Asymptotic behaviour of solutions of semilinear parabolic equations
Egorov, Yu V; Kondratiev, V A
2008-04-30
The asymptotic behaviour of solutions of a second-order semilinear parabolic equation is analyzed in a cylindrical domain that is bounded in the space variables. The dominant term of the asymptotic expansion of the solution as t{yields}+{infinity} is found. It is shown that the solution of this problem is asymptotically equivalent to the solution of a certain non-linear ordinary differential equation. Bibliography: 8 titles.
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.
Arada, N.; Raymond, J.-P. raymond@mip.ups-tlse.fr
2002-07-01
This paper is the continuation of the paper 'Dirichlet boundary control of semilinear parabolic equations. Part 1: Problems with no state constraints'. It is concerned with an optimal control problem with distributed and Dirichlet boundary controls for semilinear parabolic equations, in the presence of pointwise state constraints. We first obtain approximate optimality conditions for problems in which state constraints are penalized on subdomains. Next by using a decomposition theorem for some additive measures (based on the Stone-Cech compactification), we pass to the limit and recover Pontryagin's principles for the original problem.
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.
Arada, N.; Raymond, J.-P. raymond@mip.ups-tlse.fr
2002-07-01
This paper is concerned with distributed and Dirichlet boundary controls of semilinear parabolic equations, in the presence of pointwise state constraints. The paper is divided into two parts. In the first part we define solutions of the state equation as the limit of a sequence of solutions for equations with Robin boundary conditions. We establish Taylor expansions for solutions of the state equation with respect to perturbations of boundary control (Theorem 5.2). For problems with no state constraints, we prove three decoupled Pontryagin's principles, one for the distributed control, one for the boundary control, and the last one for the control in the initial condition (Theorem 2.1). Tools and results of Part 1 are used in the second part to derive Pontryagin's principles for problems with pointwise state constraints.
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.
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.
Local dynamics for high-order semilinear hyperbolic equations
NASA Astrophysics Data System (ADS)
Volevich, L. R.; Shirikyan, A. R.
2000-06-01
This paper is devoted to studying high-order semilinear hyperbolic equations. It is assumed that the equation is a small perturbation of an equation with real constant coefficients and that the roots of the full symbol of the unperturbed equation with respect to the variable \\tau dual to time are either separated from the imaginary axis or lie outside the domain \
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.
NASA Astrophysics Data System (ADS)
Baeumer, Boris; Geissert, Matthias; Kovács, Mihály
2015-01-01
We consider a class of semilinear Volterra type stochastic evolution equation driven by multiplicative Gaussian noise. The memory kernel, not necessarily analytic, is such that the deterministic linear equation exhibits a parabolic character. Under appropriate Lipschitz-type and linear growth assumptions on the nonlinear terms we show that the unique mild solution is mean-p Hölder continuous with values in an appropriate Sobolev space depending on the kernel and the data. In particular, we obtain pathwise space-time (Sobolev-Hölder) regularity of the solution together with a maximal type bound on the spatial Sobolev norm. As one of the main technical tools we establish a smoothing property of the derivative of the deterministic evolution operator family.
Meyer, J C; Needham, D J
2015-03-08
In this paper, we examine a semi-linear parabolic Cauchy problem with non-Lipschitz nonlinearity which arises as a generic form in a significant number of applications. Specifically, we obtain a well-posedness result and examine the qualitative structure of the solution in detail. The standard classical approach to establishing well-posedness is precluded owing to the lack of Lipschitz continuity for the nonlinearity. Here, existence and uniqueness of solutions is established via the recently developed generic approach to this class of problem (Meyer & Needham 2015 The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations. London Mathematical Society Lecture Note Series, vol. 419) which examines the difference of the maximal and minimal solutions to the problem. From this uniqueness result, the approach of Meyer & Needham allows for development of a comparison result which is then used to exhibit global continuous dependence of solutions to the problem on a suitable initial dataset. The comparison and continuous dependence results obtained here are novel to this class of problem. This class of problem arises specifically in the study of a one-step autocatalytic reaction, which is schematically given by A→B at rate a(p)b(q) (where a and b are the concentrations of A and B, respectively, with 0
Mild solutions of semilinear elliptic equations in Hilbert spaces
NASA Astrophysics Data System (ADS)
Federico, Salvatore; Gozzi, Fausto
2017-03-01
This paper extends the theory of regular solutions (C1 in a suitable sense) for a class of semilinear elliptic equations in Hilbert spaces. The notion of regularity is based on the concept of G-derivative, which is introduced and discussed. A result of existence and uniqueness of solutions is stated and proved under the assumption that the transition semigroup associated to the linear part of the equation has a smoothing property, that is, it maps continuous functions into G-differentiable ones. The validity of this smoothing assumption is fully discussed for the case of the Ornstein-Uhlenbeck transition semigroup and for the case of invertible diffusion coefficient covering cases not previously addressed by the literature. It is shown that the results apply to Hamilton-Jacobi-Bellman (HJB) equations associated to infinite horizon optimal stochastic control problems in infinite dimension and that, in particular, they cover examples of optimal boundary control of the heat equation that were not treatable with the approaches developed in the literature up to now.
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.
NASA Astrophysics Data System (ADS)
Sazaklioglu, Ali Ugur; Erdogan, Abdullah Said; Ashyralyev, Allaberen
2016-08-01
This paper deals with existence and uniqueness of the solution of an inverse problem for a semilinear equation subject to a final overdetermination in a Banach space. Moreover, the first order of accuracy Rothe difference scheme is presented for the numerical solution of this problem. The existence and uniqueness result for this difference scheme is given. This difference scheme is applied on a particular example and some numerical results are given.
On the Approximate Controllability of Some Semilinear Parabolic Boundary-Value Problems
Diaz, J. I.; Henry, J.; Ramos, A. M.
1998-01-15
We prove the approximate controllability of several nonlinear parabolic boundary-value problems by means of two different methods: the first one can be called a Cancellation method and the second one uses the Kakutani fixed-point theorem.
Improved Parabolization of the Euler Equations
2013-05-01
generalization of linear stability theory call the parabolized stability equations ( PSE ).10 PSE can partially capture nonparallel and nonlinear effects...and has been shown to accurately model many convectively unstable flows. In particular, our group has previously shown that linear PSE can produce...mode analysis. The efficiency of PSE is achieved by using a spatial marching technique in the streamwise direction. Initial conditions are specified
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.
Singularities for a 2-Dimensional Semilinear Elliptic Equation with a Non-Lipschitz Nonlinearity
NASA Astrophysics Data System (ADS)
Bidaut-Véron, Marie-Francoise; Galaktionov, Victor; Grillot, Philippe; Véron, Laurent
1999-05-01
We study the limit behaviour of solutions of the semilinear elliptic equationΔu=|x|σ |u|q-1 u in R2, q∈(0, 1), σ∈R,with a non-Lipschitz nonlinearity on the right-hand side. When |σ+2|⩽2 we give a complete classification of the types of singularities asx→0 andx→∞ which in the rescaled form are essentially non-analytic and, even more, notC∞. The proof is based on the asymptotic study of the corresponding evolution dynamical system and the Sturmian argument on zero set analysis.
Control problems for semilinear neutral differential equations in Hilbert spaces.
Jeong, Jin-Mun; Cho, Seong Ho
2014-01-01
We construct some results on the regularity of solutions and the approximate controllability for neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the controllability of the neutral equations, we first consider the existence and regularity of solutions of the neutral control system by using fractional power of operators and the local Lipschitz continuity of nonlinear term. Our purpose is to obtain the existence of solutions and the approximate controllability for neutral functional differential control systems without using many of the strong restrictions considered in the previous literature. Finally we give a simple example to which our main result can be applied.
Control Problems for Semilinear Neutral Differential Equations in Hilbert Spaces
Jeong, Jin-Mun; Cho, Seong Ho
2014-01-01
We construct some results on the regularity of solutions and the approximate controllability for neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the controllability of the neutral equations, we first consider the existence and regularity of solutions of the neutral control system by using fractional power of operators and the local Lipschitz continuity of nonlinear term. Our purpose is to obtain the existence of solutions and the approximate controllability for neutral functional differential control systems without using many of the strong restrictions considered in the previous literature. Finally we give a simple example to which our main result can be applied. PMID:24772022
Nonlinear Parabolic Equations Involving Measures as Initial Conditions.
1981-09-01
CHART N N N Afl4Uf’t 1N II Il MRC Technical Summary Report # 2277 0 NONLINEAR PARABOLIC EQUATIONS INVOLVING MEASURES AS INITIAL CONDITIONS I Haim Brezis ...NONLINEAR PARABOLIC EQUATIONS INVOLVING MEASURES AS INITIAL CONDITIONS Haim Brezis and Avner Friedman Technical Summary Report #2277 September 1981...with NRC, and not with the authors of this report. * s ’a * ’ 4| NONLINEAR PARABOLIC EQUATIONS INVOLVING MEASURES AS INITIAL CONDITIONS Haim Brezis
Bifurcation and stability for a nonlinear parabolic partial differential equation
NASA Technical Reports Server (NTRS)
Chafee, N.
1973-01-01
Theorems are developed to support bifurcation and stability of nonlinear parabolic partial differential equations in the solution of the asymptotic behavior of functions with certain specified properties.
Null Controllability for the Dissipative Semilinear Heat Equation
Sebastian, Anita; Tataru, Daniel
2002-12-19
We consider the exact null controllability problem for the semi- linear heat equation with dissipative nonlinearity in a bounded domain of R{sup n} . The main result of the article asserts that if the nonlinearity is even mildly superlinear, then global null controllability in an arbitrarily short time fails; instead we provide sharp estimates for the controllability time in terms of the size of the initial data.
Casas, E.
1999-03-15
In this paper we are concerned with some optimal control problems governed by semilinear elliptic equations. The case of a boundary control is studied. We consider pointwise constraints on the control and a finite number of equality and inequality constraints on the state. The goal is to derive first- and second-order optimality conditions satisfied by locally optimal solutions of the problem.
Upper bounds for parabolic equations and the Landau equation
NASA Astrophysics Data System (ADS)
Silvestre, Luis
2017-02-01
We consider a parabolic equation in nondivergence form, defined in the full space [ 0 , ∞) ×Rd, with a power nonlinearity as the right-hand side. We obtain an upper bound for the solution in terms of a weighted control in Lp. This upper bound is applied to the homogeneous Landau equation with moderately soft potentials. We obtain an estimate in L∞ (Rd) for the solution of the Landau equation, for positive time, which depends only on the mass, energy and entropy of the initial data.
Kozhevnikova, L M; Mukminov, F Kh
2000-02-28
A quasilinear system of parabolic equations with energy inequality is considered in a cylindrical domain {l_brace}t>0{r_brace}x{omega}. In a broad class of unbounded domains {omega} two geometric characteristics of a domain are identified which determine the rate of convergence to zero as t{yields}{infinity} of the L{sub 2}-norm of a solution. Under additional assumptions on the coefficients of the quasilinear system estimates of the derivatives and uniform estimates of the solution are obtained; they are proved to be best possible in the order of convergence to zero in the case of one semilinear equation.
NASA Astrophysics Data System (ADS)
Zhang, Qidi
2016-12-01
We show for almost every m > 0, the solution to the semi-linear Klein-Gordon equation with a quadratic potential in dimension one, exists over a longer time interval than the one given by local existence theory, using the normal form method. By using an Lp -Lq estimate for eigenfunctions of the harmonic oscillator and by carefully analysis on the nonlinearity, we improve the result obtained by the author before.
NASA Astrophysics Data System (ADS)
Hashizume, Masato
2017-02-01
We investigate the existence, the non-existence and the asymptotic behavior of the least-energy solutions of a semilinear elliptic equation with the Hardy-Sobolev critical exponent. In the boundary singularity case, it is known that the mean curvature of the boundary at origin plays a crucial role on the existence of the least-energy solutions. In this paper, we study the relation between the asymptotic behavior of the solutions and the mean curvature at origin.
NASA Astrophysics Data System (ADS)
Jiang, Tian; Zhang, Yong-Tao
2013-11-01
Implicit integration factor (IIF) methods are originally a class of efficient “exactly linear part” time discretization methods for solving time-dependent partial differential equations (PDEs) with linear high order terms and stiff lower order nonlinear terms. For complex systems (e.g. advection-diffusion-reaction (ADR) systems), the highest order derivative term can be nonlinear, and nonlinear nonstiff terms and nonlinear stiff terms are often mixed together. High order weighted essentially non-oscillatory (WENO) methods are often used to discretize the hyperbolic part in ADR systems. There are two open problems on IIF methods for solving ADR systems: (1) how to obtain higher than the second order global time discretization accuracy; (2) how to design IIF methods for solving fully nonlinear PDEs, i.e., the highest order terms are nonlinear. In this paper, we solve these two problems by developing new Krylov IIF-WENO methods to deal with both semilinear and fully nonlinear advection-diffusion-reaction equations. The methods can be designed for arbitrary order of accuracy. The stiffness of the system is resolved well and the methods are stable by using time step sizes which are just determined by the nonstiff hyperbolic part of the system. Large time step size computations are obtained. We analyze the stability and truncation errors of the schemes. Numerical examples of both scalar equations and systems in two and three spatial dimensions are shown to demonstrate the accuracy, efficiency and robustness of the methods.
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)
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.
Model Predictive Control for Nonlinear Parabolic Partial Differential Equations
NASA Astrophysics Data System (ADS)
Hashimoto, Tomoaki; Yoshioka, Yusuke; Ohtsuka, Toshiyuki
In this study, the optimal control problem of nonlinear parabolic partial differential equations (PDEs) is investigated. Optimal control of nonlinear PDEs is an open problem with applications that include fluid, thermal, biological, and chemically-reacting systems. Model predictive control with a fast numerical solution method has been well established to solve the optimal control problem of nonlinear systems described by ordinary differential equations. In this study, we develop a design method of the model predictive control for nonlinear systems described by parabolic PDEs. Our approach is a direct infinite dimensional extension of the model predictive control method for finite-dimensional systems. The objective of this paper is to develop an efficient algorithm for numerically solving the model predictive control problem of nonlinear parabolic PDEs. The effectiveness of the proposed method is verified by numerical simulations.
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.
On an algorithm for solving parabolic and elliptic equations
NASA Astrophysics Data System (ADS)
D'Ascenzo, N.; Saveliev, V. I.; Chetverushkin, B. N.
2015-08-01
The present-day rapid growth of computer power, in particular, parallel computing systems of ultrahigh performance requires a new approach to the creation of models and solution algorithms for major problems. An algorithm for solving parabolic and elliptic equations is proposed. The capabilities of the method are demonstrated by solving astrophysical problems on high-performance computer systems with massive parallelism.
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.
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.
NASA Astrophysics Data System (ADS)
Cosso, Andrea; Russo, Francesco
2016-11-01
Functional Itô calculus was introduced in order to expand a functional F(t,Xṡ+t,Xt) depending on time t, past and present values of the process X. Another possibility to expand F(t,Xṡ+t,Xt) consists in considering the path Xṡ+t = {Xx+t,x ∈ [-T, 0]} as an element of the Banach space of continuous functions on C([-T, 0]) and to use Banach space stochastic calculus. The aim of this paper is threefold. (1) To reformulate functional Itô calculus, separating time and past, making use of the regularization procedures which match more naturally the notion of horizontal derivative which is one of the tools of that calculus. (2) To exploit this reformulation in order to discuss the (not obvious) relation between the functional and the Banach space approaches. (3) To study existence and uniqueness of smooth solutions to path-dependent partial differential equations which naturally arise in the study of functional Itô calculus. More precisely, we study a path-dependent equation of Kolmogorov type which is related to the window process of the solution to an Itô stochastic differential equation with path-dependent coefficients. We also study a semilinear version of that equation.
PE Workshop II. Proceedings of the Second Parabolic Equation Workshop
1993-01-01
pp. 21-28. [11 ] M. D. Feit and J. A. Fleck, Jr., "Computation of mode properties in optical fiber waveguides by a propagating beam method," Appl...that are, at best, only typical of that region of the worlds oceans. Ocean bottom properties obtained from historical data bases are usually less...the first term of a geometric- optical series," Comm. Pure and Appl. Math. 4, 105-115. Brock, H. K. (1975). "The AESD parabolic equation model," AESD TN
Spectral Deferred Corrections for Parabolic Partial Differential Equations
2015-06-08
linear differential equation ϕ′(t) = λϕ(t), t ≥ 0 ϕ(0) = 1, (3.31) where λ ∈ C, has exact solution ϕ(t) = eλt. (3.32) Traditionally, for a fixed time step...the second-order differentiation matrix with 16 subintervals and 16 points per subinterval. From Figure 5.2, this matrix approximates the exact ...We describe a new class of algorithms for the solution of parabolic partial differential equa- tions (PDEs). This class of schemes is based on three
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.
Experimental testing of the variable rotated elastic parabolic equation.
Simpson, Harry J; Collis, Jon M; Soukup, Raymond J; Collins, Michael D; Siegmann, William L
2011-11-01
A series of laboratory experiments was conducted to obtain high-quality data for acoustic propagation in shallow water waveguides with sloping elastic bottoms. Accurate modeling of transmission loss in these waveguides can be performed with the variable rotated parabolic equation method. Results from an earlier experiment with a flat or sloped slab of polyvinyl chloride (PVC) demonstrated the necessity of accounting for elasticity in the bottom and the ability of the model to produce benchmark-quality agreement with experimental data [J. M. Collis et al., J. Acoust. Soc. Am. 122, 1987-1993 (2007)]. This paper presents results of a second experiment, using two PVC slabs joined at an angle to create a waveguide with variable bottom slope. Acoustic transmissions over the 100-300 kHz band were received on synthetic horizontal arrays for two source positions. The PVC slabs were oriented to produce three different simulated waveguides: flat bottom followed by downslope, upslope followed by flat bottom, and upslope followed by downslope. Parabolic equation solutions for treating variable slopes are benchmarked against the data.
Mahillo-Isla, R; Gonźalez-Morales, M J; Dehesa-Martínez, C
2011-06-01
The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well.
Higher order parabolic approximations of the reduced wave equation
NASA Technical Reports Server (NTRS)
Mcaninch, G. L.
1986-01-01
Asymptotic solutions of order k to the nth are developed for the reduced wave equation. 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 applied to the example of radiation from a piston, and it is demonstrated that the higher order approximations are more accurate for decreasing values of k.
Approximate controllability of a system of parabolic equations with delay
NASA Astrophysics Data System (ADS)
Carrasco, Alexander; Leiva, Hugo
2008-09-01
In this paper we give necessary and sufficient conditions for the approximate controllability of the following system of parabolic equations with delay: where [Omega] is a bounded domain in , D is an n×n nondiagonal matrix whose eigenvalues are semi-simple with nonnegative real part, the control and B[set membership, variant]L(U,Z) with , . The standard notation zt(x) defines a function from [-[tau],0] to (with x fixed) by zt(x)(s)=z(t+s,x), -[tau][less-than-or-equals, slant]s[less-than-or-equals, slant]0. Here [tau][greater-or-equal, slanted]0 is the maximum delay, which is supposed to be finite. We assume that the operator is linear and bounded, and [phi]0[set membership, variant]Z, [phi][set membership, variant]L2([-[tau],0];Z). To this end: First, we reformulate this system into a standard first-order delay equation. Secondly, the semigroup associated with the first-order delay equation on an appropriate product space is expressed as a series of strongly continuous semigroups and orthogonal projections related with the eigenvalues of the Laplacian operator (); this representation allows us to reduce the controllability of this partial differential equation with delay to a family of ordinary delay equations. Finally, we use the well-known result on the rank condition for the approximate controllability of delay system to derive our main result.
NASA Astrophysics Data System (ADS)
Wang, Zaihong
2014-02-01
In this paper, we study the existence of positive periodic solutions of resonant Duffing equations with singularities. Some Lazer-Leach type conditions are given to ensure the existence of positive periodic solutions of singular resonant Duffing equations.
2014-03-01
method to the numerical solution of nonlinear and variable coefficient wave equations ,” SIAM, vol. 15, no. 2, pp. 423, Apr. 1973. [3] D. Lee and S. T...DIFFERENT IMPLEMENTATION OPTIONS FOR DENSITY DISCONTINUITY IN SPLIT– STEP FOURIER PARABOLIC EQUATION MODELS by Matthew D. Owens March 2014...FOR DENSITY DISCONTINUITY IN SPLIT–STEP FOURIER PARABOLIC EQUATION MODELS 5. FUNDING NUMBERS 6. AUTHOR(S) Matthew D. Owens 7. PERFORMING
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.
Existence of Large Solutions to Semilinear Elliptic Equations with Multiple Terms
2006-09-01
the solutions in bounded domains in Rn was studied by Lazer and McKenna [14]. Bandle and Marcus [3] showed that 4u = g(x, u) has a unique large positive...Wood (Shaker). "Large solutions of sublinear elliptic equations," Nonlinear Analysis, 39: 745-753 (2000). 14. Lazer , A.C. and P.J. McKenna. "Asymptotic...behavior of solutions of boundary blow up problems," Differential Integral Equations, 7:1001-1020 (1994). 15. Lazer , A.C. and P.J. McKenna. "On a
Global existence of solutions for semilinear damped wave equation in 2-D exterior domain
NASA Astrophysics Data System (ADS)
Ikehata, Ryo
We consider a mixed problem of a damped wave equation utt-Δ u+ ut=| u| p in the two dimensional exterior domain case. Small global in time solutions can be constructed in the case when the power p on the nonlinear term | u| p satisfies p ∗=2
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.
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.
Galerkin/Runge-Kutta discretizations of nonlinear parabolic equations
NASA Astrophysics Data System (ADS)
Hansen, Eskil
2007-08-01
Global error bounds are derived for full Galerkin/Runge-Kutta discretizations of nonlinear parabolic problems, including the evolution governed by the p-Laplacian with p[greater-or-equal, slanted]2. The analysis presented here is not based on linearization procedures, but on the fully nonlinear framework of logarithmic Lipschitz constants and an extended B-convergence theory. The global error is bounded in L2 by [Delta]xr/2+[Delta]tq, where r is the convergence order of the Galerkin method applied to the underlying stationary problem and q is the stiff order of the algebraically stable Runge-Kutta method.
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.
On numerical solution of multipoint NBVP for hyperbolic-parabolic equations with Neumann condition
NASA Astrophysics Data System (ADS)
Ashyralyev, Allaberen; Ozdemir, Yildirim
2012-08-01
A numerical method is proposed for solving multi-dimensional hyperbolic-parabolic differential equations with the nonlocal boundary condition in t and Neumann condition in space variables. The first and second orders of accuracy difference schemes are presented. The stability estimates for the solution and its first and second orders difference derivatives are established. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of a one-dimensional hyperbolic-parabolic differential equations with variable in x coefficients.
a Note on Difference Schemes of Nonlocal Boundary Value Problems for Hyperbolic-Parabolic Equations
NASA Astrophysics Data System (ADS)
Ashyralyev, Allaberen; Ozdemir, Yildirim
2010-11-01
A numerical method is proposed for solving multi-dimensional hyperbolic-parabolic differential equations with the nonlocal boundary condition in t and Dirichlet condition in space variables. The first and second orders of accuracy difference schemes are presented. The stability estimates for the solution and its first- and second-orders difference derivatives are established. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of a one-dimensional hyperbolic-parabolic partial differential equations with variable in x coefficients.
Calderón-Zygmund estimates for parabolic measure data equations
NASA Astrophysics Data System (ADS)
Baroni, Paolo; Habermann, Jens
We consider parabolic equations of the type u-div A(x,t,Du)=μ having a Radon measure on the right-hand side and prove fractional integrability and differentiability results of Calderón-Zygmund type for weak solutions. We extend some of the integrability results for elliptic equations achieved by G. Mingione (2007) [24] to the parabolic setting and locally recover the integrability results of L. Boccardo, A. Dall'Aglio, T. Gallouët, and L. Orsina (1997) in [5].
Degtyarev, Sergey P
2010-09-02
The first initial-boundary problem for second-order parabolic and degenerate parabolic equations is investigated in a domain with a conical or angular point. The means of attack is already known and uses weighted classes of smooth or integrable functions. Sufficient conditions for a unique solution to exist and for coercive estimates for the solution to be obtained are formulated in terms of the angular measure of the solid angle and the exponent of the weight. It is also shown that if these conditions fail to hold, then the parabolic problem has elliptic properties, that is, it can have a nonzero kernel or can be nonsolvable, and, in the latter case, it is not even a Fredholm problem. A parabolic equation and an equation with some degeneracy or a singularity at a conical point are considered. Bibliography: 49 titles.
Random Rays, Geometric Acoustics, and the Parabolic Wave Equation
1984-03-01
5). Of course. Nelson’s theory is a stochastic version of the Schrodinger equation of quantum mechanics, but this equation is formally identical... equation is just the Schrodinger equation of quantum mechanics, and since we expect ray theory to be meaningful when k »1, i.e., when 1/k « 1, where (1/k...Wave Equation 5. TYPE OF REPORT & PERIOD COVERED TECHNICAL 6. PERFORMING 07G. REPORT NUMBER LAP-4 7. AUTHORfj; Thad Dankel, Jr. 8
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.
Hölder estimates for non-local parabolic equations with critical drift
NASA Astrophysics Data System (ADS)
Chang-Lara, Héctor A.; Dávila, Gonzalo
2016-03-01
In this paper we extend previous results on the regularity of solutions of integro-differential parabolic equations. The kernels are non-necessarily symmetric which could be interpreted as a non-local drift with the same order as the diffusion. We provide a growth lemma and a Harnack inequality which can be used to prove higher regularity estimates.
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.
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.
NASA Astrophysics Data System (ADS)
Dehghan, Mehdi; Tatari, Mehdi
2006-03-01
Certain types of physical problems can be modelled by a parabolic partial differential equation with temperature overspecification. In this work, the Adomian decomposition method is used to solve the two-dimensional (or three-dimensional) parabolic partial differential equation subject to the overspecification at a point in the spatial domain. This analytic technique can also be used to provide a numerical approximation for the problem without linearization or discretization. The Adomian decomposition procedure does not need to solve any linear or nonlinear system of algebraic equations. It finds the solution in a rapid convergent series. Some theoretical behaviours of the method are investigated. To support the theoretical discussion and show the superiority of the method, two test problems are given and the numerical results are presented.
NASA Astrophysics Data System (ADS)
Namazov, F. M.; Khudaverdiyev, K. I.
2010-09-01
Many problems in mathematical physics are reduced to one- or multidimensional initial and initial-boundary value problems for, generally speaking, strongly nonlinear Sobolev-type equations. In this work, local and global classical solvability is studied for the one-dimensional mixed problem with homogeneous Riquier-type boundary conditions for a class of semilinear long-wave equations U_{tt} left( {t,x} right) - U_{xx} left( {t,x} right) - α U_{ttxx} left( {t,x} right) = Fleft( {t,x,Uleft( {t,x} right),U_x left( {t,x} right),U_{xx} left( {t,x} right),U_t left( {t,x} right),U_{tx} left( {t,x} right),U_{txx} left( {t,x} right)} right) , where α > 0 is a fixed number, 0 ≤ t ≤ T, 0 ≤ x ≤ π, 0 < T < +∞, F is a given function, and U( t, x) is the sought function. A uniqueness theorem for the mixed problem is proved using the Gronwall-Bellman inequality. A local existence result is proved by applying the generalized contraction mapping principle combined with the Schauder fixed point theorem. The method of a priori estimates is used to prove the global existence of a classical solution to the mixed problem.
Improved stochastic approximation methods for discretized parabolic partial differential equations
NASA Astrophysics Data System (ADS)
Guiaş, Flavius
2016-12-01
We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).
Undetermined Coefficient Problems for Quasi-Linear Parabolic Equations
1989-12-18
recovered by an iteration scheme, and give sufficient conditions for the unique solution of the inverse problem. Equation (1.1) describes the evolution of...unique fixed point for T, and give conditions on the data for which such a fixed point exists . The solution can then be obtained by the iteration scheme...the solution pair (u, h) in the one dimensional heat equation subject to the nonlinear boundary conditions u. = h(u) on 002. The value of u(0, t) = 8
NORDA Parabolic Equation Workshop, 31 March - 3 April 1981
1982-09-01
equation). These forms will follow as a result of approximations to the pseudo-differential operator Q, whose properties preclude the solution of GPE itself...horizontal range in kin, a id Cd(r) is the soun , speed (mis) at the bottom of the duct. There are three pirts to this test case as defined by the receiver...a * very powerful, efficient, and accurate predictor of sound transmission properties . This was borne out in those test cases for which there was an
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.
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.
Solutions to higher-order anisotropic parabolic equations in unbounded domains
NASA Astrophysics Data System (ADS)
Kozhevnikova, L. M.; Leont'ev, A. A.
2014-01-01
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,\\infty)\\times\\Omega, where \\Omega\\subset R^n, n\\geq 3, is an unbounded domain. When the initial function has compact support the highest possible rate of decay of this solution as t\\to \\infty 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.
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.
Conditional stability in determination of initial data for stochastic parabolic equations
NASA Astrophysics Data System (ADS)
Yuan, Ganghua
2017-03-01
In this paper, we solve two kinds of inverse problems in determination of the initial data for stochastic parabolic equations. One is determination of the initial data by lateral boundary observation on arbitrary portion of the boundary, the second one is determination of the initial data by internal observation in a subregion inside the domain. We obtain conditional stability for the two kinds of inverse problems. To prove the results, we estimate the initial data by a terminal observation near the initial time, then we estimate this terminal observation by lateral boundary observation on arbitrary portion of the boundary or internal observation in a subregion inside the domain. To achieve those goals, we derive several new Carleman estimates for stochastic parabolic equations in this paper.
2006-10-01
equation for sound waves in inhomogeneous moving media”, Acustica united with Acta Acustica , Vol 83(3), pp 455-460,1997. [3] L. Dallois, Ph. Blanc...propagation in a turbulent atmosphere within the parabolic approximation”, Acustica united with Acta Acustica , Vol 87(1), pp 659-669, 2001 [6] M. Karweit...approaches", Acta Acustica united with Acustica , 89 (6), 980-991, (2003). [40] Ph. Voisin, Ph. Blanc-Benon, "The influence of meteorological
Acoustic Field Associated with Parabolized Stability Equation Models in Turbulent Jets
2013-05-01
discusses linear models of these wavepackets for supersonic turbulent jets based on Parabolized Stability Equations ( PSE ). In the past, results of...comparisons of the PSE models with near-field pressure fields from LES, filtered by means of Proper Orthogonal Decomposition (POD), demonstrate acceptable...fidelity of the model. Finally, the acoustic far-field associated with the PSE wavepackets is computed using a Kirchhoff surface method, capturing
Algorithm for rapid integration of turbulence model equations on parabolic regions
NASA Technical Reports Server (NTRS)
Wilcox, D. C.
1981-01-01
While developing a three-dimensional boundary layer program using a standard parabolic matching scheme, the author has found computing time with the Wilcox-Rubesin (1979) two-equation turbulence model to be very lengthy. The long computing time occurs because converged solutions are possible only when very small streamwise steps are taken. The proposed remedy reduces computing time by increasing the maximum permissible step size.
Marching iterative methods for the parabolized and thin layer Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Israeli, M.
1985-01-01
Downstream marching iterative schemes for the solution of the Parabolized or Thin Layer (PNS or TL) Navier-Stokes equations are described. Modifications of the primitive equation global relaxation sweep procedure result in efficient second-order marching schemes. These schemes take full account of the reduced order of the approximate equations as they behave like the SLOR for a single elliptic equation. The improved smoothing properties permit the introduction of Multi-Grid acceleration. The proposed algorithm is essentially Reynolds number independent and therefore can be applied to the solution of the subsonic Euler equations. The convergence rates are similar to those obtained by the Multi-Grid solution of a single elliptic equation; the storage is also comparable as only the pressure has to be stored on all levels. Extensions to three-dimensional and compressible subsonic flows are discussed. Numerical results are presented.
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.
A three dimensional parabolic equation method for sound propagation in moving inhomogeneous media.
Cheng, Rui; Morris, Philip J; Brentner, Kenneth S
2009-10-01
In this paper, a formulation of the Helmholtz equation for three dimensional sound propagation in a moving inhomogeneous medium in cylindrical coordinates is derived. Based on this formulation, a three dimensional parabolic equation (PE) is constructed. This PE can be used to model sound propagation in an inhomogeneous arbitrary moving medium. The method is used here to simulate three dimensional outdoor sound propagation above a rigid flat ground surface. The numerical results for two simple wind cases are presented and compared with analytical results to validate the methodology. Examples of propagation problems with more complicated wind are then included to demonstrate the importance of including the wind velocity directly in the PE method.
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.
Non-divergence parabolic equations of second order with critical drift in Lebesgue spaces
NASA Astrophysics Data System (ADS)
Chen, Gong
2017-02-01
We consider uniformly parabolic equations and inequalities of second order in the non-divergence form with drift \\[-u_{t}+Lu=-u_{t}+\\sum_{ij}a_{ij}D_{ij}u+\\sum b_{i}D_{i}u=0\\,(\\geq0,\\,\\leq0)\\] in some domain $\\Omega\\subset \\mathbb{R}^{n+1}$. We prove a variant of Aleksandrov-Bakelman-Pucci-Krylov-Tso estimate with $L^{p}$ norm of the inhomogeneous term for some number $p
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.
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 scaled mapping parabolic equation for sloping range-dependent environments.
Metzler, Adam M; Moran, Daniel; Collis, Jon M; Martin, P A; Siegmann, William L
2014-03-01
Parabolic equation solutions use various techniques for approximating range-dependent interfaces. One is a mapping approach [M. D. Collins et al., J. Acoust. Soc. Am. 107, 1937-1942 (2000)] where at each range the domain is vertically translated so that sloping bathymetry becomes horizontal, and range dependence is transferred to the upper surface. In this paper, a scaled mapping is suggested where the domain is vertically distorted so that both the bathymetry and upper surface are horizontal. Accuracy is demonstrated for problems involving fluid sediments. Generalizations of the approach should be useful for environments with layer thicknesses that vary with range.
Gilbert, Kenneth E; Di, Xiao
2007-05-01
A method for exactly representing a point source starting field in a Fourier parabolic equation calculation is presented. The formulation is based on an exact, analytic expression for the field in vertical wave number space (k space). The field in vertical coordinate space (z space) is obtained via a Fourier transform of the k-space field. Thus, one can directly control the Fourier components of the starting field, so that nonpropagating components are excluded. The relation of the exact starting field to the standard Gaussian starting field is demonstrated analytically. Examples of the numerical implementation of the exact starting field are given.
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.
Hybrid Ray Optics and Parabolic Equation Methods for Radar Propagation Modeling
1992-10-01
FOR PR C1)W RADAR PROPAGATION MODELING P.E: 0602-135N 6 AUTHOR(S) Wld: DN46Th760 H. V. Hitney 7. PERFORMING ORGANIZATION NAME(S) AND ADORESS(ES) a...is unlimited. 13. ABSTRACT AMazmsn 200 words) The use of parabolic equation (PE) methods has become very popular in recent years for modeling radar ...made in all regions of practical interest to radar engineers or operators with just one model. However, a significant disadvantage of the split-step
Alternating direction implicit methods for parabolic equations with a mixed derivative
NASA Technical Reports Server (NTRS)
Beam, R. M.; Warming, R. F.
1979-01-01
Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A sub 0-stable linear two-step methods in conjunction with the method of approximation factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A sub 0-stable method. The parameter space for which the resulting ADI schemes are second order accurate and unconditionally stable is determined. Some numerical examples are given.
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.
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.
NASA Astrophysics Data System (ADS)
Gou, Haide; Li, Baolin
2017-01-01
In this paper, we study local and global existence of mild solution for an impulsive fractional functional integro differential equation with non-compact semi-group in Banach spaces. We establish a general framework to find the mild solutions for impulsive fractional integro-differential equations, which will provide an effective way to deal with such problems. The theorems proved in this paper improve and extend some related conclusions on this topic. Finally, two applications are given to illustrate that our results are valuable.
Stability results for backward parabolic equations with time-dependent coefficients
NASA Astrophysics Data System (ADS)
Nho Hào, Dinh; Van Duc, Nguyen
2011-02-01
Let H be a Hilbert space with the norm || sdot || and A(t) (0 <= t <= T) be positive self-adjoint unbounded operators from D(A(t))⊂H to H. In the paper, we establish stability estimates of Hölder type and propose a regularization method for the ill-posed backward parabolic equation with time-dependent coefficients \\left\\lbrace \\begin{array}{@{}ll@{}} u_t+ A(t)u=0, & 0Our stability estimates improve the related results by Krein (1957 Dokl. Akad. Nauk SSSR 114 1162-5), and Agmon and Nirenberg (1963 Commun. Pure Appl. Math. 16 121-239). Our regularization method with a priori and a posteriori parameter choice yields error estimates of Hölder type. This is the only result when a regularization method for backward parabolic equations with time-dependent coefficients provides a convergence rate. Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th birthday.
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.
Global gradient estimates for general nonlinear parabolic equations in nonsmooth domains
NASA Astrophysics Data System (ADS)
Byun, Sun-Sig; Ok, Jihoon; Ryu, Seungjin
We establish the natural Calderón-Zygmund theory for a nonlinear parabolic equation of p-Laplacian type in divergence form, ut-diva(Du,x,t)=div(|F) in ΩT, by essentially proving that |∈Lq(ΩT) ⇒ |∈Lq(ΩT), for every q∈[1,∞). The equation under consideration is of general type and not necessarily of variation form, the involved nonlinearity a=a(ξ,x,t) is assumed to have a small BMO semi-norm with respect to (x,t)-variables and the lateral boundary ∂Ω of the domain is assumed to be δ-Reifenberg flat. As a consequence, we are able to not only relax the known regularity requirements on the nonlinearity for such a regularity theory, but also extend local results to a global one in a nonsmooth domain whose boundary has a fractal property. We also find an optimal regularity estimate in Orlicz-Sobolev spaces for such nonlinear parabolic problems.
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.
Perfectly matched layer for an elastic parabolic equation model in ocean acoustics
NASA Astrophysics Data System (ADS)
Xu, Chuanxiu; Zhang, Haigang; Piao, Shengchun; Yang, Shi'e.; Sun, Sipeng; Tang, Jun
2017-02-01
The perfectly matched layer (PML) is an effective technique for truncating unbounded domains with minimal spurious reflections. A fluid parabolic equation (PE) model applying PML technique was previously used to analyze the sound propagation problem in a range-dependent waveguide (Lu and Zhu, 2007). However, Lu and Zhu only considered a standard fluid PE to demonstrate the capability of the PML and did not take improved one-way models into consideration. They applied a [1/1] Padé approximant to the parabolic equation. The higher-order PEs are more accurate than standard ones when a very large angle propagation is considered. As for range-dependent problems, the techniques to handle the vertical interface between adjacent regions are mainly energy conserving and single-scattering. In this paper, the PML technique is generalized to the higher order elastic PE, as is to the higher order fluid PE. The correction of energy conserving is used in range-dependent waveguides. Simulation is made in both acoustic cases and seismo-acoustic cases. Range-independent and range-dependent waveguides are both adopted to test the accuracy and efficiency of this method. The numerical results illustrate that a PML is much more effective than an artificial absorbing layer (ABL) both in acoustic and seismo-acoustic sound propagation modeling.
NASA Technical Reports Server (NTRS)
Nakamura, S.
1982-01-01
A fast method for generating three-dimensional grids for fuselage-wing transonic flow calculations using parabolic difference equations is described. No iterative scheme is used in the three-dimensional sense; grids are generated from one grid surface to the next starting from the fuselage surface. The computational procedure is similar to the iterative solution of the two-dimensional heat conduction equation. The proposed method is at least 10 times faster than the elliptic grid generation method and has much smaller memory requirements. Results are presented for a fuselage and wing of NACA-0012 section and thickness ratio of 10 percent. Although only H-grids are demonstrated, the present technique should be applicable to C-grids and O-grids in three dimensions.
Renewed studies on the unsteady boundary layers governed by singular parabolic equations
NASA Astrophysics Data System (ADS)
Wang, J. C. T.
1985-06-01
Two classic problems in unsteady boundary layers, the Stewartson and the Lam and Crocco problems, are formulated with a unified new semi-similar transformation using velocity and static enthalpy as dependent variables. By this formulation, the resulting governing equations - singular parabolic in nature - for these two physically different problems are shown to closely resemble one another in all essential aspects. For both cases, the domain of the streamwise independent variable is mapped onto (0, 1) for all t. The existence of the Reynolds analogy and the exact energy integral are given; their relations are shown to be different from those in the steady boundary layers. Uniformly valid solutions are shown to be obtainable, accurately, by a standard relaxation method commonly applied to the solution of elliptical partial differential equations. Characteristics of the transition from non-similar solutions to downstream similar solutions are discussed.
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.
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
Wen, Zijuan; Fan, Meng; Asiri, Asim M; Alzahrani, Ebraheem O; El-Dessoky, Mohamed M; Kuang, Yang
2017-04-01
This paper studies the global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with appropriate initial and mixed boundary conditions. Under some practicable regularity criteria on diffusion item and nonlinearity, we establish the local existence and uniqueness of classical solutions based on a contraction mapping. This local solution can be continued for all positive time by employing the methods of energy estimates, Lp-theory, and Schauder estimate of linear parabolic equations. A straightforward application of global existence result of classical solutions to a density-dependent diffusion model of in vitro glioblastoma growth is also presented.
NASA Astrophysics Data System (ADS)
Shishkin, G. I.; Shishkina, L. P.
2010-12-01
For the one-dimensional singularly perturbed parabolic reaction-diffusion equation with a perturbation parameter ɛ, where ɛ ∈ (0, 1], the grid approximation of the Dirichlet problem on a rectangular domain in the ( x, t)-plane is examined. For small ɛ, a parabolic boundary layer emerges in a neighborhood of the lateral part of the boundary of this domain. A new approach to the construction of ɛ-uniformly converging difference schemes of higher accuracy is developed for initial boundary value problems. The asymptotic construction technique is used to design the base decomposition scheme within which the regular and singular components of the grid solution are solutions to grid subproblems defined on uniform grids. The base scheme converges ɛ-uniformly in the maximum norm at the rate of O( N -2ln2 N + N {0/-1}), where N + 1 and N 0 + 1 are the numbers of nodes in the space and time meshes, respectively. An application of the Richardson extrapolation technique to the base scheme yields a higher order scheme called the Richardson decomposition scheme. This higher order scheme convergesɛ-uniformly at the rate of O( N -4ln4 N + N {0/-2}). For fixed values of the parameter, the convergence rate is O( N -4 + N {0/-2}).
Limiting Motion for the Parabolic Ginzburg-Landau Equation with Infinite Energy Data
NASA Astrophysics Data System (ADS)
Côte, Delphine; Côte, Raphaël
2017-03-01
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).
Recovering the source and initial value simultaneously in a parabolic equation
NASA Astrophysics Data System (ADS)
Zheng, Guang-Hui; Wei, Ting
2014-06-01
In this paper, we consider an inverse problem to simultaneously reconstruct the source term and initial data associated with a parabolic equation based on the additional temperature data at a terminal time t = T and the temperature data on an accessible part of a boundary. The conditional stability and uniqueness of the inverse problem are established. We apply a variational regularization method to recover the source and initial value. The existence, uniqueness and stability of the minimizer of the corresponding variational problem are obtained. Taking the minimizer as a regularized solution for the inverse problem, under an a priori and an a posteriori parameter choice rule, the convergence rates of the regularized solution under a source condition are also given. Furthermore, the source condition is characterized by an optimal control approach. Finally, we use a conjugate gradient method and a stopping criterion given by Morozov's discrepancy principle to solve the variational problem. Numerical experiments are provided to demonstrate the feasibility of the method.
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.
Metzler, Adam M; Siegmann, William L; Collins, Michael D
2012-02-01
The parabolic equation method with a single-scattering correction allows for accurate modeling of range-dependent environments in elastic layered media. For problems with large contrasts, accuracy and efficiency are gained by subdividing vertical interfaces into a series of two or more single-scattering problems. This approach generates several computational parameters, such as the number of interface slices, an iteration convergence parameter τ, and the number of iterations n for convergence. Using a narrow-angle approximation, the choices of n=1 and τ=2 give accurate solutions. Analogous results from the narrow-angle approximation extend to environments with larger variations when slices are used as needed at vertical interfaces. The approach is applied to a generic ocean waveguide that includes the generation of a Rayleigh interface wave. Results are presented in both frequency and time domains.
Developments of parabolic equation method in the period of 2000-2016
NASA Astrophysics Data System (ADS)
Xu, Chuan-Xiu; Tang, Jun; Piao, Sheng-Chun; Liu, Jia-Qi; Zhang, Shi-Zhao
2016-12-01
Parabolic equation (PE) method is an efficient tool for modelling underwater sound propagation, particularly for problems involving range dependence. Since the PE method was first introduced into the field of underwater acoustics, it has been about 40 years, during which contributions to extending its capability has been continuously made. The most recent review paper surveyed the contributions made before 1999. In the period of 2000-2016, the development of PE method basically focuses on seismo-acoustic problems, three-dimensional problems, and realistic applications. In this paper, a review covering the contribution from 2000 to 2016 is given, and what should be done in future work is also discussed. Project supported by the Foundation of State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences (Grant No. SKLA201303) and the National Natural Science Foundation of China (Grant Nos. 11104044, 11234002, and 11474073).
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.
Helmholtz and parabolic equation solutions to a benchmark problem in ocean acoustics.
Larsson, Elisabeth; Abrahamsson, Leif
2003-05-01
The Helmholtz equation (HE) describes wave propagation in applications such as acoustics and electromagnetics. For realistic problems, solving the HE is often too expensive. Instead, approximations like the parabolic wave equation (PE) are used. For low-frequency shallow-water environments, one persistent problem is to assess the accuracy of the PE model. In this work, a recently developed HE solver that can handle a smoothly varying bathymetry, variable material properties, and layered materials, is used for an investigation of the errors in PE solutions. In the HE solver, a preconditioned Krylov subspace method is applied to the discretized equations. The preconditioner combines domain decomposition and fast transform techniques. A benchmark problem with upslope-downslope propagation over a penetrable lossy seamount is solved. The numerical experiments show that, for the same bathymetry, a soft and slow bottom gives very similar HE and PE solutions, whereas the PE model is far from accurate for a hard and fast bottom. A first attempt to estimate the error is made by computing the relative deviation from the energy balance for the PE solution. This measure gives an indication of the magnitude of the error, but cannot be used as a strict error bound.
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.
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.
On a new nonlocal boundary value problem for an equation of the mixed parabolic-hyperbolic type
NASA Astrophysics Data System (ADS)
Dildabek, Gulnar
2016-12-01
In this work a new nonlocal boundary value problem for an equation of the mixed type is formulated. This equation is parabolic-hyperbolic and belongs to the first kind because the line of type change is not a characteristic of the equation. Non-local 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. A boundary value problem for the heat equation with conditions of the Samarskii-Ionlin type arises in solving this problem. Unlike the existing publications of the other authors related to the theme it is necessary to note that in this papers the nonlocal problems were considered in rectangular domains. But in our formulation of the problem the hyperbolic part of the domain coincides with a characteristic triangle. Unique strong solvability of the formulated problem is proved.
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.
Inversion of heterogeneous parabolic-type equations using the pilot points method
NASA Astrophysics Data System (ADS)
Alcolea, Andrés; Carrera, Jesús; Medina, Agustín
2006-07-01
The inverse problem (also referred to as parameter estimation) consists of evaluating the medium properties ruling the behaviour of a given equation from direct measurements of those properties and of the dependent state variables. The problem becomes ill-posed when the properties vary spatially in an unknown manner, which is often the case when modelling natural processes. A possibility to fight this problem consists of performing stochastic conditional simulations. That is, instead of seeking a single solution (conditional estimation), one obtains an ensemble of fields, all of which honour the small scale variability (high frequency fluctuations) and direct measurements. The high frequency component of the field is different from one simulation to another, but a fixed component for all of them. Measurements of the dependent state variables are honoured by framing simulation as an inverse problem, where both model fit and parameter plausibility are maximized with respect to the coefficients of the basis functions (pilot point values). These coefficients (model parameters) are used for parameterizing the large scale variability patterns. The pilot points method, which is often used in hydrogeology, uses the kriging weights as basis functions. The performance of the method (both its variants of conditional estimation/simulation) is tested on a synthetic example using a parabolic-type equation. Results show that including the plausibility term improves the identification of the spatial variability of the unknown field function and that the weight assigned to the plausibility term does lead to optimal results both for conditional estimation and for stochastic simulations.
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.
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.
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
NASA Astrophysics Data System (ADS)
Shishkin, G. I.; Shishkina, L. P.
2015-03-01
An initial-boundary value problem is considered for a singularly perturbed parabolic reaction-diffusion equation. For this problem, a technique is developed for constructing higher order accurate difference schemes that converge ɛ-uniformly in the maximum norm (where ɛ is the perturbation parameter multiplying the highest order derivative, ɛ ∈ (0, 1]). A solution decomposition scheme is described in which the grid subproblems for the regular and singular solution components are considered on uniform meshes. The Richardson technique is used to construct a higher order accurate solution decomposition scheme whose solution converges ɛ-uniformly in the maximum norm at a rate of [InlineMediaObject not available: see fulltext.], where N + 1 and N 0 + 1 are the numbers of nodes in uniform meshes in x and t, respectively. Also, a new numerical-analytical Richardson scheme for the solution decomposition method is developed. Relying on the approach proposed, improved difference schemes can be constructed by applying the solution decomposition method and the Richardson extrapolation method when the number of embedded grids is more than two. These schemes converge ɛ-uniformly with an order close to the sixth in x and equal to the third in t.
NASA Astrophysics Data System (ADS)
Itasse, Maxime; Brazier, Jean-Philippe; Léon, Olivier; Casalis, Grégoire
2015-08-01
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 (m1, n1), (m2, n2), such that the difference in azimuth and in frequency matches the desired "target" mode (m1 - m2, n1 - n2). 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.
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.
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.
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.
Flatté, Stanley M; Vera, Michael D
2003-08-01
Line-integral approximations to the acoustic path integral have been used to estimate the magnitude of the fluctuations in an acoustic signal traveling through an ocean filled with internal waves. These approximations for the root-mean-square (rms) fluctuation and the bias of travel time, rms fluctuation in a vertical arrival angle, and the spreading of the acoustic pulse are compared here to estimates from simulations that use the parabolic equation (PE). PE propagations at 250 Hz with a maximum range of 1000 km were performed. The model environment consisted of one of two sound-speed profiles perturbed by internal waves conforming to the Garrett-Munk (GM) spectral model with strengths of 0.5, 1, and 2 times the GM reference energy level. Integral-approximation (IA) estimates of rms travel-time fluctuations were within statistical uncertainty at 1000 km for the SLICE89 profile, and in disagreement by between 20% and 60% for the Canonical profile. Bias estimates were accurate for the first few hundred kilometers of propagation, but became a strong function of time front ID beyond, with some agreeing with the PE results and others very much larger. The IA structure functions of travel time with depth are predicted to be quadratic with the form theta(2)vc0(-2)deltaz(2), where deltaz is vertical separation, c0 is a reference sound speed, and thetav is the rms fluctuation in an arrival angle. At 1000 km, the PE results were close to quadratic at small deltaz, with values of thetav in disagreement with those of the integral approximation by factors of order 2. Pulse spreads in the PE results were much smaller than predicted by the IA estimates. Results imply that acoustic tomography of internal waves at ranges up to 1000 km can use the IA estimate of travel-time variance with reasonable reliability.
Semilinear (topological) spaces and applications
NASA Technical Reports Server (NTRS)
Prakash, P.; Sertel, M. R.
1971-01-01
Semivector spaces are defined and some of their algebraic aspects are developed including some structure theory. These spaces are then topologized to obtain semilinear topological spaces for which a hierarchy of local convexity axioms is identified. A number of fixed point and minmax theorems for spaces with various local convexity properties are established. The spaces of concern arise naturally as various hyperspaces of linear and semilinear (topological) spaces. It is indicated briefly how all this can be applied in socio-economic analysis and optimization.
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.
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.
NASA Astrophysics Data System (ADS)
Ali, Zakaria Idriss; Sango, Mamadou
2016-06-01
In this paper, we investigate a class of stochastic quasilinear parabolic 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, 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 Lipschitzity of the nonlinear external forces, f and G, we obtain the uniqueness of the weak probabilistic solutions. Combining the uniqueness and the famous Yamada-Watanabe result we prove the existence of the unique strong probabilistic solution.
A New Error Bound for Reduced Basis Approximation of Parabolic Partial Differential Equations
2012-01-26
AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Massachusetts Institute of...Technology,Department of Mechanical Engineering,Cambridge,MA,02139 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND...croissance exponentielle en eµ1T et qui sont donc inutilisables en pratique . 1. Space-time formulation We first formulate a general linear parabolic
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.
NASA Astrophysics Data System (ADS)
Kawakami, Hajime; Tsuchiya, Masaaki
2010-12-01
The paper deals with an inverse problem determining the shape of a time-varying Lipschitz domain by boundary measurements of the temperature; such a domain is treated as a non-cylindrical domain in the time-space. Here we focus on the uniqueness of the shape identification. As a general treatment to show the uniqueness, a comparability condition on a pair of domains is introduced; the condition holds automatically in the time-independent case. Based on the condition, we provide several classes of domains in which the uniqueness of the shape identification holds under an appropriate initial shape condition or initial temperature condition. Each of such classes is characterized by a certain geometric condition on its each single element; in particular, it is verified that the class of polyhedral domains and any class of domains with C1 smoothness and with a common initial shape fulfil the uniqueness property. The inverse problem is studied via a parabolic equation with a mixed boundary condition. Then the unique continuation property of weak solutions and the uniqueness of weak solutions to an induced parabolic equation with the homogeneous Dirichlet boundary condition on a non-cylindrical non-Lipschitz domain play key roles. This work was partially supported by JSPS Grant-in-Aid for Scientific Research 21540160.
NASA Astrophysics Data System (ADS)
Meyer, Chad D.; Balsara, Dinshaw S.; Aslam, Tariq D.
2014-01-01
Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit solution methods can be unconditionally stable but have the disadvantage of being computationally costly or difficult to implement. Super-time-stepping methods for treating parabolic terms in mixed type partial differential equations occupy an intermediate position. In such methods each superstep takes “s” explicit Runge-Kutta-like time-steps to advance the parabolic terms by a time-step that is s2 times larger than a single explicit time-step. The expanded stability is usually obtained by mapping the short recursion relation of the explicit Runge-Kutta scheme to the recursion relation of some well-known, stable polynomial. Prior work has built temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Chebyshev polynomials. Since their stability is based on the boundedness of the Chebyshev polynomials, these methods have been called RKC1 and RKC2. In this work we build temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Legendre polynomials. We call these methods RKL1 and RKL2. The RKL1 method is first-order accurate in time; the RKL2 method is second-order accurate in time. We verify that the newly-designed RKL1 and RKL2 schemes have a very desirable monotonicity preserving property for one-dimensional problems - a solution that is monotone at the beginning of a time step retains that property at the end of that time step. It is shown that RKL1 and RKL2 methods are stable for all values of the diffusion coefficient up to the maximum value. We call this a convex monotonicity preserving property and show by examples that it is very useful in
Meyer, Chad D.; Balsara, Dinshaw S.; Aslam, Tariq D.
2014-01-15
Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit solution methods can be unconditionally stable but have the disadvantage of being computationally costly or difficult to implement. Super-time-stepping methods for treating parabolic terms in mixed type partial differential equations occupy an intermediate position. In such methods each superstep takes “s” explicit Runge–Kutta-like time-steps to advance the parabolic terms by a time-step that is s{sup 2} times larger than a single explicit time-step. The expanded stability is usually obtained by mapping the short recursion relation of the explicit Runge–Kutta scheme to the recursion relation of some well-known, stable polynomial. Prior work has built temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Chebyshev polynomials. Since their stability is based on the boundedness of the Chebyshev polynomials, these methods have been called RKC1 and RKC2. In this work we build temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Legendre polynomials. We call these methods RKL1 and RKL2. The RKL1 method is first-order accurate in time; the RKL2 method is second-order accurate in time. We verify that the newly-designed RKL1 and RKL2 schemes have a very desirable monotonicity preserving property for one-dimensional problems – a solution that is monotone at the beginning of a time step retains that property at the end of that time step. It is shown that RKL1 and RKL2 methods are stable for all values of the diffusion coefficient up to the maximum value. We call this a convex monotonicity preserving property and show by examples that it is very
Multiple solutions for resonant semilinear elliptic problems in
NASA Astrophysics Data System (ADS)
López Garza, Gabriel; Rumbos, Adolfo J.
2005-05-01
We prove the existence of multiple nontrivial solutions for the semilinear elliptic problem -[Delta]u=h([lambda]u+g(u)) in , , where h[set membership, variant]L1[intersection]L[alpha] for [alpha]>N/2, N[greater-or-equal, slanted]3, g is a function that has at most linear growth at infinity, g(0)=0, and [lambda] is an eigenvalue of the corresponding linear problem -[Delta]u=[lambda]hu in , . Existence of multiple solutions, for certain values of g'(0), is obtained by imposing a generalized Landesman-Lazer type condition. We use the saddle point theorem of Ambrosetti and Rabinowitz and the mountain pass theorem, as well as a Morse-index result of Ambrosetti [A. Ambrosetti, Differential Equations with Multiple Solutions and Nonlinear Functional Analysis, Equadiff 82, Lecture Notes in Math., vol. 1017, Springer-Verlag, Berlin, 1983] and a Leray-Schauder index theorem for mountain pass type critical points due to Hofer [H. Hofer, A note on the Topological Degree at a critical Point of Mountain Pass Type, Proc. Amer. Math. Soc. 90 (1984) 309-315]. The results of this paper are based upon multiplicity results for resonant problems on bounded domains in [E. Landesman, S. Robinson, A. Rumbos, Multiple solutions of semilinear elliptic problems at resonance, Nonlinear Anal. 24 (1995) 1049-1059] and [S. Robinson, Multiple solutions for semilinear elliptic boundary value problems at resonance, Electron. J. Differential Equations 1995 (1995) 1-14], and complement a previous existence result by the authors in [G. López Garza, A. Rumbos, Resonance and strong resonance for semilinear elliptic equations in , Electron. J. Differential Equations 2003 (2003) 1-22] for resonant problems in in which g was assumed to be bounded.
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.
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
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.
NASA Technical Reports Server (NTRS)
Stephenson, B. L.; Hassan, H. A.
1983-01-01
A method based on the Parabolized Navier-Stokes equations is used to calculate the flow field and heat transfer of lifting entry vehicles. The method is based on the Bean and Warming implicit algorithm and uses a new procedure for preventing departure solutions. Calculations are carried out for blunt on-axis and bent biconics, assuming a perfect gas and laminar flow, and compared with available heat transfer, surface pressure and shock shape measurements for a range of Mach numbers and angles of attack. In all calculations presented here, the starting solution is obtained from available inviscid and boundary layer codes. Good agreement with experiment is indicated. Thus, the method provides an accurate and rather inexpensive procedure for calculating three-dimensional flows at supersonic Mach numbers.
Blow-up rates of solutions of initial-boundary value problems for a quasi-linear parabolic equation
NASA Astrophysics Data System (ADS)
Anada, Koichi; Ishiwata, Tetsuya
2017-01-01
We consider initial-boundary value problems for a quasi linear parabolic equation, kt =k2 (kθθ + k), with zero Dirichlet boundary conditions and positive initial data. It has known that each of solutions blows up at a finite time with the rate faster than √{(T - t) - 1}. In this paper, it is proved that supθ k (θ , t) ≈√{(T - t) - 1 log log (T - t) - 1 } as t ↗ T under some assumptions. Our strategy is based on analysis for curve shortening flows that with self-crossing brought by S.B. Angenent and J.J.L. Velázquez. In addition, we prove some of numerical conjectures by Watterson which are keys to provide the blow-up rate.
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.
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...
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.
Use of splines in the solution of parabolized Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Lyttle, Ian; Reed, Helen
1996-11-01
A parabolized Navier-Stokes code is written to investigate the three-dimensional nature of boundary layers. The geometry of interest is a sharp cone, of elliptical cross-section, at zero angle-of-attack. The flow of interest is a calorically perfect ideal gas at free-stream Mach number of 4 and freestream Reynolds number of 4 × 10^6 per meter. The use of cubic splines with an adaptive grid scheme is found to induce small errors in pressure. Though large scale flow features remain unaffected, spurious small scale features can appear. The nature of these errors is investigated. As the solution is transferred between grids, splined quantities are used to reconstruct other quantities through the ideal gas relations. Non-physical oscillations appear in the reconstructed quantities. These oscillations contaminate the solution at small scales. This work is supported by the Air Force Office of Scientific Research (F49620-95-1-0033), and by the National Science Foundation Faculty Awards for Women in Science and Engineering (GER-9022523).
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.
Development of Vector Parabolic Equation Technique for Propagation in Urban and Tunnel Environments
2010-09-01
lattice when a particle undergoing random walk is endowed with two states of spin in addition to the two states of direction in a 1+1 spacetime dimension...the first and second kind from which the spacetime continuum limits of the diffusion equation and Schrödinger equation follow directly. PACS numbers...Nottale [6] and Ord [7] advanced the idea that spacetime is not differentiable but is of a fractal nature, suggesting that an infinity of geodesics
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.
The entropy solution of a hyperbolic-parabolic mixed type equation.
Zhan, Huashui
2016-01-01
The entropy solution of the equation [Formula: see text]is considered. Besides the usual initial value, only a partial boundary value is imposed. By choosing some special test functions, the stability of the solutions is obtained by Kruzkov's bi-variables method, provided that [Formula: see text] is an unit n-dimensional cube or the half space.
Collins, Michael D; Siegmann, William L
2015-01-01
The parabolic equation method is extended to handle problems in seismo-acoustics that have multiple fluid and solid layers, continuous depth dependence within layers, and sloping interfaces between layers. The medium is approximated in terms of a series of range-independent regions, and a single-scattering approximation is used to compute transmitted fields across the vertical interfaces between regions. The approach is implemented in terms of a set of dependent variables that is well suited to piecewise continuous depth dependence in the elastic parameters, but one of the fluid-solid interface conditions in that formulation involves a second derivative that complicates the treatment of sloping interfaces. This issue is resolved by using a non-centered, four-point difference formula for the second derivative. The approach is implemented using a matrix decomposition that is efficient when the parameters of the medium have a general dependence within the upper layers of the sediment but only depend on depth in the water column and deep within the sediment.
NASA Astrophysics Data System (ADS)
Shishkin, G. I.
2013-04-01
For a singularly perturbed parabolic convection-diffusion equation, the conditioning and stability of finite difference schemes on uniform meshes are analyzed. It is shown that a convergent standard monotone finite difference scheme on a uniform mesh is not ɛ-uniformly well conditioned or ɛ-uniformly stable to perturbations of the data of the grid problem (here, ɛ is a perturbation parameter, ɛ ∈ (0, 1]). An alternative finite difference scheme is proposed, namely, a scheme in which the discrete solution is decomposed into regular and singular components that solve grid subproblems considered on uniform meshes. It is shown that this solution decomposition scheme converges ɛ-uniformly in the maximum norm at an O( N -1ln N + N {0/-1}) rate, where N + 1 and N 0 + 1 are the numbers of grid nodes in x and t, respectively. This scheme is ɛ-uniformly well conditioned and ɛ-uniformly stable to perturbations of the data of the grid problem. The condition number of the solution decomposition scheme is of order O(δ-2lnδ-1 + δ{0/-1}); i.e., up to a logarithmic factor, it is the same as that of a classical scheme on uniform meshes in the case of a regular problem. Here, δ = N -1ln N and δ0 = N {0/-1} are the accuracies of the discrete solution in x and t, respectively.
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
Degtyarev, S P
2008-04-30
Instantaneous support shrinking is studied for a doubly non-linear degenerate parabolic equation in the case of slow diffusion when, in general, the Cauchy initial data are Radon measures. For a non-negative solution, a necessary and sufficient condition for instantaneous support shrinking is obtained in terms of the local behaviour of the mass of the initial data. In the same terms, estimates are obtained for the size of the support, that are sharp with respect to order. Bibliography: 24 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.
Numerical Solution of Ill Posed Problems in Partial Differential Equations.
1987-09-01
periodic solutions of semilinear wave equations in exterior domains (breathers). Necessary and sufficient conditions for the existence of such...Crandall, M.G., and Sacks, P.E., Some L1 existence and depandence results for semilinear elliptic equations under nonlinear boundary conditions , to...the former case, a convective diffusion equation with a semilinear source in the boundary condition was analyzed. A fairly complete picture of the
On maximal parabolic regularity for non-autonomous parabolic operators
NASA Astrophysics Data System (ADS)
Disser, Karoline; ter Elst, A. F. M.; Rehberg, Joachim
2017-02-01
We consider linear inhomogeneous non-autonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to time integrability exponents r ≠ 2. This allows us to prove maximal parabolic Lr-regularity for discontinuous non-autonomous second-order divergence form operators in very general geometric settings and to prove existence results for related quasilinear equations.
Analytic Parabolic Equation Solutions.
1989-11-01
problem involving a line source in a homogeneous ocean above a homogeneous , semi-infinite, fast fluid bottom has been analyzed in detail. Various...excited duct with laterally homogeneous bilinear height profile. An exact numerical reference solution can be constructed by modal summation for...have been well documented in the literature [1]. Since the final-field is constructed by beam shooting, one avoids the need for eigenray search which
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.
NASA Astrophysics Data System (ADS)
Grinevich, P. G.; Santini, P. M.
2016-10-01
Written in the evolutionary form, the multidimensional integrable dispersionless equations, exactly like the soliton equations in 2+1 dimensions, become nonlocal. In particular, the Pavlov equation is brought to the form v t = v x v y - ∂ x -1 ∂ y [ v y + v x 2], where the formal integral ∂ x -1 becomes the asymmetric integral - int_x^∞ {dx'} . We show that this result could be guessed using an apparently new integral geometry lemma. It states that the integral of a sufficiently general smooth function f( X, Y) over a parabola in the plane ( X, Y) can be expressed in terms of the integrals of f( X, Y) over straight lines not intersecting the parabola. We expect that this result can have applications in two-dimensional linear tomography problems with an opaque parabolic obstacle.
NASA Astrophysics Data System (ADS)
Ozgun, Ozlem; Apaydin, Gökhan; Kuzuoglu, Mustafa; Sevgi, Levent
2011-12-01
A MATLAB-based one-way and two-way split-step parabolic equation software tool (PETOOL) has been developed with a user-friendly graphical user interface (GUI) for the analysis and visualization of radio-wave propagation over variable terrain and through homogeneous and inhomogeneous atmosphere. The tool has a unique feature over existing one-way parabolic equation (PE)-based codes, because it utilizes the two-way split-step parabolic equation (SSPE) approach with wide-angle propagator, which is a recursive forward-backward algorithm to incorporate both forward and backward waves into the solution in the presence of variable terrain. First, the formulation of the classical one-way SSPE and the relatively-novel two-way SSPE is presented, with particular emphasis on their capabilities and the limitations. Next, the structure and the GUI capabilities of the PETOOL software tool are discussed in detail. The calibration of PETOOL is performed and demonstrated via analytical comparisons and/or representative canonical tests performed against the Geometric Optic (GO) + Uniform Theory of Diffraction (UTD). The tool can be used for research and/or educational purposes to investigate the effects of a variety of user-defined terrain and range-dependent refractivity profiles in electromagnetic wave propagation. Program summaryProgram title: PETOOL (Parabolic Equation Toolbox) Catalogue identifier: AEJS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 143 349 No. of bytes in distributed program, including test data, etc.: 23 280 251 Distribution format: tar.gz Programming language: MATLAB (MathWorks Inc.) 2010a. Partial Differential Toolbox and Curve Fitting Toolbox required Computer: PC Operating system: Windows XP and
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)
Singer, Bart A.; Choudhari, Meelan; Li, Fei
1995-01-01
A multiple-scales approach is used to approximate the effects of nonparallelism and streamwise surface curvature on the growth of stationary crossflow vortices in incompressible, three-dimesional boundary layers. The results agree with results predicted by solving the parabolized stability equations in regions where the nonparallelism is sufficiently weak. As the nonparallelism increases, the agreement between the two approaches worsens. An attempt has been made to quantify the nonparallelism on flow stability in terms of a nondimensional number that describes the rate of change of the mean flow relative to the disturbance wavelength. We find that the above nondimensional number provides useful information about the adequacy of the multiple-scales approximation for different disturbances for a given flow geometry, but the number does not collapse data for different flow geometries onto a single curve.
NASA Astrophysics Data System (ADS)
Vassiliev, V. A.
2016-10-01
We enumerate the local Petrovskii lacunas (that is, the domains of local regularity of the principal fundamental solutions of strictly hyperbolic PDEs with constant coefficients in {R}^N) close to parabolic singular points of their wavefronts (that is, at the points of types P_8^1, P_8^2, +/- X_9, X_9^1, X_9^2, J10^1 and J10^3). These points form the next most difficult family of classes in the natural classification of singular points after the so-called simple singularities A_k, D_k, E_6, E_7 and E_8, which have been investigated previously. Also we present a computer program which counts the topologically distinct morsifications of critical points of smooth functions, and hence also the local components of the complement of a generic wavefront at its singular points. Bibliography: 22 titles.
The geometry of finite difference discretizations of semilinear elliptic operators
NASA Astrophysics Data System (ADS)
Teles, Eduardo; Tomei, Carlos
2012-04-01
Discretizations by finite differences of some semilinear elliptic equations lead to maps F(u) = Au - f(u), u \\in {{R}}^n , given by nonlinear convex diagonal perturbations of symmetric matrices A. For natural nonlinearity classes, we consider the equation F(u) = y - tp, where t is a large positive number and p is a vector with negative coordinates. As the range of the derivative f'i of the coordinates of f encloses more eigenvalues of A, the number of solutions increases geometrically, eventually reaching 2n. This phenomenon, somewhat in contrast with behaviour associated with the Lazer-McKenna conjecture, has a very simple geometric explanation: a perturbation of a multiple fold gives rise to a function which sends connected components of its critical set to hypersurfaces with large rotation numbers with respect to vectors with very negative coordinates. Strictly speaking, the results have nothing to do with elliptic equations: they are properties of the interaction of a (self-adjoint) linear map with increasingly stronger nonlinear convex diagonal interactions.
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.
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.
Parabolic Herz Spaces and their Applications
NASA Astrophysics Data System (ADS)
Ragusa, Maria Alessandra
2010-09-01
The note is a natural continuations of the study started in [7]. In Herz spaces endowed with parabolic metric are proved regularity results of weak solutions to divergence form parabolic equations having discontinuous coefficients, using boundedness of integral operators and commutators generated by VMO functions and Calderón-Zygmund operators.
Numerical Solution of Ill Posed Problems in Partial Differential Equations
1988-06-30
periodic solutions of semilinear wave equations in exterior domains (breathers). Necessary and sufficient conditions for the existence of such solutions...numerically, that radial, global , positive solutions of the equation div grad u + uq u = 0 (X > 0, q > 1). ((1+1grad ul ) / exist for all X sufficiently... equation with a semilinear boundary condition , to appear in SIAM J. Math. Anal. 17] Levine, H.A. and Protter, M.H., The breakdown of solutions of
NASA Astrophysics Data System (ADS)
Beretta, Elena; Manzoni, Andrea; Ratti, Luca
2017-03-01
In this paper we develop a reconstruction algorithm for the solution of an inverse boundary value problem dealing with a semilinear elliptic partial differential equation of interest in cardiac electrophysiology. The goal is the detection of small inhomogeneities located inside a domain Ω , where the coefficients of the equation are altered, starting from observations of the solution of the equation on the boundary \\partial Ω . Exploiting theoretical results recently achieved in [13], we implement a reconstruction procedure based on the computation of the topological gradient of a suitable cost functional. Numerical results obtained for several test cases finally assess the feasibility and the accuracy of the proposed technique.
NASA Astrophysics Data System (ADS)
Mejjaoli, Hatem
2008-12-01
We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.
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.
NASA Astrophysics Data System (ADS)
Rousseau, Jérôme Le; Robbiano, Luc
2010-03-01
In a bounded domain of R n+1, n ≧ 2, we consider a second-order elliptic operator, {A=-{partial_{x_0}^2} - nabla_x \\cdot (c(x) nabla_x)}, where the (scalar) coefficient c( x) is piecewise smooth yet discontinuous across a smooth interface S. We prove a local Carleman estimate for A in the neighborhood of any point of the interface. The “observation” region can be chosen independently of the sign of the jump of the coefficient c at the considered point. The derivation of this estimate relies on the separation of the problem into three microlocal regions and the Calderón projector technique. Following the method of Lebeau and Robbiano (Comm Partial Differ Equ 20:335-356, 1995) we then prove the null controllability for the linear parabolic initial problem with Dirichlet boundary conditions associated with the operator {{partial_t - nabla_x \\cdot (c(x) nabla_x)}}.
1983-11-01
Dr h cos a (2.3d) An equation for the scale factors can...momentum equations are expressed as I hIr s (rUh2) = 0 (2.7) 2 SU I p 1 r (r u’v’) r (ru) 9 (u2 2 1 Dr 1 DU w’- Dr + (u’ -v’ ) - +- -+-- r U Ds r s 3 2U QU...Reynolds stresses in Equation (2.10) are given by V-- lu U 3CL - u’v’v -T n+U- T 9n (is 2/3k u 2V DU T s 2 -2vT 2/3k v ’ (r,U) (2.11)r 9s 2 U Dr
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.
Parabolically connected subgroups
Netai, Igor V
2011-08-31
All reductive spherical subgroups of the group SL(n) are found for which the intersections with every parabolic subgroup of SL(n) are connected. This condition guarantees that open equivariant embeddings of the corresponding homogeneous spaces into Moishezon spaces are algebraic. Bibliography: 6 titles.
Numerical analysis of the rescaling method for parabolic problems with blow-up in finite time
NASA Astrophysics Data System (ADS)
Nguyen, V. T.
2017-01-01
In this work, we study the numerical solution for parabolic equations whose solutions have a common property of blowing up in finite time and the equations are invariant under the following scaling transformation
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.
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.
NASA Astrophysics Data System (ADS)
Parsons, W. L., IV; Goetchius, W.
The further development of parabolic solar collectors to increase their efficiency and simplify their operation was the prime objective of this research project. Three primary objectives were pursued. The first of these was to investigate the simplest and most efficient techniques to build and mass-produce parabolic solar collectors. The second objective was to further develop and simplify absorber tubes used to collect and transfer the solar energy. Absorber tubes represented a significant area of this research project. The third objective was to develop accurate, low cost, and durable tracking systems for solar collectors. Solar tracking systems are covered including several schematic representations of various systems and designs. The testing systems and associated mechanisms for the designs discussed in this report are described.
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.
Tropospheric Propagation Modelling with the Parabolic Equation
1990-09-01
raised cosine window to the imaginary part of the square of the refractive index term. From the fust exponential term of (29) it is evident that this...the present implementation of the model, this low pass filtering of spatial frequency is achieved by applying a simple raised cosine window to the...range in thickness from a few metres (these tend to affect propagation above microwave frequencies) up to hundreds of metres (affecting propagation at
Reverberation Modelling Using a Parabolic Equation Method
2012-10-01
normaux adiabatiques pour les environnements dont les caractéristiques varient en fonction de la distance. Toutefois, on s’attend à ce que cette...approche échoue pour les environnements dont les caractéristiques varient fortement en fonction de la distance. D’un autre côté, les modèles à équation...les environnements dont les caractéristiques varient en fonction de la distance. Toutefois, on s’attend à ce que cette approche échoue pour les
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.
Strict parabolicity of the multifractal spectrum at the Anderson transition
NASA Astrophysics Data System (ADS)
Suslov, I. M.
2016-11-01
Using the well-known "algebra of multifractality," we derive the functional equation for anomalous dimensions Δ q , whose solution Δ = χ q( q-1) corresponds to strict parabolicity of the multifractal spectrum. This result demonstrates clearly that a correspondence of the nonlinear σ-models with the initial disordered systems is not exact.
The planar parabolic optical antenna.
Schoen, David T; Coenen, Toon; García de Abajo, F Javier; Brongersma, Mark L; Polman, Albert
2013-01-09
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 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.
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.
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.
Analysis and conceptual design of a lunar radiator parabolic shade
NASA Astrophysics Data System (ADS)
Ewert, Michael K.; Clark, Craig S.
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.
NASA Astrophysics Data System (ADS)
Dai, Qiuyi; Fu, Yuxia
This article studies positive solutions of Robin problem for semi-linear second order ordinary differential equations. Nondegeneracy and uniqueness results are proven for homogeneous differential equations. Necessary and sufficient conditions for the existence of one or two positive solutions for inhomogeneous differential equations or differential equations with concave-convex nonlinearities are obtained by making use of the nondegeneracy and uniqueness results for positive solutions of homogeneous differential equations.
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)
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.
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.
Spectral stability of periodic waves in the generalized reduced Ostrovsky equation
NASA Astrophysics Data System (ADS)
Geyer, Anna; Pelinovsky, Dmitry E.
2017-02-01
We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all smooth periodic travelling waves independent of the nonlinearity power. The argument is based on the energy convexity and does not use coordinate transformations of the reduced Ostrovsky equations to the semi-linear equations of the Klein-Gordon type.
JPL's parabolic dish test site
NASA Technical Reports Server (NTRS)
Hagen, T. L.
1980-01-01
A parabolic dish test site (PDTS) was established in the California Mojave Desert to carry out work in testing solar point focusing concentrator systems and related hardware. The site was chosen because of its high solar insolation level and year around clear sky conditions. The various facilities and equipment at the PDTS, and the concentrator experiments being performed are described.
On two parabolic systems: Convergence and blowup
NASA Astrophysics Data System (ADS)
Huang, Yamin
1998-12-01
This dissertation studies two parabolic systems. It consists of two parts. In part one (chapter one), we prove a convergence result, namely, the solution (AK,/ BK) of a system of chemical diffusion-reaction equations (with reaction rate K) converges to the solution (A, B) of a diffusion- instantaneous-reaction equation. To prove our main result, we use some L1 and L2 'energy' estimates and a compactness result due to Aubin (1). As a by-product we also prove that as K approaches infinity, the limit solution exhibits phase separation between A and B. In part two (chapter two), we study the blowup rate for a system of heat equations ut=/Delta u,/ vt=/Delta v in a bounded domain Ωtimes(0,T) coupled in the nonlinear Neumann boundary conditions [/partial u/over/partial n]=vp,/ [/partial v/over/partial n]=uq on ∂Omega×[ 0,T), where p>0,/ q>0,/ pq>1 and n is the exterior normal vector on ∂Omega. Under certain assumptions, we establish exact blowup rate which generalizes the corresponding results of some authors' recent work including Deng (2), Deng-Fila-Levine (3) and Hu-Yin (4). ftn (1) J. P. A scUBIN, Un theoreme de compacite, C. R. Acad. Sci., 256(1963), pp. 5042-5044. (2) K. D scENG, Blow-up rates for parabolic systems, Z. Angew. Math. Phys., 47(1996), No. 1, pp. 132-143. (3) K. D scENG, M. F scILA AND H. A. L scEVINE, On critical exponents for a system of heat equations coupled in the boundary conditions, Acta Math. Univ. Comenian. (N.S.), 36(1994), No. 2, pp. 169-192. (4) B. H scU scAND H. M. Y scIN, The profile near blowup time for solutions of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc., 346(1994), pp. 117-135.
Proton driven plasma wakefield generation in a parabolic plasma channel
NASA Astrophysics Data System (ADS)
Golian, Y.; Dorranian, D.
2016-11-01
An analytical model for the interaction of charged particle beams and plasma for a wakefield generation in a parabolic plasma channel is presented. In the suggested model, the plasma density profile has a minimum value on the propagation axis. A Gaussian proton beam is employed to excite the plasma wakefield in the channel. While previous works investigated on the simulation results and on the perturbation techniques in case of laser wakefield accelerations for a parabolic channel, we have carried out an analytical model and solved the accelerating field equation for proton beam in a parabolic plasma channel. The solution is expressed by Whittaker (hypergeometric) functions. Effects of plasma channel radius, proton bunch parameters and plasma parameters on the accelerating processes of proton driven plasma wakefield acceleration are studied. Results show that the higher accelerating fields could be generated in the PWFA scheme with modest reductions in the bunch size. Also, the modest increment in plasma channel radius is needed to obtain maximum accelerating gradient. In addition, the simulations of longitudinal and total radial wakefield in parabolic plasma channel are presented using LCODE. It is observed that the longitudinal wakefield generated by the bunch decreases with the distance behind the bunch while total radial wakefield increases with the distance behind the bunch.
Curvilinear parabolic approximation for surface wave transformation with wave-current interaction
Shi Fengyan . E-mail: fyshi@coastal.udel.edu; Kirby, James T.
2005-04-10
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.
Entire Blow-Up Solutions of Semilinear Elliptic Equations and Systems
2008-03-01
solR r B r u v c d= > = . (4.24) Let ,c dR be given as , supc d solR R= . (4.25) Then , , lim ( ) lim ( ) c d c dr R r R u r v r...Proof. Take ( , )c d S∉ , 0c d≠ ≠ . By Lemma 4-3, solR ≠ ∅ , and since ( , )c d S∉ , ,c dR < ∞ . Let ( , )u v be a solution of (1.2) in ,(0
Low Sidelobe Scanning Beams for Parabolic Reflectors,
Parabolic antennas, *Sidelobes, *Electronic scanners, Parabolas, Far field, Antenna feeds , Reflectors, Low level, Amplitude, Distortion, Configurations, Secondary, Compensation, Feeding , Symposia, Taper
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.
Three-dimensional rogue waves in nonstationary parabolic potentials
Yan Zhenya; Konotop, V. V.; Akhmediev, N.
2010-09-15
Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1)-dimensional inhomogeneous nonlinear Schroedinger (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.
Decay and stability for nonlinear hyperbolic equations
NASA Astrophysics Data System (ADS)
Marcati, Pierangelo
This paper deals with the asymptotic stability of the null solution of a semilinear partial differential equation. The La Salle Invariance Principle has been used to obtain the stability results. The first result is given under quite general hypotheses assuming only the precompactness of the orbits and the local existence. In the second part, under some restrictions, sufficient conditions for precompactness of the orbits and decay of solutions are given. An existence and uniqueness theorem is proved in the Appendix. Some examples are given.
Existence results for quasilinear parabolic hemivariational inequalities
NASA Astrophysics Data System (ADS)
Liu, Zhenhai
This paper is devoted to the periodic problem for quasilinear parabolic hemivariational inequalities at resonance as well as at nonresonance. By use of the theory of multi-valued pseudomonotone operators, the notion of generalized gradient of Clarke and the property of the first eigenfunction, we build a Landesman-Lazer theory in the nonsmooth framework of quasilinear parabolic hemivariational inequalities.
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.
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.
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.
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.
Parabolized Navier-Stokes methods for hypersonic flows
NASA Technical Reports Server (NTRS)
Lawrence, Scott L.
1991-01-01
A representative sampling of the techniques used in the integration of the Parabolized Navier-Stokes (PNS) equations is presented. Special atention is given to recent algorithms developed specifically for application to high speed flows, characterized by the presence of strong embedded shock waves and real gas effects. It is shown that PNS solvers are being used in the analysis of sonic boom signatures. Methods for modeling physical effects are discussed, including an overview of commonly used turbulence models and a more detailed discussion of techniques for including equilibrium and finite rate real gas effects.
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 .
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.
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.
Positive solutions of quasilinear parabolic systems with nonlinear boundary conditions
NASA Astrophysics Data System (ADS)
Pao, C. V.; Ruan, W. H.
2007-09-01
The aim of this paper is to investigate the existence, uniqueness, and asymptotic behavior of solutions for a coupled system of quasilinear parabolic equations under nonlinear boundary conditions, including a system of quasilinear parabolic and ordinary differential equations. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system as well as the uniqueness of a positive steady-state solution. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients Di(ui) may have the property Di(0)=0 for some or all i. Our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. It is shown that the time-dependent solution converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a porous medium type of problem, a heat-transfer problem, and a two-component competition model in ecology. These applications illustrate some very interesting distinctive behavior of the time-dependent solutions between density-independent and density-dependent diffusions.
Positive solutions of quasilinear parabolic systems with Dirichlet boundary condition
NASA Astrophysics Data System (ADS)
Pao, C. V.; Ruan, W. H.
Coupled systems for a class of quasilinear parabolic equations and the corresponding elliptic systems, including systems of parabolic and ordinary differential equations are investigated. The aim of this paper is to show the existence, uniqueness, and asymptotic behavior of time-dependent solutions. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients D(u) may have the property D(0)=0 for some or all i=1,…,N, and the boundary condition is u=0. Using the method of upper and lower solutions, we show that a unique global classical time-dependent solution exists and converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a scalar polynomial growth problem, a coupled system of polynomial growth problem, and a two component competition model in ecology.
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.
Tailored dispersion profile in controlling optical solitons in a tapered parabolic index fiber
NASA Astrophysics Data System (ADS)
Prakash, S. Arun; Malathi, V.; Mani Rajan, M. S.
2016-03-01
We investigate the soliton dynamics in tapered parabolic index fibers via symbolic computation for a variety of dispersion profiles to inspect how a specific dispersion profile controls the optical soliton. By means of AKNS procedure, Lax pair is constructed for nonlinear Schrödinger equation with variable coefficients. Using obtained Lax pair, multi-soliton solutions are generated via Darboux transformation technique. Using multi-soliton solutions, soliton dynamics in tapered parabolic index fiber with the hyperbolic, Gaussian, exponential, and linear profiles are discussed. Results obtained in this study will be of certain potential application on construction of the nonlinear optical devices by soliton control. Results obtained in this study will be of certain value to the studies on the propagation and application of the soliton in the tapered parabolic index fiber and dispersion-managed fiber system.
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.
Block Iterative Methods for Elliptic and Parabolic Difference Equations.
1981-09-01
Wisconsin 53706. (3) University of California, Los Alamos National Laboratory, Los Alamos, New Mexico 87545. *Will also appear as Los Alamos Scientic...Courant, K. Friedrichs, and H. Lewy, Uber die Partiellen Differenzengleichungen der Mathematischen Physik, Math. Ann., 100 (1928), pp. 32-74 = On the
Elastic Bottom Propagation Mechanisms Investigated by Parabolic Equation Methods
2014-09-30
Scholte interface waves are excited by seismic sources and have been observed by seismometers at the ocean bottom.[12, 13] Energy from interface waves has...to generate abyssal oceanic T - waves from seismic sources has been verified by comparing transmission loss results for a flat seafloor to those from...channel propagation of oceanic T waves from seismic sources in the presence of intervening seamounts or coral reef barriers is established using elastic PE
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.
Elastic Bottom Propagation Mechanisms Investigated by Parabolic Equation Methods
2013-09-30
layered elastic bottom and an intervening seamount . Range-dependence associated with the seamount begins 15 km from the source. Acoustic wave energy...interacts with the elastic layers. Channeling of elastic energy in the top elastic layer appears on the left side of the seamount and continues over...bottom on the right side of the seamount , in particular at ranges greater than 65 km. Wavenumber spectra for a depth of 2550 m obtained from
Studies of boundary-layer receptivity with parabolized stability equations
NASA Astrophysics Data System (ADS)
Herbert, Thorwald; Lin, Nay
1993-07-01
Transition prediction with DNS or PSE requires specification of a model environment that affects the transition process through initial and boundary conditions. Usually, this environment is specified in terms of normal modes at an initial position. This specification is based on empiricism and is often inappropriate. To free the transition analysis from empiricism, it is necessary to specify the environment in more physical terms and to incorporate local and area-distributed receptivity as part of the analysis. In principle, the PSE are capable to deal with linear and nonlinear receptivity mechanisms. We demonstrate this capability by analyzing the origin of Klebanoff modes, their connection to Goertler vortices, and the forcing of cross-flow vortices in swept Hiemenz flow. Our study serves to refine the PSE and to extend their scope as a tool for studies on receptivity, stability, and transition.
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.
Beam diffraction by planar and parabolic reflectors
NASA Astrophysics Data System (ADS)
Suedan, Gibreel A.; Jull, Edward V.
1991-04-01
In the complex source point (CSP) technique, an omnidirectional source diffraction solution becomes that for a directive beam when the coordinates of the source position are given appropriate complex values. This is applied to include feed directivity in reflector edge diffraction. Solutions and numerical examples for planar strip and parabolic cylinder reflectors are given, including an offset parabolic reflector. The main beams of parabolic reflectors are calculated by aperture integration and the edge diffracted fields by uniform diffraction theory. In both cases, a complex source point feed in the near or far field of the reflector may be used in the pattern calculation, with improvements in accuracy in the lateral and spillover pattern lobes.
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.
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
Incompressible Navier-Stokes and parabolized Navier-Stokes formulations and computational techniques
NASA Technical Reports Server (NTRS)
Rubin, S. G.
1984-01-01
The differential formulations and computational techniques currently used for the incompressible Navier-Stokes (NS) and parabolic Navier-Stokes (PNS) equations are reviewed. In particular, attention is given to problems associated with the choice of difference equations, the method of solution and the choice of algorithm, the coupling of dependent variables and discretized equations, the application of boundary conditions, and grid generation. A new composite velocity NS and PNS formulation in (u,v,p) variables is presented, and the applicability of a 'forward' difference global pressure iteration for the (u,v,p) PNS system is demonstrated.
Nonlinear equations of 'variable type'
NASA Astrophysics Data System (ADS)
Larkin, N. A.; Novikov, V. A.; Ianenko, N. N.
In this monograph, new scientific results related to the theory of equations of 'variable type' are presented. Equations of 'variable type' are equations for which the original type is not preserved within the entire domain of coefficient definition. This part of the theory of differential equations with partial derivatives has been developed intensively in connection with the requirements of mechanics. The relations between equations of the considered type and the problems of mathematical physics are explored, taking into account quasi-linear equations, and models of mathematical physics which lead to equations of 'variable type'. Such models are related to transonic flows, problems involving a separation of the boundary layer, gasdynamics and the van der Waals equation, shock wave phenomena, and a combustion model with a turbulent diffusion flame. Attention is also given to nonlinear parabolic equations, and nonlinear partial differential equations of the third order.
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.
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.
Discontinuous Mixed Covolume Methods for Parabolic Problems
Zhu, Ailing
2014-01-01
We present the semidiscrete and the backward Euler fully discrete discontinuous mixed covolume schemes for parabolic problems on triangular meshes. We give the error analysis of the discontinuous mixed covolume schemes and obtain optimal order error estimates in discontinuous H(div) and first-order error estimate in L2. PMID:24983008
Status of the current parabolic dish technology
NASA Technical Reports Server (NTRS)
Sumrall, C.
1981-01-01
Vu-graphs are presented that show that point focus distributed receiver distributed generation systems are cost competitive with current utilities. System cost caveats and typical power module costs are described. Major problems inhibiting commercialization of the parabolic dish technology were reviewed.
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.
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).
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.
Who dares to join a parabolic flight?
NASA Astrophysics Data System (ADS)
Montag, Christian; Zander, Tina; Schneider, Stefan
2016-12-01
Parabolic flights represent an important tool in space research to investigate zero gravity on airplanes. Research on these flights often target psychological and biological processes in humans to investigate if and how we can adapt to this unique environment. This research is costly, hard to conduct and clearly heavily relies on humans participating in experiments in this (unnatural) situation. The present study investigated N =66 participants and N =66 matched control persons to study if participants in such experimental flights differ in terms of their personality traits from non-parabonauts. The main finding of this study demonstrates that parabonauts score significantly lower on harm avoidance, a trait closely linked to being anxious. As anxious humans differ from non-anxious humans in their biology, the present observations need to be taken into account when aiming at the generalizability of psychobiological research findings conducted in zero gravity on parabolic flights.
Parabolic dish collectors - A solar option
NASA Astrophysics Data System (ADS)
Truscello, V. C.
1981-05-01
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.
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
Essential Parabolic Structures and Their Infinitesimal Automorphisms
NASA Astrophysics Data System (ADS)
Alt, Jesse
2011-04-01
Using the theory of Weyl structures, we give a natural generalization of the notion of essential conformal structures and conformal Killing fields to arbitrary parabolic geometries. We show that a parabolic structure is inessential whenever the automorphism group acts properly on the base space. As a corollary of the generalized Ferrand-Obata theorem proved by C. Frances, this proves a generalization of the ''Lichnérowicz conjecture'' for conformal Riemannian, strictly pseudo-convex CR, and quaternionic/octonionic contact manifolds in positive-definite signature. For an infinitesimal automorphism with a singularity, we give a generalization of the dictionary introduced by Frances for conformal Killing fields, which characterizes (local) essentiality via the so-called holonomy associated to a singularity of an infinitesimal automorphism.
Parabolic cylinder functions of large order
NASA Astrophysics Data System (ADS)
Jones, D. S.
2006-06-01
The asymptotic behaviour of parabolic cylinder functions of large real order is considered. Various expansions in terms of elementary functions are derived. They hold uniformly for the variable in appropriate parts of the complex plane. Some of the expansions are doubly asymptotic with respect to the order and the complex variable which is an advantage for computational purposes. Error bounds are determined for the truncated versions of the asymptotic series.
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.
The parabolic concentrating collector: A tutorial
NASA Technical Reports Server (NTRS)
Truscello, V. C.
1979-01-01
A tutorial overview of point-focusing parabolic collectors is presented. Optical and thermal characteristics are discussed. Data representing typical achievable collector efficiencies are presented and the importance of balancing collector cost with concentrator quality is argued through the development of a figure of merit. Various types of two-axis tracking collectors are described. The Department of Energy program to develop these devices is briefly discussed, as are present and projected costs for these collectors.
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 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.
Design of stigmatic grazing incidence telescopes with non-parabolic primaries
NASA Technical Reports Server (NTRS)
Winkler, C. E.; Korsch, D.
1979-01-01
A two-mirror grazing-incidence telescope having a non-parabolic primary, and designed to be free of spherical aberration has been investigated. A method for determining the second surface equation is described, when the surface equation for one mirror is given. Application to grazing incidence systems such as used in X-ray and planed for EUV astronomy is discussed. Of special interest is the design of a secondary mirror when the hyperboloid of a conventional Wolter type I system is taken as the primary.
Dynamics of wave equations with moving boundary
NASA Astrophysics Data System (ADS)
Ma, To Fu; Marín-Rubio, Pedro; Surco Chuño, Christian Manuel
2017-03-01
This paper is concerned with long-time dynamics of weakly damped semilinear wave equations defined on domains with moving boundary. Since the boundary is a function of the time variable the problem is intrinsically non-autonomous. Under the hypothesis that the lateral boundary is time-like, the solution operator of the problem generates an evolution process U (t , τ) :Xτ →Xt, where Xt are time-dependent Sobolev spaces. Then, by assuming the domains are expanding, we establish the existence of minimal pullback attractors with respect to a universe of tempered sets defined by the forcing terms. Our assumptions allow nonlinear perturbations with critical growth and unbounded time-dependent external forces.
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.
Optimal Heat Collection Element Shapes for Parabolic Trough Concentrators
Bennett, C
2007-11-15
For nearly 150 years, the cross section of the heat collection tubes used at the focus of parabolic trough solar concentrators has been circular. This type of tube is obviously simple and easily fabricated, but it is not optimal. It is shown in this article that the optimal shape, assuming a perfect parabolic figure for the concentrating mirror, is instead oblong, and is approximately given by a pair of facing parabolic segments.
Parabolic trough collectors for industrial and commercial applications
Gee, R.C.
1997-06-01
Industrial Solar Technology Corporation (IST) manufactures and installs parabolic trough solar energy systems for large-scale commercial and industrial applications. Parabolic trough collectors have advanced significantly over the last fifteen years and are the most developed and widely deployed type of solar concentrator. Collector efficiency has increased, installed costs have decreased, and system reliability has improved. These positive trends have moved parabolic trough technology to commercial viability in niche markets where energy costs are high and sunlight is abundant.
Comments on ``Barut-Girardello Coherent States for the Parabolic Cylinder Functions''
NASA Astrophysics Data System (ADS)
Fakhri, H.; Dehghani, A.; Mojaveri, B.
2009-02-01
In Chenaghlou and Faizy (Int. J. Theor. Phys. 2008), the authors claim that they have constructed the Barut-Girardello coherent states for the parabolic cylinder functions. However, we point out here that by introducing these coherent states, Schrödinger was able to put forth the idea of “coherent states of the quantum harmonic oscillator” over eighty years ago. These coherent states are derived not only from the Barut-Girardello eigenvalue equation, but also from the Schrödinger and the Klauder-Perelomov approaches. Thus, contrary to their claim, the authors have not introduced new coherent states. In particular, a wide range of the parabolic cylinder functions do not form an orthonormal basis.
Thermo-electronic solar power conversion with a parabolic concentrator
NASA Astrophysics Data System (ADS)
Olukunle, Olawole C.; De, Dilip K.
2016-02-01
We consider the energy dynamics of the power generation from the sun when the solar energy is concentrated on to the emitter of a thermo-electronic converter with the help of a parabolic mirror. We use the modified Richardson-Dushman equation. The emitter cross section is assumed to be exactly equal to the focused area at a height h from the base of the mirror to prevent loss of efficiency. We report the variation of output power with solar insolation, height h, reflectivity of the mirror, and anode temperature, initially assuming that there is no space charge effect. Our methodology allows us to predict the temperature at which the anode must be cooled in order to prevent loss of efficiency of power conversion. Novel ways of tackling the space charge problem have been discussed. The space charge effect is modeled through the introduction of a parameter f (0 < f < 1) in the thermos-electron emission equation. We find that the efficiency of the power conversion depends on solar insolation, height h, apart from radii R of the concentrator aperture and emitter, and the collector material properties. We have also considered solar thermos electronic power conversion by using single atom-layer graphene as an emitter.
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.
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.
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.
Nonlinear modes in a complex parabolic potential
Zezyulin, Dmitry A.; Alfimov, Georgy L.; Konotop, Vladimir V.
2010-01-15
We report on analysis of the mode structure of a Bose-Einstein condensate loaded in a complex parabolic potential and subjected to a constant pump. Stationary solutions for the positive and negative scattering lengths are addressed. In the case of a positive scattering length and large number of atoms the ground state is described by the Thomas-Fermi distribution, whose properties in the presence of the dissipation are very different from its conservative counterpart. It is shown that for a positive scattering length only the ground state appears to be stable.
Parabolic Refined Invariants and Macdonald Polynomials
NASA Astrophysics Data System (ADS)
Chuang, Wu-yen; Diaconescu, Duiliu-Emanuel; Donagi, Ron; Pantev, Tony
2015-05-01
A string theoretic derivation is given for the conjecture of Hausel, Letellier and Rodriguez-Villegas on the cohomology of character varieties with marked points. Their formula is identified with a refined BPS expansion in the stable pair theory of a local root stack, generalizing previous work of the first two authors in collaboration with Pan. Haiman's geometric construction for Macdonald polynomials is shown to emerge naturally in this context via geometric engineering. In particular this yields a new conjectural relation between Macdonald polynomials and refined local orbifold curve counting invariants. The string theoretic approach also leads to a new spectral cover construction for parabolic Higgs bundles in terms of holomorphic symplectic orbifolds.
NASA Astrophysics Data System (ADS)
Choi, Y. S.; Huan, Zhongdan; Lui, Roger
2003-11-01
This paper consists of two parts. In the first part, we proved the global existence of weak solutions of a strongly coupled quasilinear parabolic system in Rn using weak compactness method. In the second part, we considered the electrochemistry model studied in Choi and Lui (J. Differential Equations 116 (1995) 306) where the Poisson equation governing the electric potential is replaced by a local electro-neutrality condition. In one space dimension, the equations for the model is of the form considered in the first part of this paper except that the coefficient matrix is discontinuous at places where all the charged ions vanish. We approximate the equations by nicer operators and pass to the limit to obtain global existence of weak solutions. The non-negativity of weak solutions and L2-stability of the steady-state solutions are also shown under additional hypotheses.
NASA Astrophysics Data System (ADS)
Chernov, A. V.
2015-02-01
The optimal control of a second-order semilinear elliptic diffusion-reaction equation is considered. Sufficient conditions for the convergence of the conditional gradient method are obtained without using assumptions (traditional for optimization theory) that ensure the Lipschitz continuity of the objective functional derivative. The total (over the entire set of admissible controls) preservation of solvability, a pointwise estimate of solutions, and the uniqueness of a solution to the homogeneous Dirichlet problem for a controlled elliptic equation are proved as preliminary results, which are of interest on their own.
Focusing parabolic guide for very small samples
NASA Astrophysics Data System (ADS)
Hils, T.; Boeni, P.; Stahn, J.
2004-07-01
Modern materials can often only be grown in small quantities. Therefore, neutron-scattering experiments are difficult to perform due to the low signal. In order to increase the flux at the sample position, we have developed the concept of a small focusing guide tube with parabolically shaped walls that are coated with supermirror m=3. The major advantage of parabolic focusing is that the flux maximum occurs not at the exit of the tube. It occurs at the focal point that can be several centimeters away from the exit of the tube. We show that an intensity gain of 6 can easily be obtained. Simulations using the software package McStas demonstrate that gain factors up to more than 50 can be realised on a spot size of approximately 1.2 mm diameter. For PGAA we expect flux gains of up to three orders of magnitude if multiplexing is used. We show that elliptic ballistic guides lead to flux gains of more than 6.
On the stability of steady states in a granuloma model
NASA Astrophysics Data System (ADS)
Friedman, Avner; Lam, King-Yeung
We consider a free boundary problem for a system of two semilinear parabolic equations. The system represents a simple model of granuloma, a collection of immune cells and bacteria filling a 3-dimensional domain Ω(t) which varies in time. We prove the existence of stationary spherical solutions and study their linear asymptotic stability as time increases to infinity.
Optical, Energetic and Exergetic Analyses of Parabolic Trough Collectors
NASA Astrophysics Data System (ADS)
Murat, Öztürk; Nalan Çiçek, Bezir; Nuri, Özek
2007-07-01
Parabolic trough collectors generate thermal energy from solar energy. Especially, they are very convenient for applications in high temperature solar power systems. To determine the design parameters, parabolic trough collectors must be analysed with optical analysis. In addition, thermodynamics (energy and exergy) analysis in the development of an energy efficient system must be achieved. Solar radiation passes through Earth's atmosphere until it reaches on Earth's surface and is focused from the parabolic trough collector to the tube receiver with a transparent insulated envelope. All of them constitute a complex mechanism. We investigate the geometry of parabolic trough reflector and characteristics of solar radiation to the reflecting surface through Earth's atmosphere, and calculate the collecting total energy in the receiver. The parabolic trough collector, of which design parameters are given, is analysed in regard to the energy and exergy analysis considering the meteorological specification in May, June, July and August in Isparta/Turkey, and the results are presented.
The design of parabolic cylindrical antenna with light emitting plasma
NASA Astrophysics Data System (ADS)
Zeng, Jie; Shi, Jia-ming; Liu, Yang; Zhang, Ji-kui; Li, Zhi-gang
2016-11-01
By using the electromagnetic wave reflection characteristics of the plasma, the plasma can be used to design the reflector antenna. the paper designs a metal parabolic cylindrical antenna and a plasma luminescence parabolic cylindrical antenna, and uses CST software calculating the radiative properties of them, analysising the key parameters of plasma luminescence parabolic cylindrical antenna radiation and scattered radiation resistance. Simulation results show that selecting appropriate plasma column spacing, plasma frequency, collision frequency, the plasma luminescence parabolic cylindrical antenna has the same radiation performance with metal parabolic antenna, at the same time, the RCS of plasma antenna in working and not working are smaller compared with the metal antenna, especially in plasma does not work ,the bistatic RCS reduced to a greater extent than the previous related literature design.
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.
NASA Technical Reports Server (NTRS)
Funaro, D.; Gottlieb, D.
1988-01-01
A new method to impose boundary conditions for pseudospectral approximations to hyperbolic equations is suggested. This method involves the collocation of the equation at the boundary nodes as well as satisfying boundary conditions. Stability and convergence results are proven for the Chebyshev approximation of linear scalar hyperbolic equations. The eigenvalues of this method applied to parabolic equations are shown to be real and negative.
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.
Parabolized Navier-Stokes analysis of ducted turbulent mixing problems with finite-rate chemistry
NASA Technical Reports Server (NTRS)
Sinha, N.; Dash, S. M.
1986-01-01
A hybrid implicit/explicit approach for analyzing 2D ducted turbulent mixing problems with finite-rate chemistry is presented. The approach combines a fully-implicit parabolic mixing algorithm, an explicit viscous-characteristic based shock-capturing algorithm, and linearized implicit chemical kinetic algorithm. The resultant model provides spatial marching solutions of the parabolized Navier-Stokes (PNS) equations for supersonic combustion and viscous nozzle flowfields. Specialized procedures are incorporated to deal with the near wall sublayer and with small central pockets of subsonic flow. A parabolic option is available which can be utilized in the direct or inverse mode for design applications. The ability of the model to treat shock waves and wave/mixing layer interactions is assessed via comparisons of predictions with those of well established explicit shock-capturing Euler (SCIPPY) and PNS (SCIPVIS) models. Applications to a variety of supersonic combustion flowfield problems involving tangential or moderately inclined fuel injection, and, to a viscous nozzle flow problem, are presented. This paper serves to exhibit overall capabilities of the model developed and no comparisons with supersonic combustion data are presented. Such comparisons serve mainly to validate the modeling of the turbulence and turbulence/chemical interactions and will be the subject of a future paper.
Chirped Airy-Gaussian beam in a medium with a parabolic potential
NASA Astrophysics Data System (ADS)
Zhang, Liping; Deng, Fu; Peng, Yulian; Chen, Bo; Peng, Xi; Li, Dongdong; Deng, Dongmei
2017-01-01
By solving the normalized dimensionless linear parabolic (Schrödinger-like) equations in the paraxial approximation, we can obtain the analytic solutions of the chirped Airy-Gaussian (CAiG) beam in a medium with a parabolic potential. We study the propagation properties of the finite energy CAiG beam in a parabolic potential and the influence of the distribution factor and the chirped factor on the CAiG beam. The propagation of the CAiG beam changes drastically with the distribution factor increasing: the CAiG beam tends to the chirped Airy beam when the distribution factor is very small; while as the distribution factor increases further, the CAiG beam tends to the chirped Gaussian beam. At the same time, the CAiG beam with a chirp has big changes when the chirped factor is increasing: the multi-peak structure is not obvious, the accelerated velocity and the peak intensity are larger, but the period does not change; when the CAiG beam has a quadratic chirp, the maximum intensity of the CAiG beam becomes smaller and the envelope is gradually smoother with the increasing of the chirped factor.
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
NASA Astrophysics Data System (ADS)
Nakamura, Masanori; Asada, Keiichi
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 & 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 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 ~103 r s, while the upstream trans-Alfvénic flow speed increases linearly as a function of the distance at ~102-103 r 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.
Finite-horizon optimal investment with transaction costs: A parabolic double obstacle problem
NASA Astrophysics Data System (ADS)
Dai, Min; Yi, Fahuai
This paper concerns optimal investment problem of a CRRA investor who faces proportional transaction costs and finite time horizon. From the angle of stochastic control, it is a singular control problem, whose value function is governed by a time-dependent HJB equation with gradient constraints. We reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. This enables us to make use of the well-developed theory of obstacle problem to attack the problem. The C regularity of the value function is proven and the behaviors of the free boundaries are completely characterized.
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.
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).
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1988-01-01
An abstract approximation and convergence theory for the closed-loop solution of discrete-time linear-quadratic regulator problems for parabolic systems with unbounded input is developed. Under relatively mild stabilizability and detectability assumptions, functional analytic, operator techniques are used to demonstrate the norm convergence of Galerkin-based approximations to the optimal feedback control gains. The application of the general theory to a class of abstract boundary control systems is considered. Two examples, one involving the Neumann boundary control of a one-dimensional heat equation, and the other, the vibration control of a cantilevered viscoelastic beam via shear input at the free end, are discussed.
Dynamics of strongly coupled spatially distributed logistic equations with delay
NASA Astrophysics Data System (ADS)
Kashchenko, I. S.; Kashchenko, S. A.
2015-04-01
The dynamics of a system of two logistic delay equations with spatially distributed coupling is studied. The coupling coefficient is assumed to be sufficiently large. Special nonlinear systems of parabolic equations are constructed such that the behavior of their solutions is determined in the first approximation by the dynamical properties of the original system.
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 Astrophysics Data System (ADS)
Demler, R. L.
1981-05-01
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
NASA Technical Reports Server (NTRS)
Lackner, J. R.; Graybiel, A.
1979-01-01
On the earth, or in level flight, a blindfolded subject being rotated at constant velocity about his recumbent long body axis experiences illusory orbital motion of his body in the opposite direction. By contrast, during comparable rotation in the free-fall phase of parabolic flight, no body motion is perceived and all sense of external orientation may be lost; when touch and pressure stimulation is applied to the body surface, a sense of orientation is reestablished immediately. The increased gravitoinertial force period of a parabola produces an exaggeration of the orbital motion experienced in level flight. These observations reveal an important influence of touch, pressure, and kinesthetic information on spatial orientation and provide a basis for understanding many of the postural illusions reported by astronauts in space flight.
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.
Nuclear blast resistant parabolic antenna feed means
Dumas, T. A.; Buchmeyer, S. K.; Vet, M.
1985-03-19
The aftermath of a nuclear explosion generates a large amount of heat or infrared energy. When this heat is received by a parabolic reflector type antenna, the level of heat concentrated on the focal area of the feed is very intense. The present invention utilizes a highly heat conductive ceramic plug between the splash plate at the focal area of the feed and the waveguide so that heat can be readily conducted away from the splash plate and thereby minimize operational destruction of this splash plate due to thermal overload. The heat conductor material is a ceramic which is substantially transparent to RF signals being received by, or transmitted from the waveguide of the antenna system.
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.
Microphotonic parabolic light directors fabricated by two-photon lithography
Atwater, J. H.; Spinelli, P.; Kosten, E.; Parsons, J.; Van Lare, C.; Van de Groep, J.; Garcia de Abajo, J.; Polman, A.; Atwater, H. A.
2011-10-10
We have fabricated microphotonic parabolic light directors using two-photon lithography, thin-film processing, and aperture formation by focused ion beam lithography. Optical transmission measurements through upright parabolic directors 22 μm high and 10 μm in diameter exhibit strong beam directivity with a beam divergence of 5.6°, in reasonable agreement with ray-tracing and full-field electromagnetic simulations. The results indicate the suitability of microphotonic parabolic light directors for producing collimated beams for applications in advanced solar cell and light-emitting diode designs.
A study on optical aberrations in parabolic neutron guides
NASA Astrophysics Data System (ADS)
Wang, Yu; Wang, Hongli; Liu, Yuntao; Zu, Yong; He, Linfeng; Wei, Guohai; Sun, Kai; Han, Songbai; Chen, Dongfeng
2015-06-01
It is widely believed that a neutron beam can be focused to a small spot using a parabolic guide, which will significantly improve the flux. However, researchers have also noted challenges for the neutron inhomogeneous phase space distribution in parabolic focusing guide systems. In this paper, the sources of most prominent optical aberrations, such as an inhomogeneous phase space distribution and irregular divergence distribution, are discussed, and an optimization solution is also proposed. We indicate that optimizing the parabolic guide geometrical configuration removes almost all of the aberrations and yields a considerable intensity gain factor.
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
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.
Finite Time Blowup for Parabolic Systems in Two Dimensions
NASA Astrophysics Data System (ADS)
Mooney, Connor
2017-03-01
We construct examples of finite time singularity from smooth data for linear uniformly parabolic systems in the plane. We obtain similar examples for quasilinear systems with coefficients that depend only on the solution.
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
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
Guidelines for reporting parabolic trough solar electric system performance
Price, H.W.
1997-06-01
The purpose of this activity is to develop a generic methodology which can be used to track and compare the performance of parabolic trough power plants. The approach needs to be general enough to work for all existing and future parabolic trough plant designs, provide meaningful comparisons of year to year performance, and allow for comparisons between dissimilar plant designs. The approach presented here uses the net annual system efficiency as the primary metric for evaluating the performance of parabolic trough power plants. However, given the complex nature of large parabolic trough plants, the net annual system efficiency by itself does not adequately characterize the performance of the plant. The approach taken here is to define a number of additional performance metrics which enable a more comprehensive understanding of overall plant performance.
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.
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.
Comparison of large aperture telescopes with parabolic and spherical primaries
NASA Technical Reports Server (NTRS)
Korsch, D.
1986-01-01
Quasi-Cassegrain-type four-mirror telescopes are compared to conventional two-mirror Cassegrain telescopes for use as high performance, very large aperture space telescopes. Spherical and parabolic primaries with continuous as well as segmented surfaces are considered. Imaging characteristics and misalignment sensitivities serve as the principal criteria of comparison. The evaluation shows that parabolic primaries yield superior wide-field performance, whereas spherical primaries hold distinct advantages regarding manufacturability and regarding certain alignment aspects in the case of segmentation.
Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints
Pham, H.
2002-10-01
This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation. This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate our results with several examples of stochastic volatility models popular in the financial literature.
Visually-induced tilt during parabolic flights.
Cheung, B S; Howard, I P; Money, K E
1990-01-01
A helmet-mounted visual display system was used to study visually induced sensations of self-motion (vection) about the roll, pitch and yaw axes under normal gravity condition (1g) and during the microgravity and hypergravity phases of parabolic flights aboard the NASA KC-135 aircraft. Under each gravity condition, the following parameters were investigated: (1) the subject's perceived body vertical with eyes closed and with eyes open gazing at a stationary random dot display; (2) the magnitude of sensations of body tilt with respect to the subjective vertical, while the subject viewed displays rotating about the roll, pitch and yaw axes; (3) the magnitude of vection; (4) latency of vection. All eleven subjects perceived a definite "up and down" orientation throughout the course of the flight. During the microgravity phase, the average magnitudes of perceived body tilt and self-motion increased significantly, and there was no significant difference in vection latency. These results show that there is a rapid onset of increased dependence on visual inputs for perception of self-orientation and self-motion in weightlessness, and a decreased dependence on otolithic and somatosensory graviceptive information. Anti-motion sickness drugs appear not to affect the parameters measured.
NASA Astrophysics Data System (ADS)
Adimurthi; Karthik, A.; Giacomoni, Jacques
2016-06-01
Let n ≥ 2 and Ω ⊂Rn be a bounded domain. Then by Trudinger-Moser embedding, W01,n (Ω) is embedded in an Orlicz space consisting of exponential functions. Consider the corresponding semilinear n-Laplace equation with critical or sub-critical exponential nonlinearity in a ball B (R) with dirichlet boundary condition. In this paper, we prove that under suitable growth conditions on the nonlinearity, there exists an γ0 > 0, and a corresponding R0 (γ0) > 0 such that for all 0 < R
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.
On the Aleksandrov-Bakel'man-Pucci Estimate for Some Elliptic and Parabolic Nonlinear Operators
NASA Astrophysics Data System (ADS)
Argiolas, Roberto; Charro, Fernando; Peral, Ireneo
2011-12-01
In this work we prove the Aleksandrov-Bakel'man-Pucci estimate for (possibly degenerate) nonlinear elliptic and parabolic equations of the form -div left( Fleft( nabla u(x)right) right) =fleft(xright) quad in Ω subset mathbb{R}n and ut(x,t)-div left( Fleft( nabla u(x,t)right) right) =fleft( x,tright) quad in Qsubset mathbb{R}^{n+1} for F a {fancyscript{C}^1} monotone field under some suitable conditions. Examples of applications such as the p-Laplacian and the Mean Curvature Flow are considered, as well as extensions of the general results to equations that are not in divergence form, such as the m-curvature flow.
Neutron-transport equation in a general curvelinear coordinate system
Takahashi, H
1981-01-01
Different from a fission reactor, a fusion reactor has complex geometry, such as toroidal geometry. Neutron transport equation for the toroidal coordinate system has been derived by using coordinate transformation from the cartesian coordinate. These methods require rather tedious calculations. Presented here is a simple method to formulate the neutron transport equation in the general curvelinear coordinate system. The equations for parabolic cylinder and toroidal coordinate systems are derived as an example.
An Evolution Operator Solution for a Nonlinear Beam Equation
1990-12-01
uniqueness for the parabolic problem Ug + (-A) m u+ I I- u = f (14) on RN X (0, 1). Again, certain restrictions apply. The Schr ~ dinger equation , [68:pg 823...evolution equation because of the time dependence in the definition of the operator A. He identifies conditions for the existence of a unique solution. In...The arguments for the adjoint and dissipativity are not repeated. Because of the explicit time dependence , (71) is called an evolution equation . For
A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains
NASA Astrophysics Data System (ADS)
Bonforte, Matteo; Vázquez, Juan Luis
2015-10-01
We investigate quantitative properties of the nonnegative solutions to the nonlinear fractional diffusion equation, , posed in a bounded domain, , with m > 1 for t > 0. As we use one of the most common definitions of the fractional Laplacian , 0 < s < 1, in a bounded domain with zero Dirichlet boundary conditions. We consider a general class of very weak solutions of the equation, and obtain a priori estimates in the form of smoothing effects, absolute upper bounds, lower bounds, and Harnack inequalities. We also investigate the boundary behaviour and we obtain sharp estimates from above and below. In addition, we obtain similar estimates for fractional semilinear elliptic equations. Either the standard Laplacian case s = 1 or the linear case m = 1 are recovered as limits. The method is quite general, suitable to be applied to a number of similar problems.
Decomposition of the Visible and Dark Matter in the Einstein Ring 0047-2808 by Semilinear Inversion
NASA Astrophysics Data System (ADS)
Dye, S.; Warren, S. J.
2005-04-01
We measure the mass density profile of the lens galaxy in the Einstein ring system 0047-2808 using our semilinear inversion method developed in an earlier paper. By introducing an adaptively gridded source plane, we are able to eliminate the need for regularization of the inversion. This removes the problem of a poorly defined number of degrees of freedom, encountered by inversion methods that employ regularization, and so allows a proper statistical comparison between models. We confirm previous results indicating that the source is double and that a power-law model gives a significantly better fit than the singular isothermal ellipsoid model. We measure a slope α=2.11+/-0.04. We find, furthermore, that a dual-component constant M/L baryonic+dark halo model gives a significantly better fit than the power-law model, at the 99.7% confidence level. The inner logarithmic slope of the dark halo profile is found to be 0.87+0.69-0.61 (95% CL), consistent with the predictions of cold dark matter simulations of structure formation. We determine an unevolved B-band mass-to-light ratio for the baryons (only) of 3.05+0.53-0.90h65Msolar/LBsolar (95% CL). This is the first measurement of the baryonic M/L of a single galaxy by purely gravitational lens methods. The baryons account for 65+10-18% (95% CL) of the total projected mass, or, assuming spherical symmetry, 84+12-24% (95% CL) of the total three-dimensional mass within the mean radius of 1.16" (7.5h-165 kpc) traced by the ring. Finally, at the level of >3 σ, we find that the halo mass is rounder than the baryonic distribution and that the two components are offset in orientation from one another.
First Middle East Aircraft Parabolic Flights for ISU Participant Experiments
NASA Astrophysics Data System (ADS)
Pletser, Vladimir; Frischauf, Norbert; Cohen, Dan; Foster, Matthew; Spannagel, Ruven; Szeszko, Adam; Laufer, Rene
2017-02-01
Aircraft parabolic flights are widely used throughout the world to create microgravity environment for scientific and technology research, experiment rehearsal for space missions, and for astronaut training before space flights. As part of the Space Studies Program 2016 of the International Space University summer session at the Technion - Israel Institute of Technology, Haifa, Israel, a series of aircraft parabolic flights were organized with a glider in support of departmental activities on `Artificial and Micro-gravity' within the Space Sciences Department. Five flights were organized with manoeuvres including several parabolas with 5 to 6 s of weightlessness, bank turns with acceleration up to 2 g and disorientation inducing manoeuvres. Four demonstration experiments and two experiments proposed by SSP16 participants were performed during the flights by on board operators. This paper reports on the microgravity experiments conducted during these parabolic flights, the first conducted in the Middle East for science and pedagogical experiments.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Gvelesiani, Simon; Lippoth, Friedrich; Walker, Christoph
2015-12-01
We provide sufficient and almost optimal conditions for global existence of classical solutions in parabolic Hölder spaces to quasilinear one-dimensional parabolic problems with dynamical boundary conditions.
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.
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).
The ellipse in parabolic motion: An undergraduate experiment
NASA Astrophysics Data System (ADS)
Carrillo-Bernal, M. A.; Mancera-Piña, P. E.; Cerecedo-Núñez, H. H.; Padilla-Sosa, P.; Núñez-Yépez, H. N.; Salas-Brito, A. L.
2014-04-01
We present a simple method of experimentally studying the elliptic shape of the joined apices of parabolic projectile trajectories in the undergraduate laboratory. The experimental data agrees well with theoretical results, and we find that this experiment provides an interesting twist to the venerable undergraduate experiment on projectile motion.
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.
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…
Parabolic trough solar power for competitive U.S. markets
Price, H.W.; Kistner, R.
1999-07-01
Nine parabolic trough power plants located in the California Mojave Desert represent the only commercial development of large-scale solar power plants to date. Although all nine plants continue to operate today, no new solar power plants have been completed since 190. Over the last several years, the parabolic trough industry has focused much of its efforts on international market opportunities. Although the power market in developing countries appears to offer a number of opportunities for parabolic trough technologies due to high growth and the availability of special financial incentives for renewables, these markets are also plagued with many difficulties for developers. In recent years, there has been some renewed interest in the U.S. domestic power market as a results of an emerging green market and green pricing incentives. Unfortunately, many of these market opportunities and incentives focus on smaller, more modular technologies (such as photovoltaics or wind power), and as a result they tend to exclude or are of minimum long-term benefit to large-scale concentrating solar power technologies. This paper looks at what is necessary for large-scale parabolic trough solar power plants to compete with state-of-the-art fossil power technology in a competitive US power market.
Parabolic Trough Solar Power for Competitive U.S. Markets
Henry W. Price
1998-11-01
Nine parabolic trough power plants located in the California Mojave Desert represent the only commercial development of large-scale solar power plants to date. Although all nine plants continue to operate today, no new solar power plants have been completed since 1990. Over the last several years, the parabolic trough industry has focused much of its efforts on international market opportunities. Although the power market in developing countries appears to offer a number of opportunities for parabolic trough technologies due to high growth and the availability of special financial incentives for renewables, these markets are also plagued with many difficulties for developers. In recent years, there has been some renewed interest in the U.S. domestic power market as a result of an emerging green market and green pricing incentives. Unfortunately, many of these market opportunities and incentives focus on smaller, more modular technologies (such as photovoltaics or wind power), and as a result they tend to exclude or are of minimum long-term benefit to large-scale concentrating solar power technologies. This paper looks at what is necessary for large-scale parabolic trough solar power plants to compete with state-of-the-art fossil power technology in a competitive U.S. power market.
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.
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.
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.
Solar Thermal Power Plants with Parabolic-Trough Collectors
NASA Astrophysics Data System (ADS)
Zarza, E.; Valenzuela, L.; León, J.
2004-12-01
Parabolic-trough collectors (PTC) are solar concentrating devices suitable to work in the 150°C- 400°C temperature range. Power plants based on this type of solar collectors are a very efficient way to produce electricity with solar energy. At present, there are eight commercial solar plants (called SEGS-II, III,.. IX) producing electricity with parabolic-trough collectors and their total output power is 340 MW. Though all SEGS plants currently in operation use thermal oil as a heat transfer fluid between the solar field and the power block, direct steam generation (DSG) in the receiver tubes is a promising option to reduce the cost of electricity produced with parabolic- trough power plants. Most of technical uncertainties associated to the DSG technology were studied and solved in the DISS project and it is expected that this new technology will be commercially available in a short term. In Spain, the Royal Decree No. 436/204 (March 12th , 2004) has defined a premium of 0,18€/kWh for the electricity produced by solar thermal power plants, thus promoting the installation of solar thermal power plants up to a limit of 200 MW. Due to the current legal and financial framework defined in Spain, several projects to install commercial solar power plants with parabolic-trough collectors are currently underway.
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
Golian, Y.; Dorranian, D.; Aslaninejad, M.
2016-01-15
A model for the interaction of charged particle beams and plasma for a linear wakefield generation in a parabolic plasma channel is presented. The density profile has the maximum on the axis. A Gaussian proton beam is employed to excite the plasma wakefield in the channel. We have built a thorough analytical model and solved the governing equations for the wakefield acceleration of a charged particle beam. The longitudinal and radial wakefields are expressed by Whittaker functions, and for certain parameters of plasma and the beam, their behaviours in longitudinal and radial directions are investigated. It is observed that the radial electric field generated by the bunch increases with the distance behind the bunch.
Fast Multilevel Solvers for a Class of Discrete Fourth Order Parabolic Problems
Zheng, Bin; Chen, Luoping; Hu, Xiaozhe; Chen, Long; Nochetto, Ricardo H.; Xu, Jinchao
2016-03-05
In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to construct efficient preconditioners. We provide eigenvalue analysis for the preconditioned system and estimate the convergence rate of the preconditioned GMRes method. Furthermore, we show that these preconditioners only need to be solved inexactly by optimal multigrid algorithms. Our numerical examples indicate that the proposed preconditioners are very efficient and robust with respect to both discretization parameters and diffusion coefficients. We also investigate the performance of multigrid algorithms with either collective smoothers or distributive smoothers when solving the preconditioner systems.
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.
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.
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.
IR spectrometer using 90-degree off-axis parabolic mirrors
NASA Astrophysics Data System (ADS)
Malone, Robert M.; Dolan, Daniel H.; Hacking, Richard G.; McKenna, Ian J.
2008-08-01
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 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…
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.
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.
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.
Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.
Talaei, Behzad; Jagannathan, Sarangapani; Singler, John
2017-03-02
This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.
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.
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.
'Parabolic' trapped modes and steered Dirac cones in platonic crystals.
McPhedran, R C; Movchan, A B; Movchan, N V; Brun, M; Smith, M J A
2015-05-08
This paper discusses the properties of flexural waves governed by the biharmonic operator, and propagating in a thin plate pinned at doubly periodic sets of points. The emphases are on the design of dispersion surfaces having the Dirac cone topology, and on the related topic of trapped modes in plates for a finite set (cluster) of pinned points. The Dirac cone topologies we exhibit have at least two cones touching at a point in the reciprocal lattice, augmented by another band passing through the point. We show that these Dirac cones can be steered along symmetry lines in the Brillouin zone by varying the aspect ratio of rectangular lattices of pins, and that, as the cones are moved, the involved band surfaces tilt. We link Dirac points with a parabolic profile in their neighbourhood, and the characteristic of this parabolic profile decides the direction of propagation of the trapped mode in finite clusters.
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.
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.
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.
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.
Irrigation market for solar thermal parabolic dish systems
NASA Astrophysics Data System (ADS)
Habib-Agahi, H.; Jones, S. C.
1981-09-01
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.
Performance contracting for parabolic trough solar thermal systems
Brown, H.; Hewett, R.; Walker, A.; Gee, R.; May, K.
1997-12-31
Several applications of solar energy have proven viable in the energy marketplace, due to competitive technology and economic performance. One example is the parabolic trough solar collectors, which use focused solar energy to maximize efficiency and reduce material use in construction. Technical improvements are complemented by new business practices to make parabolic trough solar thermal systems technically and economically viable in an ever widening range of applications. Technical developments in materials and fabrication techniques reduce production cost and expand applications from swimming pool heating and service hot water, to higher-temperature applications such as absorption cooling and process steam. Simultaneously, new financing mechanisms such as a recently awarded US Department of Energy (DOE) Federal Energy Management Program (FEMP) indefinite quantity Energy Savings Performance Contract (Super ESPC) facilitate and streamline implementation of the technology in federal facilities such as prisons and military bases.
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.
Second-generation parabolic trough solar energy systems optimization analysis
NASA Astrophysics Data System (ADS)
Peters, R. R.
1982-04-01
In the near future high-efficiency, low-cost, parabolic trough collectors will probably become available. The economic feasibility of these parabolic trough solar-energy systems is affected by many parameters which include component cost, load shape, fraction of the load supplied by solar energy, average temperature of the collector field and its axis of rotation, and for solar Rankine cogeneration systems, the electrical-to-thermal energy output ratio. The sensitivity of economic feasibility and system design to changes in these and other relevant parameters is discussed. System design and economics generally were found to be sensitive to component cost. They were also found to be quite sensitive to some of the other parameters in restricted ranges.
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.
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.
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.
Evolution of laser pulse shape in a parabolic plasma channel
NASA Astrophysics Data System (ADS)
Kaur, M.; Gupta, D. N.; Suk, H.
2017-01-01
During high-intensity laser propagation in a plasma, the group velocity of a laser pulse is subjected to change with the laser intensity due to alteration in refractive index associated with the variation of the nonlinear plasma density. The pulse front sharpened while the back of the pulse broadened due to difference in the group velocity at different parts of the laser pulse. Thus the distortion in the shape of the laser pulse is expected. We present 2D particle-in-cell simulations demonstrating the controlling the shape distortion of a Gaussian laser pulse using a parabolic plasma channel. We show the results of the intensity distribution of laser pulse in a plasma with and without a plasma channel. It has been observed that the plasma channel helps in controlling the laser pulse shape distortion. The understanding of evolution of laser pulse shape may be crucial while applying the parabolic plasma channel for guiding the laser pulse in plasma based accelerators.
Configuration selection study for isolated loads using parabolic dish modules
NASA Technical Reports Server (NTRS)
Revere, W.; Bowyer, J.; Fujita, T.; Awaya, H.
1981-01-01
A configuration tradeoff study has been conducted to determine optimum solar thermal parabolic dish power systems for isolated load applications. The specific application of an essentially constant power demand as required for MX missile shelters is treated. Supplying a continuous level of power with high reliability is shown to require a power system comprising modular parabolic dish power units where the heat engines of the modular power units can be driven by fossil fuels as well as solar-derived heat. Since constraints on reliability result in the provision of a power generating capability that exceeds the constant demand level, efficient utilization of the power system requires battery storage. Tradeoffs regarding the optimum size of storage are investigated as a function of the number of power modules and the cost of the fossil fuel which is used to meet the demand when insolation is unavailable and storage is depleted.
Configuration selection study for isolated loads using parabolic dish modules
NASA Technical Reports Server (NTRS)
Revere, W.; Bowyer, J.; Fujita, T.; Awaya, H.
1982-01-01
A configuration tradeoff study was conducted to determine optimum solar thermal parabolic dish power systems for isolated load applications. The specific application of an essentially constant power demand as required for MX missile shelters is treated. Supplying a continuous level of power with high reliability is shown to require a power system comprising modular parabolic dish power units where the heat engines of the modular power units can be driven by fossil fuels as well as solar-derived heat. Since constraints on reliability result in the provision of a power generating capability that exceeds the constant demand level, efficient utilization of the power system requires battery storage. Tradeoffs regarding the optimum size of storage are investigated as a function of the number of power modules and the cost of the fossil fuel.
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.
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
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.
Radiative Heat Transfer During Atmosphere Entry at Parabolic Velocity
NASA Technical Reports Server (NTRS)
Yoshikawa, Kenneth K.; Wick, Bradford H.
1961-01-01
Stagnation point radiative heating rates for manned vehicles entering the earth's atmosphere at parabolic velocity are presented and compared with corresponding laminar convective heating rates. The calculations were made for both nonlifting and lifting entry trajectories for vehicles of varying nose radius, weight-to-area ratio, and drag. It is concluded from the results presented that radiative heating will be important for the entry conditions considered.
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.
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.
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.
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.
Circulatory filling pressures during transient microgravity induced by parabolic flight.
Latham, R D; Fanton, J W; White, C D; Vernalis, M 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 conditions. The result is an increase in blood volume in the thoracic and cardiac chambers. This increase in central volume shift should result in an increase in central atrial filling pressures. However, experimental data has been somewhat contradictory and nonconclusive to date. Early investigations of peripheral venous pressure and estimates of central venous pressure (CVP) from these data did not show an increase in CVP in the microgravity condition. However, CVP recorded in human volunteers during the parabolic flight by Norsk revealed an increase in CVP during the microgravity state. On the June 1991 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 subjects had increased CVP recordings and two other subjects had decreased CVP measurements. In April 1991, our laboratory performed parabolic flight studies in several chronic-instrumented baboon subjects. It was again noted that centrally recorded right atrial pressure varied with exposure to microgravity, some animals having an increase and others having a decrease. Thus, data presently available has demonstrated a variable response in the mechanism not clearly defined. In April 1992, we determined a test hypothesis relating the possible mechanism of these variable pressure responses to venous pressure-volume relationships.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Ungan, F.; Martínez-Orozco, J. C.; Restrepo, R. L.; Mora-Ramos, M. E.; Kasapoglu, E.; Duque, C. A.
2015-05-01
The effects of electric and magnetic fields on the nonlinear optical rectification and second harmonic generation coefficients related with intersubband transitions in a semi-parabolic quantum well under intense laser field are theoretically studied. The energy levels and corresponding wave functions are obtained by solving the conduction band Schrödinger-like equation in the parabolic approximation and the envelope function approach. Numerical calculations are presented for a typical GaAs/Ga1-xAlxAs quantum well. The results show that both the non-resonant intense laser field and the static external fields have significant influences on the magnitude and resonant peak energy positions of the coefficients under study.
An implicit upwind parabolized Navier-Stokes code for chemically nonequilibrium flows
NASA Astrophysics Data System (ADS)
Chen, Bing; Wang, Li; Xu, Xu
2013-02-01
The previously developed single-sweep parabolized Navier-Stokes (SSPNS) space marching code for ideal gas flows has been extended to compute chemically nonequilibrium flows. In the code, the strongly coupled set of gas dynamics, species conservation, and turbulence equations is integrated with the implicit lower-upper symmetric Gauss-Seidel (LU-SGS) method in the streamwise direction in a space marching manner. The AUSMPW+ scheme is used to calculate the inviscid fluxes in the crossflow direction, while the conventional central scheme for the viscous fluxes. The k- g two-equation turbulence model is used. The revised SSPNS code is validated by computing the Burrows-Kurkov non-premixed H2/air supersonic combustion flows, premixed H2/air hypersonic combustion flows in a three-dimensional duct with a 15° compression ramp, as well as the hypersonic laminar chemically nonequilibrium air flows around two 10° half-angle cones. The results of these calculations are in good agreement with those of experiments, NASA UPS or Prabhu's PNS codes. It can be concluded that the SSPNS code is highly efficient for steady supersonic/hypersonic chemically reaction flows when there is no large streamwise separation.
Heavy-particle collisions and quantum optics: The parabolic noncrossing model
Nesbitt, B.S.; Crothers, D.S.; ORourke, S.F.; Berman, P.R.
1997-08-01
The problem of deriving analytic formulas for transition probabilities in two-level systems is studied. The two-level systems are described by a pair of first-order differential equations coupled by a time-dependent potential. One such model is given by da{sub m}/dt={minus}i{beta}f(t)a{sub n}e{sup ({minus}1){sup n}i{alpha}t} (m,n=1,2; m{ne}/n), which describes certain types of ion-atom collisions and some quantum-optics two-level problems. It will be shown that the correct approach in solving the coupled equations is to adopt a Zwaan-Stueckelberg phase-integral analysis of the four-transition-point problem based on the parabolic noncrossing model of Crothers [J. Phys. B {bold 9}, 635 (1976)]. Alternatively, one may obtain an approximation by employing adiabatic perturbation theory, but such an approach can at best provide only weak-coupling solutions and can never guarantee unitarity in the probability amplitudes. The advantage of the phase-integral method is that it produces a strong-coupling approximation by embracing the appropriate asymptotic expansions for cylinder functions of large order and argument [D. S. F. Crothers, J. Phys. A {bold 5}, 1680 (1972)] and it also ensures analyticity, unitarity, and symmetry. {copyright} {ital 1997} {ital The American Physical Society}
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.
Far-Field Boundary Conditions in Numerical Solutions of the Navier-Stokes Equations.
2014-09-26
nonlinear system of mixed parabolic- hyperbolic type in two space dimensions and time, with four independent variables must be solved in an exterior...conditions. * III THE NAVIER-STOKES EQUATIONS AND CHARACTERISTIC VARIABLES : We now begin our discussion of the equations of gas dynamics. We will neglect...8217 Far-Field Boundary Conditions in Numerical Solutions of the Navier-Stokes Equations L°O * (. P.J. McKenna LA. DTIC * E.LECTE Final Report AFOSR Grant
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.
Dynamics of the logistic delay equation with a large spatially distributed control coefficient
NASA Astrophysics Data System (ADS)
Kashchenko, I. S.; Kashchenko, S. A.
2014-05-01
The local dynamics of the logistic delay equation with a large spatially distributed control coefficient is asymptotically studied. The basic bifurcation scenarios are analyzed depending on the relations between the parameters of the equation. It is shown that the equilibrium states can lose stability even for asymptotically small values of the delay parameter. The corresponding critical cases can have an infinite dimension. Special nonlinear parabolic equations are constructed whose nonlocal dynamics determine the local behavior of solutions to the original boundary value problem.
1991-11-20
3 1M. Spivack , "Accuracy of the Moments from Simulation of Waves in Random Media," J. Opt Soc Am A 7, 790-793 (1990). 32D. Rouseff and R. P. Porter...34Anomalous Microwave Propagation through Atmospheric Ducts," Johns Hopkins APL Tech. Dig. 4, 12-26 (1983). 31M. Spivack , "Accuracy of the Moments from
1997-03-01
uiiy a R +1% (b ~H= 2%,(c 6R ±%.On extpae: d) R1= +% () RH.±...... 33....... (d) 2 -.. ..... .. .. . . .. . ...... .. ....0~~.. 20..... 406 0.0.2 10...When a surface evaporation duct is present, height calculations become much more critical since the vertical gradient of refractivity is 44 F ...sE RE-4 I l4 . .~V / r A DAWE REF HM RE 1BAi 4#14 5SE REF 19 R 124 Ht1 :,4 RE L EV=: 0. 5"I DEG.J = t.5 I~ .’ __o_ _..._ _ _ _ __.._:_ 124.nmi.223
On a Fully Nonlinear Parabolic Equation and the Asymptotic Behaviour of its Solutions
1981-10-01
151 J. I. Dias. Propiedades cualitativas do ciertos problemes parabolicog no lineales: Una clasificacion par& los modelos de difusion del calor...Memory no. XIV of the Real Aced. Ciencias , Madrid (1980). (161 G. Duvaut and J. L. Lions. Lea Inequatione en Mecanique et en Physique. Dunod, Paris
2006-05-31
to the Displacement Vector r u ........... 124 8. SUMMARY AND FUTURE TRENDS...example, away from the ocean bottom and towards the air-sea interface). Denote the two-dimensional vector transverse to the range by ( ),TR y z= e. The...speed of light are set equal to one) the reference wave number 0k becomes the rest mass, time takes the place of the range x , the transverse space is
1991-05-01
3 3. Raytrace diagram for a transmitter at 25 meters (in) in a 100-m surface-based duct resulting from an elevated layer...4 4. Raytrace diagram for a transmitter at 25 m, standard atmosphere conditions ........ 5 5. M-profile for a typical evaporation...within the last decade) that the radar community has applied the PE method to tropospheric radiowave propagation [5-81. The importance of the split
Recent Progress in the Development and Application of the Parabolic Equation
1984-05-07
Z2 _ 2- (35) Using Eq. (28) we fina that the leaoing term (1) has the form ’ 2 = ikon n (36)k r )’ 0 As with the farfiela approximation, a...un,2 + (i/k )(p1 )( 2 u) / 2 2 2 n+ 2 Ikon +l)(P2 - 2)(6~) I2il .. m Finally, the average of these two yields the Crank-Nicolson difference
On a Nonlinear Degenerate Parabolic Equation in Infiltration or Evaporation through a Porous Medium.
1983-04-01
generalized solutions. Work Unit Number 1 (Applied Analysis) (1) Facultad de Matematicas, Universidad Complutense de Madrid, SPAIN (2) Computer and Automation...write. 0 = + Then we obtain (1.1) as div aoe rde - €e -i (0(8) grad 0) + - K(8) where (1.2) D(e) - K(e).- (e) (i) Facultai de Matematicas, Universidad ... Complutense de Madrid, SPAIN (2) Computer and Automation Institute of the Hungarian Academy of S1cienoes, Budapest, HUNGARY. (’) Partalaly sponsored by
3-D Acoustic Scattering from 2-D Rough Surfaces Using A Parabolic Equation Model
2013-12-01
acoustic propagation signals, especially at mid- frequencies and higher (e.g., acoustic communications systems). For many years, the effects of rough...of the effect of surface scattering on 3-D propagation , which is critical in evaluating the variability in underwater acoustic propagation . Results...14. SUBJECT TERMS Acoustic Propagation , Acoustic Scattering, Sea Surface Perturbations, Split- Step Fourier Algorithm, Finite Difference Algorithm
Evolution of basic equations for nearshore wave field
ISOBE, Masahiko
2013-01-01
In this paper, a systematic, overall view of theories for periodic waves of permanent form, such as Stokes and cnoidal waves, is described first with their validity ranges. To deal with random waves, a method for estimating directional spectra is given. Then, various wave equations are introduced according to the assumptions included in their derivations. The mild-slope equation is derived for combined refraction and diffraction of linear periodic waves. Various parabolic approximations and time-dependent forms are proposed to include randomness and nonlinearity of waves as well as to simplify numerical calculation. Boussinesq equations are the equations developed for calculating nonlinear wave transformations in shallow water. Nonlinear mild-slope equations are derived as a set of wave equations to predict transformation of nonlinear random waves in the nearshore region. Finally, wave equations are classified systematically for a clear theoretical understanding and appropriate selection for specific applications. PMID:23318680
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.
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.
Dexterous Manipulation in Microgravity in Parabolic Flights and on ISS
NASA Astrophysics Data System (ADS)
Pletser, V.; Sundblad, P.; Thonnard, J.-L.; Lefevre, P.; McIntyre, J.; Kassel, R.; Derkinderen, W.; Penta, M.; Andre, T.
It has been shown that during exposure to microgravity in parabolic flights the control of interaction forces when manipulating an object adapts partially to the lack of gravity, yet evidence indicates that anticipation of gravity's effects persists in the short term. The motivation for these experiments to be performed in long-duration space flight is to understand how the central nervous system adapts to an environment without gravity and what will be the consequences of long-term adaptation when an individual returns to a normal (Earth) or partial (Moon or Mars) gravitational field. The experiment “Dexterous Manipulation in Microgravity” (DEX) will target specific questions about the effects of gravity on dexterous manipulation, questions that cannot be addressed in the normal terrestrial environment. Some of the scientific questions have already been studied since nearly ten years and will continue to be addressed in experiments conducted in parabolic flights, during which it will be examined how the nervous system copes with repeated transitions between different gravitational environments. Results from these experiments provide initial data about short-term adaptation to 0g. The experiments proposed for ISS draw from these short-term precursor experiments, but will emphasize long-term adaptation of sensorimotor processes to 0g and re-adaptation to 1g. A first conceptual definition phase of a DEX instrument has been completed under an ESA contract and is now ready to enter into the design and development phase in view of a launch on ISS in the 2013-2014 timeframe. In this paper, the science background will be recalled and several experiments performed during parabolic flights will be presented, showing how these early breadboards testing in microgravity have helped to refine the DEX conceptual design and how it could be used on ISS.
The well-posedness of the Kuramoto-Sivashinsky equation
NASA Technical Reports Server (NTRS)
Tadmor, E.
1984-01-01
The Kuramoto-Sivashinsky equation arises in a variety of applications, among which are modeling reaction diffusion systems, flame propagation and viscous flow problems. It is considered here, as a prototype to the larger class of generalized Burgers equations: those consist of a quadratic nonlinearity and an arbitrary linear parabolic part. It is shown that such equations are well posed, thus admitting a unique smooth solution, continuously dependent on its initial data. As an attractive alternative to standard energy methods, existence and stability are derived in this case, by patching in the large short time solutions without loss of derivatives.
Limits of Femtosecond Fiber Amplification by Parabolic Pre-Shaping
Fu, Walter; Tang, Yuxing; McComb, Timothy S.; Lowder, Tyson L.; Wise, Frank W.
2017-01-01
We explore parabolic pre-shaping as a means of generating and amplifying ultrashort pulses. We develop a theoretical framework for modeling the technique and use its conclusions to design a femtosecond fiber amplifier. Starting from 9 ps pulses, we obtain 4.3 μJ, nearly transform-limited pulses 275 fs in duration, simultaneously achieving over 40 dB gain and 33-fold compression. Finally, we show that this amplification scheme is limited by Raman scattering, and outline a method by which the pulse duration and energy may be further improved and tailored for a given application. PMID:28331242
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.
Fuzzy control of parabolic antenna with backlash compensation
NASA Astrophysics Data System (ADS)
Ahmed, Mohammed; Noor, Samsul Bahari B. Mohd
2015-05-01
A fuzzy logic based controller (FLC) was proposed for position control of a parabolic dish antenna system with the major aim of eradicating the effect backlash disturbance which may be present in the system. The disturbance is nonlinear and is capable of generating steady state positional errors. Simulation results obtained using SIMULINK/MATLAB 2012a were compared with those obtained when the controller was proportional-derivative controller (PDC). The fuzzy controller portrays that it has the capability of reducing the noise due to backlash and possibly others more than the proportional-derivative controller.
Scattering Parabolic Solutions for the Spatial N-Centre Problem
NASA Astrophysics Data System (ADS)
Boscaggin, Alberto; Dambrosio, Walter; Terracini, Susanna
2017-03-01
For the N-centre problem in the three dimensional space, {ddot{x}} = -sum_{i=1}N m_i (x-c_i)/\\vert x - c_i \\vert^{α+2}, qquad x in R^3 {setminus} {c_1,ldots,c_N}, where {N ≥q 2}, {m_i > 0} and {α in [1,2)}, we prove the existence of entire parabolic trajectories having prescribed asymptotic directions. The proof relies on a variational argument of min-max type. Morse index estimates and regularization techniques are used in order to rule out the possible occurrence of collisions.
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.
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.
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),
Simulation of point light concentration with parabolic trough collector
NASA Astrophysics Data System (ADS)
Danylyuk, Andriy; Zettl, Marcus; Lynass, Mark
2010-08-01
As the amount of solar generated energy usage increases worldwide, researches are turning to more advanced methods to increase collection efficiencies and drive down system costs. In this paper, four different optical system designs for solar concentrator applications are discussed. Each of the designs studied utilizes a parabolic trough optical element. The use of the parabolic trough in conjunction with a secondary optical component eliminates the need for expensive complicated 2-axis tracking, whilst still allowing the precise point focus normally only possible with more complex paraboloid systems. The result is an optical system, which offers all the advantages of a linear focus geometry combined with the possibility to utilize point focus concentration. The results were obtained using photometric geometrical ray tracing methods. Ideal surface simulations were initially used to separate surface from geometrical loss contributions. Later, more realistic simulations, including surface and reflectivity data of typical manufacturing methods and materials, were used to compare optical output power densities and system losses. For the systems studied, the minimum and maximum optical efficiencies obtained were 76.73% and 81% respectively. The AM 1.5 solar spectrum power densities in the absorption plane ranged from 50 to 195.8Wm-2.
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.
Altered osteoblast structure and function in parabolic flight
NASA Astrophysics Data System (ADS)
Zhong-Quan, Dai; Ying-Hui, Li; Fen, Yang; Bai, Ding; Ying-Jun, Tan
Introduction Bone loss has a significant impact on astronauts during spaceflight being one of the main obstacles preventing interplanetary missions However the exact mechanism is not well understood In the present study we investigated the effects of acute gravitational changes generated by parabolic flight on the structure and function of osteoblasts ROS17 2 8 carried by airbus A300 Methods The alteration of microfilament cytoskeleton was observed by the Texas red conjugated Phalloidin and Alexa Fluor 488 conjugated DNase I immunofluorescence stain ALP activity and expression COL1A1 expression osteocalcin secrete which presenting the osteoblast function were detected by modified calcium and cobalt method RT-PCR and radioimmunity methods respectively Results The changed gravity induced the reorganization of microfilament cytoskeleton of osteoblast After 3 hours parabolic flight F-actin of osteoblast cytoskeleton became more thickness and directivity whereas G-actin reduced and relatively concentrated at the edge of nucleus observed by confocal fluorescence microscopy This phenomenon is identical with structure alternation observed in hypergravity but the osteoblast function decrease The excretion of osteocalcin the activity and mRNA expression of ALP decrease but the COL1A1 expression has no changes These results were similar to the changes in simulated or real microgravity Conclusion Above results suggest that short time gravity alternative change induce osteoblast structure and function
Thermal storage requirements for parabolic dish solar power plants
NASA Technical Reports Server (NTRS)
Wen, L.; Steele, H.
1980-01-01
The cost effectiveness of a high temperature thermal storage system is investigated for a representative parabolic dish solar power plant. The plant supplies electrical power in accordance with a specific, seasonally varying demand profile. The solar power received by the plant is supplemented by power from fuel combustion. The cost of electricity generated by the solar power plant is calculated, using the cost of mass-producible subsystems (specifically, parabolic dishes, receivers, and power conversion units) now being designed for this type of solar plant. The trade-off between fuel and thermal storage is derived in terms of storage effectiveness, the cost of storage devices, and the cost of fuel. Thermal storage requirements, such as storage capacity, storage effectiveness, and storage cost are established based on the cost of fuel and the overall objective of minimizing the cost of the electricity produced by the system. As the cost of fuel increases at a rate faster than general inflation, thermal storage systems in the $40 to $70/kWthr range could become cost effective in the near future.
Innovative design of parabolic reflector light guiding structure
NASA Astrophysics Data System (ADS)
Whang, Allen J.; Tso, Chun-Hsien; Chen, Yi-Yung
2008-02-01
Due to the idea of everlasting green architecture, it is of increasing importance to guild natural light into indoors. The advantages are multifold - to have better color rendering index, excellent energy savings from environments viewpoints and make humans more healthy, etc. Our search is to design an innovative structure, to convert outdoor sun light impinges on larger surfaces, into near linear light beam sources, later convert this light beam into near point sources which enters the indoor spaces then can be used as lighting sources indoors. We are not involved with the opto-electrical transformation, to the guild light into to the building, to perform the illumination, as well as the imaging function. Because non-imaging optics, well known for apply to the solar concentrators, that can use non-imaging structures to fulfill our needs, which can also be used as energy collectors in solar energy devices. Here, we have designed a pair of large and small parabolic reflector, which can be used to collect daylight and change area from large to small. Then we make a light-guide system that is been designed by us use of this parabolic reflector to guide the collection light, can pick up the performance for large surface source change to near linear source and a larger collection area.
A parabolic velocity-decomposition method for wind turbines
NASA Astrophysics Data System (ADS)
Mittal, Anshul; Briley, W. Roger; Sreenivas, Kidambi; Taylor, Lafayette K.
2017-02-01
An economical parabolized Navier-Stokes approximation for steady incompressible flow is combined with a compatible wind turbine model to simulate wind turbine flows, both upstream of the turbine and in downstream wake regions. The inviscid parabolizing approximation is based on a Helmholtz decomposition of the secondary velocity vector and physical order-of-magnitude estimates, rather than an axial pressure gradient approximation. The wind turbine is modeled by distributed source-term forces incorporating time-averaged aerodynamic forces generated by a blade-element momentum turbine model. A solution algorithm is given whose dependent variables are streamwise velocity, streamwise vorticity, and pressure, with secondary velocity determined by two-dimensional scalar and vector potentials. In addition to laminar and turbulent boundary-layer test cases, solutions for a streamwise vortex-convection test problem are assessed by mesh refinement and comparison with Navier-Stokes solutions using the same grid. Computed results for a single turbine and a three-turbine array are presented using the NREL offshore 5-MW baseline wind turbine. These are also compared with an unsteady Reynolds-averaged Navier-Stokes solution computed with full rotor resolution. On balance, the agreement in turbine wake predictions for these test cases is very encouraging given the substantial differences in physical modeling fidelity and computer resources required.
Spectral methods for time dependent partial differential equations
NASA Technical Reports Server (NTRS)
Gottlieb, D.; Turkel, E.
1983-01-01
The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.
On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations
NASA Astrophysics Data System (ADS)
Glatt-Holtz, Nathan; Mattingly, Jonathan C.; Richards, Geordie
2017-02-01
We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart possesses a finite number of determining modes. Examples exhibiting parabolic and hyperbolic structure are studied in detail. In the later situation we also present a simple framework for establishing the existence of invariant measures when the usual approach relying on the Krylov-Bogolyubov procedure and compactness fails.
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.
NASA Astrophysics Data System (ADS)
Prentis, Jeffrey J.
1996-05-01
One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.
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.
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.
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.
Singh, Arvinder E-mail: naveens222@rediffmail.com; Gupta, Naveen E-mail: naveens222@rediffmail.com
2015-01-15
This paper presents an investigation of relativistic self-focusing effect of a q-Gaussian laser beam on second harmonic generation in a preformed parabolic plasma channel. An expression has been derived for density perturbation associated with the plasma wave excited by the laser beam. This in turn acts as a source of second harmonic generation. The moment theory approach has been used to derive a differential equation that governs the evolution of spot size of the laser beam with the distance of propagation. The detailed effects of intensity distribution deviation from Gaussian distribution, intensity of laser beam, density, and depth of the channel have been studied on self-focusing as well as on second harmonic generation.
Novel second-stage solar concentrator for parabolic troughs
NASA Astrophysics Data System (ADS)
Collares-Pereira, Manuel; Mendes, Joao F.
1995-08-01
Conventional parabolic troughs can be combined with second stage concentrators (SSC), to increase temperature and pressure inside the absorber, making possible the direct production of steam, improving substantially the overall system efficiency and leading to a new generation of distributed solar power plants. To attain this objective, research is needed at the optical, thermodynamic, system control, and engineering levels. In what concerns the receiver of such a system, different practical solutions have been proposed recently and in the past for the geometry of the second stage concentrator: CPC type and others. In this work we discuss these solutions and we propose a new one, 100% efficient in energy collection while reaching a total concentration ratio which is almost 65% of the thermodynamic limit. This SSC has an asymmetric elliptical geometry, rendering possible a smooth solution for the reflectors while maintaining a reasonable size for the receiver.
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.
Shock Analysis of Sentinel-3 SLSTR Parabolic Mirror Assembly
NASA Astrophysics Data System (ADS)
Braun, Benjamin; Kiel, Daniel
2014-06-01
This paper presents the different steps that have been undertaken to demonstrate the successful shock qualification of the Parabolic Mirror Assembly (PMA) in the frame of the Sentinel-3 SLSTR development. The unit has failed the first qualification shock test in terms of shift of natural frequencies and optical alignment. The objectives of the subsequent analyses are:- to correlate the finite element model with the PMA shock test on unit level,- to determine the interface loads between different parts of the PMA assembly for the PMA shock test on unit level,- to assess the PMA interface loads induced by the instrument level shock test,- to derive a reduced shock input spectrum for the PMA shock test on unit level with respect to a second qualification test.
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.
Intracranial pressure increases during weightlessness: A parabolic flights study
NASA Astrophysics Data System (ADS)
Denise, P.; Normand, H.; Buzer, L.; Duretete, A.; Avan, P.
2005-08-01
The fluid shift induced by weightlessness likely induces an elevated intracranial pressure (ICP). This factor may contribute to space adaptation syndrome (SAS). Recently, it has been shown that ICP can be monitored every few seconds non invasively by otoacoustic emissions (OAE). The OAE of 6 subjects were measured along the course of parabolic flights aboard the zero-gravity A300 Airbus. Built-in noise rejection and signal processing techniques enabled valid OAE signals to be collected and analyzed online in 4 of 6 subjects. On average, the phase of 1 kHz- OAE rotated by -41° from 1 to 1.8 g, and by +78.7° at 0 g relative to 1 g. From reference invasive ICP measurements in a control group of neurosurgery patients, it is possible to infer that ICP increased by about 34 mmHg in transient weightlessness.
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.
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
Multigrid methods for parabolic distributed optimal control problems
NASA Astrophysics Data System (ADS)
Borzì, Alfio
2003-08-01
Multigrid schemes that solve parabolic distributed optimality systems discretized by finite differences are investigated. Accuracy properties of finite difference approximation are discussed and validated. Two multigrid methods are considered which are based on a robust relaxation technique and use two different coarsening strategies: semicoarsening and standard coarsening. The resulting multigrid algorithms show robustness with respect to changes of the value of [nu], the weight of the cost of the control, is sufficiently small. Fourier mode analysis is used to investigate the dependence of the linear twogrid convergence factor on [nu] and on the discretization parameters. Results of numerical experiments are reported that demonstrate sharpness of Fourier analysis estimates. A multigrid algorithm that solves optimal control problems with box constraints on the control is considered.
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.
Electronic Nose Functionality for Breath Gas Analysis during Parabolic Flight
NASA Astrophysics Data System (ADS)
Dolch, Michael E.; Hummel, Thomas; Fetter, Viktor; Helwig, Andreas; Lenic, Joachim; Moukhamedieva, Lana; Tsarkow, Dimitrij; Chouker, Alexander; Schelling, Gustav
2017-02-01
The presence of humans in space represents a constant threat for their health and safety. Environmental factors such as living in a closed confinement, as well as exposure to microgravity and radiation, are associated with significant changes in bone metabolism, muscular atrophy, and altered immune response, which has impacts on human performance and possibly results in severe illness. Thus, maintaining and monitoring of crew health status has the highest priority to ensure whole mission success. With manned deep space missions to moon or mars appearing at the horizon where short-term repatriation back to earth is impossible the availability of appropriate diagnostic platforms for crew health status is urgently needed. In response to this need, the present experiment evaluated the functionality and practicability of a metal oxide based sensor system (eNose) together with a newly developed breath gas collecting device under the condition of altering acceleration. Parabolic flights were performed with an Airbus A300 ZeroG at Bordeaux, France. Ambient air and exhaled breath of five healthy volunteers was analyzed during steady state flight and parabolic flight maneuvres. All volunteers completed the study, the breath gas collecting device valves worked appropriately, and breathing through the collecting device was easy and did not induce discomfort. During breath gas measurements, significant changes in metal oxide sensors, mainly sensitive to aromatic and sulphur containing compounds, were observed with alternating conditions of acceleration. Similarly, metal oxide sensors showed significant changes in all sensors during ambient air measurements. The eNose as well as the newly developed breath gas collecting device, showed appropriate functionality and practicability during alternating conditions of acceleration which is a prerequisite for the intended use of the eNose aboard the International Space Station (ISS) for breath gas analysis and crew health status
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).
A constrained backpropagation approach for the adaptive solution of partial differential equations.
Rudd, Keith; Di Muro, Gianluca; Ferrari, Silvia
2014-03-01
This paper presents a constrained backpropagation (CPROP) methodology for solving nonlinear elliptic and parabolic partial differential equations (PDEs) adaptively, subject to changes in the PDE parameters or external forcing. Unlike existing methods based on penalty functions or Lagrange multipliers, CPROP solves the constrained optimization problem associated with training a neural network to approximate the PDE solution by means of direct elimination. As a result, CPROP reduces the dimensionality of the optimization problem, while satisfying the equality constraints associated with the boundary and initial conditions exactly, at every iteration of the algorithm. The effectiveness of this method is demonstrated through several examples, including nonlinear elliptic and parabolic PDEs with changing parameters and nonhomogeneous terms.
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
NASA Astrophysics Data System (ADS)
Dobrev, V. K.
2013-02-01
In the present paper we continue the project of systematic construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we call 'conformal Lie algebras' (CLA), which have very similar properties to the conformal algebras of Minkowski space-time, though our aim is to go beyond this class in a natural way. For this we introduce the new notion of parabolic relation between two non-compact semisimple Lie algebras G and G ' that have the same complexification and possess maximal parabolic subalgebras with the same complexification. Thus, we consider the exceptional algebra E 7(7) which is parabolically related to the CLA E 7(-25) , the parabolic subalgebras including E 6(6) and E 6(-26). Other interesting examples are the orthogonal algebras so(p, q) all of which are parabolically related to the conformal algebra so( n, 2) with p + q = n + 2, the parabolic subalgebras including the Lorentz subalgebra so( n - 1, 1) and its analogs so( p - 1, q - 1). We consider also E6(6) and E6(2) which are parabolically related to the hermitian symmetric case E6(-14) , the parabolic subalgebras including real forms of sl(6). We also give a formula for the number of representations in the main multiplets valid for CLAs and all algebras that are parabolically related to them. In all considered cases we give the main multiplets of indecomposable elementary representations including the necessary data for all relevant invariant differential operators. In the case of so( p, q) we give also the reduced multiplets. We should stress that the multiplets are given in the most economic way in pairs of shadow fields. Furthermore we should stress that the classification of all invariant differential operators includes as special cases all possible conservation laws and conserved currents, unitary or not.
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.
Nonimaging secondary concentrators for large rim angle parabolic troughs with tubular absorbers
NASA Astrophysics Data System (ADS)
Ries, Harald; Spirkl, Wolfgang
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. concentrators, solar trough collectors, tailored reflectors.
Vortex shedding and galloping of open semi-circular and parabolic cylinders in cross-flow
NASA Astrophysics Data System (ADS)
Weaver, D. S.; Veljkovic, I.
2005-11-01
An experimental wind-tunnel study was undertaken to investigate the flow-induced vibration behaviour of open semi-circular and parabolic cylinders in cross-flow. The motivation for the research was to investigate the cause of the fatigue failures of a number of parabolic section rotary mixing blades in a large mixing vessel. Results are presented for force coefficients as a function of angle of incidence of the flow, Strouhal number and amplitude response. It is shown that the parabolic cylinder is subject to large amplitude vortex shedding resonance and, when the elastic axis is sufficiently downstream of the section's centre of gravity, galloping instability.
NASA Technical Reports Server (NTRS)
Baker, A. J.; Soliman, M. O.
1978-01-01
A study of accuracy and convergence of linear functional finite element solution to linear parabolic and hyperbolic partial differential equations is presented. A variable-implicit integration procedure is employed for the resultant system of ordinary differential equations. Accuracy and convergence is compared for the consistent and two lumped assembly procedures for the identified initial-value matrix structure. Truncation error estimation is accomplished using Richardson extrapolation.
Diffusive instabilities in hyperbolic reaction-diffusion equations.
Zemskov, Evgeny P; Horsthemke, Werner
2016-03-01
We investigate two-variable reaction-diffusion systems of the hyperbolic type. A linear stability analysis is performed, and the conditions for diffusion-driven instabilities are derived. Two basic types of eigenvalues, real and complex, are described. Dispersion curves for both types of eigenvalues are plotted and their behavior is analyzed. The real case is related to the Turing instability, and the complex one corresponds to the wave instability. We emphasize the interesting feature that the wave instability in the hyperbolic equations occurs in two-variable systems, whereas in the parabolic case one needs three reaction-diffusion equations.
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.
NASA Astrophysics Data System (ADS)
Rosnitskiy, P. B.; Yuldashev, P. V.; Vysokanov, B. A.; Khokhlova, V. A.
2016-03-01
An equivalent source model is developed for setting boundary conditions on the parabolic diffraction equation in order to simulate ultrasound fields radiated by strongly focused medical transducers. The equivalent source is defined in a plane; corresponding boundary conditions for pressure amplitude, aperture, and focal distance are chosen so that the axial solution to the parabolic model in the focal region of the beam matches the solution to the full diffraction model (Rayleigh integral) for a spherically curved uniformly vibrating source. It is shown that the proposed approach to transferring the boundary condition from a spherical surface to a plane makes it possible to match the solutions over an interval of several diffraction maxima around the focus even for focused sources with F-numbers less than unity. This method can be used to accurately simulate nonlinear effects in the fields of strongly focused therapeutic transducers using the parabolic Khokhlov-Zabolotskaya equation.
NASA Astrophysics Data System (ADS)
Mironov, M. A.
2017-01-01
Flexural wave propagation along a bar whose thickness smoothly decreases down to zero within its end piece is considered. The propagation velocity tends to zero as the tapered end of the bar is approached, and the time of wave propagation to the tapered end is infinite. As a consequence, waves propagating along the bar are not reflected from the end. Previous quantitative study of the effect in the WKB approximation shows that, in the case of parabolic tapering, the WKB approximation yields a uniform asymptotics, which is valid (or invalid) for any of the bar's cross sections. In the case of a bar with parabolic tapering, the equation of flexural vibrations of the bar has exact analytic solutions in the form of power functions. Based on these solutions, a modified WKB approximation is proposed to solve equations for bars with nonparabolic thickness variation laws. The input impedance of a bar with a parabolic tapering is calculated and analyzed.
NASA Astrophysics Data System (ADS)
Granero-Belinchón, Rafael
2017-02-01
We introduce new lower bounds for the fractional Fisher information. Equipped with these bounds we study a hyperbolic-parabolic model of chemotaxis and prove the global existence of solutions in certain dissipation regimes.
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.
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
Current and Future Economics of Parabolic Trough Technology
Price, H.; Mehos, M.; Kutscher, C.; Blair, N.
2007-01-01
Solar energy is the largest energy resource on the planet. Unfortunately, it is largely untapped at present, in part because sunlight is a very diffuse energy source. Concentrating solar power (CSP) systems use low cost reflectors to concentrate the sun's energy to allow it to be used more effectively. Concentrating solar power systems are also well suited for large solar power plants that can be connected into the existing utility infrastructure. These two facts mean that CSP systems can be used to make a meaningful difference in energy supply in a relatively short period. CSP plants are best suited for the arid climates in the Southwestern United States, Northern Mexico, and many desert regions around the globe. A recent Western Governors' Association siting study [1] found that the solar potential in the U.S. Southwest is at least 4 times the total U.S. electric demand even after eliminating urban areas, environmentally sensitive areas, and all regions with a ground slope greater than 1%.While it is currently not practical to power the whole county from the desert southwest, only a small portion of this area is needed to make a substantial contribution to future U.S. electric needs. Many of the best sites are near existing high-voltage transmission lines and close to major power load centers in the Southwest (Los Angeles, Las Vegas, and Phoenix). In addition, the power provided by CSP technologies has strong coincidence with peak electric demand, especially in the Southwest where peak demand corresponds in large part to air conditioning loads. Parabolic troughs currently represent the most cost-effective CSP technology for developing large utility-scale solar electric power systems. These systems are also one of the most mature solar technologies, with commercial utility-scale plants that have been operating for over 20 years. In addition, substantial improvements have been made to the technology in recent years including improved efficiency and the addition of
Parabolic tailored-potential quantum-wires grown in inverted pyramids
NASA Astrophysics Data System (ADS)
Lazarev, M.; Szeszko, J.; Rudra, A.; Karlsson, K. F.; Kapon, E.
2015-03-01
Quasi-one-dimensional AlGaAs quantum wires (QWRs) with parabolic heterostructure profiles along their axis were fabricated using metallorganic vapor phase epitaxy (MOVPE) on patterned (111)B GaAs substrates. Tailoring of the confined electronic states via modification in the parabolic potential profile is demonstrated using model calculations and photoluminescence spectroscopy. These novel nanostructures are useful for studying the optical properties of systems with dimensionality between zero and one.
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.
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.
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).
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
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Hibiya, Taketoshi; Watanabe, Masahito; Ozawa, Shumpei; Adachi, Masayoshi; Takenaga, Noriaki; Aoyagai, Tomowo; Mizuno, Akitoshi; Higuchi, Kensuke
Use of a levitation technique is an elegant way to determine thermophysical properties of high temperature melts, because this containerless technique can avoid contamination from a container and assures measurement in a wide temperature range including superheated and undercooled conditions. In particular, electromagnetic levitation is suitable for electrically conductive materials, such as molten metals, alloys and semiconductors. For surface tension measurement, the Rayleigh equation can be applicable only under microgravity condition [1]. However, when this technique is applied on earth, the l = 2 mode frequency is split into five frequencies, because a droplet is deformed from a spherical shape into an egg shape due to gravitational force and the Lorentz force. Surface tension must be calculated taking account of correction term [2]. Therefore, measurement under microgravity is required to minimize uncertainty. Furthermore, surface tension is sensitive to oxygen partial pressure of an ambient atmosphere. However, there has been less report on surface tension measurement under microgravity in an atmosphere with controlled oxygen partial pressure. We are going to measure surface tension of high temperature metallic melts under microgravity using a parabolic flight of a jet aircraft, the Gulf Stream II, operated by Diamond Air Service in Japan. In September of 2007, through parabolic flight experiments we confirmed that droplets of Cu and Ag were successfully levitated using a newly designed coil under the 1G and 10-2G conditions. Droplets were also assured to be levitated in the pull-up period (1.5G); we can melt samples before entering microgravity condition, so that we can use 20 second microgravity only for measurement. On earth, surface tension of molten silicon was successfully measured using electromagnetic levitation in an ambient atmosphere with various oxygen partial pressures; surface tension of molten silicon showed a marked dependence of oxygen
A Process Heat Application Using Parabolic Trough Collector
NASA Astrophysics Data System (ADS)
Yılmaz, İbrahim Halil; Söylemez, Mehmet Sait; Hayta, Hakan; Yumrutaş, Recep
A pilot study has been performed based on a heat process application that is designed, installed and tested at Gaziantep University to establish the technical and economic feasibility of high temperature solar-assisted cooking process. The system has been designed to be satisfying the process conditions integrated with parabolic trough solar collector (PTSC). It is primarily consists of the PTSC array, auxiliary heater, plate type heat exchanger, cooking system and water heating tanks. In the operation of the process heat application, the energy required to cook wheat (used as cooking material) has been supplied from solar energy which is transferred to heat transfer fluid (HTF) by heat exchanging units and finally discharged to water in order to produce bulgur. The performance parameters of the sub-systems and the process compatibility have been accomplished depending on the system operation. In addition that the system performance of the high temperature solar heat process has been presented and the recommendations on its improvement have been evaluated by performing an experimental study. As a result that the use of solar energy in process heat application has been projected and its contribution to economics view with respect to conventional cooking systems has been conducted.
Heat and Chemical Exergy Analysis of Parabolic Trough Collector
NASA Astrophysics Data System (ADS)
Öztürk, M.; Üçgül, I.; Özek, N.
2007-04-01
Emissions of greenhouse gases and other pollutants, derived from the combustion of fossil fuels for heat and electricity generation, can be significantly reduced or even completely eliminated by substituting fossil fuels with a clean energy source, e.g. solar energy. However, solar radiation reaching the earth is diluted, intermittent, and, unequally distributed. These disadvantages can be overcome by converting solar energy into chemical energy carriers, i.e. solar fuels, such as solar hydrogen and solar methanol, which can be long-termed stored and long-ranged transported. Since the energy conversion efficiency of thermochemical processes is limited by the Carnot efficiency, the use of concentrated solar radiation as the source of high-temperature process heat provides a thermodynamically efficient path for the conversion of solar energy into chemical fuels. In this study, water-gas shift reaction in parabolic trough collector is evaluated with regarding the heat exergy and chemical exergy analyses and the results are given as tables and graphs.
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.
A parabolized stability analysis of a trailing vortex wake
NASA Astrophysics Data System (ADS)
Edstrand, Adam; Schmid, Peter; Taira, Kunihiko; Cattafesta, Louis
2016-11-01
To aid in understanding how best to control a trailing vortex, we perform a parabolized stability analysis on a flow past a wing at a chord-based Reynolds number of 1000. At the upstream position, the wake instability branch dominates, with only a single vortex instability present in the spectrum. With downstream progression, the growth rate of the wake instability decays, but remains unstable 10 chords downstream. With the wake mode being unstable so far downstream, these results imply that the excitation of the wake instability, despite the varying base flow, will continue to see growth and potentially disrupt the trailing vortex. Conversely, the vortex instability in its formative region rapidly decays to the stable half-plane, then at 11 chords downstream becomes unstable again. We hypothesized the renewed instability growth far downstream is developing as a result of vortex instabilities, however the excitation of these instabilities proves to be challenging in the vortex far field. From these results, control near the two-dimensional wake behind the airfoil may better interfere with the trailing vortex formation; however, to determine the optimal disturbances, an adjoint analysis is required and is included in the future work of the project. ONR Grants N00014-10-1-0832 and N00014-15-1-2403.
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.
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.
High Speed Analysis Of Free Flights With A Parabolic Thruster
Scharring, Stefan; Eckel, Hans-Albert; Roeser, Hans-Peter
2010-05-06
A laser-based rangefinder with high temporal resolution, synchronized with a laser burst, is employed for fast on-site analysis of pulsed free flights. Additional high speed recordings from two different angles of view allow for full 3D-reconstruction of the trajectory and calibration of the rangefinder data. This reveals the whole dynamics of the flyer including the lateral and angular impulse coupling components as well as information on the detonation process. The employment of an ignition pin enhances the reproducibility of the momentum coupling due to a more reliable plasma ignition during the flight. The impact of initial lateral offset is studied and shows beam-riding properties of the parabolic craft within a small range. Back-driving forces are derived and compared with the theoretical model. The flight stability is evaluated with respect to the minimization and compensation of the lateral and angular momentum in a hovering experiment. Stable laser acceleration ranges up to 3 m altitude. Ballistic free flights close to the laboratory ceiling at 7.8 m are reported.
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.
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.
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
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.
Lipschitz regularity of solutions for mixed integro-differential equations
NASA Astrophysics Data System (ADS)
Barles, Guy; Chasseigne, Emmanuel; Ciomaga, Adina; Imbert, Cyril
We establish new Hölder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method. We thus extend the Hölder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the local and nonlocal term, but their overall behavior is driven by the local-nonlocal interaction, e.g. the fractional diffusion may give the ellipticity in one direction and the classical diffusion in the complementary one.
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.
Results of the parabolic flight tests of the rapunzel deployer
NASA Astrophysics Data System (ADS)
Sabath, D.; Krischke, M.; Kast, W.; Kowalczyk, M.; Kruijff, M.; van der Heide, E.
The tether assisted re-entry of small payloads is a highly interesting tool for space transportation especially for the return of small payloads from Space Station ISSA. The small tether mission Rapunzel was initiated in 1991 by the Institute of Astronautics, TU München and the Kayser-Threde Company, to design a low cost and feasible tether experiment for the verification of the tether assisted re-entry. Together with the Samara State Aerospace University, Russia, a mission concept on a Russian Resurs or Photon capsule was developed. Based on this mission a deployer has been designed, mainly based on technology of the textile industry, which insures high reliability at low cost. Recently a similar configuration is being discussed for the ESA-TSE mission. The main work during the recent time was the development and test of the breadboard model of the deployer system. After successfully completing initial ground tests with the deployer, further tests during the ESA Parabolic Flight campaign in November 1995 were conducted. After a short introduction of the overall mission scenario, the planned configuration in orbit, this paper will present the results of the microgravity test campaign onboard the KC-135 aircraft and compare them with the ground test. The deployer showed a good performance during all tests, including ejection of the end-mass, deployment, and braking. Problems that occurred during the tests will be discussed, and solutions for the detected flaws and the results of the redesign now in progress will be presented. These verifications have shown the feasibility of the concept and will lay the base for the planned development of the flight model of the deployer.
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.
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.
Local discontinuous Galerkin approximations to Richards’ equation
NASA Astrophysics Data System (ADS)
Li, H.; Farthing, M. W.; Dawson, C. N.; Miller, C. T.
2007-03-01
We consider the numerical approximation to Richards' equation because of its hydrological significance and intrinsic merit as a nonlinear parabolic model that admits sharp fronts in space and time that pose a special challenge to conventional numerical methods. We combine a robust and established variable order, variable step-size backward difference method for time integration with an evolving spatial discretization approach based upon the local discontinuous Galerkin (LDG) method. We formulate the approximation using a method of lines approach to uncouple the time integration from the spatial discretization. The spatial discretization is formulated as a set of four differential algebraic equations, which includes a mass conservation constraint. We demonstrate how this system of equations can be reduced to the solution of a single coupled unknown in space and time and a series of local constraint equations. We examine a variety of approximations at discontinuous element boundaries, permeability approximations, and numerical quadrature schemes. We demonstrate an optimal rate of convergence for smooth problems, and compare accuracy and efficiency for a wide variety of approaches applied to a set of common test problems. We obtain robust and efficient results that improve upon existing methods, and we recommend a future path that should yield significant additional improvements.
NASA Astrophysics Data System (ADS)
Kogoj, Alessia E.
2017-02-01
We show how to apply harmonic spaces potential theory in the study of the Dirichlet problem for a general class of evolution hypoelliptic partial differential equations of second order. We construct Perron-Wiener solution and we provide a sufficient condition for the regularity of the boundary points. Our criterion extends and generalizes the classical parabolic-cone criterion for the Heat equation due to Effros and Kazdan.
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.
Bouri, C.; Selles, P.; Malegat, L.; Kwato Njock, M. G.
2006-09-15
Spherical and parabolic partial cross sections and asymmetry parameters, defined in the ejected electron frame, are presented for photoionization excitation of the helium atom at 0.1 eV above its double ionization threshold. A quantitative law giving the dominant spherical partial wave l{sub dom} for each excitation level n is obtained. The parabolic partial cross sections are shown to satisfy the same approximate selection rules as the related Rydberg series of doubly excited states (K,T){sub n}{sup A}. The analysis of radial and angular correlations reveals the close relationship between double excitation, ionization excitation, and double ionization. Opposite to a widespread belief, the observed value of the asymmetry parameter is shown to result from the interplay of radial correlations and symmetry constraints, irrespective of angular correlations. Finally, the measurement of parabolic partial cross sections is proposed as a challenge to experimentalists.
Wind load design methods for ground-based heliostats and parabolic dish collectors
Peterka, J A; Derickson, R G
1992-09-01
The purpose of this design method is to define wind loads on flat heliostat and parabolic dish collectors in a simplified form. Wind loads are defined for both mean and peak loads accounting for the protective influence of upwind collectors, wind protective fences, or other wind-blockage elements. The method used to define wind loads was to generalize wind load data obtained during tests on model collectors, heliostats or parabolic dishes, placed in a modeled atmospheric wind in a boundary-layer wind-tunnel at Colorado State University. For both heliostats and parabolic dishes, loads are reported for solitary collectors and for collectors as elements of a field. All collectors were solid with negligible porosity; thus the effects of porosity in the collectors is not addressed.
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.
A Grinding Apparatus For Making A Middle-Size Parabolic Mirror Using The Link Mechanism Method
NASA Astrophysics Data System (ADS)
Shishido, Kora; Sugiura, Masao
1987-01-01
A large solar furnace that has a parabolic mirror with a diameter of 10m, a focal length of 3.2m and a heliostat mirror with an area of 15x15m was made by the authors at T6hoku University in 1962, and subsequently a small solar furnace having a parabolic mirror with a diameter of 1.5m, a focal -length of 0.5m and a heliostat mirror with an area of 2x2m was constructed at T6hoku Gakuin University in 1986. The large solar furnace could melt tungsten with a melting point of 3400°C, and the small solar furnace drove a stirling engine made in West Germany that had a rated power of 400W. The parabolic mirror of the segment type at TohokU University was made by a grinding apparatus that used a cam mechanism, and the parabolic mirror at T6hoku Gakuin University was made by an apparatus (hand-made by students)which employed a link mechanism to draw the parabolic curve. In this paper, the grinding apparatus used for making the segmental parabolic mirror with a diameter of 2-3m and a focal length of 0.5-1.0 m is reported. This mirror was used in a middle-size solar heat engine. The heat engine in this system was a Stirling engine with a rated power of 1-3KW, and the grinding apparatus (the precision parts moved in a linear track ) employed a compact link mechanism.
UPC BarcelonaTech Platform. Innovative aerobatic parabolic flights for life sciences experiments.
NASA Astrophysics Data System (ADS)
Perez-Poch, Antoni; Gonzalez, Daniel
We present an innovative method of performing parabolic flights with aerobatic single-engine planes. A parabolic platform has been established in Sabadell Airport (Barcelona, Spain) to provide an infraestructure ready to allow Life Sciences reduced gravity experiments to be conducted in parabolic flights. Test flights have demonstrated that up to 8 seconds of reduced gravity can be achieved by using a two-seat CAP10B aircraft, with a gravity range between 0.1 and 0.01g in the three axis. A parabolic flight campaign may be implemented with a significant reduction in budget compared to conventional parabolic flight campaigns, and with a very short time-to-access to the platform. Operational skills and proficiency of the pilot controling the aircraft during the maneuvre, sensitivity to wind gusts, and aircraft balance are the key issues that make a parabola successful. Efforts are focused on improving the total “zero-g” time and the quality of reduced gravity achieved, as well as providing more space for experiments. We report results of test flights that have been conducted in order to optimize the quality and total microgravity time. A computer sofware has been developed and implemented to help the pilot optimize his or her performance. Finally, we summarize the life science experiments that have been conducted in this platform. Specific focus is given to the very successful 'Barcelona ZeroG Challenge', this year in its third edition. This educational contest gives undergraduate and graduate students worldwide the opportunity to design their research within our platform and test it on flight, thus becoming real researchers. We conclude that aerobatic parabolic flights have proven to be a safe, unexpensive and reliable way to conduct life sciences reduced gravity experiments.
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]).
Gawlik, K.
2010-08-01
Tested parabolic trough products provided by SkyFuel, a manufacturer of parabolic trough systems in the concentrating solar thermal power industry. The testing evaluated the performance of the system at the Optical Efficiency Test Loop at Solar Industrial Mesa Top Area.
Validation of the FLAGSOL parabolic trough solar power plant performance model
Price, H.W.; Svoboda, P.; Kearney, D.
1994-10-01
This paper describes the results of a validation of the FLAGSOL parabolic trough solar power plant performance model. The validation was accomplished by simulating an operating solar electric generating system (SEGS) parabolic trough solar thermal power plant and comparing the model output results with actual plant operating data. This comparison includes instantaneous, daily, and annual total solar thermal electric output, gross solar electric generation, and solar mode parasitic electric consumption. The results indicate that the FLAGSOL model adequately predicts the gross solar electric output of an operating plant, both on a daily and an annual basis.
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.
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.
On Decay Estimates of Solutions to One-dimensional Linear Parabolic Feedback Control Systems
NASA Astrophysics Data System (ADS)
Nambu, Takao
In feedback stabilization for linear parabolic systems,a control scheme is designed so that the “state” of the system decays with a designated decay rate as t → ∞. An arbitrary linear functional of the state, which is subordinate to the state, also decays at least with the same decay rate. We study in the paper a class of linear parabolic systems of one dimension, and construct a specific control scheme such that a nontrivial linear functional decays exactly faster than the state.
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.
NASA Astrophysics Data System (ADS)
Kashchenko, Sergey A.
2016-12-01
The dynamics of second-order equations with nonlinear delayed feedback and a large coefficient of a delayed equation is investigated using asymptotic methods. Based on special methods of quasi-normal forms, a new construction is elaborated for obtaining the main terms of asymptotic expansions of asymptotic residual solutions. It is shown that the dynamical properties of the above equations are determined mostly by the behavior of the solutions of some special families of parabolic boundary value problems. A comparative analysis of the dynamics of equations with the delayed feedback of three types is carried out.
Global in time solutions to Kolmogorov-Feller pseudodifferential equations with small parameter
NASA Astrophysics Data System (ADS)
Albeverio, S.; Danilov, V. G.
2011-03-01
The goal in this paper is to demonstrate a new method for constructing globalin-time approximate (asymptotic) solutions of (pseudodifferential) parabolic equations with a small parameter. We show that, in the leading term, such a solution can be constructed by using characteristics, more precisely, by using solutions of the corresponding Hamiltonian system and without using any integral representation. For completeness, we also briefly describe the well-known scheme developed by V. P. Maslov for constructing global-in-time solutions.
The heat equation source determination for the case of non-smooth boundary and initial conditions
NASA Astrophysics Data System (ADS)
Solovi’ev, V. V.; Tkachenko, D. S.
2017-01-01
An inverse problem of reconstructing the source of a special kind for parabolic equations in a bounded region with smooth boundary is considered. Solutions are sought in the Holder classes. We prove an uniqueness criterion for the solution and sufficient conditions of Fredholm property of the task at hand. As a consequence of the sufficient conditions for existence and uniqueness of solution of the inhomogeneous inverse problems are found.
NASA Astrophysics Data System (ADS)
DiLisi, Gregory; Dempsey, Robert; Rarick, Richard; Rosenblatt, Charles
2015-06-01
Liquid bridges were flown aboard a Boeing 727-200 aircraft in a series of parabolic arcs that produced multiple periods of microgravity. During the microgravity portion of each arc, g eff, the effective total body acceleration due to external forces became negligibly small so that cylindrical liquid bridges could be suspended across two coaxial support posts. Near the bottom of each arc, g eff slowly increased to a maximum of 1.84g, causing the liquid bridges to deform and in some cases collapse. Although the physics of liquid bridges subject to varying total body force is well-established and has been analyzed extensively both theoretically and experimentally, specific hardware was designed to vary g eff in a precise way that overcomes the gravity-related limitations and high g-jitter associated with parabolic flights. Bridge-stability was examined for axial and lateral orientations with respect to g eff by measuring the slenderness ratio as a function of Bond number at the instant of bridge collapse. Results exhibit remarkable agreement with theory as well as with the experimental results obtained in a magnetic levitation-based experiment. The parabolic flight method offers technical originality and provides experimental insights for researchers in the microgravity field. Here we present hardware development, experimental considerations, and results, and demonstrate that parabolic flight is a viable alternative to extant techniques for quantitative experiments on fluids.
Negatively charged donors in parabolic quantum-well wires under magnetic fields
NASA Astrophysics Data System (ADS)
Zhai, Li-Xue; Liu, Jian-Jun
2007-09-01
The ground state of a negatively charged donor (D-) in a parabolic GaAs quantum-well wire in the presence of a magnetic field is investigated using the finite difference method within the quasi-one-dimensional effective potential model. The magnetic effects on the binding energies of the ground state of a D- center are calculated for various parabolic potentials. The distance between the electrons and the donor ion and the distance between the two electrons are also calculated, respectively, as a function of the strength of the parabolic potential and the magnetic field. We find that the interplay of the spatial confinement and the magnetic confinement of electrons in quantum-well wires leads to complicated behavior of the binding energies of the D- center and that the increase of the electron-donor ion attraction dominates the increase of the electron-electron repulsion as the spatial and magnetic confinement increases for the ground state of a D- center in a parabolic quantum-well wire.
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.)
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.
Estimation of discontinuous coefficients in parabolic systems: Applications to reservoir simulation
NASA Technical Reports Server (NTRS)
Lamm, P. D.
1984-01-01
Spline based techniques for estimating spatially varying parameters that appear in parabolic distributed systems (typical of those found in reservoir simulation problems) are presented. The problem of determining discontinuous coefficients, estimating both the functional shape and points of discontinuity for such parameters is discussed. Convergence results and a summary of numerical performance of the resulting algorithms are given.
Simulating Parabolic Flight like g-Profiles on Ground - A Combination of Centrifuge and Clinostat
NASA Astrophysics Data System (ADS)
Brungs, Sonja; Petrat, Guido; der Wiesche, Melanie von; Anken, Ralf; Kolanus, Waldemar; Hemmersbach, Ruth
2016-06-01
Clinostats and centrifuges are widely used to create simulated microgravity or hypergravity, respectively, in order to study the impact of gravity on biosystems. Here, we used a clinostat and a centrifuge in alternating modes of operation in order to create a simulated parabolic flight like g-profile. To our knowledge, it is the first time that both devices were run in connection. In order to test the method, we investigated the production of reactive oxygen species of immune cells (macrophages) during oxidative burst in an on-line kinetic approach, which has been extensively studied under real (parabolic flight) and simulated microgravity (clinostat) as well as under hypergravity conditions (centrifuge). Our results indicate that clinostat and centrifuge can be operated in an alternating way to simulate the repetitive changes of gravity during parabolic flight. Although the switch from one gravity level to the other could not be carried out as quickly as it takes place during actual parabolic flight due to technical and operational reasons, it can be concluded that running experiments in a clinostat aboard a centrifuge on ground are suitable for studying gravity-related phenomena.
The First European Parabolic Flight Campaign with the Airbus A310 ZERO-G
NASA Astrophysics Data System (ADS)
Pletser, Vladimir; Rouquette, Sebastien; Friedrich, Ulrike; Clervoy, Jean-Francois; Gharib, Thierry; Gai, Frederic; Mora, Christophe
2016-12-01
Aircraft parabolic flights repetitively provide up to 23 seconds of reduced gravity during ballistic flight manoeuvres. Parabolic flights are used to conduct short microgravity investigations in Physical and Life Sciences and in Technology, to test instrumentation prior to space flights and to train astronauts before a space mission. The use of parabolic flights is complementary to other microgravity carriers (drop towers, sounding rockets), and preparatory to manned space missions on board the International Space Station and other manned spacecraft, such as Shenzhou and the future Chinese Space Station. After 17 years of using the Airbus A300 ZERO-G, the French company Novespace, a subsidiary of the ' Centre National d'Etudes Spatiales' (CNES, French Space Agency), based in Bordeaux, France, purchased a new aircraft, an Airbus A310, to perform parabolic flights for microgravity research in Europe. Since April 2015, the European Space Agency (ESA), CNES and the ` Deutsches Zentrum für Luft- und Raumfahrt e.V.' (DLR, the German Aerospace Center) use this new aircraft, the Airbus A310 ZERO-G, for research experiments in microgravity. The first campaign was a Cooperative campaign shared by the three agencies, followed by respectively a CNES, an ESA and a DLR campaign. This paper presents the new Airbus A310 ZERO-G and its main characteristics and interfaces for scientific experiments. The experiments conducted during the first European campaign are presented.
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.