation direction agree well with those from our theoretical predication.
Spaces of initial data for differential equations in a Hilbert space
Shamin, R V
2003-10-31
Spaces of initial data for differential equations in a Hilbert space are considered. Necessary and sufficient conditions for the strong solubility of parabolic differential-difference equations and parabolic functional differential equations with dilated and contracted variables are obtained.
NASA Astrophysics Data System (ADS)
Shubina, Maria
2016-09-01
In this paper, we investigate the one-dimensional parabolic-parabolic Patlak-Keller-Segel model of chemotaxis. For the case when the diffusion coefficient of chemical substance is equal to two, in terms of travelling wave variables the reduced system appears integrable and allows the analytical solution. We obtain the exact soliton solutions, one of which is exactly the one-soliton solution of the Korteweg-de Vries equation.
Masiero, Federica
2007-05-15
Semilinear elliptic partial differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. These results are applied to a stochastic optimal control problem with infinite horizon. Applications to controlled stochastic heat and wave equations are given.
Session: Parabolic Troughs (Presentation)
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.
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.
For Which X-Values Does a Least-Squares Parabolic Fit Exist?
ERIC Educational Resources Information Center
Farnsworth, David L.
2005-01-01
The normal equations discussed in this paper for a least-squares parabolic fit have a unique solution if and only if there are at least three different x-values in the observations. This requirement is satisfied by most real sets of quantitative observations. For particular data sets, the appropriateness of parabolic fits should be assessed with…
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].
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.
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.
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.
The planar parabolic optical antenna.
Schoen, David T; Coenen, Toon; García de Abajo, F Javier; Brongersma, Mark L; Polman, Albert
2013-01-01
One of the simplest and most common structures used for directing light in macroscale applications is the parabolic reflector. Parabolic reflectors are ubiquitous in many technologies, from satellite dishes to hand-held flashlights. Today, there is a growing interest in the use of ultracompact metallic structures for manipulating light on the wavelength scale. Significant progress has been made in scaling radiowave antennas to the nanoscale for operation in the visible range, but similar scaling of parabolic reflectors employing ray-optics concepts has not yet been accomplished because of the difficulty in fabricating nanoscale three-dimensional surfaces. Here, we demonstrate that plasmon physics can be employed to realize a resonant elliptical cavity functioning as an essentially planar nanometallic structure that serves as a broadband unidirectional parabolic antenna at optical frequencies.
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.
Parabolic metamaterials and Dirac bridges
NASA Astrophysics Data System (ADS)
Colquitt, D. J.; Movchan, N. V.; Movchan, A. B.
2016-10-01
A new class of multi-scale structures, referred to as `parabolic metamaterials' is introduced and studied in this paper. For an elastic two-dimensional triangular lattice, we identify dynamic regimes, which corresponds to so-called `Dirac Bridges' on the dispersion surfaces. Such regimes lead to a highly localised and focussed unidirectional beam when the lattice is excited. We also show that the flexural rigidities of elastic ligaments are essential in establishing the `parabolic metamaterial' regimes.
Testing Parabolic-Dish Concentrators
NASA Technical Reports Server (NTRS)
Selcuk, M. Kudret
1988-01-01
Report describes test equipment and tests at Parabolic Dish Test Site at Edwards Air Force Base in California. Site established in 1978 for testing point-focusing solar concentrators operating at temperatures above 600 degree F. Used for six years to evaluate parabolic-dish concentrators, receivers, power-conversion units, and solar/fossil-fuel hybrid units. Report describes evolution of test program at site, lists experiments conducted there in chronological order, and summarizes experimental data.
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.
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.
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.
Analysis and conceptual design of a lunar radiator parabolic shade
NASA Technical Reports Server (NTRS)
Ewert, Michael K.; Clark, Craig S.
1991-01-01
On the moon, the available heat sink temperature for a vertical unshaded radiator at the equator is 322 K. A method of reducing this heat sink temperature using a parabolic trough shading device was investigated. A steady state heat balance was performed to predict the available heat sink temperature. The effect of optical surface properties on system performance was investigated. Various geometric configurations were also evaluated. A flexible shade conceptual design is presented which greatly reduces the weight and stowed volume of the system. The concept makes use of the natural catenary shape assumed by a flexible material when supported at two points. The catenary shape is very near parabolic. The lunar radiator parabolic shade design presented integrates the energy collection and rejection of a solar dynamic power cycle with the moderate temperature waste heat rejection of a lunar habitat.
Existence and dynamics of quasilinear parabolic systems with time delays
NASA Astrophysics Data System (ADS)
Pao, C. V.; Ruan, W. H.
2015-05-01
This paper is concerned with a coupled system of quasilinear parabolic equations where the effect of time delays is taken into consideration in the reaction functions of the system. The partial differential operators in the system may be degenerate and the reaction functions possess some mixed quasimonotone property, including quasimonotone nondecreasing functions. The aim of the paper is to show the existence and uniqueness of a global solution to the parabolic system, the existence of positive quasisolutions or maximal-minimal solutions of the corresponding elliptic system, and the asymptotic behavior of the solution of the parabolic system in relation to the quasisolutions or maximal-minimal solutions of the elliptic system. Applications are given to three reaction-diffusion models arising from mathematical biology and ecology where the diffusion coefficients are density dependent and are degenerate. This degenerate density-dependent diffusion leads to some interesting distinct asymptotic behavior of the time-dependent solution when compared with density-independent diffusion.
Application of the Parabolic Approximation to Predict Acoustical Propagation in the Ocean.
ERIC Educational Resources Information Center
McDaniel, Suzanne T.
1979-01-01
A simplified derivation of the parabolic approximation to the acoustical wave equation is presented. Exact solutions to this approximate equation are compared with solutions to the wave equation to demonstrate the applicability of this method to the study of underwater sound propagation. (Author/BB)
Engineering parabolic beams with dynamic intensity profiles.
Ruelas, Adrian; Lopez-Aguayo, Servando; Gutiérrez-Vega, Julio C
2013-08-01
We present optical fields formed by superposing nondiffracting parabolic beams with distinct longitudinal wave-vector components, generating light profiles that display intensity fluxes following parabolic paths in the transverse plane. Their propagation dynamics vary depending on the physical mechanism originating interference, where the possibilities include constructive and destructive interference between traveling parabolic beams, interference between stationary parabolic modes, and combinations of these. The dark parabolic region exhibited by parabolic beams permits a straightforward superposition of intensity fluxes, allowing formation of a variety of profiles, which can exhibit circular, elliptic, and other symmetries.
Shenandoah parabolic dish solar collector
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.
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.
Self-similar parabolic plasmonic beams.
Davoyan, Arthur R; Turitsyn, Sergei K; Kivshar, Yuri S
2013-02-15
We demonstrate that an interplay between diffraction and defocusing nonlinearity can support stable self-similar plasmonic waves with a parabolic profile. Simplicity of a parabolic shape combined with the corresponding parabolic spatial phase distribution creates opportunities for controllable manipulation of plasmons through a combined action of diffraction and nonlinearity.
Transversal filter for parabolic phase equalization
NASA Technical Reports Server (NTRS)
Kelly, Larry R. (Inventor); Waugh, Geoffrey S. (Inventor)
1993-01-01
An equalizer (10) for removing parabolic phase distortion from an analog signal (3), utilizing a pair of series connected transversal filters. The parabolic phase distortion is cancelled by generating an inverse parabolic approximation using a sinusoidal phase control filter (18). The signal (3) is then passed through an amplitude control filter (21) to remove magnitude ripple components.
Parabolic tapers for overmoded waveguides
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.
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.
NASA Astrophysics Data System (ADS)
Wang, JinRong; Ibrahim, A. G.; Fečkan, Michal
2015-10-01
In this paper we present two existence results of nonlocal Cauchy problems for semilinear differential inclusions with fractional order in Banach spaces. The first result relies on a growth condition on the whole time interval. Our second result relies on a revised growth condition which is divided into two parts, one for the subintervals containing the points associated with the nonlocal conditions, and the other for the rest of the interval. The used technique is based on fractional calculus, the properties of the measure of noncompactness and a powerful fixed point theorem for multifunctions due to O'Regan-Precup. Finally, we apply the theoretical results to fractional differential inclusions on lattices with global neighborhood interactions.
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.
Shock wave convergence in water with parabolic wall boundaries
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.
Optimize design of the parabolic gradient-index coupling lens for a laser diode to single-mode fiber
NASA Astrophysics Data System (ADS)
Huang, Yantang; Chen, Chao
2002-09-01
In this paper, we theoretically study the optimize design of the parabolic gradient-index lens used as laser diode to single mode fiber coupling lens. In order to enhance the coupling efficiency between the LD and the SMF, we have calculated the aberration (longitudinal spherical aberration (LSA), offense against sine condition (OSC) and optimized the parameter of the parabolic gradient-index coupling lens by solving the ray equation with the standard Runge-Kutta method. From analysis of the parabolic GRIN coupling lens, it turns out as follow: i) axis GRIN constant L can affect the aberration, ii) the plane-convex parabolic GRIN coupling lens with small end towards LD is the best design, iii) we obtain groups of optimized biplane, plane-convex parabolic GRIN coupling lens.
Multibump solutions for quasilinear elliptic equations with critical growth
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.
Parabolic dishes: technology and economics
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.
Three-dimensional rogue waves in nonstationary parabolic potentials.
Yan, Zhenya; Konotop, V V; Akhmediev, N
2010-09-01
Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1) -dimensional inhomogeneous nonlinear Schrödinger (NLS) equation with variable coefficients and parabolic potential to the (1+1) -dimensional NLS equation with constant coefficients. This transformation allows us to relate certain class of localized exact solutions of the (3+1) -dimensional case to the variety of solutions of integrable NLS equation of the (1+1) -dimensional case. As an example, we illustrated our technique using two lowest-order rational solutions of the NLS equation as seeding functions to obtain rogue wavelike solutions localized in three dimensions that have complicated evolution in time including interactions between two time-dependent rogue wave solutions. The obtained three-dimensional rogue wavelike solutions may raise the possibility of relative experiments and potential applications in nonlinear optics and Bose-Einstein condensates.
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.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Sommariva, Sara; Sorrentino, Alberto
2014-11-01
We discuss the use of a recent class of sequential Monte Carlo methods for solving inverse problems characterized by a semi-linear structure, i.e. where the data depend linearly on a subset of variables and nonlinearly on the remaining ones. In this type of problems, under proper Gaussian assumptions one can marginalize the linear variables. This means that the Monte Carlo procedure needs only to be applied to the nonlinear variables, while the linear ones can be treated analytically; as a result, the Monte Carlo variance and/or the computational cost decrease. We use this approach to solve the inverse problem of magnetoencephalography, with a multi-dipole model for the sources. Here, data depend nonlinearly on the number of sources and their locations, and depend linearly on their current vectors. The semi-analytic approach enables us to estimate the number of dipoles and their location from a whole time-series, rather than a single time point, while keeping a low computational cost.
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.
Dynamics of parabolic problems with memory. Subcritical and critical nonlinearities
NASA Astrophysics Data System (ADS)
Li, Xiaojun
2016-08-01
In this paper, we study the long-time behavior of the solutions of non-autonomous parabolic equations with memory in cases when the nonlinear term satisfies subcritical and critical growth conditions. In order to do this, we show that the family of processes associated to original systems with heat source f(x, t) being translation bounded in Lloc 2 ( R ; L 2 ( Ω ) ) is dissipative in higher energy space M α , 0 < α ≤ 1, and possesses a compact uniform attractor in M 0 .
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.
On a Parabolic-Elliptic system with chemotaxis and logistic type growth
NASA Astrophysics Data System (ADS)
Galakhov, Evgeny; Salieva, Olga; Tello, J. Ignacio
2016-10-01
We consider a nonlinear PDEs system of two equations of Parabolic-Elliptic type with chemotactic terms. The system models the movement of a biological population "u" towards a higher concentration of a chemical agent "w" in a bounded and regular domain Ω ⊂RN for arbitrary N ∈ N. After normalization, the system is as follows
Photovoltaic applications of Compound Parabolic Concentrator (CPC)
NASA Technical Reports Server (NTRS)
Winston, R.
1975-01-01
The use of a compound parabolic concentrator as field collector, in conjunction with a primary focusing concentrator for photovoltaic applications is studied. The primary focusing concentrator can be a parabolic reflector, an array of Fresnel mirrors, a Fresnel lens or some other lens. Silicon solar cell grid structures are proposed that increase efficiency with concentration up to 10 suns. A ray tracing program has been developed to determine energy distribution at the exit of a compound parabolic concentrator. Projected total cost of a CPC/solar cell system will be between 4 and 5 times lower than for flat plate silicon cell arrays.
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.
On a Modified Form of Navier-Stokes Equations for Three-Dimensional Flows
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
Self-similar propagation and amplification of parabolic pulses in optical fibers.
Fermann, M E; Kruglov, V I; Thomsen, B C; Dudley, J M; Harvey, J D
2000-06-26
Ultrashort pulse propagation in high gain optical fiber amplifiers with normal dispersion is studied by self-similarity analysis of the nonlinear Schrödinger equation with gain. An exact asymptotic solution is found, corresponding to a linearly chirped parabolic pulse which propagates self-similarly subject to simple scaling rules. The solution has been confirmed by numerical simulations and experiments studying propagation in a Yb-doped fiber amplifier. Additional experiments show that the pulses remain parabolic after propagation through standard single mode fiber with normal dispersion.
Reflective Properties of a Parabolic Mirror.
ERIC Educational Resources Information Center
Ramsey, Gordon P.
1991-01-01
An incident light ray parallel to the optical axis of a parabolic mirror will be reflected at the focal point and vice versa. Presents a mathematical proof that uses calculus, algebra, and geometry to prove this reflective property. (MDH)
A reformulation of the parabolic approximation for waves in stratified moving media
NASA Technical Reports Server (NTRS)
Mcaninch, G. L.
1986-01-01
An asymptotic, large wave number approximation for the equations governing the propagation of acoustic disturbances through a stratified moving medium is developed. The theory is an extension of the geometric acoustics approximation and provides corrections to that approximation in the form of multiplicative functions which satisfy parabolic differential equations of second order. By properly accounting for variations in the acoustic field in directions normal to the rays both caustic surfaces and the secularity of the geometric theory may be avoided.
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.
Lipoxygenase activity during parabolic flights.
Maccarrone, M; Tacconi, M; Battista, N; Valgattarri, F; Falciani, P; Finazzi-Agro, A
2001-07-01
Experiments in Space clearly show that various cellular processes, such as growth rates, signaling pathways and gene expression, are modified when cells are placed under conditions of weightlessness. As yet, there is no coherent explanation for these observations, though recent experiments, showing that microtubule self-organization is gravity-dependent suggest that investigations at the molecular level might fill the gap between observation and understanding of Space effects. Lipoxygenases are a family of dioxygenases which have been implicated in the pathogenesis of several inflammatory conditions, in atherosclerosis, in brain aging and in HIV infection. In plants, lipoxy-genases favour germination, participate in the synthesis of traumatin and jasmonic acid and in the response to abiotic stress. Here, we took advantage of a fibre optics spectrometer developed on purpose, the EMEC (Effect of Microgravity on Enzymatic Catalysis) module, to measure the dioxygenation reaction by pure soybean lipoxygenase-1 (LOX-1) during the 28th parabolic flight campaign of the European Space Agency (ESA). The aim was to ascertain whether microgravity can affect enzyme catalysis.
QSAGE iterative method applied to fuzzy parabolic equation
NASA Astrophysics Data System (ADS)
Dahalan, A. A.; Muthuvalu, M. S.; Sulaiman, J.
2016-02-01
The aim of this paper is to examine the effectiveness of the Quarter-Sweep Alternating Group Explicit (QSAGE) iterative method by solving linear system generated from the discretization of one-dimensional fuzzy diffusion problems. In addition, the formulation and implementation of the proposed method are also presented. The results obtained are then compared with Full-Sweep Gauss-Seidel (FSGS), Full-Sweep AGE (FSAGE) and Half-Sweep AGE (HSAGE) to illustrate their feasibility.
Test results, Industrial Solar Technology parabolic trough solar collector
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.
Dagrau, Franck; Rénier, Mathieu; Marchiano, Régis; Coulouvrat, François
2011-07-01
Numerical simulation of nonlinear acoustics and shock waves in a weakly heterogeneous and lossless medium is considered. The wave equation is formulated so as to separate homogeneous diffraction, heterogeneous effects, and nonlinearities. A numerical method called heterogeneous one-way approximation for resolution of diffraction (HOWARD) is developed, that solves the homogeneous part of the equation in the spectral domain (both in time and space) through a one-way approximation neglecting backscattering. A second-order parabolic approximation is performed but only on the small, heterogeneous part. So the resulting equation is more precise than the usual standard or wide-angle parabolic approximation. It has the same dispersion equation as the exact wave equation for all forward propagating waves, including evanescent waves. Finally, nonlinear terms are treated through an analytical, shock-fitting method. Several validation tests are performed through comparisons with analytical solutions in the linear case and outputs of the standard or wide-angle parabolic approximation in the nonlinear case. Numerical convergence tests and physical analysis are finally performed in the fully heterogeneous and nonlinear case of shock wave focusing through an acoustical lens.
Large mass self-similar solutions of the parabolic-parabolic Keller-Segel model of chemotaxis.
Biler, Piotr; Corrias, Lucilla; Dolbeault, Jean
2011-07-01
In two space dimensions, the parabolic-parabolic Keller-Segel system shares many properties with the parabolic-elliptic Keller-Segel system. In particular, solutions globally exist in both cases as long as their mass is less than a critical threshold M(c). However, this threshold is not as clear in the parabolic-parabolic case as it is in the parabolic-elliptic case, in which solutions with mass above M(c) always blow up. Here we study forward self-similar solutions of the parabolic-parabolic Keller-Segel system and prove that, in some cases, such solutions globally exist even if their total mass is above M(c), which is forbidden in the parabolic-elliptic case.
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.
Parabolic flight as a spaceflight analog.
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.
Parabolic Ejecta Features on Titan? Probably Not
NASA Astrophysics Data System (ADS)
Lorenz, R. D.; Melosh, H. J.
1996-03-01
Radar mapping of Venus by Magellan indicated a number of dark parabolic features, associated with impact craters. A suggested mechanism for generating such features is that ejecta from the impact event is 'winnowed' by the zonal wind field, with smaller ejecta particles falling out of the atmosphere more slowly, and hence drifting further. What discriminates such features from simple wind streaks is the 'stingray' or parabolic shape. This is due to the ejecta's spatial distribution prior to being winnowed during fallout, and this distribution is generated by the explosion plume of the impact piercing the atmosphere, allowing the ejecta to disperse pseudoballistically before re-entering the atmosphere, decelerating to terminal velocity and then being winnowed. Here we apply this model to Titan, which has a zonal wind field similar to that of Venus. We find that Cassini will probably not find parabolic features, as the winds stretch the deposition so far that ejecta will form streaks or bands instead.
Soliton solutions for quasilinear Schrödinger equations with critical growth
NASA Astrophysics Data System (ADS)
do Ó, João M. Bezerra; Miyagaki, Olímpio H.; Soares, Sérgio H. M.
In this paper we establish the existence of standing wave solutions for quasilinear Schrödinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration-compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9].
Exact controllability of partial integrodifferential equations with mixed boundary conditions
NASA Astrophysics Data System (ADS)
Sakthivel, K.; Balachandran, K.; Lavanya, R.
2007-01-01
In this work the exact controllability of linear parabolic integrodifferential equations with mixed boundary conditions are studied. Carleman estimate for the linearized problem providing the observability results is fundamental to the analysis and by duality it provides exact global controllability.
ON NONLINEAR EQUATIONS OF THE FORM F(x,\\, u,\\, Du,\\, \\Delta u) = 0
NASA Astrophysics Data System (ADS)
Soltanov, K. N.
1995-02-01
The Dirichlet problem for equations of the form F(x,\\, u,\\, Du,\\, \\Delta u) = 0 and also the initial boundary value problem for a parabolic equation with a nonlinearity are studied.Bibliography: 11 titles.
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.
Discontinuous mixed covolume methods for parabolic problems.
Zhu, Ailing; Jiang, Ziwen
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 L(2).
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.
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.
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.
A cosmological hydrodynamic code based on the piecewise parabolic method
NASA Astrophysics Data System (ADS)
Gheller, Claudio; Pantano, Ornella; Moscardini, Lauro
1998-04-01
We present a hydrodynamical code for cosmological simulations which uses the piecewise parabolic method (PPM) to follow the dynamics of the gas component and an N-body particle-mesh algorithm for the evolution of the collisionless component. The gravitational interaction between the two components is regulated by the Poisson equation, which is solved by a standard fast Fourier transform (FFT) procedure. In order to simulate cosmological flows, we have introduced several modifications to the original PPM scheme, which we describe in detail. Various tests of the code are presented, including adiabatic expansion, single and multiple pancake formation, and three-dimensional cosmological simulations with initial conditions based on the cold dark matter scenario.
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).
Modeling of concentration polarization in a reverse osmosis channel with parabolic crossflow.
Liu, Cui; Morse, Audra; Rainwater, Ken; Song, Lianfa
2014-01-01
Concentration polarization in narrow reverse osmosis channels with parabolic crossflow was numerically simulated with finite different equations related to permeate velocity, crossflow velocity, average salt concentration, and wall salt concentration. A significant new theoretical development was the determination of two correction functions, F2 and F3, in the governing equation for average salt concentration. Simulations of concentration polarization under various conditions were then presented to describe the features of the new model as well as discussions about the differences of concentration polarizations of the more realistic parabolic flow with those when plug flow or shear flow was assumed. The situations in which the simpler models based on shear or plug flow can be used were indicated. Concentration polarization was also simulated for various conditions to show the applicability of the model and general features of concentration polarization in a narrow, long reverse osmosis channel.
Well-posedness of nonlocal parabolic differential problems with dependent operators.
Ashyralyev, Allaberen; Hanalyev, Asker
2014-01-01
The nonlocal boundary value problem for the parabolic differential equation v'(t) + A(t)v(t) = f(t) (0 ≤ t ≤ T), v(0) = v(λ) + φ, 0 < λ ≤ T in an arbitrary Banach space E with the dependent linear positive operator A(t) is investigated. The well-posedness of this problem is established in Banach spaces C 0 (β,γ) (E α-β ) of all E α-β -valued continuous functions φ(t) on [0, T] satisfying a Hölder condition with a weight (t + τ)(γ). New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.
Pathwise random periodic solutions of stochastic differential equations
NASA Astrophysics Data System (ADS)
Feng, Chunrong; Zhao, Huaizhong; Zhou, Bo
In this paper, we study the existence of random periodic solutions for semilinear stochastic differential equations. We identify these as the solutions of coupled forward-backward infinite horizon stochastic integral equations in general cases. We then use the argument of the relative compactness of Wiener-Sobolev spaces in C([0,T],L(Ω)) and generalized Schauder's fixed point theorem to prove the existence of a solution of the coupled stochastic forward-backward infinite horizon integral equations. The condition on F is then further weakened by applying the coupling method of forward and backward Gronwall inequalities. The results are also valid for stationary solutions as a special case when the period τ can be an arbitrary number.
Investigation of a Parabolic Iterative Solver for Three-dimensional Configurations
NASA Technical Reports Server (NTRS)
Nark, Douglas M.; Watson, Willie R.; Mani, Ramani
2007-01-01
A parabolic iterative solution procedure is investigated that seeks to extend the parabolic approximation used within the internal propagation module of the duct noise propagation and radiation code CDUCT-LaRC. The governing convected Helmholtz equation is split into a set of coupled equations governing propagation in the positive and negative directions. The proposed method utilizes an iterative procedure to solve the coupled equations in an attempt to account for possible reflections from internal bifurcations, impedance discontinuities, and duct terminations. A geometry consistent with the NASA Langley Curved Duct Test Rig is considered and the effects of acoustic treatment and non-anechoic termination are included. Two numerical implementations are studied and preliminary results indicate that improved accuracy in predicted amplitude and phase can be obtained for modes at a cut-off ratio of 1.7. Further predictions for modes at a cut-off ratio of 1.1 show improvement in predicted phase at the expense of increased amplitude error. Possible methods of improvement are suggested based on analytic and numerical analysis. It is hoped that coupling the parabolic iterative approach with less efficient, high fidelity finite element approaches will ultimately provide the capability to perform efficient, higher fidelity acoustic calculations within complex 3-D geometries for impedance eduction and noise propagation and radiation predictions.
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.
Focusing a TM(01) beam with a slightly tilted parabolic mirror.
April, Alexandre; Bilodeau, Pierrick; Piché, Michel
2011-05-01
A parabolic mirror illuminated with an incident collimated beam whose axis of propagation does not exactly coincide with the axis of revolution of the mirror shows distortion and strong coma. To understand the behavior of such a focused beam, a detailed description of the electric field in the focal region of a parabolic mirror illuminated with a beam having a nonzero angle of incidence is required. We use the Richards-Wolf vector field equation to investigate the electric energy density distribution of a beam focused with a parabolic mirror. The explicit aberration function of this focused field is provided along with numerically calculated electric energy densities in the focal region for different angles of incidence. The location of the peak intensity, the Strehl ratio and the full-width at half-maximum as a function of the angle of incidence are given and discussed. The results confirm that the focal spot of a strongly focused beam is affected by severe coma, even for very small tilting of the mirror. This analysis provides a clearer understanding of the effect of the angle of incidence on the focusing properties of a parabolic mirror as such a focusing device is of growing interest in microscopy.
Mechatronic Prototype of Parabolic Solar Tracker
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
Mechatronic Prototype of Parabolic Solar Tracker.
Morón, Carlos; Díaz, Jorge Pablo; Ferrández, Daniel; Ramos, Mari Paz
2016-06-15
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.
Parabolic dish collectors - A solar option
NASA Technical Reports Server (NTRS)
Truscello, V. C.
1981-01-01
A description is given of several parabolic-dish high temperature solar thermal systems currently undergoing performance trials. A single parabolic dish has the potential for generating 20 to 30 kW of electricity with fluid temperatures from 300 to 1650 C. Each dish is a complete power-producing unit, and may function either independently or as part of a group of linked modules. The two dish designs under consideration are of 11 and 12 meter diameters, yielding receiver operating temperatures of 925 and 815 C, respectively. The receiver designs described include (1) an organic working fluid (toluene) Rankine cycle engine; (2) a Brayton open cycle unit incorporating a hybrid combustion chamber and nozzle and a shaft-coupled permanent magnet alternator; and (3) a modified Stirling cycle device originally designed for automotive use. Also considered are thermal buffer energy storage and thermochemical transport and storage.
Nanofocusing Parabolic Refractive X-Ray Lenses
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.
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.
Mechatronic Prototype of Parabolic Solar Tracker.
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
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.
Parabolic Trough Organic Rankine Cycle Power Plant
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.
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.
Parabolic resection for mitral valve repair.
Drake, Daniel H; Drake, Charles G; Recchia, Dino
2010-02-01
Parabolic resection, named for the shape of the cut edges of the excised tissue, expands on a common 'trick' used by experienced mitral surgeons to preserve tissue and increase the probability of successful repair. Our objective was to describe and clinically analyze this simple modification of conventional resection. Thirty-six patients with mitral regurgitation underwent valve repair using parabolic resection in combination with other techniques. Institution specific mitral data, Society of Thoracic Surgeons data and preoperative, post-cardiopulmonary bypass (PCPB) and postoperative echocardiography data were collected and analyzed. Preoperative echocardiography demonstrated mitral regurgitation ranging from moderate to severe. PCPB transesophageal echocardiography demonstrated no regurgitation or mild regurgitation in all patients. Thirty-day surgical mortality was 2.8%. Serial echocardiograms demonstrated excellent repair stability. One patient (2.9%) with rheumatic disease progressed to moderate regurgitation 33 months following surgery. Echocardiography on all others demonstrated no or mild regurgitation at a mean follow-up of 22.8+/-12.8 months. No patient required mitral reintervention. Longitudinal analysis demonstrated 80% freedom from cardiac death, reintervention and greater than moderate regurgitation at four years following repair. Parabolic resection is a simple technique that can be very useful during complex mitral reconstruction. Early and intermediate echocardiographic studies demonstrate excellent results.
Simulation of parabolic reflectors for ultraviolet phototherapy.
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.
Simulation of parabolic reflectors for ultraviolet phototherapy.
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
Higher-order parabolic approximations for sound propagation in stratified moving media
NASA Technical Reports Server (NTRS)
Mcaninch, G. L.
1984-01-01
Asymptotic solutions of order k-n are developed for the equations governing the propagation of sound through a stratified moving medium. Here k is a dimensionless wave number and n is the arbitrary order of the approximation. These approximations are an extension of geometric acoustics theory and provide corrections to that theory in the form of multiplicative functions which satisfy parabolic partial differential equations. These corrections account for the diffraction effects caused by variation of the field normal to the ray path and the interaction of these transverse variations with the variation of the field along the ray. The theory is illustrated by application to simple examples.
Numerical Modeling of Unsaturated Flows in Variable Gravity During Parabolic Flight
NASA Astrophysics Data System (ADS)
Jones, S. B.; Heinse, R.; Šimunek, J.; Tuller, M.; Or, D.
2007-12-01
Parabolic flight experiments were conducted to study effects of reduced gravity on multiphase fluid distribution and transport. Notwithstanding the limited duration of microgravity (~20 s), measurements of porous-media fluid behavior have been successful in demonstrating significant differences between μ- and 1-g. Further understanding of reduced gravity effects can be gained through numerical modeling of hydrodynamic data. The gravitational acceleration during parabolic flight cycles between hypergravity (1.8-g) and microgravity (~10-6-g). Impacts of variable gravity on measurements focusing on the microgravity portion of the flight were ambiguous and difficult to interpret. One-dimensional numerical modeling using the Richards equation with a variable gravity term was compared with matric potential and water content measurements obtained during several parabolic flights. Introducing a time-dependent variable gravity term facilitated modeling of the hypergravity phase, which extends to 1.8-g and precedes each microgravity cycle. This 'complete' treatment of flight data allowed more accurate modeling of secondary water retention scanning curves. This is important because during parabolic flight, wetting and draining processes occur simultaneously in different volumes of the porous medium. Both baked clay aggregates and glass beads were packed into containers with heights varying from 1 to 7 cm. Hydrostatic and matric potentials were measured using micro-tensiometers and water content was determined either volumetrically or using TDR. Hydrus-1D was used to model the hydrodynamics with time- dependent gravity input in sub-second increments of time. Our results suggest that the impact of a preceding hypergravity-phase on microgravity hydrodynamics during parabolic flight should not be ignored and requires due attention for adequate modeling of matric potential and water content measurements in porous media.
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.
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.
Well-posedness of backward stochastic differential equations with general filtration
NASA Astrophysics Data System (ADS)
Lü, Qi; Zhang, Xu
This paper is addressed to the well-posedness of some linear and semilinear backward stochastic differential equations with general filtration, without using the Martingale Representation Theorem. The point of our approach is to introduce a new notion of solution, i.e., the transposition solution, which coincides with the usual strong solution when the filtration is natural but it is more flexible for the case of general filtration than the existing notion of solutions. A comparison theorem for transposition solutions and a Pontryagin-type stochastic maximum principle are also presented.
An evolution infinity Laplace equation modelling dynamic elasto-plastic torsion
NASA Astrophysics Data System (ADS)
Messelmi, Farid
2016-09-01
We consider in this paper a parabolic partial differential equation involving the infinity Laplace operator and a Leray-Lions operator with no coercitive assumption. We prove the existence and uniqueness of the corresponding approached problem and we show that at the limit the solution solves the parabolic variational inequality arising in the elasto-plastic torsion problem.
Wang, Jun-Wei; Wu, Huai-Ning; Li, Han-Xiong
2012-06-01
In this paper, a distributed fuzzy control design based on Proportional-spatial Derivative (P-sD) is proposed for the exponential stabilization of a class of nonlinear spatially distributed systems described by parabolic partial differential equations (PDEs). Initially, a Takagi-Sugeno (T-S) fuzzy parabolic PDE model is proposed to accurately represent the nonlinear parabolic PDE system. Then, based on the T-S fuzzy PDE model, a novel distributed fuzzy P-sD state feedback controller is developed by combining the PDE theory and the Lyapunov technique, such that the closed-loop PDE system is exponentially stable with a given decay rate. The sufficient condition on the existence of an exponentially stabilizing fuzzy controller is given in terms of a set of spatial differential linear matrix inequalities (SDLMIs). A recursive algorithm based on the finite-difference approximation and the linear matrix inequality (LMI) techniques is also provided to solve these SDLMIs. Finally, the developed design methodology is successfully applied to the feedback control of the Fitz-Hugh-Nagumo equation.
Femtosecond parabolic pulse shaping in normally dispersive optical fibers.
Sukhoivanov, Igor A; Iakushev, Sergii O; Shulika, Oleksiy V; Díez, Antonio; Andrés, Miguel
2013-07-29
Formation of parabolic pulses at femtosecond time scale by means of passive nonlinear reshaping in normally dispersive optical fibers is analyzed. Two approaches are examined and compared: the parabolic waveform formation in transient propagation regime and parabolic waveform formation in the steady-state propagation regime. It is found that both approaches could produce parabolic pulses as short as few hundred femtoseconds applying commercially available fibers, specially designed all-normal dispersion photonic crystal fiber and modern femtosecond lasers for pumping. The ranges of parameters providing parabolic pulse formation at the femtosecond time scale are found depending on the initial pulse duration, chirp and energy. Applicability of different fibers for femtosecond pulse shaping is analyzed. Recommendation for shortest parabolic pulse formation is made based on the analysis presented.
Parabolic Trough VSHOT Optical Characterization in 2005-2006 (Presentation)
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.
Parasympathetic heart rate modulation during parabolic flights.
Beckers, F; Seps, B; Ramaekers, D; Verheyden, B; Aubert, A E
2003-09-01
During parabolic flight short periods of microgravity and hypergravity are created. These changes influence cardiovascular function differently according to posture. During the 29th parabolic flight campaign of the European Space Agency (ESA), the electrocardiogram (ECG) was recorded continuously in seven healthy volunteers in two positions (standing and supine). Five different phases were differentiated: 1 g (1 g=9.81 m/s(2)) before and after each parabola, 1.8 g at the ascending leg of the parabola (hypergravity), 0 g at the apex, 1.6 g at the descending leg (hypergravity). We assessed heart rate variability (HRV) by indices of temporal analysis [mean RR interval (meanRR), the standard deviation of the intervals (SDRR), and the square root of the mean squared differences of successive intervals (rMSSD) and coefficient of variation (CV)]. In the supine position no significant differences were shown between different gravity phases for all HRV indices. In the standing position the 0 g phase showed a tendency towards higher values of meanRR compared to the control and to the other phases ( p=NS). SDRR, rMSSD and CV were significantly higher compared to control ( p<0.05). Significantly higher values for meanRR in the supine position at 1 g and hypergravity ( p<0.05) were found when compared to standing. SDRR was significantly higher at 0 g in the standing position compared to supine [95 (44) ms vs. 50 (15) ms; p<0.05] and lower in other phases. rMSSD and CV showed the same trend ( p=NS). We confirm that, during parabolic flights, position matters for cardiovascular measurements. Time domain indices of HRV during different gravity phases showed: (1) higher vagal modulation of the autonomic nervous system in microgravity, when compared with normo- or hypergravity in standing subjects; and (2) no differences in supine subjects between different g phases.
Alignment method for parabolic trough solar concentrators
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.
Manipulation of dielectric particles with nondiffracting parabolic beams.
Ortiz-Ambriz, Antonio; Gutiérrez-Vega, Julio C; Petrov, Dmitri
2014-12-01
The trapping and manipulation of microscopic particles embedded in the structure of nondiffracting parabolic beams is reported. The particles acquire orbital angular momentum and exhibit an open trajectory following the parabolic fringes of the beam. We observe an asymmetry in the terminal velocity of the particles caused by the counteracting gradient and scattering forces.
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.
High-order parabolic beam approximation for aero-optics
White, Michael D.
2010-08-01
The parabolic beam equations are solved using high-order compact differences for the Laplacians and Runge-Kutta integration along the beam path. The solution method is verified by comparison to analytical solutions for apertured beams and both constant and complex index of refraction. An adaptive 4th-order Runge-Kutta using an embedded 2nd-order method is presented that has demonstrated itself to be very robust. For apertured beams, the results show that the method fails to capture near aperture effects due to a violation of the paraxial approximation in that region. Initial results indicate that the problem appears to be correctable by successive approximations. A preliminary assessment of the effect of turbulent scales is undertaken using high-order Lagrangian interpolation. The results show that while high fidelity methods are necessary to accurately capture the large scale flow structure, the method may not require the same level of fidelity in sampling the density for the index of refraction. The solution is used to calculate a phase difference that is directly compared with that commonly calculated via the optical path difference. Propagation through a supersonic boundary layer shows that for longer wavelengths, the traditional method to calculate the optical path is less accurate than for shorter wavelengths. While unlikely to supplant more traditional methods for most aero-optics applications, the current method can be used to give a quantitative assessment of the other methods as well as being amenable to the addition of more physics.
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%.
THE PARABOLIC JET STRUCTURE IN M87 AS A MAGNETOHYDRODYNAMIC NOZZLE
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.
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.
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).
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.
Self-similar propagation of high-power parabolic pulses in optical fiber amplifiers.
Kruglov, V I; Peacock, A C; Dudley, J M; Harvey, J D
2000-12-15
Self-similarity techniques are used to study pulse propagation in a normal-dispersion optical fiber amplifier with an arbitrary longitudinal gain profile. Analysis of the nonlinear Schrödinger equation that describes such an amplifier leads to an exact solution in the high-power limit that corresponds to a linearly chirped parabolic pulse. The self-similar scaling of the propagating pulse in the amplifier is found to be determined by the functional form of the gain profile, and the solution is confirmed by numerical simulations. The implications for achieving chirp-free pulses after compression of the amplifier output are discussed.
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.
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.
Parabolic dish module experiment. Final test report
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.
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.
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.
Parabolic flight: loss of sense of orientation.
Lackner, J R; Graybiel, A
1979-11-30
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.
A stabilized explicit Lagrange multiplier based domain decomposition method for parabolic problems
NASA Astrophysics Data System (ADS)
Zheng, Zheming; Simeon, Bernd; Petzold, Linda
2008-05-01
A fully explicit, stabilized domain decomposition method for solving moderately stiff parabolic partial differential equations (PDEs) is presented. Writing the semi-discretized equations as a differential-algebraic equation (DAE) system where the interface continuity constraints between subdomains are enforced by Lagrange multipliers, the method uses the Runge-Kutta-Chebyshev projection scheme to integrate the DAE explicitly and to enforce the constraints by a projection. With mass lumping techniques and node-to-node matching grids, the method is fully explicit without solving any linear system. A stability analysis is presented to show the extended stability property of the method. The method is straightforward to implement and to parallelize. Numerical results demonstrate that it has excellent performance.
Graviresponses of Paramecium biaurelia during parabolic flights.
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.
Multigrid methods for a semilinear PDE in the theory of pseudoplastic fluids
NASA Technical Reports Server (NTRS)
Henson, Van Emden; Shaker, A. W.
1993-01-01
We show that by certain transformations the boundary layer equations for the class of non-Newtonian fluids named pseudoplastic can be generalized in the form the vector differential operator(u) + p(x)u(exp -lambda) = 0, where x is a member of the set Omega and Omega is a subset of R(exp n), n is greater than or equal to 1 under the classical conditions for steady flow over a semi-infinite flat plate. We provide a survey of the existence, uniqueness, and analyticity of the solutions for this problem. We also establish numerical solutions in one- and two-dimensional regions using multigrid methods.
Parabolic features and the erosion rate on Venus
NASA Technical Reports Server (NTRS)
Strom, Robert G.
1993-01-01
The impact cratering record on Venus consists of 919 craters covering 98 percent of the surface. These craters are remarkably well preserved, and most show pristine structures including fresh ejecta blankets. Only 35 craters (3.8 percent) have had their ejecta blankets embayed by lava and most of these occur in the Atla-Beta Regio region; an area thought to be recently active. parabolic features are associated with 66 of the 919 craters. These craters range in size from 6 to 105 km diameter. The parabolic features are thought to be the result of the deposition of fine-grained ejecta by winds in the dense venusian atmosphere. The deposits cover about 9 percent of the surface and none appear to be embayed by younger volcanic materials. However, there appears to be a paucity of these deposits in the Atla-Beta Regio region, and this may be due to the more recent volcanism in this area of Venus. Since parabolic features are probably fine-grain, wind-deposited ejecta, then all impact craters on Venus probably had these deposits at some time in the past. The older deposits have probably been either eroded or buried by eolian processes. Therefore, the present population of these features is probably associated with the most recent impact craters on the planet. Furthermore, the size/frequency distribution of craters with parabolic features is virtually identical to that of the total crater population. This suggests that there has been little loss of small parabolic features compared to large ones, otherwise there should be a significant and systematic paucity of craters with parabolic features with decreasing size compared to the total crater population. Whatever is erasing the parabolic features apparently does so uniformly regardless of the areal extent of the deposit. The lifetime of parabolic features and the eolian erosion rate on Venus can be estimated from the average age of the surface and the present population of parabolic features.
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.
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
Hardy Uncertainty Principle, Convexity and Parabolic Evolutions
NASA Astrophysics Data System (ADS)
Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L.
2016-09-01
We give a new proof of the L 2 version of Hardy's uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new log-convexity properties and the derivation of optimal Gaussian decay bounds for solutions to the heat equation with Gaussian decay at a future time.We extend the result to heat equations with lower order variable coefficient.
Extension of Gauss' method for the solution of Kepler's equation
NASA Technical Reports Server (NTRS)
Battin, R. H.; Fill, T. J.
1978-01-01
Gauss' method for solving Kepler's equation is extended to arbitrary epochs and orbital eccentricities. Although originally developed for near parabolic orbits in the vicinity of pericenter, a generalization of the method leads to a highly efficient algorithm which compares favorably to other methods in current use. A key virtue of the technique is that convergence is obtained by a method of successive substitutions with an initial approximation that is independent of the orbital parameters. The equations of the algorithm are universal, i.e., independent of the nature of the orbit whether elliptic, hyperbolic, parabolic or rectilinear.
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.
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.
Antenna cab interior showing waveguide from external parabolic antenna (later ...
Antenna cab interior showing waveguide from external parabolic antenna (later addition), looking north. - Western Union Telegraph Company, Jennerstown Relay, Laurel Summit Road off U.S. 30, Laughlintown, Westmoreland County, PA
Detail, external parabolic antenna (later addition). Note how waveguide was ...
Detail, external parabolic antenna (later addition). Note how waveguide was cut to remove active portion of antenna. - Western Union Telegraph Company, Jennerstown Relay, Laurel Summit Road off U.S. 30, Laughlintown, Westmoreland County, PA
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.
33. July 1958 PARABOLIC BRICK VAULT IN SERVICE MAGAZINE UNDER ...
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
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.
Parabolic dish test site: History and operating experience
NASA Technical Reports Server (NTRS)
Selcuk, M. K. (Compiler)
1985-01-01
The parabolic dish test site (PDTS) was established for testing point-focusing solar concentrator systems operating at temperatures approaching 1650 C. Among tests run were evaluation and performance characterization of parabolic dish concentrators, receivers, power conversion units, and solar/fossil-fuel hybrid systems. The PDTS was fully operational until its closure in June, 1984. The evolution of the test program, a chronological listing of the experiments run, and data summaries for most of the tests conducted are presented.
Testing the figure of parabolic reflectors for solar concentrators.
Bodenheimer, J S; Eisenberg, N P; Gur, J
1982-12-15
A novel method for testing the optical quality of large parabolic solar concentrators is presented, based on autocollimation. An optical system continuously scans the reflector along a fixed reference axis. At each position along the axis, the spread function is obtained. Analysis of the location, width, and intensity changes of this function gives quantitative information about the reflector's defects. A figure of merit describing the performance of parabolic trough reflectors is proposed.
Solargenix Energy Advanced Parabolic Trough Development
Gee, R. C.; Hale, M. J.
2005-11-01
The Solargenix Advanced Trough Development Project was initiated in the Year 2000 with the support of the DOE CSP Program and, more recently, with the added support of the Nevada Southwest Energy Partnership. Parabolic trough plants are the most mature solar power technology, but no large-scale plants have been built in over a decade. Given this lengthy lull in deployment, our first Project objective was development of improved trough technology for near-term deployment, closely patterned after the best of the prior-generation troughs. The second objective is to develop further improvements in next-generation trough technology that will lead to even larger reductions in the cost of the delivered energy. To date, this Project has successfully developed an advanced trough, which is being deployed on a 1-MW plant in Arizona and will soon be deployed in a 64-MW plant in Nevada. This advanced trough offers a 10% increase in performance and over an 20% decrease in cost, relative to prior-generation troughs.
Changes in cerebral oxygenation during parabolic flight.
Schneider, Stefan; Abeln, Vera; Askew, Christopher D; Vogt, Tobias; Hoffmann, Uwe; Denise, Pierre; Strüder, Heiko K
2013-06-01
Assessing changes in brain activity under extreme conditions like weightlessness is a desirable, but difficult undertaking. Results from previous studies report specific changes in brain activity connected to an increase or decrease in gravity forces. Nevertheless, so far it remains unclear (1) whether this is connected to a redistribution of blood volume during micro- or hypergravity and (2) whether this redistribution might account for neurocognitive alterations. This study aimed to display changes in brain oxygenation caused by altered gravity conditions during parabolic flight. It was hypothesized that an increase in gravity would be accompanied by a decrease in brain oxygenation, whereas microgravity would lead to an increase in brain oxygenation. Oxygenized and deoxygenized haemoglobin were measured using two near infrared spectroscopy (NIRS) probes on the left and right prefrontal cortex throughout ten parabolas in nine subjects. Results show a decrease of 1.44 μmol/l in oxygenized haemoglobin with the onset of hypergravity, followed by a considerable increase during microgravity (up to 5.34 μmol/l). In contrast, deoxygenized haemoglobin was not altered during the first but only during the second hypergravity phase and showed only minor changes during microgravity. Changes in oxygenized and deoxygenized haemoglobin indicate an increase in arterial flow to the brain and a decrease in venous outflow during microgravity.
NASA Astrophysics Data System (ADS)
Gal, Ciprian G.; Warma, Mahamadi
2016-08-01
We investigate the long term behavior in terms of finite dimensional global and exponential attractors, as time goes to infinity, of solutions to a semilinear reaction-diffusion equation on non-smooth domains subject to nonlocal Robin boundary conditions, characterized by the presence of fractional diffusion on the boundary. Our results are of general character and apply to a large class of irregular domains, including domains whose boundary is Hölder continuous and domains which have fractal-like geometry. In addition to recovering most of the existing results on existence, regularity, uniqueness, stability, attractor existence, and dimension, for the well-known reaction-diffusion equation in smooth domains, the framework we develop also makes possible a number of new results for all diffusion models in other non-smooth settings.
Weak self-adjoint differential equations
NASA Astrophysics Data System (ADS)
Gandarias, M. L.
2011-07-01
The concepts of self-adjoint and quasi self-adjoint equations were introduced by Ibragimov (2006 J. Math. Anal. Appl. 318 742-57 2007 Arch. ALGA 4 55-60). In Ibragimov (2007 J. Math. Anal. Appl. 333 311-28), a general theorem on conservation laws was proved. In this paper, we generalize the concept of self-adjoint and quasi self-adjoint equations by introducing the definition of weak self-adjoint equations. We find a class of weak self-adjoint quasi-linear parabolic equations. The property of a differential equation to be weak self-adjoint is important for constructing conservation laws associated with symmetries of the differential equation.
Diffusive limits of nonlinear hyperbolic systems with variable coefficients
NASA Astrophysics Data System (ADS)
Miyoshi, Hironari; Tsutsumi, Masayoshi
2016-09-01
We consider the initial-boundary value problem for a 2-speed system of first-order nonhomogeneous semilinear hyperbolic equations whose leading terms have a small positive parameter. Using energy estimates and a compactness lemma, we show that the diffusion limit of the sum of the solutions of the hyperbolic system, as the parameter tends to zero, verifies the nonlinear parabolic equation of the p-Laplacian type.
Bakhos, Tania; Saibaba, Arvind K.; Kitanidis, Peter K.
2015-10-15
We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in solving these inverse problems using Newton-type methods is the computational cost associated with solving the forward problem and with repeated construction of the Jacobian, which represents the sensitivity of the measurements to the unknown parameters. Forming the Jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time-dependent parabolic partial differential equations corresponding to multiple sources and receivers. We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently. Our proposed solver speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time. We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests. The algorithms discussed are applied to a synthetic example taken from THT to demonstrate the resulting computational gains of this proposed method.
Status of APS 1-Mwe Parabolic Trough Project
Canada, S.; Brosseau, D.; Kolb, G.; Moore, L.; Cable, R.; Price, H.
2005-11-01
Arizona Public Service (APS) is currently installing new power facilities to generate a portion of its electricity from solar resources that will satisfy its obligation under the Arizona Environmental Portfolio Standard (EPS). During FY04, APS began construction on a 1-MWe parabolic trough concentrating solar power plant. This plant represents the first parabolic trough plant to begin construction since 1991. Site preparation and construction activities continued throughout much of FY05, and startup activities are planned for Fall 2005 (with completion early in FY06). The plant will be the first commercial deployment of the Solargenix parabolic trough collector technology developed under contract to the National Renewable Energy Laboratory. The plant will use an organic Rankine cycle (ORC) power plant, provided by Ormat. The ORC power plant is much simpler than the conventional steam Rankine cycle plant and allows unattended operation of the facility.
Stable parabolic Higgs bundles as asymptotically stable decorated swamps
NASA Astrophysics Data System (ADS)
Beck, Nikolai
2016-06-01
Parabolic Higgs bundles can be described in terms of decorated swamps, which we studied in a recent paper. This description induces a notion of stability of parabolic Higgs bundles depending on a parameter, and we construct their moduli space inside the moduli space of decorated swamps. We then introduce asymptotic stability of decorated swamps in order to study the behaviour of the stability condition as one parameter approaches infinity. The main result is the existence of a constant, such that stability with respect to parameters greater than this constant is equivalent to asymptotic stability. This implies boundedness of all decorated swamps which are semistable with respect to some parameter. Finally, we recover the usual stability condition of parabolic Higgs bundles as asymptotic stability.
Federal technology alert. Parabolic-trough solar water heating
1998-04-01
Parabolic-trough solar water heating is a well-proven renewable energy technology with considerable potential for application at Federal facilities. For the US, parabolic-trough water-heating systems are most cost effective in the Southwest where direct solar radiation is high. Jails, hospitals, barracks, and other facilities that consistently use large volumes of hot water are particularly good candidates, as are facilities with central plants for district heating. As with any renewable energy or energy efficiency technology requiring significant initial capital investment, the primary condition that will make a parabolic-trough system economically viable is if it is replacing expensive conventional water heating. In combination with absorption cooling systems, parabolic-trough collectors can also be used for air-conditioning. Industrial Solar Technology (IST) of Golden, Colorado, is the sole current manufacturer of parabolic-trough solar water heating systems. IST has an Indefinite Delivery/Indefinite Quantity (IDIQ) contract with the Federal Energy Management Program (FEMP) of the US Department of Energy (DOE) to finance and install parabolic-trough solar water heating on an Energy Savings Performance Contract (ESPC) basis for any Federal facility that requests it and for which it proves viable. For an ESPC project, the facility does not pay for design, capital equipment, or installation. Instead, it pays only for guaranteed energy savings. Preparing and implementing delivery or task orders against the IDIQ is much simpler than the standard procurement process. This Federal Technology Alert (FTA) of the New Technology Demonstration Program is one of a series of guides to renewable energy and new energy-efficient technologies.
One-dimensional parabolic-beam photonic crystal laser.
Ahn, Byeong-Hyeon; Kang, Ju-Hyung; Kim, Myung-Ki; Song, Jung-Hwan; Min, Bumki; Kim, Ki-Soo; Lee, Yong-Hee
2010-03-15
We report one-dimensional (1-D) parabolic-beam photonic crystal (PhC) lasers in which the width of the PhC slab waveguide is parabolically tapered. A few high-Q resonant modes are confirmed in the vicinity of the tapered region where Gaussian-shaped photonic well is formed. These resonant modes originate from the dielectric PhC guided mode and overlap with the gain medium efficiently. It is also shown that the far-field radiation profile is closely associated with the symmetry of the structural perturbation.
Focusing of Intense Laser via Parabolic Plasma Concave Surface
NASA Astrophysics Data System (ADS)
Zhou, Weimin; Gu, Yuqiu; Wu, Fengjuan; Zhang, Zhimeng; Shan, Lianqiang; Cao, Leifeng; Zhang, Baohan
2015-12-01
Since laser intensity plays an important role in laser plasma interactions, a method of increasing laser intensity - focusing of an intense laser via a parabolic plasma concave surface - is proposed and investigated by three-dimensional particle-in-cell simulations. The geometric focusing via a parabolic concave surface and the temporal compression of high harmonics increased the peak intensity of the laser pulse by about two orders of magnitude. Compared with the improvement via laser optics approaches, this scheme is much more economic and appropriate for most femtosecond laser facilities. supported by National Natural Science Foundation of China (Nos. 11174259, 11175165), and the Dual Hundred Foundation of China Academy of Engineering Physics
The Poincaré-Bendixson Theorem and the non-linear Cauchy-Riemann equations
NASA Astrophysics Data System (ADS)
van den Berg, J. B.; Munaò, S.; Vandervorst, R. C. A. M.
2016-11-01
Fiedler and Mallet-Paret (1989) prove a version of the classical Poincaré-Bendixson Theorem for scalar parabolic equations. We prove that a similar result holds for bounded solutions of the non-linear Cauchy-Riemann equations. The latter is an application of an abstract theorem for flows with a(n) (unbounded) discrete Lyapunov function.
The Minkowski dimension of interior singular points in the incompressible Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Koh, Youngwoo; Yang, Minsuk
2016-09-01
We study the possible interior singular points of suitable weak solutions to the three dimensional incompressible Navier-Stokes equations. We present an improved parabolic upper Minkowski dimension of the possible singular set, which is bounded by 95/63. The result also continue to hold for the three dimensional incompressible magnetohydrodynamic equations without any difficulty.
Model Problem for Integro-Differential Zakai Equation with Discontinuous Observation Processes
Mikulevicius, R.; Pragarauskas, H.
2011-08-15
The existence and uniqueness in Hoelder spaces of solutions of the Cauchy problem to a stochastic parabolic integro-differential equation of the order {alpha}{<=}2 is investigated. The equation considered arises in a filtering problem with a jump signal process and a jump observation process.
Global solution curves for self-similar equations
NASA Astrophysics Data System (ADS)
Korman, Philip
2014-10-01
We consider positive solutions of a semilinear Dirichlet problem Δu+λf(u)=0, for |x|<1, u=0, when |x|=1 on a unit ball in Rn. For four classes of self-similar equations it is possible to parameterize the entire (global) solution curve through the solution of a single initial value problem. This allows us to derive results on the multiplicity of solutions, and on their Morse indices. In particular, we easily recover the classical results of D.D. Joseph and T.S. Lundgren [6] on the Gelfand problem. Surprisingly, the situation turns out to be different for the generalized Gelfand problem, where infinitely many turns are possible for any space dimension n≥3. We also derive detailed results for the equation modeling electrostatic micro-electromechanical systems (MEMS), in particular we easily recover the main result of Z. Guo and J. Wei [4], and we show that the Morse index of the solutions increases by one at each turn. We also consider the self-similar Henon's equation.
The dynamics of parabolic flight: Flight characteristics and passenger percepts
NASA Astrophysics Data System (ADS)
Karmali, Faisal; Shelhamer, Mark
2008-09-01
Flying a parabolic trajectory in an aircraft is one of the few ways to create freefall on Earth, which is important for astronaut training and scientific research. Here we review the physics underlying parabolic flight, explain the resulting flight dynamics, and describe several counterintuitive findings, which we corroborate using experimental data. Typically, the aircraft flies parabolic arcs that produce approximately 25 s of freefall (0 g) followed by 40 s of enhanced force (1.8 g), repeated 30-60 times. Although passengers perceive gravity to be zero, in actuality acceleration, and not gravity, has changed, and thus we caution against the terms "microgravity" and "zero gravity." Despite the aircraft trajectory including large (45°) pitch-up and pitch-down attitudes, the occupants experience a net force perpendicular to the floor of the aircraft. This is because the aircraft generates appropriate lift and thrust to produce the desired vertical and longitudinal accelerations, respectively, although we measured moderate (0.2 g) aft-ward accelerations during certain parts of these trajectories. Aircraft pitch rotation (average 3°/s) is barely detectable by the vestibular system, but could influence some physics experiments. Investigators should consider such details in the planning, analysis, and interpretation of parabolic-flight experiments.
The dynamics of parabolic flight: flight characteristics and passenger percepts.
Karmali, Faisal; Shelhamer, Mark
2008-09-01
Flying a parabolic trajectory in an aircraft is one of the few ways to create freefall on Earth, which is important for astronaut training and scientific research. Here we review the physics underlying parabolic flight, explain the resulting flight dynamics, and describe several counterintuitive findings, which we corroborate using experimental data. Typically, the aircraft flies parabolic arcs that produce approximately 25 seconds of freefall (0 g) followed by 40 seconds of enhanced force (1.8 g), repeated 30-60 times. Although passengers perceive gravity to be zero, in actuality acceleration, and not gravity, has changed, and thus we caution against the terms "microgravity" and "zero gravity. " Despite the aircraft trajectory including large (45°) pitch-up and pitch-down attitudes, the occupants experience a net force perpendicular to the floor of the aircraft. This is because the aircraft generates appropriate lift and thrust to produce the desired vertical and longitudinal accelerations, respectively, although we measured moderate (0.2 g) aft-ward accelerations during certain parts of these trajectories. Aircraft pitch rotation (average 3°/s) is barely detectable by the vestibular system, but could influence some physics experiments. Investigators should consider such details in the planning, analysis, and interpretation of parabolic-flight experiments.
Low-crosstalk Si arrayed waveguide grating with parabolic tapers.
Ye, Tong; Fu, Yunfei; Qiao, Lei; Chu, Tao
2014-12-29
A silicon arrayed waveguide grating (AWG) with low channel crosstalk was demonstrated by using ultra-short parabolic tapers to connect the AWG's free propagation regions and single-mode waveguides. The tapers satisfied the requirements of low-loss mode conversion and lower channel crosstalk from the coupling of neighboring waveguides in the AWGs. In this work, three different tapers, including parabolic tapers, linear tapers, and exponential tapers, were theoretically analyzed and experimentally investigated for a comparison of their effects when implemented in AWGs. The experimental results showed that the AWG with parabolic tapers had a crosstalk improvement up to 7.1 dB compared with the others. Based on the advantages of parabolic tapers, a 400-GHz 8 × 8 cyclic AWG with 2.4 dB on-chip loss and -17.6~-25.1 dB crosstalk was fabricated using a simple one-step etching process. Its performance was comparable with that of existing AWGs with bi-level tapers, which require complicated two-step etching fabrication processes.
Compound parabolic concentrator with cavity for tubular absorbers
Winston, Roland
1983-01-01
A compond parabolic concentrator with a V-shaped cavity is provided in which an optical receiver is emplaced. The cavity redirects all energy entering between the receiver and the cavity structure onto the receiver, if the optical receiver is emplaced a distance from the cavity not greater than 0.27 r (where r is the radius of the receiver).
Polarization properties of linearly polarized parabolic scaling Bessel beams
NASA Astrophysics Data System (ADS)
Guo, Mengwen; Zhao, Daomu
2016-10-01
The intensity profiles for the dominant polarization, cross polarization, and longitudinal components of modified parabolic scaling Bessel beams with linear polarization are investigated theoretically. The transverse intensity distributions of the three electric components are intimately connected to the topological charge. In particular, the intensity patterns of the cross polarization and longitudinal components near the apodization plane reflect the sign of the topological charge.
Orthostatic intolerance and motion sickness after parabolic flight
NASA Technical Reports Server (NTRS)
Schlegel, T. T.; Brown, T. E.; Wood, S. J.; Benavides, E. W.; Bondar, R. L.; Stein, F.; Moradshahi, P.; Harm, D. L.; Fritsch-Yelle, J. M.; Low, P. A.
2001-01-01
Because it is not clear that the induction of orthostatic intolerance in returning astronauts always requires prolonged exposure to microgravity, we investigated orthostatic tolerance and autonomic cardiovascular function in 16 healthy subjects before and after the brief micro- and hypergravity of parabolic flight. Concomitantly, we investigated the effect of parabolic flight-induced vomiting on orthostatic tolerance, R-wave-R-wave interval and arterial pressure power spectra, and carotid-cardiac baroreflex and Valsalva responses. After parabolic flight 1) 8 of 16 subjects could not tolerate 30 min of upright tilt (compared to 2 of 16 before flight); 2) 6 of 16 subjects vomited; 3) new intolerance to upright tilt was associated with exaggerated falls in total peripheral resistance, whereas vomiting was associated with increased R-wave-R-wave interval variability and carotid-cardiac baroreflex responsiveness; and 4) the proximate mode of new orthostatic failure differed in subjects who did and did not vomit, with vomiters experiencing comparatively isolated upright hypocapnia and cerebral vasoconstriction and nonvomiters experiencing signs and symptoms reminiscent of the clinical postural tachycardia syndrome. Results suggest, first, that syndromes of orthostatic intolerance resembling those developing after space flight can develop after a brief (i.e., 2-h) parabolic flight and, second, that recent vomiting can influence the results of tests of autonomic cardiovascular function commonly utilized in returning astronauts.
Lateral migration of a capsule in a parabolic flow.
Nix, S; Imai, Y; Ishikawa, T
2016-07-26
Red blood cells migrate to the center of the blood vessel in a process called axial migration, while other blood cells, such as white blood cells and platelets, are disproportionately found near the blood vessel wall. However, much is still unknown concerning the lateral migration of cells in the blood; the specific effect of hydrodynamic factors such as a wall or a shear gradient is still unclear. In this study, we investigate the lateral migration of a capsule using the boundary integral method, in order to compute exactly an infinite computational domain for an unbounded parabolic flow and a semi-infinite computational domain for a near-wall parabolic flow in the limit of Stokes flow. We show that the capsule lift velocity in an unbounded parabolic flow is linear with respect to the shear gradient, while the lift velocity in a near-wall parabolic flow is dependent on the distance to the wall. Then, using these relations, we give an estimation of the relative effect of the shear gradient as a function of channel width and distance between the capsule and the wall. This estimation can be used to determine cases in which the effect of the shear gradient or wall can be neglected; for example, the formation of the cell-free layer in blood vessels is determined to be unaffected by the magnitude of the shear gradient.
An Application of Calculus: Optimum Parabolic Path Problem
ERIC Educational Resources Information Center
Atasever, Merve; Pakdemirli, Mehmet; Yurtsever, Hasan Ali
2009-01-01
A practical and technological application of calculus problem is posed to motivate freshman students or junior high school students. A variable coefficient of friction is used in modelling air friction. The case in which the coefficient of friction is a decreasing function of altitude is considered. The optimum parabolic path for a flying object…
Orthostatic Intolerance and Motion Sickness After Parabolic Flight
NASA Technical Reports Server (NTRS)
Schlegel, Todd T.; Brown, Troy E.; Wood, Scott J.; Benavides, Edgar W.; Bondar, Roberta L.; Stein, Flo; Moradshahi, Peyman; Harm, Deborah L.; Low, Phillip A.
1999-01-01
Orthostatic intolerance is common in astronauts after prolonged space flight. However, the "push-pull effect" in military aviators suggests that brief exposures to transitions between hypo- and hypergravity are sufficient to induce untoward autonomic cardiovascular physiology in susceptible individuals. We therefore investigated orthostatic tolerance and autonomic cardiovascular function in 16 healthy test subjects before and after a seated 2-hr parabolic flight. At the same time, we also investigated relationships between parabolic flight-induced vomiting and changes in orthostatic and autonomic cardiovascular function. After parabolic flight, 8 of 16 subjects could not tolerate a 30-min upright tilt test, compared to 2 of 16 before flight. Whereas new intolerance in non-Vomiters resembled the clinical postural tachycardia syndrome (POTS), new intolerance in Vomiters was characterized by comparatively isolated upright hypocapnia and cerebral vasoconstriction. As a group, Vomiters also had evidence for increased postflight fluctuations in efferent vagal-cardiac nerve traffic occurring independently of any superimposed change in respiration. Results suggest that syndromes of orthostatic intolerance resembling those occurring after space flight can occur after a brief (i.e., 2-hr) parabolic flight.
Boundary control of parabolic systems - Finite-element approximation
NASA Technical Reports Server (NTRS)
Lasiecka, I.
1980-01-01
The finite element approximation of a Dirichlet type boundary control problem for parabolic systems is considered. An approach based on the direct approximation of an input-output semigroup formula is applied. Error estimates are derived for optimal state and optimal control, and it is noted that these estimates are actually optimal with respect to the approximation theoretic properties.
Parabolic Dish Solar Thermal Power Annual Program Review Proceedings
NASA Technical Reports Server (NTRS)
Lucas, J. W.
1982-01-01
The results of activities of the parabolic dish technology and applications development element of DOE's Solar Thermal Energy System Program are presented. Topics include the development and testing of concentrators, receivers, and power conversion units; system design and development for engineering experiments; economic analysis and marketing assessment; and advanced development activities. A panel discussion concerning industrial support sector requirements is also documented.
The dynamics of parabolic flight: flight characteristics and passenger percepts
Karmali, Faisal; Shelhamer, Mark
2008-01-01
Flying a parabolic trajectory in an aircraft is one of the few ways to create freefall on Earth, which is important for astronaut training and scientific research. Here we review the physics underlying parabolic flight, explain the resulting flight dynamics, and describe several counterintuitive findings, which we corroborate using experimental data. Typically, the aircraft flies parabolic arcs that produce approximately 25 seconds of freefall (0 g) followed by 40 seconds of enhanced force (1.8 g), repeated 30–60 times. Although passengers perceive gravity to be zero, in actuality acceleration, and not gravity, has changed, and thus we caution against the terms "microgravity" and "zero gravity. " Despite the aircraft trajectory including large (45°) pitch-up and pitch-down attitudes, the occupants experience a net force perpendicular to the floor of the aircraft. This is because the aircraft generates appropriate lift and thrust to produce the desired vertical and longitudinal accelerations, respectively, although we measured moderate (0.2 g) aft-ward accelerations during certain parts of these trajectories. Aircraft pitch rotation (average 3°/s) is barely detectable by the vestibular system, but could influence some physics experiments. Investigators should consider such details in the planning, analysis, and interpretation of parabolic-flight experiments. PMID:19727328
Dynamics of the energy relaxation in a parabolic quantum well laser
NASA Astrophysics Data System (ADS)
Trifonov, A. V.; Cherotchenko, E. D.; Carthy, J. L.; Ignatiev, I. V.; Tzimis, A.; Tsintzos, S.; Hatzopoulos, Z.; Savvidis, P. G.; Kavokin, A. V.
2016-03-01
We explore two parabolic quantum well (PQW) samples, with and without Bragg mirrors, in order to optimize the building blocks of a bosonic cascade laser. The photoluminescence spectra of a PQW microcavity sample is compared against that of a conventional microcavity with embedded quantum wells (QWs) to demonstrate that the weak coupling lasing in a PQW sample can be achieved. The relaxation dynamics in a conventional QW microcavity and in the PQW microcavity was studied by a nonresonant pump-pump excitation method. Strong difference in the relaxation characteristics between the two samples was found. The semiclassical Boltzmann equations were adapted to reproduce the evolution of excitonic populations within the PQW as a function of the pump power and the output intensity evolution as a function of the pump-pump pulse delay. Fitting the PQW data confirms the anticipated cascade relaxation, paving the way for such a system to produce terahertz radiation.
Nonuniqueness and multi-bump solutions in parabolic problems with the p-Laplacian
NASA Astrophysics Data System (ADS)
Benedikt, Jiří; Girg, Petr; Kotrla, Lukáš; Takáč, Peter
2016-01-01
The validity of the weak and strong comparison principles for degenerate parabolic partial differential equations with the p-Laplace operator Δp is investigated for p > 2. This problem is reduced to the comparison of the trivial solution (≡0, by hypothesis) with a nontrivial nonnegative solution u (x, t). The problem is closely related also to the question of uniqueness of a nonnegative solution via the weak comparison principle. In this article, realistic counterexamples to the uniqueness of a nonnegative solution, the weak comparison principle, and the strong maximum principle are constructed with a nonsmooth reaction function that satisfies neither a Lipschitz nor an Osgood standard "uniqueness" condition. Nonnegative multi-bump solutions with spatially disconnected compact supports and zero initial data are constructed between sub- and supersolutions that have supports of the same type.
Parabolized Navier-Stokes solutions of separation and trailing-edge flows
NASA Technical Reports Server (NTRS)
Brown, J. L.
1983-01-01
A robust, iterative solution procedure is presented for the parabolized Navier-Stokes or higher order boundary layer equations as applied to subsonic viscous-inviscid interaction flows. The robustness of the present procedure is due, in part, to an improved algorithmic formulation. The present formulation is based on a reinterpretation of stability requirements for this class of algorithms and requires only second order accurate backward or central differences for all streamwise derivatives. Upstream influence is provided for through the algorithmic formulation and iterative sweeps in x. The primary contribution to robustness, however, is the boundary condition treatment, which imposes global constraints to control the convergence path. Discussed are successful calculations of subsonic, strong viscous-inviscid interactions, including separation. These results are consistent with Navier-Stokes solutions and triple deck theory.
Cotta, R.M.; Gerk, J.E.V. . Dept. de Engenharia Mecanica)
1994-06-01
The integral transform method is employed in conjunction with second-order-accurate explicit finite-differences schemes, to handle accurately a class of parabolic-hyperbolic problems that appear in connection with transient forced convection inside ducts. The integral transformation process eliminates the independent variables in which the diffusion phenomena predominate. A system of coupled hyperbolic equations then results, involving time and the space coordinates in which convection is dominant, which is solved numerically through a modified upwind second-order finite-difference scheme. Stability and convergence characteristics of the proposed mixed approach are also examined. Typical applications in two- and three-dimensional geometries are considered, for both slug and laminar flow situations.
Pierantozzi, T.; Vazquez, L.
2005-11-01
Through fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D'Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case.
Askari, Nasim; Eslami, Esmaeil; Mirzaie, Reza
2015-11-15
The photonic band gap of obliquely incident terahertz electromagnetic waves in a one-dimensional plasma photonic crystal is studied. The periodic structure consists of lossless dielectric and inhomogeneous plasma with a parabolic density profile. The dispersion relation and the THz wave transmittance are analyzed based on the electromagnetic equations and transfer matrix method. The dependence of effective plasma frequency and photonic band gap characteristics on dielectric and plasma thickness, plasma density, and incident angle are discussed in detail. A theoretical calculation for effective plasma frequency is presented and compared with numerical results. Results of these two methods are in good agreement.
IR Spectrometer Using 90-Degree Off-Axis Parabolic Mirrors
Robert M. Malone, Ian J. McKenna
2008-03-01
A gated spectrometer has been designed for real-time, pulsed infrared (IR) studies at the National Synchrotron Light Source at the Brookhaven National Laboratory. A pair of 90-degree, off-axis parabolic mirrors are used to relay the light from an entrance slit to an output recording camera. With an initial wavelength range of 1500–4500 nm required, gratings could not be used in the spectrometer because grating orders would overlap. A magnesium oxide prism, placed between these parabolic mirrors, serves as the dispersion element. The spectrometer is doubly telecentric. With proper choice of the air spacing between the prism and the second parabolic mirror, any spectral region of interest within the InSb camera array’s sensitivity region can be recorded. The wavelengths leaving the second parabolic mirror are collimated, thereby relaxing the camera positioning tolerance. To set up the instrument, two different wavelength (visible) lasers are introduced at the entrance slit and made collinear with the optical axis via flip mirrors. After dispersion by the prism, these two laser beams are directed to tick marks located on the outside housing of the gated IR camera. This provides first-order wavelength calibration for the instrument. Light that is reflected off the front prism face is coupled into a high-speed detector to verify steady radiance during the gated spectral imaging. Alignment features include tick marks on the prism and parabolic mirrors. This instrument was designed to complement single-point pyrometry, which provides continuous time histories of a small collection of spots from shock-heated targets.
IR Spectrometer Using 90-degree Off-axis Parabolic Mirrors
Robert M. Malone, Richard, G. Hacking, Ian J. McKenna, and Daniel H. Dolan
2008-09-02
A gated spectrometer has been designed for real-time, pulsed infrared (IR) studies at the National Synchrotron Light ource at the Brookhaven National Laboratory. A pair of 90-degree, off-axis parabolic mirrors are used to relay the light from an entrance slit to an output IR recording camera. With an initial wavelength range of 1500–4500 nm required, gratings could not be used in the spectrometer because grating orders would overlap. A magnesium oxide prism, placed between these parabolic mirrors, serves as the dispersion element. The spectrometer is doubly telecentric. With proper choice of the air spacing between the prism and the second parabolic mirror, any spectral region of interest within the InSb camera array’s sensitivity region can be recorded. The wavelengths leaving the second parabolic mirror are collimated, thereby relaxing the camera positioning tolerance. To set up the instrument, two different wavelength (visible) lasers are introduced at the entrance slit and made collinear with the optical axis via flip mirrors. After dispersion by the prism, these two laser beams are directed to tick marks located on the outside housing of the gated IR camera. This provides first-order wavelength calibration for the instrument. Light that is reflected off the front prism face is coupled into a high-speed detector to verify steady radiance during the gated spectral imaging. Alignment features include tick marks on the prism and parabolic mirrors. This instrument was designed to complement singlepoint pyrometry, which provides continuous time histories of a small collection of spots from shock-heated targets.
ERIC Educational Resources Information Center
De Luca, R.; Fedullo, A.
2009-01-01
A vertical light ray coming from infinity is reflected by a primary parabolic mirror M[subscript 1] having focus at F[subscript 1]. At a small distance from F[subscript 1] a secondary mirror M[subscript 2], symmetric with respect to the vertical axis, is placed. One would like to find the analytic equation of the mirror M[subscript 2], so that all…
Ground states for irregular and indefinite superlinear Schrödinger equations
NASA Astrophysics Data System (ADS)
Ackermann, Nils; Chagoya, Julián
2016-11-01
We consider the existence of a ground state for the subcritical stationary semilinear Schrödinger equation - Δu + u = a (x) | u| p - 2 u in H1, where a ∈L∞ (RN) may change sign. Our focus is on the case where loss of compactness occurs at the ground state energy. By providing a new variant of the Splitting Lemma we do not need to assume the existence of a limit problem at infinity, be it in the form of a pointwise limit for a as | x | → ∞ or of asymptotic periodicity. That is, our problem may be irregular at infinity. In addition, we allow a to change sign near infinity, a case that has never been treated before.
Electromagnetic Casimir forces of parabolic cylinder and knife-edge geometries
Graham, Noah; Shpunt, Alexander; Kardar, Mehran; Emig, Thorsten; Rahi, Sahand Jamal; Jaffe, Robert L.
2011-06-15
An exact calculation of electromagnetic scattering from a perfectly conducting parabolic cylinder is employed to compute Casimir forces in several configurations. These include interactions between a parabolic cylinder and a plane, two parabolic cylinders, and a parabolic cylinder and an ordinary cylinder. To elucidate the effect of boundaries, special attention is focused on the 'knife-edge' limit in which the parabolic cylinder becomes a half-plane. Geometrical effects are illustrated by considering arbitrary rotations of a parabolic cylinder around its focal axis, and arbitrary translations perpendicular to this axis. A quite different geometrical arrangement is explored for the case of an ordinary cylinder placed in the interior of a parabolic cylinder. All of these results extend simply to nonzero temperatures.
Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations
NASA Astrophysics Data System (ADS)
Ablowitz, Mark J.; Demirci, Ali; Ma, Yi-Ping
2016-10-01
Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using step like initial data along a parabolic front. Employing a parabolic similarity reduction exactly reduces the study of such DSWs in two space one time (2 + 1) dimensions to finding DSW solutions of (1 + 1) dimensional equations. With this ansatz, the KP and 2DBO equations can be exactly reduced to the cylindrical Korteweg-de Vries (cKdV) and cylindrical Benjamin-Ono (cBO) equations, respectively. Whitham modulation equations which describe DSW evolution in the cKdV and cBO equations are derived and Riemann type variables are introduced. DSWs obtained from the numerical solutions of the corresponding Whitham systems and direct numerical simulations of the cKdV and cBO equations are compared with very good agreement obtained. In turn, DSWs obtained from direct numerical simulations of the KP and 2DBO equations are compared with the cKdV and cBO equations, again with good agreement. It is concluded that the (2 + 1) DSW behavior along self similar parabolic fronts can be effectively described by the DSW solutions of the reduced (1 + 1) dimensional equations.
Verification and Validation of a Chemical Reaction Solver Coupled to the Piecewise Parabolic Method
NASA Astrophysics Data System (ADS)
Attal, Nitesh; Ramaprabhu, Praveen; Hossain, Jahed; Karkhanis, Varad; Roy, Sukesh; Gord, James; Uddin, Mesbah
2012-11-01
We present a detailed chemical kinetics reaction solver coupled to the Piecewise Parabolic Method (PPM) embedded in the widely used astrophysical FLASH code. The FLASH code solves the compressible Euler equations with a directionally split, PPM with Adaptive Mesh Refinement (AMR). The reaction network is solved using a library of coupled ODE solvers, specialized for handling stiff systems of equations. Finally, the diffusion of heat, mass, and momentum is handled either through an update of the fluxes of each quantity, or by directly solving a diffusion equation for each. The resulting product is capable of handling a variety of physics such as gas-phase chemical kinetics, diffusive transport of mass, momentum, and heat, shocks, sharp interfaces, multi-species mixtures, and thermal radiation. We will present results from verification and validation of the above capabilities through comparison with analytical solutions, and published numerical and experimental data. Our validation cases include advection of reacting fronts in 1-D and 2D, laminar premixed flames in a Bunsen burner configuration, and shock-driven combustion. We acknowledge funding from Spectral Energies LLC.
NASA Technical Reports Server (NTRS)
Amitai, Dganit; Averbuch, Amir; Itzikowitz, Samuel; Turkel, Eli
1991-01-01
A major problem in achieving significant speed-up on parallel machines is the overhead involved with synchronizing the concurrent process. Removing the synchronization constraint has the potential of speeding up the computation. The authors present asynchronous (AS) and corrected-asynchronous (CA) finite difference schemes for the multi-dimensional heat equation. Although the discussion concentrates on the Euler scheme for the solution of the heat equation, it has the potential for being extended to other schemes and other parabolic partial differential equations (PDEs). These schemes are analyzed and implemented on the shared memory multi-user Sequent Balance machine. Numerical results for one and two dimensional problems are presented. It is shown experimentally that the synchronization penalty can be about 50 percent of run time: in most cases, the asynchronous scheme runs twice as fast as the parallel synchronous scheme. In general, the efficiency of the parallel schemes increases with processor load, with the time level, and with the problem dimension. The efficiency of the AS may reach 90 percent and over, but it provides accurate results only for steady-state values. The CA, on the other hand, is less efficient, but provides more accurate results for intermediate (non steady-state) values.
NASA Technical Reports Server (NTRS)
Baumeister, Kenneth J.; Kreider, Kevin L.
1996-01-01
An explicit finite difference iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.
Parabolic dish systems at work - Applying the concepts
NASA Technical Reports Server (NTRS)
Marriott, A. T.
1981-01-01
An overview is given of parabolic dish solar concentrator application experiments being conducted by the U.S. Department of Energy. The 'engineering experiments' comprise the testing of (1) a small-community powerplant system, in conjunction with a grid-connected utility; (2) stand-alone applications at remote sites such as military installations, radar stations and villages; and (3) dish modules that can deliver heat for direct use in industrial processes. Applicability projections are based on a dish and receiver that use a Brayton engine with an engine/generator efficiency of 25% and a production level of up to 25,000 units per year. Analyses indicate that parabolic-dish power systems can potentially replace small, oil-fired power plants in all regions of the U.S. between 1985 and 1991.
Water Cooled TJ Dense Array Modules for Parabolic Dishes
Loeckenhoff, Ruediger; Kubera, Tim; Rasch, Klaus Dieter
2010-10-14
AZUR SPACE Solar Power GmbH has developed a novel type of dense array module for use in parabolic dishes. Such dishes never produce a perfectly homogeneous, rectangular light spot but an inhomogeneous light distribution. A regular module would use this light distribution very inefficiently. Therefore AZUR SPACE developed a dense array module concept which can be adapted to inhomogeneous light spots. It is populated with state of the art triple junction solar cells.The modules are designed for light intensities in the range of 50-100 W/cm{sup 2} and are actively water cooled. Prototypes are installed in 11 m{sup 2} parabolic dishes produced by Zenith Solar. A peak output of 2.3 kW electrical and 5.5 kW thermal power could be demonstrated. The thermal power may be used for solar heating, solar cooling or warm water.
Parabolic Trouogh Optical Characterization at the National Renewable Energy Laboratory
Wendelin, T. J.
2005-01-01
Solar parabolic trough power plant projects are soon to be implemented in the United States and internationally. In addition to these new projects, parabolic trough power plants totaling approximately 350 MW already exist within the United States and have operated for close to 20 years. As such, the status of the technology exists within several different phases. Theses phases include R&D, manufacturing and installation, and operations and maintenance. One aspect of successful deployment of this technology is achieving and maintaining optical performance. Different optical tools are needed to assist in improving initial designs, provide quality control during manufacture and assembly, and help maintain performance during operation. This paper discusses several such tools developed at SunLab (a joint project of the National Renewable Laboratory and Sandia National Laboratories) for these purposes. Preliminary testing results are presented. Finally, plans for further tool development are discussed.
Physiologic Pressure and Flow Changes During Parabolic Flight (Pilot Study)
NASA Technical Reports Server (NTRS)
Pantalos, George; Sharp, M. Keith; Mathias, John R.; Hargens, Alan R.; Watenpaugh, Donald E.; Buckey, Jay C.
1999-01-01
The objective of this study was to obtain measurement of cutaneous tissue perfusion central and peripheral venous pressure, and esophageal and abdominal pressure in human test subjects during parabolic flight. Hemodynamic data recorded during SLS-I and SLS-2 missions have resulted in the paradoxical finding of increased cardiac stroke volume in the presence of a decreased central venous pressure (CVP) following entry in weightlessness. The investigators have proposed that in the absence of gravity, acceleration-induced peripheral vascular compression is relieved, increasing peripheral vascular capacity and flow while reducing central and peripheral venous pressure, This pilot study seeks to measure blood pressure and flow in human test subjects during parabolic flight for different postures.
Parabolic discounting of monetary rewards by physical effort.
Hartmann, Matthias N; Hager, Oliver M; Tobler, Philippe N; Kaiser, Stefan
2013-11-01
When humans and other animals make decisions in their natural environments prospective rewards have to be weighed against costs. It is well established that increasing costs lead to devaluation or discounting of reward. While our knowledge about discount functions for time and probability costs is quite advanced, little is known about how physical effort discounts reward. In the present study we compared three different models in a binary choice task in which human participants had to squeeze a handgrip to earn monetary rewards: a linear, a hyperbolic, and a parabolic model. On the group as well as the individual level, the concave parabolic model explained most variance of the choice data, thus contrasting with the typical hyperbolic discounting of reward value by delay. Research on effort discounting is not only important to basic science but also holds the potential to quantify aberrant motivational states in neuropsychiatric disorders.
Treatment of motion sickness in parabolic flight with buccal scopolamine
NASA Technical Reports Server (NTRS)
Norfleet, William T.; Degioanni, Joseph J.; Reschke, Millard F.; Bungo, Michael W.; Kutyna, Frank A.; Homick, Jerry L.; Calkins, D. S.
1992-01-01
Treatment of acute motion sickness induced by parabolic flight with a preparation of scopolamine placed in the buccal pouch was investigated. Twenty-one subjects flew aboard a KC-135 aircraft operated by NASA which performed parabolic maneuvers resulting in periods of 0-g, 1-g, and 1.8-g. Each subject flew once with a tablet containing scopolamine and once with a placebo in a random order, crossover design. Signs and symptoms of motion sickness were systematically recorded during each parabola by an investigator who was blind to the content of the tablet. Compared with flights using placebo, flights with buccal scopolamine resulted in significantly lower scores for nausea (31-35 percent reduction) and vomiting (50 percent reduction in number of parabolas with vomiting). Side effects of the drug during flight were negligible. It is concluded that buccal scopolamine is more effective than a placebo in treating ongoing motion sickness.
Development and testing of Parabolic Dish Concentrator No. 1
NASA Technical Reports Server (NTRS)
Dennison, E. W.; Thostesen, T. O.
1984-01-01
Parabolic Dish Concentrator No. 1 (PDC-1) is a 12-m-diameter prototype concentrator with low life-cycle costs for use with thermal-to-electric energy conversion devices. The concentrator assembly features panels made of a resin transfer molded balsa core/fiberglass sandwich with plastic reflective film as the reflective surface and a ribbed framework to hold the panels in place. The concentrator assembly tracks in azimuth and elevation on a base frame riding on a circular track. It is shown that the panels do not exhibit the proper parabolic contour. However, thermal gradients were discovered in the panels with daily temperature changes. The PDC-1 has sufficient optical quality to operate satisfactorily in a dish-electric system. The PDC-1 development provides the impetus for creating innovative optical testing methods and valuable information for use in designing and fabricating concentrators of future dish-electric systems.
All-fiber ring Raman laser generating parabolic pulses
Kruglov, V. I.; Mechin, D.; Harvey, J. D.
2010-02-15
We present theoretical and numerical results for an all-fiber laser using self-similar parabolic pulses ('similaritons') designed to operate using self-similar propagation regimes. The similariton laser features a frequency filter and a Sagnac loop which operate together to generate an integrated all-fiber mode-locked laser. Numerical studies show that this laser generates parabolic pulses with linear chirp in good agreement with analytical predictions. The period for propagating similariton pulses in stable regimes can vary from one to two round trips for different laser parameters. Two-round-trip-period operation in the mode-locked laser appears at bifurcation points for certain cavity parameters. The stability of the similariton regimes has been confirmed by numerical simulations for large numbers of round trips.
Irrigation market for solar thermal parabolic dish systems
NASA Technical Reports Server (NTRS)
Habib-Agahi, H.; Jones, S. C.
1981-01-01
The potential size of the onfarm-pumped irrigation market for solar thermal parabolic dish systems in seven high-insolation states is estimated. The study is restricted to the displacement of three specific fuels: gasoline, diesel and natural gas. The model was developed to estimate the optimal number of parabolic dish modules per farm based on the minimum cost mix of conventional and solar thermal energy required to meet irrigation needs. The study concludes that the potential market size for onfarm-pumped irrigation applications ranges from 101,000 modules when a 14 percent real discount rate is assumed to 220,000 modules when the real discount rate drops to 8 percent. Arizona, Kansas, Nebraska, New Mexico and Texas account for 98 percent of the total demand for this application, with the natural gas replacement market accounting for the largest segment (71 percent) of the total market.
A Review of Psycho-Physiological Responses to Parabolic Flight
NASA Astrophysics Data System (ADS)
Brummer, Vera; Schneider, Stefan; Guardiera, Simon; Struder, Heiko K.
2008-06-01
This review combines and correlates data of several studies conducted in the recent years where we were able to show an increase in stress hormone concentrations, EEG activity and a decrease in mood during parabolic flights. The aim of these studies was to consider whether previous results showing a decrease in mental and perceptual motor performance during weightlessness were solely due to the changes in gravity itself or were also, at least partly, explainable by an increase of stress and/or arousal during parabolic flights. A correlation between stress hormones and mood but not between EEG activity and mood nor between stress hormones and EEG activity could be found. We propose two different stressors: First an activation of the adrenomedullary system, secondly a general increase of cortical arousal. Whereas the first one is perceived by subjects, this is not the case for the second one.
Absorber Alignment Measurement Tool for Solar Parabolic Trough Collectors: Preprint
Stynes, J. K.; Ihas, B.
2012-04-01
As we pursue efforts to lower the capital and installation costs of parabolic trough solar collectors, it is essential to maintain high optical performance. While there are many optical tools available to measure the reflector slope errors of parabolic trough solar collectors, there are few tools to measure the absorber alignment. A new method is presented here to measure the absorber alignment in two dimensions to within 0.5 cm. The absorber alignment is measured using a digital camera and four photogrammetric targets. Physical contact with the receiver absorber or glass is not necessary. The alignment of the absorber is measured along its full length so that sagging of the absorber can be quantified with this technique. The resulting absorber alignment measurement provides critical information required to accurately determine the intercept factor of a collector.
NASA Technical Reports Server (NTRS)
Grosse, Ralf
1990-01-01
Propagation of sound through the turbulent atmosphere is a statistical problem. The randomness of the refractive index field causes sound pressure fluctuations. Although no general theory to predict sound pressure statistics from given refractive index statistics exists, there are several approximate solutions to the problem. The most common approximation is the parabolic equation method. Results obtained by this method are restricted to small refractive index fluctuations and to small wave lengths. While the first condition is generally met in the atmosphere, it is desirable to overcome the second. A generalization of the parabolic equation method with respect to the small wave length restriction is presented.
Proceedings: Fourth Parabolic Dish Solar Thermal Power Program Review
NASA Technical Reports Server (NTRS)
1983-01-01
The results of activities within the parabolic dish technology and applications development program are presented. Stirling, organic Rankine and Brayton module technologies, associated hardware and test results to date; concentrator development and progress; economic analyses; and international dish development activities are covered. Two panel discussions, concerning industry issues affecting solar thermal dish development and dish technology from a utility/user perspective, are also included.
Sea urchin fertilization during a KC-135 parabolic flight.
Schatten, H; Zoran, S; Levine, H G; Anderson, K; Chakrabarti, A
1999-07-01
For long-term exposure to space it is crucial to understand the underlying mechanisms for altered physiological functions. We have chosen the sea urchin system to study the effects of microgravity on various cellular processes visible during fertilization and subsequent development. We report here on experiments performed on NASA's KC-135 during parabolic flight trajectories to validate procedures to be implemented as part of the first Aquatic Research Facility Space Shuttle experiment on STS-77. PMID:11543042
Thermal distortion analysis of a deployable parabolic reflector
NASA Technical Reports Server (NTRS)
Bruck, L. R.; Honeycutt, G. H.
1973-01-01
A thermal distortion analysis of the ATS-6 Satellite parabolic reflector was performed using NASTRAN level 15.1. The same NASTRAN finite element method was used to conduct a one g static load analysis and a dynamic analysis of the reflector. In addition, a parametric study was made to determine which parameters had the greatest effect on the thermal distortions. The method used to model the construction of the reflector is described and the results of the analyses are presented.
Performance of a blood chemistry analyzer during parabolic flight
NASA Technical Reports Server (NTRS)
Spooner, Brian S.; Claassen, Dale E.; Guikema, James A.
1990-01-01
The performance of the Vision System Blood Analyzer during parabolic flight on a KC-135 aircraft (NASA 930) has been tested. This fully automated instrument performed flawlessly in these trials, demonstrating its potential for efficient, reliable use in a microgravity environment. In addition to instrument capability, it is demonstrated that investigators could readily fill specially modified test packs with fluid during zero gravity, and that filled test packs could be easily loaded into VISION during an episode of microgravity.
Synergies between optical and physical variables in intercepting parabolic targets.
Gómez, José; López-Moliner, Joan
2013-01-01
Interception requires precise estimation of time-to-contact (TTC) information. A long-standing view posits that all relevant information for extracting TTC is available in the angular variables, which result from the projection of distal objects onto the retina. The different timing models rooted in this tradition have consequently relied on combining visual angle and its rate of expansion in different ways with tau being the most well-known solution for TTC. The generalization of these models to timing parabolic trajectories is not straightforward. For example, these different combinations rely on isotropic expansion and usually assume first-order information only, neglecting acceleration. As a consequence no optical formulations have been put forward so far to specify TTC of parabolic targets with enough accuracy. It is only recently that context-dependent physical variables have been shown to play an important role in TTC estimation. Known physical size and gravity can adequately explain observed data of linear and free-falling trajectories, respectively. Yet, a full timing model for specifying parabolic TTC has remained elusive. We here derive two formulations that specify TTC for parabolic ball trajectories. The first specification extends previous models in which known size is combined with thresholding visual angle or its rate of expansion to the case of fly balls. To efficiently use this model, observers need to recover the 3D radial velocity component of the trajectory which conveys the isotropic expansion. The second one uses knowledge of size and gravity combined with ball visual angle and elevation angle. Taking into account the noise due to sensory measurements, we simulate the expected performance of these models in terms of accuracy and precision. While the model that combines expansion information and size knowledge is more efficient during the late trajectory, the second one is shown to be efficient along all the flight.
Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques
NASA Technical Reports Server (NTRS)
Banks, H. T.; Wang, C.
1989-01-01
A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.
Discontinuous Galerkin Finite Element Method for Parabolic Problems
NASA Technical Reports Server (NTRS)
Kaneko, Hideaki; Bey, Kim S.; Hou, Gene J. W.
2004-01-01
In this paper, we develop a time and its corresponding spatial discretization scheme, based upon the assumption of a certain weak singularity of parallel ut(t) parallel Lz(omega) = parallel ut parallel2, for the discontinuous Galerkin finite element method for one-dimensional parabolic problems. Optimal convergence rates in both time and spatial variables are obtained. A discussion of automatic time-step control method is also included.
Performance of a blood chemistry analyzer during parabolic flight.
Spooner, B S; Claassen, D E; Guikema, J A
1990-01-01
We have tested the performance of the VISION System Blood Analyzer, produced by Abbott Laboratories, during parabolic flight on a KC-135 aircraft (NASA 930). This fully automated instrument performed flawlessly in these trials, demonstrating its potential for efficient, reliable use in a microgravity environment. In addition to instrument capability, we demonstrated that investigators could readily fill specially modified test packs with fluid during zero gravity, and that filled test packs could be easily loaded into VISION during an episode of microgravity.
Synergies between optical and physical variables in intercepting parabolic targets
Gómez, José; López-Moliner, Joan
2013-01-01
Interception requires precise estimation of time-to-contact (TTC) information. A long-standing view posits that all relevant information for extracting TTC is available in the angular variables, which result from the projection of distal objects onto the retina. The different timing models rooted in this tradition have consequently relied on combining visual angle and its rate of expansion in different ways with tau being the most well-known solution for TTC. The generalization of these models to timing parabolic trajectories is not straightforward. For example, these different combinations rely on isotropic expansion and usually assume first-order information only, neglecting acceleration. As a consequence no optical formulations have been put forward so far to specify TTC of parabolic targets with enough accuracy. It is only recently that context-dependent physical variables have been shown to play an important role in TTC estimation. Known physical size and gravity can adequately explain observed data of linear and free-falling trajectories, respectively. Yet, a full timing model for specifying parabolic TTC has remained elusive. We here derive two formulations that specify TTC for parabolic ball trajectories. The first specification extends previous models in which known size is combined with thresholding visual angle or its rate of expansion to the case of fly balls. To efficiently use this model, observers need to recover the 3D radial velocity component of the trajectory which conveys the isotropic expansion. The second one uses knowledge of size and gravity combined with ball visual angle and elevation angle. Taking into account the noise due to sensory measurements, we simulate the expected performance of these models in terms of accuracy and precision. While the model that combines expansion information and size knowledge is more efficient during the late trajectory, the second one is shown to be efficient along all the flight. PMID:23720614
Criteria for evaluation of reflective surface for parabolic dish concentrators
NASA Technical Reports Server (NTRS)
Bouquet, F.
1980-01-01
Commercial, second surface glass mirror are emphasized, but aluminum and metallized polymeric films are also included. Criteria for sealing solar mirrors in order to prevent environmental degradation and criteria for bonding sagged or bent mirrors to substrate materials are described. An overview of the technical areas involved in evaluating small mirror samples, sections, and entire large gores is presented. A basis for mirror criteria was established that eventually may become part of inspection and evaluation techniques for three dimensional parabolic reflective surfaces.
Gas Turbine/Solar Parabolic Trough Hybrid Designs: Preprint
Turchi, C. S.; Ma, Z.; Erbes, M.
2011-03-01
A strength of parabolic trough concentrating solar power (CSP) plants is the ability to provide reliable power by incorporating either thermal energy storage or backup heat from fossil fuels. Yet these benefits have not been fully realized because thermal energy storage remains expensive at trough operating temperatures and gas usage in CSP plants is less efficient than in dedicated combined cycle plants. For example, while a modern combined cycle plant can achieve an overall efficiency in excess of 55%; auxiliary heaters in a parabolic trough plant convert gas to electricity at below 40%. Thus, one can argue the more effective use of natural gas is in a combined cycle plant, not as backup to a CSP plant. Integrated solar combined cycle (ISCC) systems avoid this pitfall by injecting solar steam into the fossil power cycle; however, these designs are limited to about 10% total solar enhancement. Without reliable, cost-effective energy storage or backup power, renewable sources will struggle to achieve a high penetration in the electric grid. This paper describes a novel gas turbine / parabolic trough hybrid design that combines solar contribution of 57% and higher with gas heat rates that rival that for combined cycle natural gas plants. The design integrates proven solar and fossil technologies, thereby offering high reliability and low financial risk while promoting deployment of solar thermal power.
Circulatory filling pressures during transient microgravity induced by parabolic flight
NASA Technical Reports Server (NTRS)
Latham, Ricky D.; Fanton, John W.; White, C. D.; Vernalis, Mariana N.; Crisman, R. P.; Koenig, S. C.
1993-01-01
Theoretical concepts hold that blood in the gravity dependent portion of the body would relocate to more cephalad compartments under microgravity. The result is an increase in blood volume in the thoraic and cardiac chambers. However, experimental data has been somewhat contradictory and nonconclusive. Early studies of peripheral venous pressure and estimates of central venous pressure (CVP) from these data did not show an increase in CVP under microgravity. However, CVP recorded in human volunteers during a parabolic flight revealed an increase in CVP during the microgravity state. On the STS 40 shuttle mission, a payload specialist wore a fluid line that recorded CVP during the first few hours of orbital insertion. These data revealed decreased CVP. When this CVP catheter was tested during parabolic flight in four subjects, two had increased CVP recordings and two had decreased CVP measurements. In 1991, our laboratory performed parabolic flight studies in several chronic-instrumented baboons. It was again noted that centrally recorded right atrial pressure varied with exposure to microgravity, some animals having an increase, and others a decrease.
Application of parabolic reflector on Raman analysis of gas samples
NASA Astrophysics Data System (ADS)
Yu, Anlan; Zuo, Duluo; Gao, Jun; Li, Bin; Wang, Xingbing
2016-05-01
Studies on the application of a parabolic reflector in spontaneous Raman scattering for low background Raman analysis of gas samples are reported. As an effective signal enhancing sample cell, photonic bandgap fiber (HC-PBF) or metallined capillary normally result in a strong continuous background in spectra caused by the strong Raman/fluorescence signal from the silica wall and the polymer protective film. In order to obtain enhanced signal with low background, a specially designed sample cell with double-pass and large collecting solid angle constructed by a parabolic reflector and a planar reflector was applied, of which the optical surfaces had been processed by diamond turning and coated by silver film and protective film of high-purity alumina. The influences of optical structure, polarization characteristic, collecting solid-angle and collecting efficiency of the sample cell on light propagation and signal enhancement were studied. A Raman spectrum of ambient air with signal to background ratio of 94 was acquired with an exposure time of 1 sec by an imaging spectrograph. Besides, the 3σ limits of detection (LOD) of 7 ppm for H2, 8 ppm for CO2 and 12 ppm for CO were also obtained. The sample cell mainly based on parabolic reflector will be helpful for compact and high-sensitive Raman system.
Parabolic similariton Yb-fiber laser with triangular pulse evolution
NASA Astrophysics Data System (ADS)
Wang, Sijia; Wang, Lei
2016-04-01
We propose a novel mode-locked fiber laser design which features a passive nonlinear triangular pulse formation and self-similar parabolic pulse amplification intra cavity. Attribute to the nonlinear reshaping progress in the passive fiber, a triangular-profiled pulse with negative-chirp is generated and paved the way for rapid and efficient self-similar parabolic evolution in a following short-length high-gain fiber. In the meanwhile, the accompanied significantly compressed narrow spectrum from this passive nonlinear reshaping also gives the promise of pulse stabilization and gain-shaping robustness without strong filtering. The resulting short average intra-cavity pulse duration, low amplified spontaneous emission (ASE) and low intra-cavity power loss are essential for the low-noise operation. Simulations predict this modelocked fiber laser allows for high-energy ultra-short transform-limited pulse generation exceeding the gain bandwidth. The output pulse has a de-chirped duration (full-width at half maximum, FWHM) of 27 fs. In addition to the ultrafast laser applications, the proposed fiber laser scheme can support low-noise parabolic and triangular pulse trains at the same time, which are also attractive in optical pulse shaping, all-optical signal processing and high-speed communication applications.
Price, H.; Kearney, D.
1999-01-31
Technology roadmapping is a needs-driven technology planning process to help identify, select, and develop technology alternatives to satisfy a set of market needs. The DOE's Office of Power Technologies' Concentrating Solar Power (CSP) Program recently sponsored a technology roadmapping workshop for parabolic trough technology. The workshop was attended by an impressive cross section of industry and research experts. The goals of the workshop were to evaluate the market potential for trough power projects, develop a better understanding of the current state of the technology, and to develop a conceptual plan for advancing the state of parabolic trough technology. This report documents and extends the roadmap that was conceptually developed during the workshop.
NASA Technical Reports Server (NTRS)
Dinar, N.
1978-01-01
Several aspects of multigrid methods are briefly described. The main subjects include the development of very efficient multigrid algorithms for systems of elliptic equations (Cauchy-Riemann, Stokes, Navier-Stokes), as well as the development of control and prediction tools (based on local mode Fourier analysis), used to analyze, check and improve these algorithms. Preliminary research on multigrid algorithms for time dependent parabolic equations is also described. Improvements in existing multigrid processes and algorithms for elliptic equations were studied.
A fourth-order box method for solving the boundary layer equations
NASA Technical Reports Server (NTRS)
Wornom, S. F.
1977-01-01
A fourth order box method for calculating high accuracy numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations is presented. The method is the natural extension of the second order Keller Box scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary layer equations. Numerical results for high accuracy test cases show the method to be significantly faster than other higher order and second order methods.
The dynamics of patterns for two phase separation equations
Eyre, D.J.
1992-12-31
Two parabolic partial differential equations, the Allen-Cahn equation and the Cahn-Hilliard equation, are studied. Solutions of these equations form spatial patterns that evolve in time. For the Allen-Cahn equation, the analysis is on an initial value problem that is appropriate for development of the spatial patterns from constant stationary solutions. A model is developed to predict the patterns that form. For the Cahn-Hilliard equation, the analysis is concentrated on the pattern dynamics once a well formed pattern exists. Discrete and continuous models of the pattern dynamics are considered. Predictions of these models include a period doubling phenomena and a self-similar pattern. All the results given here are for one spatial dimension. These equations have applications in the material sciences and these applications are discussed.
Numerical investigation of internal high-speed viscous flows using a parabolic technique
NASA Technical Reports Server (NTRS)
Anderson, O. L.; Power, G. D.
1985-01-01
A feasibility study has been 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 are present. A set of test problems with weak shock and expansion waves have been analyzed with this modified ADD method and stable and accurate solutions were demonstrated provided the streamwise step size was maintained at levels larger than the boundary layer displacement thickness. Calculations made with further reductions in step size encountered departure solutions consistent with strong interaction theory. Calculations were also performed for a flow field with a flame front in which a specific heat release was imposed to simulate a SCRAMJET combustor. In this case the flame front generated relatively thick shear layers which aggravated the departure solution problem. Qualitatively correct results were obtained for these cases using a marching technique with the convective terms in the normal momentum equation suppressed. 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.
Solution Methods for Certain Evolution Equations
NASA Astrophysics Data System (ADS)
Vega-Guzman, Jose Manuel
Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value
Young, C.W.
1997-10-01
In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.
Processing of data from innovative parabolic strip telescope.
NASA Astrophysics Data System (ADS)
Kosejk, Vladislav; Novy, J.; Chadzitaskos, Goce
2015-12-01
This paper presents an innovative telescope design based on the usage of a parabolic strip fulfilling the function of an objective. Isaac Newton was the first to solve the problem of chromatic aberration, which is caused by a difference in the refractive index of lenses. This problem was solved by a new kind of telescope with a mirror used as an objective. There are many different kinds of telescopes. The most basic one is the lens telescope. This type of a telescope uses a set of lenses. Another type is the mirror telescope, which employs the concave mirror, spherical parabolic mirror or hyperbolically shaped mirror as its objective. The lens speed depends directly on the surface of a mirror. Both types can be combined to form a telescope composed of at least two mirrors and a set of lenses. The light is reflected from the primary mirror to the secondary one and then to the lens system. This type is smaller-sized, with a respectively reduced lens speed. The telescope design presented in this paper uses a parabolic strip fulfilling the function of an objective. Observed objects are projected as lines in a picture plane. Each of the lines of a size equal to the size of the strip corresponds to the sum of intensities of the light coming perpendicular to the objective from an observed object. A series of pictures taken with a different rotation and processed by a special reconstruction algorithm is needed to get 2D pictures. The telescope can also be used for fast detection of objects. In this mode, the rotation and multiple pictures are not needed, just one picture in the focus of a mirror is required to be taken.
Error Analysis for Discontinuous Galerkin Method for Parabolic Problems
NASA Technical Reports Server (NTRS)
Kaneko, Hideaki
2004-01-01
In the proposal, the following three objectives are stated: (1) A p-version of the discontinuous Galerkin method for a one dimensional parabolic problem will be established. It should be recalled that the h-version in space was used for the discontinuous Galerkin method. An a priori error estimate as well as a posteriori estimate of this p-finite element discontinuous Galerkin method will be given. (2) The parameter alpha that describes the behavior double vertical line u(sub t)(t) double vertical line 2 was computed exactly. This was made feasible because of the explicitly specified initial condition. For practical heat transfer problems, the initial condition may have to be approximated. Also, if the parabolic problem is proposed on a multi-dimensional region, the parameter alpha, for most cases, would be difficult to compute exactly even in the case that the initial condition is known exactly. The second objective of this proposed research is to establish a method to estimate this parameter. This will be done by computing two discontinuous Galerkin approximate solutions at two different time steps starting from the initial time and use them to derive alpha. (3) The third objective is to consider the heat transfer problem over a two dimensional thin plate. The technique developed by Vogelius and Babuska will be used to establish a discontinuous Galerkin method in which the p-element will be used for through thickness approximation. This h-p finite element approach, that results in a dimensional reduction method, was used for elliptic problems, but the application appears new for the parabolic problem. The dimension reduction method will be discussed together with the time discretization method.
Shock-layer bounds for a singularly perturbed equation
NASA Technical Reports Server (NTRS)
Scroggs, Jeffrey S.
1990-01-01
The size of the shock-layer governed by a conservation law is studied. The conservation law is a parabolic reaction-convection-diffusion equation with a small parameter multiplying the diffusion term and convex flux. Rigorous upper and lower bounding functions for the solution of the conservation law are established based on maximum-principle arguments. The bounding functions demonstrate that the size of the shock-layer is proportional to the parameter multiplying the diffusion term.
Luo, Biao; Wu, Huai-Ning
2012-12-01
This paper addresses the approximate optimal control problem for a class of parabolic partial differential equation (PDE) systems with nonlinear spatial differential operators. An approximate optimal control design method is proposed on the basis of the empirical eigenfunctions (EEFs) and neural network (NN). First, based on the data collected from the PDE system, the Karhunen-Loève decomposition is used to compute the EEFs. With those EEFs, the PDE system is formulated as a high-order ordinary differential equation (ODE) system. To further reduce its dimension, the singular perturbation (SP) technique is employed to derive a reduced-order model (ROM), which can accurately describe the dominant dynamics of the PDE system. Second, the Hamilton-Jacobi-Bellman (HJB) method is applied to synthesize an optimal controller based on the ROM, where the closed-loop asymptotic stability of the high-order ODE system can be guaranteed by the SP theory. By dividing the optimal control law into two parts, the linear part is obtained by solving an algebraic Riccati equation, and a new type of HJB-like equation is derived for designing the nonlinear part. Third, a control update strategy based on successive approximation is proposed to solve the HJB-like equation, and its convergence is proved. Furthermore, an NN approach is used to approximate the cost function. Finally, we apply the developed approximate optimal control method to a diffusion-reaction process with a nonlinear spatial operator, and the simulation results illustrate its effectiveness. PMID:22588610
Overview of software development at the parabolic dish test site
NASA Technical Reports Server (NTRS)
Miyazono, C. K.
1985-01-01
The development history of the data acquisition and data analysis software is discussed. The software development occurred between 1978 and 1984 in support of solar energy module testing at the Jet Propulsion Laboratory's Parabolic Dish Test Site, located within Edwards Test Station. The development went through incremental stages, starting with a simple single-user BASIC set of programs, and progressing to the relative complex multi-user FORTRAN system that was used until the termination of the project. Additional software in support of testing is discussed including software in support of a meteorological subsystem and the Test Bed Concentrator Control Console interface. Conclusions and recommendations for further development are discussed.
Analytical model and performance data for a cylindrical parabolic collector
Ford, F.M.; Stewart, W.E. Jr.
1980-01-01
Concentrating solar collectors provide higher fluid temperatures than flat-plate, an important advantage in many applications. The parabolic cylinder is one of the most popular types of concentrating collectors because of its relatively simple construction and tracking configuration. A mathematical model was developed for one such collector in order to predict thermal efficiency as a function of solar insolation. An experiment was then devised in an attempt to verify this model. Discrepancies between predicted and observed values are discussed, and suggestions are made for improving the model and the experimental procedure.
Piecewise-parabolic methods for astrophysical fluid dynamics
Woodward, P.R.
1983-11-01
A general description of some modern numerical techniques for the simulation of astrophysical fluid flow is presented. The methods are introduced with a thorough discussion of the especially simple case of advection. Attention is focused on the piecewise-parabolic method (PPM). A description of the SLIC method for treating multifluid problems is also given. The discussion is illustrated by a number of advection and hydrodynamics test problems. Finally, a study of Kelvin-Helmholtz instability of supersonic jets using PPM with SLIC fluid interfaces is presented.
Numerical solution of the scalar-wave equation for inhomogeneous cylindrical dielectric waveguides.
Rose, J W; Mitra, S S
1981-09-01
An initial-value algorithm derived from the Ricatti transformation of the scalar-wave equation is used to find the eigenvalues of inhomogeneous cylindrical dielectric waveguides. The numerical accuracy of the technique is investigated for cladded parabolic and step-index cylindrical refractive-index profiles.
NASA Technical Reports Server (NTRS)
Banks, H. T.; Kunisch, K.
1982-01-01
Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.
Optical properties of Dirac electrons in a parabolic well.
Kim, S C; Lee, J W; Yang, S-R Eric
2013-09-01
A single electron transitor may be fabricated using qunatum dots. A good model for the confinement potential of a quantum dot is a parabolic well. Here we consider such a parabolic dot made of graphene. Recently, we found counter intuitively that resonant quasi-boundstates of both positive and negative energies exist in the energy spectrum. The presence of resonant quasi-boundstates of negative energies is a unique property of massless Dirac fermions. As magnetic field B gets smaller the energy width of these states become broader and for sufficiently weak value of B resonant quasi-bound states disappear into a quasi-continuum. In the limit of small B resonant and nonresonant states transform into discrete anomalous states with a narrow probability density peak inside the well and another broad peak under the potential barrier. In this paper we compute the optical strength between resonant quasi-bound states as a function of B, and investigate how the signature of resonant quasi-bound states of Dirac electrons may appear in optical measurements.
Development effort of sheet molding compound (SMC) parabolic trough panels
Kirsch, P.A.; Champion, R.L.
1982-01-01
The objectives of the development effort are to: investigate the problems of molding parabolic trough solar reflector panels of sheet molding compound (SMC); develop molding techniques and processes by which silvered glass reflector sheets can be integrally molded into SMC trough panels; provide representative prototype panels for evaluation; and provide information regarding the technical feasibility of molding SMC panels in high volume production. The approach taken to meet the objectives was to design the parabolic panel, fabricate a prototype die, choose an SMC formulation and mold the glass and SMC together into a vertex to rim mirrored panel. The main thrust of the program was to successfully co-mold a mirrored glass sheet with the SMC. Results indicate that mirrored glass sheets, if properly strengthened to withstand the temperature and pressure of the molding process, can be successfully molded with SMC in a single press stroke using standard compression molding techniques. The finalized design of the trough panel is given. The SMC formulation chosen is a low shrink, low profile SMC using 40% by weight one inch chopped glass fibers in a uv stabilized polyester resin matrix. A program to test for the adhesion between mirrored glass sheets and the SMC is discussed briefly. (LEW)
Exergetic analysis of parabolic trough solar thermal power plants
NASA Astrophysics Data System (ADS)
Petrakopoulou, F.; Ruperez, B.; San Miguel, G.
2014-12-01
A very important component to achieve sustainable development in the energy sector is the improvement of energy efficiency of widely applied thermodynamic processes. Evaluation and optimization methods of energy processes play a crucial role in fulfilling this goal. A suitable method for the evaluation and optimization of energy conversion systems has been proven to be the exergetic analysis. In this work, two parabolic trough solar thermal power plants are simulated in detail using commercial software, and they are further analysed and compared using an exergetic analysis. The first plant uses a thermal fluid to produce the steam required in a steam generator, while the second one produces the steam directly in the solar field. The analysis involves the evaluation of the individual components of the power plants, as well as the performance evaluation of the overall structures. The main goal is to detect thermodynamic inefficiencies of the two different configurations and propose measures to minimize those. We find that the two examined plants have similar main sources of exergy destruction: the solar field (parabolic trough solar collectors), followed by the steam generator. This reveals the importance of an optimal design of these particular components, which could reduce inefficiencies present in the system. The differences in the exergy destruction and exergetic efficiencies of individual components of the two plants are analyzed in detail based on comparable operational conditions.
Parabolic growth patterns in 96-well plate cell growth experiments.
Faessel, H M; Levasseur, L M; Slocum, H K; Greco, W R
1999-05-01
In preparing for the routine use of the ubiquitous in vitro cell growth inhibition assay for the study of anticancer agents, we characterized the statistical properties of the assay and found some surprising results. Parabolic well-to-well cell growth patterns were discovered, which could profoundly affect the results of routine growth inhibition studies of anticancer and other agents. Four human ovarian cell lines, A2780/WT, A2780/DX5, A2780/DX5B, and A121, and one human ileocecal adenocarcinoma cell line, HCT-8, were seeded into plastic 96-well plates with a 12-channel pipette, without drugs, and grown from 1-5 d. The wells were washed with a plate washer, cells stained with sulforhodamine B (SRB), and dye absorbance measured with a plate reader. Variance models were fit to the data from replicates to determine the nature of the heteroscedastic error structure. Exponential growth models were fit to data to estimate doubling times for each cell line. Polynomial models were fit to data from 10-plate stacks of 96-well plates to explore nonuniformity of cell growth in wells in different regions of the stacks. Each separate step in the assay was examined for precision, patterns, and underlying causes of variation. Differential evaporation of water from wells is likely a major, but not exclusive, contributor to the systematic well-to-well cell growth patterns. Because the fundamental underlying causes of the parabolic growth patterns were not conclusively found, a randomization step for the growth assay was developed.
NASA Astrophysics Data System (ADS)
Dobrev, V. K.
2014-05-01
In the present paper we review the progress of the project of classification and construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we called earlier 'conformal Lie algebras' (CLA), which have very similar properties to the conformal algebras of Minkowski space-time, though our aim is to go beyond this class in a natural way. For this we introduced recently the new notion of parabolic relation between two non-compact semisimple Lie algebras G and G' that have the same complexification and possess maximal parabolic subalgebras with the same complexification. Thus, we consider the exceptional algebra E7(7) which is parabolically related to the CLA E7(-25). Other interesting examples are the orthogonal algebras so(p, q) all of which are parabolically related to the conformal algebra so(n, 2) with p + q = n + 2, the parabolic subalgebras including the Lorentz subalgebra so(n - 1,1) and its analogs so(p - 1, q - 1). Further we consider the algebras sl(2n, Bbb R) and for n = 2k the algebras su* (4k) which are parabolically related to the CLA su(n,n). Further we consider the algebras sp(r,r) which are parabolically related to the CLA sp(2r, Bbb R). We consider also E6(6) and E6(2) which are parabolically related to the hermitian symmetric case E6(-14),
Buono, Pietro-Luciano; Eftimie, Raluca
2015-10-01
The study of self-organised collective animal behaviour, such as swarms of insects or schools of fish, has become over the last decade a very active research area in mathematical biology. Parabolic and hyperbolic models have been used intensively to describe the formation and movement of various aggregative behaviours. While both types of models can exhibit aggregation-type patterns, studies on hyperbolic models suggest that these models can display a larger variety of spatial and spatio-temporal patterns compared to their parabolic counterparts. Here we use stability, symmetry and bifurcation theory to investigate this observation more rigorously, an approach not attempted before to compare and contrast aggregation patterns in models for collective animal behaviors. To this end, we consider a class of nonlocal hyperbolic models for self-organised aggregations that incorporate various inter-individual communication mechanisms, and take the formal parabolic limit to transform them into nonlocal parabolic models. We then discuss the symmetry of these nonlocal hyperbolic and parabolic models, and the types of bifurcations present or lost when taking the parabolic limit. We show that the parabolic limit leads to a homogenisation of the inter-individual communication, and to a loss of bifurcation dynamics (in particular loss of Hopf bifurcations). This explains the less rich patterns exhibited by the nonlocal parabolic models. However, for multiple interacting populations, by breaking the population interchange symmetry of the model, one can preserve the Hopf bifurcations that lead to the formation of complex spatio-temporal patterns that describe moving aggregations.
Least-squares/parabolized Navier-Stokes procedure for optimizing hypersonic wind tunnel nozzles
NASA Technical Reports Server (NTRS)
Korte, John J.; Kumar, Ajay; Singh, D. J.; Grossman, B.
1991-01-01
A new procedure is demonstrated for optimizing hypersonic wind-tunnel-nozzle contours. The procedure couples a CFD computer code to an optimization algorithm, and is applied to both conical and contoured hypersonic nozzles for the purpose of determining an optimal set of parameters to describe the surface geometry. A design-objective function is specified based on the deviation from the desired test-section flow-field conditions. The objective function is minimized by optimizing the parameters used to describe the nozzle contour based on the solution to a nonlinear least-squares problem. The effect of the changes in the nozzle wall parameters are evaluated by computing the nozzle flow using the parabolized Navier-Stokes equations. The advantage of the new procedure is that it directly takes into account the displacement effect of the boundary layer on the wall contour. The new procedure provides a method for optimizing hypersonic nozzles of high Mach numbers which have been designed by classical procedures, but are shown to produce poor flow quality due to the large boundary layers present in the test section. The procedure is demonstrated by finding the optimum design parameters for a Mach 10 conical nozzle and a Mach 6 and a Mach 15 contoured nozzle.
Wadawadigi, G.; Tannehill, J.C.; Buelow, P.E.; Lawrence, S.L. NASA, Ames Research Center, Moffett Field, CA )
1992-07-01
A new upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the three-dimensional (3D) chemically reacting flow in scramjet (supersonic combustion ramjet) engines. The code is a modification of the 3D upwind PNS (UPS) airflow code which has been extended in the present study to permit internal flow calculations with hydrogen-air chemistry. With these additions, the new code has the capability of computing aerodynamic and propulsive flowfields simultaneously. The algorithm solves the PNS equations using a finite-volume, upwind TVD method based on Roe's approximate Riemann solver that has been modified to account for 'real gas' effects. The fluid medium is assumed to be a chemically reacting mixture of thermally perfect (but calorically imperfect) gases in thermal equilibrium. The new code has been applied to two test cases. These include the Burrows-Kurkov supersonic combustion experiment and a generic 3D scramjet flowfield. The computed results compare favorably with the available experimental data. 38 refs.
NASA Astrophysics Data System (ADS)
Viljamaa, Panu; Jacobs, J. Richard; Chris; JamesHyman; Halma, Matthew; EricNolan; Coxon, Paul
2014-07-01
In reply to a Physics World infographic (part of which is given above) about a study showing that Euler's equation was deemed most beautiful by a group of mathematicians who had been hooked up to a functional magnetic-resonance image (fMRI) machine while viewing mathematical expressions (14 May, http://ow.ly/xHUFi).
Bartel, T.J.; Walker, M.A.; Homicz, G.F.
1988-01-01
This paper compares the hypersonic flow field solutions obtained from both a kinetic and a continuum model of the rarefied flow about geometries typical of those found in aerospace applications. Experimental data, where available, are also compared to the predictions. The kinetic model used is Bird's Direct-Simulation Monte-Carlo (DSMC) algorithm. The continuum model is based on the widely-used Parabolized Navier-Stokes (PNS) equations. The configurations include a sharped cone, and spherically-blunted biconic and triconic configurations; all assume 2-D axisymmetric flow at zero angle-of-attack. The Knudsen number of the flows, based on freestream conditions, varied from approximately 10/sup -3/ to 1. While the comparisons with experimental data are limited to global quantities such as the drag coefficient, numerical results are also presented for surface distributions of pressure and heat transfer, and density and temperature profiles in the flow field. Difficulties encountered with both solution procedures are discussed.
NASA Astrophysics Data System (ADS)
Schmidt, E. J. P. Georg
This paper is concerned with the total—and strict total—positivity of the integral kernels which relate the solutions of parabolic initial boundary value problems to the initial and boundary data. Maximum principle arguments, in conjunction with a characterisation of total positivity in terms of variation diminishing properties, are used to prove total positivity of both the initial value and boundary value kernels under mild assumptions; similar methods yield strict total positivity when the coefficients appearing in the equation are analytic in either the time or the space variable. In this way we extend results of Karlin and McGregor on the total positivity of the kernel associated with the initial data; their proofs used the determinantal definition of total positivity and exploited the work of Gohberg and Krein on the Green's functions of Sturm-Liouville operators.
The hyperbolic Allen–Cahn equation: exact solutions
NASA Astrophysics Data System (ADS)
Nizovtseva, I. G.; Galenko, P. K.; Alexandrov, D. V.
2016-10-01
Using the first integral method, a general set of analytical solutions is obtained for the hyperbolic Allen–Cahn equation. The solutions are presented by (i) the class of continual solutions described by \\tanh -profiles for traveling waves of the order parameter, and (ii) the class of singular solutions which exhibit unbounded discontinuity in the profile of the order parameter at the origin of the coordinate system. It is shown that the solutions include the previous analytical results for the parabolic Allen–Cahn equation as a limited class of \\tanh -functions, in which the inertial effects are omitted.
Masiero, Federica
2010-10-15
We consider a controlled state equation of parabolic type on the halfline (0,+{infinity}) with boundary conditions of Dirichlet type in which the unknown is equal to the sum of the control and of a white noise in time. We study finite horizon and infinite horizon optimal control problem related by means of backward stochastic differential equations.
The JPL parabolic dish project. [solar collectors technology development
NASA Technical Reports Server (NTRS)
Truscello, V. C.; Williams, A. N.
1980-01-01
The parabolic dish solar collector is a highly versatile concentrating collector system that can produce heat for many thermal processes and electricity by coupling the collector to a suitable heat engine. This paper discusses a project for the development of these collector systems and summarizes contracts with industry for developing the dish subsystems which include concentrator, receiver, and heat engine. An early market for dishes is the dispersed small community market which depends heavily on oil to operate diesel or steam turbine plants in order to generate electricity. The present contracts with industry for conducting engineering experiments using the developed dish hardware to demonstrate the technology in these early opportunity markets is also discussed.
Parabolic dish Stirling module development and test results
Washom, B.
1984-08-01
Private industry and the U.S. Department of Energy are presently cost sharing the design, manufacture and test of a 25 Kwe parabolic dish Stirling module, known as Vanguard. The Vanguard module achieved a world's record sunlight to electric conversion efficiency of 31.6% in February 1984 at the Rancho Mirage, California test site. The module is presently operating daily in sunrise to sunset tests to determine the long term performance and O and M requirements of this distributed receiver system. Each module can be easily integrated into a larger field of modules to provide power generation opportunities from a single 25 Kwe unit for isolated loads to 30 Mwe systems for integrated utility power generation.
Determination of error tolerances for optical design of parabolic troughs
Guven, H.M.; Bannerot, R.B.; Mistree, F.
1983-11-01
A study is presented where potential optical errors in parabolic troughs are divided into two groups: random and non-random. Small-scale slope errors, mirror nonspecularity, apparent changes in sun's width, and small occasional tracking errors are classified as random errors. Reflector profile errors, misalignment of the receiver with the effective focus of the reflector, and misalignment of the trough with the sun are classified as non-random errors. Random errors are analyzed using statistics and assuming a normally distributed error. Non-random errors are analyzed by building provisions into the optical model which allow for the analysis of such errors. Universal design curves showing the effect of random and non-random errors on the optical performance (efficiency) of the trough are presented.
Fifth parabolic dish solar thermal power program annual review: proceedings
1984-03-01
The primary objective of the Review was to present the results of activities within the Parabolic Dish Technology and Module/Systems Development element of the Department of Energy's Solar Thermal Energy Systems Program. The Review consisted of nine technical sessions covering overall Project and Program aspects, Stirling and Brayton module development, concentrator and engine/receiver development, and associated hardware and test results to date; distributed systems operating experience; international dish development activities; and non-DOE-sponsored domestic dish activities. A panel discussion concerning business views of solar electric generation was held. These Proceedings contain the texts of presentations made at the Review, as submitted by their authors at the beginning of the Review; therefore, they may vary slightly from the actual presentations in the technical sessions.
Generic parabolic points are isolated in positive characteristic
NASA Astrophysics Data System (ADS)
Lindahl, Karl-Olof; Rivera-Letelier, Juan
2016-05-01
We study analytic germs in one variable with a parabolic fixed point at the origin, over an ultrametric ground field of positive characteristic. It is conjectured that for such a germ the origin is isolated as a periodic point. Our main result is an affirmative solution of this conjecture in the case of a generic germ with a prescribed multiplier. The genericity condition is explicit: the power series is minimally ramified, i.e. the degree of the first nonlinear term of each of its iterates is as small as possible. Our main technical result is a computation of the first significant terms of a minimally ramified power series. From this we obtain a lower bound for the norm of nonzero periodic points, from which we deduce our main result. As a by-product we give a new and self-contained proof of a characterization of minimally ramified power series in terms of the iterative residue.
Ray analysis of parabolic-index segmented planar waveguides.
Rastogi, V; Ghatak, A K; Ostrowsky, D B; Thyagarajan, K; Shenoy, M R
1998-07-20
A ray analysis of periodically segmented waveguides with parabolic-index variation in the high-index region is presented. We carried out the analysis using ray transfer matrices, which is convenient to implement and which can be extended to study different types of graded-index segmented waveguide. Results of this ray tracing approach clearly illustrate the waveguiding properties and the existence of stable and unstable regions of operation in segmented waveguides. We also illustrate the tapering action exhibited by segmented waveguides in which the duty cycle varies along the length of the waveguide. This analysis, although restricted to multimode structures, provides a clear visualization of the waveguiding properties in terms of ray propagation in segmented waveguides.
Large Phased Array Radar Using Networked Small Parabolic Reflectors
NASA Technical Reports Server (NTRS)
Amoozegar, Farid
2006-01-01
Multifunction phased array systems with radar, telecom, and imaging applications have already been established for flat plate phased arrays of dipoles, or waveguides. In this paper the design trades and candidate options for combining the radar and telecom functions of the Deep Space Network (DSN) into a single large transmit array of small parabolic reflectors will be discussed. In particular the effect of combing the radar and telecom functions on the sizes of individual antenna apertures and the corresponding spacing between the antenna elements of the array will be analyzed. A heterogeneous architecture for the DSN large transmit array is proposed to meet the radar and telecom requirements while considering the budget, scheduling, and strategic planning constrains.
Context-specific adaptation of saccade gain in parabolic flight
NASA Technical Reports Server (NTRS)
Shelhamer, Mark; Clendaniel, Richard A.; Roberts, Dale C.
2002-01-01
Previous studies established that vestibular reflexes can have two adapted states (e.g., gains) simultaneously, and that a context cue (e.g., vertical eye position) can switch between the two states. Our earlier work demonstrated this phenomenon of context-specific adaptation for saccadic eye movements: we asked for gain decrease in one context state and gain increase in another context state, and then determined if a change in the context state would invoke switching between the adapted states. Horizontal and vertical eye position and head orientation could serve, to varying degrees, as cues for switching between two different saccade gains. In the present study, we asked whether gravity magnitude could serve as a context cue: saccade adaptation was performed during parabolic flight, which provides alternating levels of gravitoinertial force (0 g and 1.8 g). Results were less robust than those from ground experiments, but established that different saccade magnitudes could be associated with different gravity levels.
The third ESA Student Parabolic-Flight Campaign.
Ockels, W J; Jagger-Meziere, L
2001-02-01
Today's students will become tomorrow's workforce and hence they should be involved in the global space programme as early as possible so that they will be motivated to follow space careers and create a space-educated next generation for working within the space domain. Getting students involved in today's space programmes is important not only for the space industry in terms of providing a talented workforce for the future, but also for the general public who will be the future voters and potential political supporters of future European space activities. With this in mind, ESA's Office for Education and Outreach organises and runs many space-related activities for young people in order to stimulate their interest in space in particular and in science in general. One of these activities is the 'Student Parabolic-Flight Campaign'.
Active matter in lateral parabolic confinement: From subdiffusion to superdiffusion
NASA Astrophysics Data System (ADS)
Ribeiro, H. E.; Potiguar, F. Q.
2016-11-01
In this work we studied the diffusive behavior of active brownian particles under lateral parabolic confinement. The results showed that we go from subdiffusion to ballistic motion as we vary the angular noise strength and confinement intensity. We argued that the subdiffusion regimes appear as consequence of the restricted space available for diffusion (achieved either through large confinement and/or large noise); we saw that when there are large confinement and noise intensity, a similar configuration to single file diffusion appears; on the other hand, normal and superdiffusive regimes may occur due to low noise (longer persistent motion), either through exploring a wider region around the potential minimum in the transverse direction (low confinement), or by forming independent clusters (high confinement).
Solar parabolic dish thermal power systems - Technology and applications
NASA Technical Reports Server (NTRS)
Lucas, J. W.; Marriott, A. T.
1979-01-01
Activities of two projects at JPL in support of DOE's Small Power Systems Program are reported. These two projects are the Point-Focusing Distributed Receiver (PFDR) Technology Project and the Point-Focusing Thermal and Electric Applications (PFTEA) Project. The PFDR Technology Project's major activity is developing the technology of solar concentrators, receivers and power conversion subsystems suitable for parabolic dish or point-focusing distributed receiver power systems. Other PFDR activities include system integration and cost estimation under mass production, as well as the testing of the hardware. The PFTEA Project's first major activity is applications analysis, that is seeking ways to introduce PFDR systems into appropriate user sectors. The second activity is systems engineering and development wherein power plant systems are analyzed for specific applications. The third activity is the installation of a series of engineering experiments in various user environments to obtain actual operating experience
Complex ray and evanescent wave analysis of parabolic reflector antennas
NASA Astrophysics Data System (ADS)
Hasselmann, F. J. V.; Felsen, L. B.
The Complex-Source-Point (CSP) method is applied to the analysis of the vector field reflected from a parabolic reflector antenna offset-fed by a Gaussian beam centered at the reflector focus. The asymptotic CSP solutions from both the general and paraxially approximated analysis have been implemented on a computer using numerical data from the literature. The results from the general procedure are compared at 28.5 GHz with those deduced by semi-heuristic superposition of ideal beam mode fields with even and odd vector symmetry, and with corresponding experimental data. The total field results show coincidence between the two analytical procedures for points down to -50 dB, and the agreement holds for cross-polarization patterns as well. The validity of a simplified paraxial analysis for the total field and the cross-polarization peaks is important for tractable applications to satellite communication systems since the relevant phenomena occur in the paraxial region.
Hypersonic flows generated by parabolic and paraboloidal shock waves
NASA Technical Reports Server (NTRS)
Schwartz, L. W.
1974-01-01
A computer algorithm has been developed to determine the blunt-body flowfields supporting symmetric parabolic and paraboloidal shock waves at infinite free-stream Mach number. Solutions are expressed in an analytic form as high-order power series, in the coordinate normal to the shock, whose coefficients can be determined exactly. Analytic continuation is provided by the use of Pade approximations. Test cases provide solutions of very high accuracy. In the axisymmetric case for gamma equals 715 the solution has been found far downstream, where it agrees with the modified blast-wave results. For plane flow, on the other hand, a limit line appears within the shock layer, a short distance past the sonic line, suggesting the presence of an imbedded shock. Local solutions in the downstream limit are discussed.
Motor skills under varied gravitoinertial force in parabolic flight
NASA Astrophysics Data System (ADS)
Ross, Helen E.
Parabolic flight produces brief alternating periods of high and low gravitoinertial force. Subjects were tested on various paper-and-pencil aiming and tapping tasks during both normal and varied gravity in flight. It was found that changes in g level caused directional errors in the z body axis (the gravity axis), the arm aiming too high under 0g and too low under 2g. The standard deviation also increased for both vertical and lateral movements in the mid-frontal plane. Both variable and directional errors were greater under 0g than 2g. In an unpaced reciprocal tapping task subjects tended to increase their error rate rather than their movement time, but showed a non-significant trend towards slower speeds under 0g for all movement orientations. Larger variable errors or slower speeds were probably due to the difficulty of re-organising a motor skill in an unfamiliar force environment, combined with anchorage difficulties under 0g.
Microgravity Active Vibration Isolation System on Parabolic Flights
NASA Astrophysics Data System (ADS)
Dong, Wenbo; Pletser, Vladimir; Yang, Yang
2016-07-01
The Microgravity Active Vibration Isolation System (MAIS) aims at reducing on-orbit vibrations, providing a better controlled lower gravity environment for microgravity physical science experiments. The MAIS will be launched on Tianzhou-1, the first cargo ship of the China Manned Space Program. The principle of the MAIS is to suspend with electro-magnetic actuators a scientific payload, isolating it from the vibrating stator. The MAIS's vibration isolation capability is frequency-dependent and a decrease of vibration of about 40dB can be attained. The MAIS can accommodate 20kg of scientific payload or sample unit, and provide 30W of power and 1Mbps of data transmission. The MAIS is developed to support microgravity scientific experiments on manned platforms in low earth orbit, in order to meet the scientific requirements for fluid physics, materials science, and fundamental physics investigations, which usually need a very quiet environment, increasing their chances of success and their scientific outcomes. The results of scientific experiments and technology tests obtained with the MAIS will be used to improve future space based research. As the suspension force acting on the payload is very small, the MAIS can only be operative and tested in a weightless environment. The 'Deutsches Zentrum für Luft- und Raumfahrt e.V.' (DLR, German Aerospace Centre) granted a flight opportunity to the MAIS experiment to be tested during its 27th parabolic flight campaign of September 2015 performed on the A310 ZERO-G aircraft managed by the French company Novespace, a subsidiary of the 'Centre National d'Etudes Spatiales' (CNES, French Space Agency). The experiment results confirmed that the 6 degrees of freedom motion control technique was effective, and that the vibration isolation performance fulfilled perfectly the expectations based on theoretical analyses and simulations. This paper will present the design of the MAIS and the experiment results obtained during the
Cerebral vasoconstriction precedes orthostatic intolerance after parabolic flight
NASA Technical Reports Server (NTRS)
Serrador, J. M.; Shoemaker, J. K.; Brown, T. E.; Kassam, M. S.; Bondar, R. L.; Schlegel, T. T.
2000-01-01
The effects of brief but repeated bouts of micro- and hypergravity on cerebrovascular responses to head-up tilt (HUT) were examined in 13 individuals after (compared to before) parabolic flight. Middle cerebral artery mean flow velocity (MCA MFV; transcranial Doppler ultrasound), eye level blood pressure (BP) and end tidal CO(2) (P(ET)CO(2)) were measured while supine and during 80 degrees HUT for 30 min or until presyncope. In the postflight tests subjects were classified as being orthostatically tolerant (OT) (n = 7) or intolerant (OI) (n = 6). BP was diminished with HUT in the OT group in both tests (p < 0.05) whereas postflight BP was not different from supine in the OI group. Postflight compared to preflight, the reduction in P(ET)CO(2) with HUT (p < 0.05) increased in both groups, although significantly so only in the OI group (p < 0.05). The OI group also had a significant decrease in supine MCA MFV postflight (p < 0.05) that was unaccompanied by a change in supine P(ET)CO(2). The decrease in MCA MFV that occurred during HUT in both groups preflight (p < 0.05) was accentuated only in the OI group postflight, particularly during the final 30 s of HUT (p < 0.05). However, this accentuated decrease in MCA MFV was not correlated to the greater decrease in P(ET)CO(2) during the same period (R = 0.20, p = 0.42). Although cerebral vascular resistance (CVR) also increased in the OI group during the last 30 s of HUT postflight (p < 0.05), the dynamic autoregulatory gain was not simultaneously changed. Therefore, we conclude that in the OI individuals, parabolic flight was associated with cerebral hypoperfusion following a paradoxical augmentation of CVR by a mechanism that was not related to changes in autoregulation nor strictly to changes in P(ET)CO(2).
Parabolic flight induces changes in gene expression patterns in Arabidopsis thaliana.
Paul, Anna-Lisa; Manak, Michael S; Mayfield, John D; Reyes, Matthew F; Gurley, William B; Ferl, Robert J
2011-10-01
Our primary objective was to evaluate gene expression changes in Arabidopsis thaliana in response to parabolic flight as part of a comprehensive approach to the molecular biology of spaceflight-related adaptations. In addition, we wished to establish parabolic flight as a tractable operations platform for molecular biology studies. In a succession of experiments on NASA's KC-135 and C-9 parabolic aircraft, Arabidopsis plants were presented with replicated exposure to parabolic flight. Transcriptome profiling revealed that parabolic flight caused changes in gene expression patterns that stood the statistical tests of replication on three different flight days. The earliest response, after 20 parabolas, was characterized by a prominence of genes associated with signal transduction. After 40 parabolas, this prominence was largely replaced by genes associated with biotic and abiotic stimuli and stress. Among these responses, three metabolic processes stand out in particular: the induction of auxin metabolism and signaling, the differential expression of genes associated with calcium-mediated signaling, and the repression of genes associated with disease resistance and cell wall biochemistry. Many, but not all, of these responses are known to be involved in gravity sensing in plants. Changes in auxin-related gene expression were also recorded by reporter genes tuned to auxin signal pathways. These data demonstrate that the parabolic flight environment is appropriate for molecular biology research involving the transition to microgravity, in that with replication, proper controls, and analyses, gene expression changes can be observed in the time frames of typical parabolic flight experiments.
DOE R&D Accomplishments Database
1998-09-21
In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.
A compact representation of drawing movements with sequences of parabolic primitives.
Polyakov, Felix; Drori, Rotem; Ben-Shaul, Yoram; Abeles, Moshe; Flash, Tamar
2009-07-01
Some studies suggest that complex arm movements in humans and monkeys may optimize several objective functions, while others claim that arm movements satisfy geometric constraints and are composed of elementary components. However, the ability to unify different constraints has remained an open question. The criterion for a maximally smooth (minimizing jerk) motion is satisfied for parabolic trajectories having constant equi-affine speed, which thus comply with the geometric constraint known as the two-thirds power law. Here we empirically test the hypothesis that parabolic segments provide a compact representation of spontaneous drawing movements. Monkey scribblings performed during a period of practice were recorded. Practiced hand paths could be approximated well by relatively long parabolic segments. Following practice, the orientations and spatial locations of the fitted parabolic segments could be drawn from only 2-4 clusters, and there was less discrepancy between the fitted parabolic segments and the executed paths. This enabled us to show that well-practiced spontaneous scribbling movements can be represented as sequences ("words") of a small number of elementary parabolic primitives ("letters"). A movement primitive can be defined as a movement entity that cannot be intentionally stopped before its completion. We found that in a well-trained monkey a movement was usually decelerated after receiving a reward, but it stopped only after the completion of a sequence composed of several parabolic segments. Piece-wise parabolic segments can be generated by applying affine geometric transformations to a single parabolic template. Thus, complex movements might be constructed by applying sequences of suitable geometric transformations to a few templates. Our findings therefore suggest that the motor system aims at achieving more parsimonious internal representations through practice, that parabolas serve as geometric primitives and that non-Euclidean variables are
Observation of spectral self-imaging by nonlinear parabolic cross-phase modulation.
Lei, Lei; Huh, Jeonghyun; Cortés, Luis Romero; Maram, Reza; Wetzel, Benjamin; Duchesne, David; Morandotti, Roberto; Azaña, José
2015-11-15
We report an experimental demonstration of spectral self-imaging on a periodic frequency comb induced by a nonlinear all-optical process, i.e., parabolic cross-phase modulation in a highly nonlinear fiber. The comb free spectral range is reconfigured by simply tuning the temporal period of the pump parabolic pulse train. In particular, undistorted FSR divisions by factors of 2 and 3 are successfully performed on a 10 GHz frequency comb, realizing new frequency combs with an FSR of 5 and 3.3 GHz, respectively. The pump power requirement associated to the SSI phenomena is also shown to be significantly relaxed by the use of dark parabolic pulses.
Nonimaging secondary concentrators for large rim angle parabolic troughs with tubular absorbers.
Ries, H; Spirkl, W
1996-05-01
For parabolic trough solar collectors with tubular absorbers, we design new tailored secondary concentrators. The design is applicable for any rim angle of a parabolic reflector. With the secondary, the concentration can be increased by a factor of more than 2 with a compact secondary reflector consisting of a single piece, even for the important case of a rim angle of 90 deg. The parabolic reflector can be used without changes; the reduced absorber is still tubular but smaller than the original absorber and slightly displaced toward the primary.
NASA Technical Reports Server (NTRS)
Kreider, Kevin L.; Baumeister, Kenneth J.
1996-01-01
An explicit finite difference real time iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for future large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable for a harmonic monochromatic sound field, a parabolic (in time) approximation is introduced to reduce the order of the governing equation. The analysis begins with a harmonic sound source radiating into a quiescent duct. This fully explicit iteration method then calculates stepwise in time to obtain the 'steady state' harmonic solutions of the acoustic field. For stability, applications of conventional impedance boundary conditions requires coupling to explicit hyperbolic difference equations at the boundary. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.
Applications of the contravariant form of the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Katsanis, T.
1983-01-01
The contravariant Navier-Stokes equations in weak conservation form are well suited to certain fluid flow analysis problems. Three dimensional contravariant momentum equations may be used to obtain Navier-Stokes equations in weak conservation form on a nonplanar two dimensional surface with varying streamsheet thickness. Thus a three dimensional flow can be simulated with two dimensional equations to obtain a quasi-three dimensional solution for viscous flow. When the Navier-Stokes equations on the two dimensional nonplanar surface are transformed to a generalized body fitted mesh coordinate system, the resulting equations are similar to the equations for a body fitted mesh coordinate system on the Euclidean plane. Contravariant momentum components are also useful for analyzing compressible, three dimensional viscous flow through an internal duct by parabolic marching. This type of flow is efficiently analyzed by parabolic marching methods, where the streamwise momentum equation is uncoupled from the two crossflow momentum equations. This can be done, even for ducts with a large amount of turning, if the Navier-Stokes equations are written with contravariant components.
Biosignal alterations generated by parabolic flights of small aerobatic aircrafts
NASA Astrophysics Data System (ADS)
Simon, M. Jose; Perez-Poch, Antoni; Ruiz, Xavier; Gavalda, Fina; Saez, Nuria
Since the pioneering works of Prof. Strughold in 1948, the aerospace medicine aimed to characterize the modifications induced in the human body by changes in the gravity level. In this respect, it is nowadays well known that one of the most serious problems of these kind of environments is the fluid shift. If this effect is enough severe and persistent, serious changes in the hemodynamic of the brain (cerebral blood flow and blood oxigenation level) appear which could be detected as alterations in the electroencephalogram, EEG [1]. Also, this fluid redistribution, together with the relocation of the heart in the thorax, induces detectable changes in the electrocardiogram, ECG [2]. Other kind of important problems are related with vestibular instability, kinetosis and illusory sensations. In particular since the seventies [3,4] it is known that in parabolic flights and due to eye movements triggered by the changing input from the otholith system, fixed real targets appeared to have moved downward while visual afterimages appeared to have moved upward (oculogravic illusions). In order to cover all the above-mentioned potential alterations, the present work, together with the gravity level, continuously monitors the electroencephalogram, EEG, the electrocardiogram, ECG and the electrooculogram, EOG of a normal subject trying to detect correlations between the different alterations observed in these signals and the changes of gravity during parabolic flights. The small aerobatic aircraft used is a CAP10B and during the flight the subject is located near the pilot. To properly cover all the range of accelerations we have used two sensitive triaxial accelerometers covering the high and low ranges of acceleration. Biosignals have been gathered using a Biopac data unit together with the Acknowledge software package (from BionicÔ). It is important to finally remark that, due to the obvious difference between the power of the different engines, the accelerometric
American lookback option with fixed strike price—2-D parabolic variational inequality
NASA Astrophysics Data System (ADS)
Chen, Xiaoshan; Yi, Fahuai; Wang, Lihe
In this paper we study a 2-dimensional parabolic variational inequality with financial background. We define a suitable weak formula and obtain existence and uniqueness of the problem. Moreover we analyze the behaviors of the free boundary surface.
Shaping of parabolic cylindrical membrane reflectors for the DART precision test bed
NASA Technical Reports Server (NTRS)
White, C.; Salama, M.; Dragovan, M.; Schroeder, J.; Barber, D.; Dooley, J.
2003-01-01
The DART is a new telescope architecture consisting of two cylindrical parabolic reflectors. The system is ideally suited to using tensioned membranes for the reflective surfaces, owing to the zero Gaussian curvature of a cylindrical parabola.
A position transducer for studying parabolic motion and rolling down a grooved track
NASA Astrophysics Data System (ADS)
Basta, M.; Di Gennaro, M.; Picciarelli, V.
1994-09-01
We describe a computerized system based on a position transducer on-line and discuss its applications in two experiments (parabolic motion and rolling down a grooved track) performed in an introductory physics laboratory course.
Wind Tunnel Tests of Parabolic Trough Solar Collectors: March 2001--August 2003
Hosoya, N.; Peterka, J. A.; Gee, R. C.; Kearney, D.
2008-05-01
Conducted extensive wind-tunnel tests on parabolic trough solar collectors to determine practical wind loads applicable to structural design for stress and deformation, and local component design for concentrator reflectors.
NASA Astrophysics Data System (ADS)
Panin, Alexander; Bergquist, Jonathon
2007-10-01
Solar cells are still too expensive (5-20/watt) to compete with traditional fossil fuel power generating methods (˜1/watt). Parabolic trough solar concentrator has the advantage of modest concentration ratio (10-100) which is well suited for coupling with solar cell. Thus using small area solar cell placed in the focal line of parabolic trough may be economically viable alternative to flat solar panels. We experiment with flexible solar cell (backed by water cooling pipe) placed in the focus of parabolic trough reflector. Another advantage of parabolic trough concentrator is very relaxed tracking requirement. For example, east-west oriented concentrator (aligned with the ecliptic plane) does not even need any tracking during core 4-6 hours around noon (when maximum illumination is available). The design and the performance of the prototype, as well as possible economical benefits of full scale projects are discussed in the presentation.
NASA Technical Reports Server (NTRS)
Kohl, Randall L.
1987-01-01
The concentrations of adrenocorticotropic hormone (ACTH), vasopressin (AVP), epinephrine (EPI), and norepinephrine (NE) in 22 subjects administered 10 to 20 mg of metoclopramide prior to parabolic flight are measured. The effect of metoclopramide on motion sickness is examined. It is observed that metoclopramide is ineffective in the modulation of motion sickness due to stressful linear and angular acceleration and orbital flight, and it does not affect serum hormones prior to parabolic flight. It is detected that the serum level of AVP declines following emesis induced by parabolic flight and stressful angular acceleration; the serum levels of ACTH and EPI are elevated by parabolic flight and stressful angular acceleration; and serum NE is significantly elevated immediately following emesis. The possible roles of these hormones in the etiology of space motion sickness are discussed.
Interpolated Differential Operator (IDO) scheme for solving partial differential equations
NASA Astrophysics Data System (ADS)
Aoki, Takayuki
1997-05-01
We present a numerical scheme applicable to a wide variety of partial differential equations (PDEs) in space and time. The scheme is based on a high accurate interpolation of the profile for the independent variables over a local area and repetitive differential operations regarding PDEs as differential operators. We demonstrate that the scheme is uniformly applicable to hyperbolic, ellipsoidal and parabolic equations. The equations are solved in terms of the primitive independent variables, so that the scheme has flexibility for various types of equations including source terms. We find out that the conservation holds accurate when a Hermite interpolation is used. For compressible fluid problems, the shock interface is found to be sharply described by adding an artificial viscosity term.
Transport equations with second-order differential collision operators
Cosner, C.; Lenhart, S.M.; Protopopescu, V.
1988-07-01
This paper discusses existence, uniqueness, and a priori estimates for time-dependent and time-independent transport equations with unbounded collision operators. These collision operators are described by second-order differential operators resulting from diffusion in the velocity space. The transport equations are degenerate parabolic-elliptic partial differential equations, that are treated by modifications of the Fichera-Oleinik-Radkevic Theory of second-order equations with nonnegative characteristic form. They consider weak solutions in spaces that are extensions of L/sup rho/ to include traces on certain parts of the boundary. This extension is necessary due to the nonclassical boundary conditions imposed by the transport problem, which requires a specific analysis of the behavior of our weak solutions.
Comparison of Fresnel lenses and parabolic mirrors as solar energy concentrators.
Lorenzo, E; Luque, A
1982-05-15
This paper compares the gain that can be achieved with a one- or two-stage concentrator, when the first stage is a Fresnel lens or a parabolic mirror, as a function of the luminosity of the concentrator. The results show that the achievable gain using a parabolic mirror is greater than that obtained using a flat or roof lens but is lower than that obtained using a curved lens. PMID:20389950
NASA Astrophysics Data System (ADS)
Mossoulina, O. A.; Kirilenko, M. S.; Khonina, S. N.
2016-08-01
We use radial Fractional Fourier transform to model vortex laser beams propagation in optical waveguides with parabolic dependence of the refractive index. To overcome calculation difficulties at distances proportional to a quarter of the period we use varied calculation step. Numerical results for vortex modes superposition propagation in a parabolic optical fiber show that the transverse beam structure can be changed significantly during the propagation. To provide stable transverse distribution input scale modes should be in accordance with fiber parameters.
Parabolic movement primitives and cortical states: merging optimality with geometric invariance.
Polyakov, Felix; Stark, Eran; Drori, Rotem; Abeles, Moshe; Flash, Tamar
2009-02-01
Previous studies have suggested that several types of rules govern the generation of complex arm movements. One class of rules consists of optimizing an objective function (e.g., maximizing motion smoothness). Another class consists of geometric and kinematic constraints, for instance the coupling between speed and curvature during drawing movements as expressed by the two-thirds power law. It has also been suggested that complex movements are composed of simpler elements or primitives. However, the ability to unify the different rules has remained an open problem. We address this issue by identifying movement paths whose generation according to the two-thirds power law yields maximally smooth trajectories. Using equi-affine differential geometry we derive a mathematical condition which these paths must obey. Among all possible solutions only parabolic paths minimize hand jerk, obey the two-thirds power law and are invariant under equi-affine transformations (which preserve the fit to the two-thirds power law). Affine transformations can be used to generate any parabolic stroke from an arbitrary parabolic template, and a few parabolic strokes may be concatenated to compactly form a complex path. To test the possibility that parabolic elements are used to generate planar movements, we analyze monkeys' scribbling trajectories. Practiced scribbles are well approximated by long parabolic strokes. Of the motor cortical neurons recorded during scribbling more were related to equi-affine than to Euclidean speed. Unsupervised segmentation of simulta- neously recorded multiple neuron activity yields states related to distinct parabolic elements. We thus suggest that the cortical representation of movements is state-dependent and that parabolic elements are building blocks used by the motor system to generate complex movements.
Combined optical solitons with parabolic law nonlinearity and spatio-temporal dispersion
NASA Astrophysics Data System (ADS)
Zhou, Qin; Zhu, Qiuping
2015-03-01
In this work, combined optical solitons are constructed in a weakly nonlocal nonlinear medium. The spatio-temporal dispersion (STD), parabolic law nonlinearity, detuning, nonlinear dispersion as well as inter-modal dispersion are taken into account. The integration tool that is applied is the complex envelope function ansatz. The influences of different parameters on dynamical behavior of combined optical solitons are discussed. The results are useful in describing the propagation of combined optical solitons with STD and parabolic law nonlinearity.
McCabe, G.J., Jr.
1989-01-01
Errors of the Thornthwaite model can be analyzed using adjusted pan evaporation as an index of potential evapotranspiration. An examination of ratios of adjusted pan evaporation to Thornthwaite potential evapotranspiration indicates that the ratios are highest in the winter and lowest during summer months. This trend suggests a parabolic pattern. In this study a parabolic function is used to adjust Thornthwaite estimates of potential evapotranspiration. Forty locations east of the Rocky Mountains are analyzed. -from Author
Explicit Nonlinear Finite Element Geometric Analysis of Parabolic Leaf Springs under Various Loads
Kong, Y. S.; Omar, M. Z.; Chua, L. B.; Abdullah, S.
2013-01-01
This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability. PMID:24298209
Comparison of parabolic filtration methods for 3D filtered back projection in pulsed EPR imaging.
Qiao, Zhiwei; Redler, Gage; Epel, Boris; Halpern, Howard J
2014-11-01
Pulse electron paramagnetic resonance imaging (Pulse EPRI) is a robust method for noninvasively measuring local oxygen concentrations in vivo. For 3D tomographic EPRI, the most commonly used reconstruction algorithm is filtered back projection (FBP), in which the parabolic filtration process strongly influences image quality. In this work, we designed and compared 7 parabolic filtration methods to reconstruct both simulated and real phantoms. To evaluate these methods, we designed 3 error criteria and 1 spatial resolution criterion. It was determined that the 2 point derivative filtration method and the two-ramp-filter method have unavoidable negative effects resulting in diminished spatial resolution and increased artifacts respectively. For the noiseless phantom the rectangular-window parabolic filtration method and sinc-window parabolic filtration method were found to be optimal, providing high spatial resolution and small errors. In the presence of noise, the 3 point derivative method and Hamming-window parabolic filtration method resulted in the best compromise between low image noise and high spatial resolution. The 3 point derivative method is faster than Hamming-window parabolic filtration method, so we conclude that the 3 point derivative method is optimal for 3D FBP.
Explicit nonlinear finite element geometric analysis of parabolic leaf springs under various loads.
Kong, Y S; Omar, M Z; Chua, L B; Abdullah, S
2013-01-01
This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability.
Rosnitskiy, P. Yuldashev, P. Khokhlova, V.
2015-10-28
An equivalent source model was proposed as a boundary condition to the nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation to simulate high intensity focused ultrasound (HIFU) fields generated by medical ultrasound transducers with the shape of a spherical shell. The boundary condition was set in the initial plane; the aperture, the focal distance, and the initial pressure of the source were chosen based on the best match of the axial pressure amplitude and phase distributions in the Rayleigh integral analytic solution for a spherical transducer and the linear parabolic approximation solution for the equivalent source. Analytic expressions for the equivalent source parameters were derived. It was shown that the proposed approach allowed us to transfer the boundary condition from the spherical surface to the plane and to achieve a very good match between the linear field solutions of the parabolic and full diffraction models even for highly focused sources with F-number less than unity. The proposed method can be further used to expand the capabilities of the KZ nonlinear parabolic equation for efficient modeling of HIFU fields generated by strongly focused sources.
Piracetam and fish orientation during parabolic aircraft flight
NASA Technical Reports Server (NTRS)
Hoffman, R. B.; Salinas, G. A.; Homick, J. L.
1980-01-01
Goldfish were flown in parabolic Keplerian trajectories in a KC-135 aircraft to assay both the effectiveness of piracetam as an antimotion sickness drug and the effectiveness of state-dependent training during periods of oscillating gravity levels. Single-frame analyses of infrared films were performed for two classes of responses - role rates in hypogravity or hypogravity orienting responses (LGR) and climbing responses in hypergravity or hypergravity orienting responses (HGR). In Experiment I, preflight training with the vestibular stressor facilitated suppression of LGR by the 10th parabola. An inverse correlation was found between the magnitudes of LGR and HGR. Piracetam was not effective in a state-dependent design, but the drug did significantly increase HGR when injected into trained fish shortly before flight. In Experiment II, injections of saline, piracetam, and modifiers of gamma-aminobutyric acid - aminooxyacetic acid (AOAA) and isonicotinic acid did not modify LGR. AOAA did significantly increase HGR. Thus, the preflight training has a beneficial effect in reducing disorientation in the fish in weightlessness, but the drugs employed were ineffective.
Mechanism of Hydrogen Formation in Solar Parabolic Trough Receivers
Moens, L.; Blake, D. M.
2008-03-01
Solar parabolic trough systems for electricity production are receiving renewed attention, and new solar plants are under construction to help meet the growing demands of the power market in the Western United States. The growing solar trough industry will rely on operating experience it has gained over the last two decades. Recently, researchers found that trough plants that use organic heat transfer fluids (HTF) such as Therminol VP-1 are experiencing significant heat losses in the receiver tubes. The cause has been traced back to the accumulation of excess hydrogen gas in the vacuum annulus that surrounds the steel receiver tube, thus compromising the thermal insulation of the receiver. The hydrogen gas is formed during the thermal decomposition of the organic HTF that circulates inside the receiver loop, and the installation of hydrogen getters inside the annulus has proven to be insufficient for controlling the hydrogen build-up over the lifetime of the receivers. This paper will provide an overview of the chemical literature dealing with the thermal decomposition of diphenyl oxide and biphenyl, the two constituents of Therminol VP-1.
Perception of Egocentric Distance during Gravitational Changes in Parabolic Flight.
Clément, Gilles; Loureiro, Nuno; Sousa, Duarte; Zandvliet, Andre
2016-01-01
We explored the effect of gravity on the perceived representation of the absolute distance of objects to the observers within the range from 1.5-6 m. Experiments were performed on board the CNES Airbus Zero-G during parabolic flights eliciting repeated exposures to short periods of microgravity (0 g), hypergravity (1.8 g), and normal gravity (1 g). Two methods for obtaining estimates of perceived egocentric distance were used: verbal reports and visually directed motion toward a memorized visual target. For the latter method, because normal walking is not possible in 0 g, blindfolded subjects translated toward the visual target by pulling on a rope with their arms. The results showed that distance estimates using both verbal reports and blind pulling were significantly different between normal gravity, microgravity, and hypergravity. Compared to the 1 g measurements, the estimates of perceived distance using blind pulling were shorter for all distances in 1.8 g, whereas in 0 g they were longer for distances up to 4 m and shorter for distances beyond. These findings suggest that gravity plays a role in both the sensorimotor system and the perceptual/cognitive system for estimating egocentric distance. PMID:27463106
Norwich Technologies' Advanced Low-Cost Receivers for Parabolic Troughs
Stettenheim, Joel; McBride, Troy O.; Brambles, Oliver J.; Cashin, Emil A.
2013-12-31
This report summarizes the successful results of our SunShot project, Advanced Low-Cost Receivers for Parabolic Troughs. With a limited budget of $252K and in only 12 months, we have (1) developed validated optical and thermal models and completed rigorous optimization analysis to identify key performance characteristics as part of developing first-generation laboratory prototype designs, (2) built optical and thermal laboratory prototypes and test systems with associated innovative testing protocols, and (3) performed extensive statistically relevant testing. We have produced fully functioning optical and thermal prototypes and accurate, validated models shown to capture important underlying physical mechanisms. The test results from the first-generation prototype establish performance exceeding the FOA requirement of thermal efficiency >90% for a CSP receiver while delivering an exit fluid temperature of > 650 °C and a cost < $150/kWth. Our vacuum-free SunTrap receiver design provides improvements over conventional vacuum-tube collectors, allowing dramatic reductions in thermal losses at high operating temperature.
Motion sickness susceptibility in parabolic flight and velocity storage activity
NASA Technical Reports Server (NTRS)
Dizio, Paul; Lackner, James R.
1991-01-01
In parabolic flight experiments, postrotary nystagmus is as found to be differentially suppressed in free fall (G) and in a high gravitoinertial force (1.8 G) background relative to 1 G. In addition, the influence of postrotary head movements on nystagmus suppression was found to be contingent on G-dependency of the velocity storage and dumping mechanisms. Here, susceptibility to motion sickness during head movements in 0 G and 1.8 G was rank-correlated with the following: (1) the decay time constant of the slow phase velocity of postrotary nystagmus under 1 G, no head movement, baseline conditions, (2) the extent of time constant reduction elicited in 0 G and 1.8 G; (3) the extent of time constant reduction elicited by head tilts in 1 G; and (4) changes in the extent of time constants reduction in 0 G and 1.8 G over repeated tests. Susceptibility was significantly correlated with the extent to which a head movement reduced the time constant in 1 G, was weakly correlated with the baseline time constant, but was not correlated with the extent of reduction in 0 G or 1.8 G. This pattern suggests a link between mechanisms evoking symptoms of space motion sickness and the mechanisms of velocity storage and dumping. Experimental means of evaluating this link are described.
Evaluation of aerosolized medications during parabolic flight maneuvers
NASA Technical Reports Server (NTRS)
Lloyd, Charles W.; Martin, William J.; Gosbee, John
1991-01-01
The goal was to visually evaluate the effect gravity has on delivery of medications by the use of various aerosol devices. During parabolic flight the same four aerosols were retested as performed in studio ground tests. It appears that the Cetacaine spray and the Ventolin inhaler function without failure during all test. The pump spray (Nostril) appeared to function normally when the container was full, however it appeared to begin to fail to deliver a full mist with larger droplet size when the container was nearly empty. The simple hand spray bottle appeared to work when the container was full and performed progressively worse as the container was emptied. During Apollo flights, it was reported that standard spray bottles did not work well, however, they did not indicate why. It appears that we would also conclude that standard spray bottles do not function as well in zero gravity by failing to produce a normal mist spray. The standard spray bottle allowed the fluid to come out in a narrow fluid stream when held with the nozzle either level or slightly tilted upward.
Perception of Egocentric Distance during Gravitational Changes in Parabolic Flight.
Clément, Gilles; Loureiro, Nuno; Sousa, Duarte; Zandvliet, Andre
2016-01-01
We explored the effect of gravity on the perceived representation of the absolute distance of objects to the observers within the range from 1.5-6 m. Experiments were performed on board the CNES Airbus Zero-G during parabolic flights eliciting repeated exposures to short periods of microgravity (0 g), hypergravity (1.8 g), and normal gravity (1 g). Two methods for obtaining estimates of perceived egocentric distance were used: verbal reports and visually directed motion toward a memorized visual target. For the latter method, because normal walking is not possible in 0 g, blindfolded subjects translated toward the visual target by pulling on a rope with their arms. The results showed that distance estimates using both verbal reports and blind pulling were significantly different between normal gravity, microgravity, and hypergravity. Compared to the 1 g measurements, the estimates of perceived distance using blind pulling were shorter for all distances in 1.8 g, whereas in 0 g they were longer for distances up to 4 m and shorter for distances beyond. These findings suggest that gravity plays a role in both the sensorimotor system and the perceptual/cognitive system for estimating egocentric distance.
Perception of Egocentric Distance during Gravitational Changes in Parabolic Flight
Clément, Gilles; Loureiro, Nuno; Sousa, Duarte; Zandvliet, Andre
2016-01-01
We explored the effect of gravity on the perceived representation of the absolute distance of objects to the observers within the range from 1.5–6 m. Experiments were performed on board the CNES Airbus Zero-G during parabolic flights eliciting repeated exposures to short periods of microgravity (0 g), hypergravity (1.8 g), and normal gravity (1 g). Two methods for obtaining estimates of perceived egocentric distance were used: verbal reports and visually directed motion toward a memorized visual target. For the latter method, because normal walking is not possible in 0 g, blindfolded subjects translated toward the visual target by pulling on a rope with their arms. The results showed that distance estimates using both verbal reports and blind pulling were significantly different between normal gravity, microgravity, and hypergravity. Compared to the 1 g measurements, the estimates of perceived distance using blind pulling were shorter for all distances in 1.8 g, whereas in 0 g they were longer for distances up to 4 m and shorter for distances beyond. These findings suggest that gravity plays a role in both the sensorimotor system and the perceptual/cognitive system for estimating egocentric distance. PMID:27463106
Slope Error Measurement Tool for Solar Parabolic Trough Collectors: Preprint
Stynes, J. K.; Ihas, B.
2012-04-01
The National Renewable Energy Laboratory (NREL) has developed an optical measurement tool for parabolic solar collectors that measures the combined errors due to absorber misalignment and reflector slope error. The combined absorber alignment and reflector slope errors are measured using a digital camera to photograph the reflected image of the absorber in the collector. Previous work using the image of the reflection of the absorber finds the reflector slope errors from the reflection of the absorber and an independent measurement of the absorber location. The accuracy of the reflector slope error measurement is thus dependent on the accuracy of the absorber location measurement. By measuring the combined reflector-absorber errors, the uncertainty in the absorber location measurement is eliminated. The related performance merit, the intercept factor, depends on the combined effects of the absorber alignment and reflector slope errors. Measuring the combined effect provides a simpler measurement and a more accurate input to the intercept factor estimate. The minimal equipment and setup required for this measurement technique make it ideal for field measurements.
Geometric visual illusions in microgravity during parabolic flight.
Villard, Eric; Garcia-Moreno, Francesc Tintó; Peter, Nicolas; Clément, Gilles
2005-08-22
This investigation explores whether the absence of gravitational information in a microgravity environment affects the perception of several classical visual illusions based on the arrangement of horizontal and vertical lines. Because the perception of horizontal and vertical orientation changes in microgravity, our prediction was that the strength of visual illusions based on the arrangement of horizontal and vertical lines would be altered when study participants were free-floating during parabolic flight. The frequency of appearance of reversed-T, Müller-Lyer, Ponzo, and Hering illusions substantially decreased when observers were free-floating, whereas the Zöllner and the Poggendorff illusions were not affected. Because the former illusions rely more heavily on perspective cues for generating inaccurate judgments of depth and size, these results suggest an alteration in the role of linear perspective for three-dimensional vision in microgravity. They also confirm that the visual system normally relies on otolith and somatosensory information for providing accurate judgments about the size and distance of objects when presented with planar presentations of geometric figures.
Recent Solar Measurements Results at the Parabolic Dish Test Site
NASA Technical Reports Server (NTRS)
Ross, D. L.
1984-01-01
After the Mexican volcanic eruptions of March 28, April 3 and 4, 1982, the question of its effect on insolation levels at the Parabolic Dish Test Site (PDTS) naturally arose. Clearly, the answer to the original question is that the Mexican volcanic explosion had a significant impact on energy and insolation levels at the PDTS and, furthermore, it has been quite long lasting. The first really significant decrease in energy and insolation levels occurred in June 1982 when the energy level decreased by 19.7% while the peak insolation levels went down by 4.0%. June of 1982 was also the first month (of 13 consecutive months) when peak insolation levels did not equal or exceed 1,000 W/sq m. Signs of a recovery from the effects of the volcanic explosion began to appear in May of 1983, when the energy level exceeded that of May 1981 as well as May 1982. It would appear that energy and insolation levels are improving at the PDTS, but have not quite reached normal or pre-volcanic levels. At this time the data would seem to suggest a return to normal energy and insolation levels will occur in the very near future.
Optimal trajectories based on linear equations
NASA Technical Reports Server (NTRS)
Carter, Thomas E.
1990-01-01
The Principal results of a recent theory of fuel optimal space trajectories for linear differential equations are presented. Both impulsive and bounded-thrust problems are treated. A new form of the Lawden Primer vector is found that is identical for both problems. For this reason, starting iteratives from the solution of the impulsive problem are highly effective in the solution of the two-point boundary-value problem associated with bounded thrust. These results were applied to the problem of fuel optimal maneuvers of a spacecraft near a satellite in circular orbit using the Clohessy-Wiltshire equations. For this case two-point boundary-value problems were solved using a microcomputer, and optimal trajectory shapes displayed. The results of this theory can also be applied if the satellite is in an arbitrary Keplerian orbit through the use of the Tschauner-Hempel equations. A new form of the solution of these equations has been found that is identical for elliptical, parabolic, and hyperbolic orbits except in the way that a certain integral is evaluated. For elliptical orbits this integral is evaluated through the use of the eccentric anomaly. An analogous evaluation is performed for hyperbolic orbits.
NASA Technical Reports Server (NTRS)
Newsome, Richard W.; Walters, Robert W.; Thomas, James L.
1987-01-01
A previously developed upwind/relaxation algorithm for solving the unsteady, compressible, thin-layer Navier-Stokes equations is presently modified so that the downstream influence of the subsonic part of the boundary layer in an otherwise supersonic flow is suppressed by restricting the streamwise pressure gradient. A 'parabolized' solution is then efficiently obtained by marching downstream and iterating locally in each crossflow plane until achieving convergence. This parabolized solution is an excellent final one for problems without large adverse streamwise pressure gradients.
Hypervelocity Stars and the Restricted Parabolic Three-Body Problem
NASA Astrophysics Data System (ADS)
Sari, Re'em; Kobayashi, Shiho; Rossi, Elena M.
2010-01-01
Motivated by detections of hypervelocity stars that may originate from the Galactic center, we revisit the problem of a binary disruption by a passage near a much more massive point mass. The six orders of magnitude mass ratio between the Galactic center black hole (BH) and the binary stars allows us to formulate the problem in the restricted parabolic three-body approximation. In this framework, results can be simply rescaled in terms of binary masses, their initial separation, and the binary-to-black hole mass ratio. Consequently, an advantage over the full three-body calculation is that a much smaller set of simulations is needed to explore the relevant parameter space. Contrary to previous claims, we show that, upon binary disruption, the lighter star does not remain preferentially bound to the black hole. In fact, it is ejected in exactly 50% of the cases. Nonetheless, lighter objects have higher ejection velocities, since the energy distribution is independent of mass. Focusing on the planar case, we provide the probability distributions for disruption of circular binaries and for the ejection energy. We show that even binaries that penetrate deeply into the tidal sphere of the BH are not doomed to disruption, but survive in 20% of the cases. Nor do these deep encounters produce the highest ejection energies, which are instead obtained for binaries arriving to 0.1-0.5 of the tidal radius in a prograde orbit. Interestingly, such deep-reaching binaries separate widely after penetrating the tidal radius, but always approach each other again on their way out from the BH. Finally, our analytic method allows us to account for a finite size of the stars and recast the ejection energy in terms of a minimal possible separation. We find that, for a given minimal separation, the ejection energy is relatively insensitive to the initial binary separation.
Cluster eye camera using microlenses on parabolic surface
NASA Astrophysics Data System (ADS)
Shen, Hui-Kai; Su, Guo-Dung J.
2013-10-01
There are two main types of imaging systems that exist in nature: the single aperture eye and the compound eye. Usually, cameras and most of artificial imaging systems are similar to the single aperture eye. But compound lenses can be more compact than single lenses. Our design is based on insect compound eyes, which also have a wide field of view (FOV). With the rise of micro-optical techniques, fabricating compound lenses has become easier. The simplest form of a curved microlens array is a parabolic surface. In this paper, we proposed a multi-channel imaging system, which combines the principles of the insect compound eye and the human eye. The optical system enables the reduction of track length of the imaging optics to achieve miniaturization. With the aid of optical engineering software ZEMAX, the multi-channel structure is simulated by a curved microlens array, and we use a Hypergon lens as the main lens to simulate the human eye, which can achieve the purpose of the wide FOV. With this architecture, each microlens of a microlens array transmits a segment of the overall FOV. The partial images that are separately recorded in different channels are stitched together to form the final image of the whole FOV by software processing. A 2.74 mm thin imaging system with 59 channels and 90° FOV is optimized using ZEMAX sequential ray tracing software on a 6.16 mm × 4.62 mm image plane. Finally, we will discuss the simulation results of this system and compare it with the optical cluster eye system and a mobile phone patent.
Shore, B.W.
1981-01-30
The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence.
Spatial complexity of solutions of higher order partial differential equations
NASA Astrophysics Data System (ADS)
Kukavica, Igor
2004-03-01
We address spatial oscillation properties of solutions of higher order parabolic partial differential equations. In the case of the Kuramoto-Sivashinsky equation ut + uxxxx + uxx + u ux = 0, we prove that for solutions u on the global attractor, the quantity card {x epsi [0, L]:u(x, t) = lgr}, where L > 0 is the spatial period, can be bounded by a polynomial function of L for all \\lambda\\in{\\Bbb R} . A similar property is proven for a general higher order partial differential equation u_t+(-1)^{s}\\partial_x^{2s}u+ \\sum_{k=0}^{2s-1}v_k(x,t)\\partial_x^k u =0 .
Interband magneto-spectroscopy in InSb square and parabolic quantum wells
Kasturiarachchi, T.; Edirisooriya, M.; Mishima, T. D.; Doezema, R. E.; Santos, M. B.; Saha, D.; Pan, X.; Sanders, G. D.; Stanton, C. J.
2015-06-07
We measure the magneto-optical absorption due to intersubband optical transitions between conduction and valence subband Landau levels in InSb square and parabolic quantum wells. InSb has the narrowest band gap (0.24 eV at low temperature) of the III–V semiconductors leading to a small effective mass (0.014 m{sub 0}) and a large g–factor (−51). As a result, the Landau level spacing is large at relatively small magnetic fields (<8 T), and one can observe spin-splitting of the Landau levels. We examine two structures: (i) a multiple-square-well structure and (ii) a structure containing multiple parabolic wells. The energies and intensities of the strongest features are well explained by a modified Pidgeon-Brown model based on an 8-band k•p model that explicitly incorporates pseudomorphic strain. The strain is essential for obtaining agreement between theory and experiment. While modeling the square well is relatively straight-forward, the parabolic well consists of 43 different layers of various thickness to approximate a parabolic potential. Agreement between theory and experiment for the parabolic well validates the applicability of the model to complicated structures, which demonstrates the robustness of our model and confirms its relevance for developing electronic and spintronic devices that seek to exploit the properties of the InSb band structure.
Parallelizing across time when solving time-dependent partial differential equations
Worley, P.H.
1991-09-01
The standard numerical algorithms for solving time-dependent partial differential equations (PDEs) are inherently sequential in the time direction. This paper describes algorithms for the time-accurate solution of certain classes of linear hyperbolic and parabolic PDEs that can be parallelized in both time and space and have serial complexities that are proportional to the serial complexities of the best known algorithms. The algorithms for parabolic PDEs are variants of the waveform relaxation multigrid method (WFMG) of Lubich and Ostermann where the scalar ordinary differential equations (ODEs) that make up the kernel of WFMG are solved using a cyclic reduction type algorithm. The algorithms for hyperbolic PDEs use the cyclic reduction algorithm to solve ODEs along characteristics. 43 refs.
Tau approximation techniques for identification of coefficients in parabolic PDE
NASA Technical Reports Server (NTRS)
Banks, H. T.; Wade, J. G.
1989-01-01
A variant of the Tau method, called the weak Tau method, is developed on the basis of the weak form of the PDE for use in least-squares parameter estimation; also presented is a suitable abstract convergence framework. The emphasis is on the theoretical framework that allows treatment of the weak Tau method when it is applied to a wide class of inverse problems, including those for diffusion-advection equations, the Fokker-Planck model for population dynamics, and damped beam equations. Extensive numerical testing of the weak Tau method has demonstrated that it compares quite favorably with existing methods.
NASA Astrophysics Data System (ADS)
Yan, Na; Baas, Andreas
2015-04-01
Parabolic dunes are one of a few common aeolian landforms which are highly controlled by eco-geomorphic interactions. Parabolic dunes, on the one hand, can be developed from highly mobile dune landforms, barchans for instance, in an ameliorated vegetation condition; or on the other hand, they can be reactivated and transformed back into mobile dunes due to vegetation deterioration. The fundamental mechanisms and eco-geomorphic interactions controlling both dune transformations remain poorly understood. To bridge the gap between complex processes involved in dune transformations on a relatively long temporal scale and real world monitoring records on a very limited temporal scale, this research has extended the DECAL model to incorporate 'dynamic' growth functions and the different 'growth' of perennial shrubs between growing and non-growing seasons, informed by field measurements and remote sensing analysis, to explore environmental controls and eco-geomorphic interactions of both types of dune transformation. A non-dimensional 'dune stabilising index' is proposed to capture the interactions between environmental controls (i.e. the capabilities of vegetation to withstand wind erosion and sand burial, the sandy substratum thickness, the height of the initial dune, and the sand transport potential), and establish the linkage between these controls and the geometry of a stabilising dune. An example demonstrates how to use the power-law relationship between the dune stabilising index and the normalised migration distance to assist in extrapolating the historical trajectories of transforming dunes. The modelling results also show that a slight increase in vegetation cover of an initial parabolic dune can significantly increase the reactivation threshold of climatic impact (both drought stress and wind strength) required to reactivate a stabilising parabolic dune into a barchan. Four eco-geomorphic interaction zones that govern a barchan-to-parabolic dune transformation
The 3D heat flux density distribution on a novel parabolic trough wavy absorber
NASA Astrophysics Data System (ADS)
Demagh, Yassine; Kabar, Yassine; Bordja, Lyes; Noui, Samira
2016-05-01
The non-uniform concentrated solar flux distribution on the outer surface of the absorber pipe can lead to large circumferential gradient temperature and high concentrated temperature of the absorber pipe wall, which is one of the primary causes of parabolic trough solar receiver breakdown. In this study, a novel shape of the parabolic trough absorber pipe is proposed as a solution to well homogenize the solar flux distribution, as well as, the temperature in the absorber wall. The conventional straight absorber located along the focal line of the parabola is replaced by wavy one (invention patent by Y. Demagh [1]) for which the heat flux density distribution on the outer surface varies in both axial and azimuthal directions (3D) while it varies only in the azimuthal direction on the former (2D). As far as we know, there is not previous study which has used a longitudinally wavy pipe as an absorber into the parabolic trough collector unit.
A parabolic analogue of the higher-order comparison theorem of De Silva and Savin
NASA Astrophysics Data System (ADS)
Banerjee, Agnid; Garofalo, Nicola
2016-01-01
We show that the quotient of two caloric functions which vanish on a portion of the lateral boundary of a H k + α domain is H k + α up to the boundary for k ≥ 2. In the case k = 1, we show that the quotient is in H 1 + α if the domain is assumed to be space-time C 1, α regular. This can be thought of as a parabolic analogue of a recent important result in [8], and we closely follow the ideas in that paper. We also give counterexamples to the fact that analogous results are not true at points on the parabolic boundary which are not on the lateral boundary, i.e., points which are at the corner and base of the parabolic boundary.
Fan beam generated by a linear-array fed parabolic reflector
NASA Technical Reports Server (NTRS)
Huang, John; Rahmat-Samii, Yahya
1990-01-01
The theoretical background and the results of computer simulations and experimental studies for a parabolic reflector fed by a linear array are detailed. The concept of using a parabolic reflector antenna fed by a small linear array to generate fan-beam patterns is validated. Large angle scan along the broad-beam direction of the fan beam can be achieved by offsetting the linear array laterally. It is both empirically and numerically demonstrated that the array feed must be displaced in the reflector's axial direction to an optimum location from the focal plane in order to achieve the best antenna gain performance. As a result, the linear-array-fed parabolic reflector can be used in place of a long planar array in a multifunctional reflector antenna system.
Dynamic parabolic pulse generation using temporal shaping of wavelength to time mapped pulses.
Nguyen, Dat; Piracha, Mohammad Umar; Mandridis, Dimitrios; Delfyett, Peter J
2011-06-20
Self-phase modulation in fiber amplifiers can significantly degrade the quality of compressed pulses in chirped pulse amplification systems. Parabolic pulses with linear frequency chirp are suitable for suppressing nonlinearities, and to achieve high peak power pulses after compression. In this paper, we present an active time domain technique to generate parabolic pulses for chirped pulse amplification applications. Pulses from a mode-locked laser are temporally stretched and launched into an amplitude modulator, where the drive voltage is designed using the spectral shape of the input pulse and the transfer function of the modulator, resulting in the generation of parabolic pulses. Experimental results of pulse shaping with a pulse train from a mode-locked laser are presented, with a residual error of less than 5%. Moreover, an extinction ratio of 27 dB is achieved, which is ideal for chirped pulse amplification applications.
Wind interaction with falling ejecta - Origin of the parabolic features on Venus
NASA Technical Reports Server (NTRS)
Vervack, Ronald J., Jr.; Melosh, H. J.
1992-01-01
A quantitative model in which the parabolic features are produced by the interaction of the zonal winds with material ejected ballistically from the impact crater is proposed. As the ejecta particles fall through the atmosphere, the winds transport them downwind from their entry point, smaller particles being transported a greater distance. Since the ejecta distribution is initially axially symmetric and smaller particles are thrown farther from the crater, the winds blow the particles on the upwind side back upon one another, leading to a pile-up of material. On the downwind side, the winds disperse the ejecta particles and no pile-up occurs. The resulting thickness distribution on the Venusian surface matches the observed parabolic features closely. The dual parabolic features associated with the crater Carson is also explained by this model.
Parabolic problems with parameters arising in evolution model for phytromediation
NASA Astrophysics Data System (ADS)
Sahmurova, Aida; Shakhmurov, Veli
2012-12-01
The past few decades, efforts have been made to clean sites polluted by heavy metals as chromium. One of the new innovative methods of eradicating metals from soil is phytoremediation. This uses plants to pull metals from the soil through the roots. This work develops a system of differential equations with parameters to model the plant metal interaction of phytoremediation (see [1]).
Parabolic replicator dynamics and the principle of minimum Tsallis information gain
2013-01-01
Background Non-linear, parabolic (sub-exponential) and hyperbolic (super-exponential) models of prebiological evolution of molecular replicators have been proposed and extensively studied. The parabolic models appear to be the most realistic approximations of real-life replicator systems due primarily to product inhibition. Unlike the more traditional exponential models, the distribution of individual frequencies in an evolving parabolic population is not described by the Maximum Entropy (MaxEnt) Principle in its traditional form, whereby the distribution with the maximum Shannon entropy is chosen among all the distributions that are possible under the given constraints. We sought to identify a more general form of the MaxEnt principle that would be applicable to parabolic growth. Results We consider a model of a population that reproduces according to the parabolic growth law and show that the frequencies of individuals in the population minimize the Tsallis relative entropy (non-additive information gain) at each time moment. Next, we consider a model of a parabolically growing population that maintains a constant total size and provide an “implicit” solution for this system. We show that in this case, the frequencies of the individuals in the population also minimize the Tsallis information gain at each moment of the ‘internal time” of the population. Conclusions The results of this analysis show that the general MaxEnt principle is the underlying law for the evolution of a broad class of replicator systems including not only exponential but also parabolic and hyperbolic systems. The choice of the appropriate entropy (information) function depends on the growth dynamics of a particular class of systems. The Tsallis entropy is non-additive for independent subsystems, i.e. the information on the subsystems is insufficient to describe the system as a whole. In the context of prebiotic evolution, this “non-reductionist” nature of parabolic replicator
NASA Technical Reports Server (NTRS)
Litvin, Faydor L.; Lee, Hong-Tao
1989-01-01
A new approach for determination of machine-tool settings for spiral bevel gears is proposed. The proposed settings provide a predesigned parabolic function of transmission errors and the desired location and orientation of the bearing contact. The predesigned parabolic function of transmission errors is able to absorb piece-wise linear functions of transmission errors that are caused by the gear misalignment and reduce gear noise. The gears are face-milled by head cutters with conical surfaces or surfaces of revolution. A computer program for simulation of meshing, bearing contact and determination of transmission errors for misaligned gear has been developed.
Dynamic selective etching: a facile route to parabolic optical fiber nano-probe.
Zhu, Wei; Shi, Tielin; Tang, Zirong; Gong, Bo; Liao, Guanglan; Tully, John
2013-03-25
A dynamic etching approach is proposed through the appropriate variation of etchant composition ratio during the etching process, resulting in the parabolic shape of optical fiber nano-probe with a favorable changing of cone angle. The probe formation mechanism is thoroughly analyzed to illustrate the controllability and simplicity of this method. Optical properties of as-made probes are simulated and experimentally characterized and compared with the linear shape probes of different cone angles. It shows that the parabolic shape probes are superior to the linear shape ones with respect to the transmission efficiency and light focusing capability.
NASA Technical Reports Server (NTRS)
Vernalis, Marina N.; Latham, Ricky D.; Fanton, John W.; Geffney, F. Andrew
1993-01-01
Transthoracic echocardiography (TTE) is a feasible method to noninvasively examine cardiac anatomy during parabolic flight. However, transducer placement on the chest wall is very difficult to maintain during transition to microgravity. In addition, TTE requires the use of low frequency transponders which limit resolution. Transesophical echocardiography (TEE) is an established imaging technique which obtains echocardiographic information from the esophagus. It is a safe procedure and provides higher quality images of cardiac structure than obtained with TTE. This study is designed to determine whether TEE was feasible to perform during parabolic flight and to determine whether acute central volume responses occur in acute transition to zero gravity by direct visualization of the cardiac chambers.
On Some Properties of the Landau Kinetic Equation
NASA Astrophysics Data System (ADS)
Bobylev, Alexander; Gamba, Irene; Potapenko, Irina
2015-12-01
We discuss some general properties of the Landau kinetic equation. In particular, the difference between the "true" Landau equation, which formally follows from classical mechanics, and the "generalized" Landau equation, which is just an interesting mathematical object, is stressed. We show how to approximate solutions to the Landau equation by the Wild sums. It is the so-called quasi-Maxwellian approximation related to Monte Carlo methods. This approximation can be also useful for mathematical problems. A model equation which can be reduced to a local nonlinear parabolic equation is also constructed in connection with existence of the strong solution to the initial value problem. A self-similar asymptotic solution to the Landau equation for large v and t is discussed in detail. The solution, earlier confirmed by numerical experiments, describes a formation of Maxwellian tails for a wide class of initial data concentrated in the thermal domain. It is shown that the corresponding rate of relaxation (fractional exponential function) is in exact agreement with recent mathematically rigorous estimates.
NASA Technical Reports Server (NTRS)
Hamrock, B. J.; Dowson, D.
1981-01-01
Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.
NASA Astrophysics Data System (ADS)
Ou, Yongsheng
The need for new sources of energy is expected to become a critical problem within the next few decades. Nuclear fusion arises as a potential source of energy with sufficient energy density to supply the world population with its steadily increasing energy demands. The need to optimize the tokamak concept for the design of an economical, possibly steady state, fusion power plant have motivated extensive international research aimed at finding the so-called "advanced tokamak (AT) operation scenarios." It has been demonstrated that simultaneous real-time control of the current and pressure profiles could lead to the steady state sustainment of an internal transport barrier (ITB), and so to a stationary optimized plasma regime. It has also been suggested that global current profile control, eventually combined with pressure profile control, can be an effective mechanism for neoclassical tearing mode (NTM) control and avoidance. The control of linear or quasi-linear parabolic diffusion-reaction partial differential equations (PDE) has been extensively studied using interior control (see [1] and references therein) or boundary control (see [2] and references therein). Recently, the control of bilinear parabolic partial differential equations via actuation of the diffusive coefficient term, named diffusivity control here, has caught increasing interest. The diffusive coefficient term in a parabolic PDE is not necessary fixed or uncontrollable. For example, the diffusivity control problem arises in the control of the current density profile in magnetically confined fusion plasmas [3], where physical actuators such as plasma total current, line-averaged density and non-inductive total power are used to steer the plasma current density to a desired profile in a designated time period. By modulating these physical actuators it is possible not only to vary the amount of non-inductive current driven into the system (interior control) and the total plasma current (boundary
Robust algorithms for solving stochastic partial differential equations
Werner, M.J.; Drummond, P.D.
1997-04-01
A robust semi-implicit central partial difference algorithm for the numerical solution of coupled stochastic parabolic partial differential equations (PDEs) is described. This can be used for calculating correlation functions of systems of interacting stochastic fields. Such field equations can arise in the description of Hamiltonian and open systems in the physics of nonlinear processes, and may include multiplicative noise sources. The algorithm can be used for studying the properties of nonlinear quantum or classical field theories. The general approach is outlined and applied to a specific example, namely the quantum statistical fluctuations of ultra-short optical pulses in X{sup 2} parametric waveguides. This example uses non-diagonal coherent state representation, and correctly predicts the sub-shot noise level spectral fluctuations observed in homodyne detection measurements. It is expected that the methods used will be applicable for higher-order correlation functions and other physical problems as well. A stochastic differencing technique for reducing sampling errors is also introduced. This involves solving nonlinear stochastic parabolic PDEs in combination with a reference process, which uses the Wigner representation in the example presented here. A computer implementation on MIMD parallel architectures is discussed. 27 refs., 4 figs.
Quasilinear parabolic variational inequalities with multi-valued lower-order terms
NASA Astrophysics Data System (ADS)
Carl, Siegfried; Le, Vy K.
2014-10-01
In this paper, we provide an analytical frame work for the following multi-valued parabolic variational inequality in a cylindrical domain : Find and an such that where is some closed and convex subset, A is a time-dependent quasilinear elliptic operator, and the multi-valued function is assumed to be upper semicontinuous only, so that Clarke's generalized gradient is included as a special case. Thus, parabolic variational-hemivariational inequalities are special cases of the problem considered here. The extension of parabolic variational-hemivariational inequalities to the general class of multi-valued problems considered in this paper is not only of disciplinary interest, but is motivated by the need in applications. The main goals are as follows. First, we provide an existence theory for the above-stated problem under coercivity assumptions. Second, in the noncoercive case, we establish an appropriate sub-supersolution method that allows us to get existence, comparison, and enclosure results. Third, the order structure of the solution set enclosed by sub-supersolutions is revealed. In particular, it is shown that the solution set within the sector of sub-supersolutions is a directed set. As an application, a multi-valued parabolic obstacle problem is treated.
Stability of shock waves for multi-dimensional hyperbolic-parabolic conservation laws
NASA Astrophysics Data System (ADS)
Li, Dening
1988-01-01
The uniform linear stability of shock waves is considerd for quasilinear hyperbolic-parabolic coupled conservation laws in multi-dimensional space. As an example, the stability condition and its dynamic meaning for isothermal shock wave in radiative hydrodynamics are analyzed.
Parabolic flight experience is related to increased release of stress hormones.
Schneider, Stefan; Brümmer, Vera; Göbel, Simon; Carnahan, Heather; Dubrowski, Adam; Strüder, Heiko K
2007-06-01
Numerous studies have shown significant effects of weightlessness on adaptational processes of the CNS, cardiovascular and/or muscular system. Most of these studies have been carried out during parabolic flights, using the recurring 20 s of weightlessness at each parabola. Although some of these studies reported on potential influences not only of weightlessness but also of the stressful situation within a parabolic flight, especially provoked by the ongoing changes between 1.8, 1 and 0 G, so far there seems to be only marginal information about objective parameters of stress evoked by parabolic flights. By collecting blood samples from a permanent venous catheter several times during parabolic flights, we were able to show an increase of prolactin, cortisol and ACTH in the course of a 120 min flight. We conclude, therefore, that previous reported effects of weightlessness on adaptational processes may be affected not only by weightlessness but also by the exposure to other stressors experienced within the environment of a Zero-G airbus.
Shift in arm-pointing movements during gravity changes produced by aircraft parabolic flight.
Chen, Y; Mori, S; Koga, K; Ohta, Y; Wada, Y; Tanaka, M
1999-06-01
It has been shown that target-pointing arm movements without visual feedback shift downward in space microgravity and upward in centrifuge hypergravity. Under gravity changes in aircraft parabolic flight, however, arm movements have been reported shifting upward in hypergravity as well, but a downward shift under microgravity is contradicted. In order to explain this discrepancy, we reexamined the pointing movements using an experimental design which was different from prior ones. Arm-pointing movements were measured by goniometry around the shoulder joint of subjects with and without eyes closed or with a weight in the hand, during hyper- and microgravity in parabolic flight. Subjects were fastened securely to the seat with the neck fixed and the elbow maintained in an extended position, and the eyes were kept closed for a period of time before each episode of parabolic flight. Under these new conditions, the arm consistently shifted downward during microgravity and mostly upward during hypergravity, as expected. We concluded that arm-pointing deviation induced by parabolic flight could be also be valid for studying the mechanism underlying disorientation under varying gravity conditions.
Ex Vivo Assessment of a Parabolic-Tip Inflow Cannula for Pediatric Continuous-Flow VADs.
Griffin, Michael T; Grzywinski, Matthew F; Voorhees, Hannah J; Kameneva, Marina V; Olia, Salim E
2016-01-01
To address the challenge of unloading the left ventricle during pediatric mechanical circulatory support using next-generation rotary blood pumps, a novel inflow cannula was developed. This unique inflow cannula for pediatric, continuous-flow, left ventricular assist devices (VADs) with a parabolic-shaped inlet entrance was evaluated alongside a bevel-tip and fenestrated-tip cannula via an ex vivo, isolated-heart experimental setup. Performance was characterized using two clinical scenarios of over-pumping and hypovolemia, created by varying pump speed and filling preload pressure, respectively, at ideal and off-axis cannula placement to assess ventricular unloading and positional sensitivity. Quantitative and qualitative assessments were performed on the resultant hemodynamics and intra-ventricular boroscopic images to classify conditions of nonsuction, partial, gradual or severe entrainment, and ventricular collapse. The parabolic-tip cannula was found to be significantly less sensitive to placement position (p < 0.001) than the bevel-tip cannula under all conditions, while not statistically different from the fenestrated cannula. Visual analysis of the parabolic-tip cannula showed complete resistance to entrainment, whereas the fenestrated-tip had partial entrainment in 90% and 87% of the over-pumping and hypovolemic studies, respectively. We conclude that future pediatric VAD designs may benefit from incorporating the parabolic-tip inflow cannula design to maximize unloading of the left ventricle in ideal and nonoptimal conditions.
ERIC Educational Resources Information Center
Flugsrud, Marcia R.
This study is designed to determine whether data obtained cross-sectionally from a sample of subjects in the middle childhood range on selected personality characteristics could be well described by a concave parabolic curve and thus linked to the closure behaviour elicited from the subjects. Specifically, the investigation seeks to determine if…
Takashima, Ryoichi; Takiguchi, Tetsuya; Ariki, Yasuo
2010-02-01
This paper presents a sound-source-direction estimation method using only a single microphone with a parabolic reflection board. A simple signal-power-based method using a parabolic antenna has been proposed in the radar field. But the signal-power-based method is not effective for finding the direction of a talking person due to the varying power of the uttered speech signals. In this paper, the sound-source-direction estimation method focuses on the acoustic transfer function instead of the signal power. The use of the parabolic reflection board leads to a difference in the acoustic transfer functions of the target direction and the non-target directions, where the parabolic reflector and its associated microphone rotate together and observe the speech at each angle. The acoustic transfer function is estimated from the observed speech using the statistics of clean speech signals. Its effectiveness has been confirmed by monaural sound-source-direction estimation experiments in a room environment.
Simple Verification of the Parabolic Shape of a Rotating Liquid and a Boat on Its Surface
ERIC Educational Resources Information Center
Sabatka, Z.; Dvorak, L.
2010-01-01
This article describes a simple and inexpensive way to create and to verify the parabolic surface of a rotating liquid. The liquid is water. The second part of the article deals with the problem of a boat on the surface of a rotating liquid. (Contains 1 table, 10 figures and 5 footnotes.)
NASA Astrophysics Data System (ADS)
Muthucumaraswamy, R.; Sivakumar, P.
2016-02-01
The problem of MHD free convection flow with a parabolic starting motion of an infinite isothermal vertical plate in the presence of thermal radiation and chemical reaction has been examined in detail in this paper. The fluid considered here is a gray, absorbing emitting radiation but a non-scattering medium. The dimensionless governing coupled linear partial differential equations are solved using the Laplace transform technique. A parametric study is performed to illustrate the influence of the radiation parameter, magnetic parameter, chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number and time on the velocity, temperature, concentration. The results are discussed graphically and qualitatively. The numerical results reveal that the radiation induces a rise in both the velocity and temperature, and a decrease in the concentration. The model finds applications in solar energy collection systems, geophysics and astrophysics, aerospace and also in the design of high temperature chemical process systems.
NASA Astrophysics Data System (ADS)
Yan, Na; Baas, Andreas C. W.
2016-04-01
Parabolic dunes are a quintessential example of the co-evolution of soil, landform, and vegetation, and they are found around the world, on coasts, river valleys, lake shores, and margins of deserts and steppes. These areas are often sensitive to changes in natural and anthropogenic forcings and socio-economic activities. Some studies have indicated parabolic dunes can lose vegetation and transform into barchan and transverse dunes by environmental change such as decreased precipitation or lowered water table, as well as anthropogenic stress such as increased burning and grazing. These transformations and shifts between states of eco-geomorphic systems may have significant implications on land management and social-economic development. This study utilises the Extended-DECAL - parameterised by field measurements of dune topography and vegetation characteristics combined with remote sensing - to explore how increases in drought stress, wind strength, and grazing stress may lead to the activation of stabilised parabolic dunes into highly mobile barchans. The modelling results show that the mobility of an initial parabolic dune at the outset of perturbations determines to a large extent the capacity of a system to absorb the environmental change, and a slight increase in vegetation cover of an initial parabolic dune can increase the activation threshold significantly. Plants with a higher deposition tolerance increase the activation threshold for the climatic impact and sand transport rate, whereas the erosion tolerance of plants influences the patterns of resulting barchans. The change in the characteristics of eco-geomorphic interaction zones may indirectly reflect the dune stability and predict an ongoing transformation, whilst the activation angle may be potentially used as a proxy of environmental stresses. In contrast to the natural environmental changes which tend to affect relatively weak and young plants, grazing stress can exert a broader impact on all
Design of a Thermal Imaging Diagnostic Using 90-Degree, Off-Axis, Parabolic Mirrors
Malone, Robert M.; Becker, Steven A.; Dolan, Daniel H.; Hacking, Richard G.; Hickman, Randy J.; Kaufman, Morris I.; Stevens, Gerald D.; Turley, William D.
2006-09-01
Thermal imaging is an important, though challenging, diagnostic for shockwave experiments. Shock-compressed materials undergo transient temperature changes that cannot be recorded with standard (greater than ms response time) infrared detectors. A further complication arises when optical elements near the experiment are destroyed. We have designed a thermal-imaging system for studying shock temperatures produced inside a gas gun at Sandia National Laboratories. Inexpensive, diamond-turned, parabolic mirrors relay an image of the shocked target to the exterior of the gas gun chamber through a sapphire vacuum port. The 3000–5000-nm portion of this image is directed to an infrared camera which acquires a snapshot of the target with a minimum exposure time of 150 ns. A special mask is inserted at the last intermediate image plane, to provide dynamic thermal background recording during the event. Other wavelength bands of this image are split into high-speed detectors operating at 900–1700 nm, and at 1700–3000 nm for timeresolved pyrometry measurements. This system incorporates 90-degree, off-axis parabolic mirrors, which can collect low f/# light over a broad spectral range, for high-speed imaging. Matched mirror pairs must be used so that aberrations cancel. To eliminate image plane tilt, proper tip-to-tip orientation of the parabolic mirrors is required. If one parabolic mirror is rotated 180 degrees about the optical axis connecting the pair of parabolic mirrors, the resulting image is tilted by 60 degrees. Different focal-length mirrors cannot be used to magnify the image without substantially sacrificing image quality. This paper analyzes performance and aberrations of this imaging diagnostic.
Spike-adding in parabolic bursters: The role of folded-saddle canards
NASA Astrophysics Data System (ADS)
Desroches, Mathieu; Krupa, Martin; Rodrigues, Serafim
2016-09-01
The present work develops a new approach to studying parabolic bursting, and also proposes a novel four-dimensional canonical and polynomial-based parabolic burster. In addition to this new polynomial system, we also consider the conductance-based model of the Aplysia R15 neuron known as the Plant model, and a reduction of this prototypical biophysical parabolic burster to three variables, including one phase variable, namely the Baer-Rinzel-Carillo (BRC) phase model. Revisiting these models from the perspective of slow-fast dynamics reveals that the number of spikes per burst may vary upon parameter changes, however the spike-adding process occurs in an explosive fashion that involves special solutions called canards. This spike-adding canard explosion phenomenon is analysed by using tools from geometric singular perturbation theory in tandem with numerical bifurcation techniques. We find that the bifurcation structure persists across all considered systems, that is, spikes within the burst are incremented via the crossing of an excitability threshold given by a particular type of canard orbit, namely the true canard of a folded-saddle singularity. However there can be a difference in the spike-adding transitions in parameter space from one case to another, according to whether the process is continuous or discontinuous, which depends upon the geometry of the folded-saddle canard. Using these findings, we construct a new polynomial approximation of the Plant model, which retains all the key elements for parabolic bursting, including the spike-adding transitions mediated by folded-saddle canards. Finally, we briefly investigate the presence of spike-adding via canards in planar phase models of parabolic bursting, namely the theta model by Ermentrout and Kopell.
Schneider, Stefan; Brümmer, Vera; Mierau, Andreas; Carnahan, Heather; Dubrowski, Adam; Strüder, Heiko K
2008-03-01
Previous studies showed that changing forces of gravity as they typically occur during parabolic flights might be responsible for adaptional processes of the CNS. However, until now it has not been differentiated between primary influences of weightlessness and secondary influences due to psycho-physiological factors (e.g., physical or mental strain). With the aim of detecting parabolic flight related changes in central cortical activity, a resting EEG was deduced in 16 subjects before, during and after parabolic flights. After subdividing EEG into alpha-, beta-,delta- and theta-wave bands, an increase in beta-power was noticeable inflight, whereas alpha(1)-power was increased postflight. No changes could be observed for the control group. To control possible effects of cortical activation, a manual tracking task with mirror inversion was performed during either the phase of weightlessness or during the normal gravity phase of a parabolic flight. No differences in performance nor in adaptation could be observed between both groups. A third group, performing under normal and stress-free conditions in a lab showed similar tracking values. We assume that the specific increase in brain activity is a sign of an increase in arousal inflight. This does support previous assumptions of non-specific stressors during parabolic flights and has to be considered as a relevant factor for experiments on central nerve adaptation. Although no influences of stress and/or weightlessness on motor performance and adaptation could be observed, we suggest that an "inflight" control group seems to be more adequate than a laboratory control group to investigate gravity-dependent changes in motor control.
Stabilization and asymptotic behavior of a generalized telegraph equation
NASA Astrophysics Data System (ADS)
Nicaise, Serge
2015-12-01
We analyze the stability of different models of the telegraph equation set in a real interval. They correspond to the coupling between a first-order hyperbolic system and a first-order differential equation of parabolic type. We show that some models have an exponential decay rate, while other ones are only polynomially stable. When the parameters are constant, we show that the obtained polynomial decay is optimal and in the case of an exponential decay that the decay rate is equal to the spectral abscissa. These optimality results are based on a careful spectral analysis of the operator. In particular, we characterize its full spectrum that is made of a discrete set of eigenvalues and an essential spectrum reduced to one point.
Optimal Regularity and Long-Time Behavior of Solutions for the Westervelt Equation
Meyer, Stefan Wilke, Mathias
2011-10-15
We investigate an initial-boundary value problem for the quasilinear Westervelt equation which models the propagation of sound in fluidic media. We prove that, if the initial data are sufficiently small and regular, then there exists a unique global solution with optimal L{sub p}-regularity. We show furthermore that the solution converges to zero at an exponential rate as time tends to infinity. Our techniques are based on maximal L{sub p}-regularity for abstract quasilinear parabolic equations.
Survey of the status of finite element methods for partial differential equations
NASA Technical Reports Server (NTRS)
Temam, Roger
1986-01-01
The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.
ERIC Educational Resources Information Center
Blakley, G. R.
1982-01-01
Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)
NASA Astrophysics Data System (ADS)
Dagrau, Franck; Coulouvrat, François; Marchiano, Régis; Héron, Nicolas
2008-06-01
Dassault Aviation as a civil aircraft manufacturer is studying the feasibility of a supersonic business jet with the target of an "acceptable" sonic boom at the ground level, and in particular in case of focusing. A sonic boom computational process has been performed, that takes into account meteorological effects and aircraft manoeuvres. Turn manoeuvres and aircraft acceleration create zones of convergence of rays (caustics) which are the place of sound amplification. Therefore two elements have to be evaluated: firstly the geometrical position of the caustics, and secondly the noise level in the neighbourhood of the caustics. The modelling of the sonic boom propagation is based essentially on the assumptions of geometrical acoustics. Ray tracing is obtained according to Fermat's principle as paths that minimise the propagation time between the source (the aircraft) and the receiver. Wave amplitude and time waveform result from the solution of the inviscid Burgers' equation written along each individual ray. The "age variable" measuring the cumulative nonlinear effects is linked to the ray tube area. Caustics are located as the place where the ray tube area vanishes. Since geometrical acoustics does not take into account diffraction effects, it breaks down in the neighbourhood of caustics where it would predict unphysical infinite pressure amplitude. The aim of this study is to describe an original method for computing the focused noise level. The approach involves three main steps that can be summarised as follows. The propagation equation is solved by a forward marching procedure split into three successive steps: linear propagation in a homogeneous medium, linear perturbation due to the weak heterogeneity of the medium, and non-linear effects. The first step is solved using an "exact" angular spectrum algorithm. Parabolic approximation is applied only for the weak perturbation due to the heterogeneities. Finally, non linear effects are performed by solving the
Sinc-Galerkin estimation of diffusivity in parabolic problems
NASA Technical Reports Server (NTRS)
Smith, Ralph C.; Bowers, Kenneth L.
1991-01-01
A fully Sinc-Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newton/trust region algorithm. The L-curve technique for determining an approximate value of the regularization parameter is briefly discussed, and numerical examples are given which show the applicability of the method both for problems with noise-free data as well as for those whose data contains white noise.
Iterative methods for distributed parameter estimation in parabolic PDE
Vogel, C.R.; Wade, J.G.
1994-12-31
The goal of the work presented is the development of effective iterative techniques for large-scale inverse or parameter estimation problems. In this extended abstract, a detailed description of the mathematical framework in which the authors view these problem is presented, followed by an outline of the ideas and algorithms developed. Distributed parameter estimation problems often arise in mathematical modeling with partial differential equations. They can be viewed as inverse problems; the `forward problem` is that of using the fully specified model to predict the behavior of the system. The inverse or parameter estimation problem is: given the form of the model and some observed data from the system being modeled, determine the unknown parameters of the model. These problems are of great practical and mathematical interest, and the development of efficient computational algorithms is an active area of study.
Kinetic energy equations for the average-passage equation system
NASA Technical Reports Server (NTRS)
Johnson, Richard W.; Adamczyk, John J.
1989-01-01
Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.
Iwata, Chihiro; Abe, Chikara; Tanaka, Kunihiko; Morita, Hironobu
2011-05-16
Arterial pressure (AP) is known to fluctuate during parabolic-flight-induced gravitational changes in human subjects, increasing during hypergravity and decreasing during microgravity. In this study, we examined whether the vestibular system participates in the AP response to the gravitational changes induced by parabolic flight in human subjects. Eight subjects performed parabolic flights in a supine position as their AP was measured. Their vestibular inputs during the gravitational changes were reversibly masked by artificial electrical stimulation (galvanic vestibular stimulation, GVS). The AP responses during the parabolas were then compared between the GVS-off and GVS-on conditions. AP increased during hypergravity and decreased during microgravity. The AP responses at the onset of hypergravity and microgravity were abolished by GVS. These results indicate that the vestibular system elicits pressor and depressor responses during parabolic-flight-induced hypergravity and microgravity, respectively.
A parabolic model of drag coefficient for storm surge simulation in the South China Sea
Peng, Shiqiu; Li, Yineng
2015-01-01
Drag coefficient (Cd) is an essential metric in the calculation of momentum exchange over the air-sea interface and thus has large impacts on the simulation or forecast of the upper ocean state associated with sea surface winds such as storm surges. Generally, Cd is a function of wind speed. However, the exact relationship between Cd and wind speed is still in dispute, and the widely-used formula that is a linear function of wind speed in an ocean model could lead to large bias at high wind speed. Here we establish a parabolic model of Cd based on storm surge observations and simulation in the South China Sea (SCS) through a number of tropical cyclone cases. Simulation of storm surges for independent Tropical cyclones (TCs) cases indicates that the new parabolic model of Cd outperforms traditional linear models. PMID:26499262
NASA Technical Reports Server (NTRS)
Robertson, J. S.; Siegman, W. L.; Jacobson, M. J.
1989-01-01
There is substantial interest in the analytical and numerical modeling of low-frequency, long-range atmospheric acoustic propagation. Ray-based models, because of frequency limitations, do not always give an adequate prediction of quantities such as sound pressure or intensity levels. However, the parabolic approximation method, widely used in ocean acoustics, and often more accurate than ray models for lower frequencies of interest, can be applied to acoustic propagation in the atmosphere. Modifications of an existing implicit finite-difference implementation for computing solutions to the parabolic approximation are discussed. A locally-reacting boundary is used together with a one-parameter impedance model. Intensity calculations are performed for a number of flow resistivity values in both quiescent and windy atmospheres. Variations in the value of this parameter are shown to have substantial effects on the spatial variation of the acoustic signal.
A parabolic model of drag coefficient for storm surge simulation in the South China Sea.
Peng, Shiqiu; Li, Yineng
2015-01-01
Drag coefficient (Cd) is an essential metric in the calculation of momentum exchange over the air-sea interface and thus has large impacts on the simulation or forecast of the upper ocean state associated with sea surface winds such as storm surges. Generally, Cd is a function of wind speed. However, the exact relationship between Cd and wind speed is still in dispute, and the widely-used formula that is a linear function of wind speed in an ocean model could lead to large bias at high wind speed. Here we establish a parabolic model of Cd based on storm surge observations and simulation in the South China Sea (SCS) through a number of tropical cyclone cases. Simulation of storm surges for independent Tropical cyclones (TCs) cases indicates that the new parabolic model of Cd outperforms traditional linear models. PMID:26499262
Evaluation of the three-dimensional parabolic flow computer program SHIP
NASA Technical Reports Server (NTRS)
Pan, Y. S.
1978-01-01
The three-dimensional parabolic flow program SHIP designed for predicting supersonic combustor flow fields is evaluated to determine its capabilities. The mathematical foundation and numerical procedure are reviewed; simplifications are pointed out and commented upon. The program is then evaluated numerically by applying it to several subsonic and supersonic, turbulent, reacting and nonreacting flow problems. Computational results are compared with available experimental or other analytical data. Good agreements are obtained when the simplifications on which the program is based are justified. Limitations of the program and the needs for improvement and extension are pointed out. The present three dimensional parabolic flow program appears to be potentially useful for the development of supersonic combustors.
A parabolic model of drag coefficient for storm surge simulation in the South China Sea.
Peng, Shiqiu; Li, Yineng
2015-10-26
Drag coefficient (Cd) is an essential metric in the calculation of momentum exchange over the air-sea interface and thus has large impacts on the simulation or forecast of the upper ocean state associated with sea surface winds such as storm surges. Generally, Cd is a function of wind speed. However, the exact relationship between Cd and wind speed is still in dispute, and the widely-used formula that is a linear function of wind speed in an ocean model could lead to large bias at high wind speed. Here we establish a parabolic model of Cd based on storm surge observations and simulation in the South China Sea (SCS) through a number of tropical cyclone cases. Simulation of storm surges for independent Tropical cyclones (TCs) cases indicates that the new parabolic model of Cd outperforms traditional linear models.
Automatic Fourier transform and self-Fourier beams due to parabolic potential
NASA Astrophysics Data System (ADS)
Zhang, Yiqi; Liu, Xing; Belić, Milivoj R.; Zhong, Weiping; Petrović, Milan S.; Zhang, Yanpeng
2015-12-01
We investigate the propagation of light beams including Hermite-Gauss, Bessel-Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams-that is, the beams whose Fourier transforms are the beams themselves.
Tzimis, A.; Savvidis, P. G.; Trifonov, A. V.; Ignatiev, I. V.; Christmann, G.; Tsintzos, S. I.; Hatzopoulos, Z.; Kavokin, A. V.
2015-09-07
We report observation of strong light-matter coupling in an AlGaAs microcavity (MC) with an embedded single parabolic quantum well. The parabolic potential is achieved by varying aluminum concentration along the growth direction providing equally spaced energy levels, as confirmed by Brewster angle reflectivity from a reference sample without MC. It acts as an active region of the structure which potentially allows cascaded emission of terahertz (THz) light. Spectrally and time resolved pump-probe spectroscopy reveals characteristic quantum beats whose frequencies range from 0.9 to 4.5 THz, corresponding to energy separation between relevant excitonic levels. The structure exhibits strong stimulated nonlinear emission with simultaneous transition to weak coupling regime. The present study highlights the potential of such devices for creating cascaded relaxation of bosons, which could be utilized for THz emission.
Reduction of effective terahertz focal spot size by means of nested concentric parabolic reflectors
Neumann, V. A.; Laurita, N. J.; Pan, LiDong; Armitage, N. P.
2015-09-15
An ongoing limitation of terahertz spectroscopy is that the technique is generally limited to the study of relatively large samples of order 4 mm across due to the generally large size of the focal beam spot. We present a nested concentric parabolic reflector design which can reduce the terahertz focal spot size. This parabolic reflector design takes advantage of the feature that reflected rays experience a relative time delay which is the same for all paths. The increase in effective optical path for reflected light is equivalent to the aperture diameter itself. We have shown that the light throughput of an aperture of 2 mm can be increased by a factor 15 as compared to a regular aperture of the same size at low frequencies. This technique can potentially be used to reduce the focal spot size in terahertz spectroscopy and enable the study of smaller samples.
Gas Turbine/Solar Parabolic Trough Hybrid Design Using Molten Salt Heat Transfer Fluid: Preprint
Turchi, C. S.; Ma, Z.
2011-08-01
Parabolic trough power plants can provide reliable power by incorporating either thermal energy storage (TES) or backup heat from fossil fuels. This paper describes a gas turbine / parabolic trough hybrid design that combines a solar contribution greater than 50% with gas heat rates that rival those of natural gas combined-cycle plants. Previous work illustrated benefits of integrating gas turbines with conventional oil heat-transfer-fluid (HTF) troughs running at 390?C. This work extends that analysis to examine the integration of gas turbines with salt-HTF troughs running at 450 degrees C and including TES. Using gas turbine waste heat to supplement the TES system provides greater operating flexibility while enhancing the efficiency of gas utilization. The analysis indicates that the hybrid plant design produces solar-derived electricity and gas-derived electricity at lower cost than either system operating alone.
Analytic expressions for mode conversion in a plasma at the peak of a parabolic density profile
Hinkel-Lipsker, D.E.; Fried, B.D.; Morales, G.J. )
1992-07-01
For mode conversion in an unmagnetized plasma with a parabolic density profile of scale length {ital L}, analytic expressions, in terms of parabolic cylinder functions, for the energy flux coefficients (reflection, transmission, and mode conversion) and the fields for both the direct'' problem (incident electromagnetic wave converting to a Langmuir wave) and the inverse'' problem (incident Langmuir wave converting to an electromagnetic wave) are derived for the case where the incident wave frequency {omega} matches the electron plasma frequency {omega}{sub {ital p}} at the peak of the density profile. The mode conversion coefficient for the direct problem is equal in magnitude to that of the inverse problem, and the corresponding reflection and transmission coefficients satisfy energy conservation. In contrast to the linear profile problem, the conversion efficiency depends explicitly on the value of the collision frequency (in the cold, collisional limit) or electron temperature (in the warm, collisionless limit), but a transformation of parameters relates the results for these two limits.
Inverse parabolic quantum dot: The transition energy under magnetic field effect
NASA Astrophysics Data System (ADS)
Safwan, S. A.; El Meshed, Nagwa
2016-08-01
We present here, the evolution of the transition energy with a static magnetic field, when the electron and the hole are confined in inverse parabolic quantum dot (IPQD). The unexpected behavior is found, at the weak confinement regime the conduction band minimum and the top of valance band change from s-state to p-state or d-state for confined electron and hole inside IPQD, respectively. The strength of the inverse parabolic potential (potential hump) inside a quantum dot has the upper hand in tuning the ground state momentum for both electron and hole, and consequently their interband transition energy is changed. Knowing that this is not the case for the other types of potentials. The quantum size, the magnetic field and inverse potential hump effects on electron and hole ground and excited states are discussed.
Classical and quantum chaos in the generalized parabolic lemon-shaped billiard
NASA Astrophysics Data System (ADS)
Lopac, V.; Mrkonjić, I.; Radić, D.
1999-01-01
Two-dimensional billiards of a generalized parabolic lemonlike shape are investigated classically and quantum mechanically depending on the shape parameter δ. Quantal spectra are analyzed by means of the nearest-neighbor spacing distribution method. Calculated results are well accounted for by the proposed new two-parameter distribution function P(s), which is a generalization of Brody and Berry-Robnik distributions. Classically, Poincaré diagrams are shown and interpreted in terms of the lowest periodic orbits. For δ=2, the billiard has some unique characteristics resulting from the focusing property of the parabolic mirror. Comparison of the classical and quantal results shows an accordance with the Bohigas, Giannoni, and Schmit conjecture and confirms the relevance of the new distribution for the analysis of realistic spectral data.
Cost/performance of solar reflective surfaces for parabolic dish concentrators
NASA Technical Reports Server (NTRS)
Bouquet, F.
1980-01-01
Materials for highly reflective surfaces for use in parabolic dish solar concentrators are discussed. Some important factors concerning performance of the mirrors are summarized, and typical costs are treated briefly. Capital investment cost/performance ratios for various materials are computed specifically for the double curvature parabolic concentrators using a mathematical model. The results are given in terms of initial investment cost for reflective surfaces per thermal kilowatt delivered to the receiver cavity for various operating temperatures from 400 to 1400 C. Although second surface glass mirrors are emphasized, first surface, chemically brightened and anodized aluminum surfaces as well as second surface, metallized polymeric films are treated. Conventional glass mirrors have the lowest cost/performance ratios, followed closely by aluminum reflectors. Ranges in the data due to uncertainties in cost and mirror reflectance factors are given.
Dynamic analysis of ocular torsion in parabolic flight using video-oculography
NASA Astrophysics Data System (ADS)
Teiwes, W.; Clarke, A. H.; Scherer, H.
Dynamic ocular torsion was investigated in a group of healthy subjects during the course of parabolic flight by means of our video-based eye movement recording method—video-oculography. This technique enables a non-invasive dynamic measurement of all three dimensions of eye movement in a harsh experimental environment such as parabolic flight. The test subjects were positioned so that the changing resultant gravito-inertial field in the aircraft was aligned with their interaural ( y) axis, primarily stimulating the utricular organs. The analysis of the torsional component of eye movement during the change of gravity between 1.8-0 and 0-1.8 g demonstrated a static component—well known as the ocular counter roll—and a dynamic component, which leads to a slight overshoot in the torsional response. These static and dynamic component of ocular torsion correlate with previous neurophysiological findings.