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.
Semilinear Parabolic Equations with Preisach Hysteresis
NASA Astrophysics Data System (ADS)
Little, Thomas Dan
A coupled system consisting of a nonlinear parabolic partial differential equation and a family of ordinary differential equations is realized as an abstract Cauchy problem. We establish coercivity and accretiveness estimates for the multi-valued operator in the abstract Cauchy problem, and then apply the Crandall-Liggett theorem to recover the integral solution for the abstract Cauchy problem. A special case of the coupled system corresponds to the Super -Stefan problem, i.e. the delayed phase transition model for a material subjected to super-heating and super-cooling. In this case, the nonlinearity in the parabolic partial differential equation appears as the time derivative of a simple relay hysteresis functional produced by one member of the family of ordinary differential equations. Another special case of the coupled system corresponds to a one-dimensional derivation from Maxwell's equations for a ferromagnetic body under slowly varying field conditions. In this case, the nonlinearity is the time derivative of the classical Preisach hysteresis functional, and the family of ordinary differential equations produce a family of simple relay hysteresis functionals present in the construction of the Preisach hysteresis functional.
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.
Some blow-up problems for a semilinear parabolic equation with a potential
NASA Astrophysics Data System (ADS)
Cheng, Ting; Zheng, Gao-Feng
The blow-up rate estimate for the solution to a semilinear parabolic equation u=Δu+V(x)|u in Ω×(0,T) with 0-Dirichlet boundary condition is obtained. As an application, it is shown that the asymptotic behavior of blow-up time and blow-up set of the problem with nonnegative initial data u(x,0)=Mφ(x) as M goes to infinity, which have been found in [C. Cortazar, M. Elgueta, J.D. Rossi, The blow-up problem for a semilinear parabolic equation with a potential, preprint, arXiv: math.AP/0607055, July 2006], is improved under some reasonable and weaker conditions compared with [C. Cortazar, M. Elgueta, J.D. Rossi, The blow-up problem for a semilinear parabolic equation with a potential, preprint, arXiv: math.AP/0607055, July 2006].
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.
Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle
NASA Astrophysics Data System (ADS)
Fiedler, Bernold; Rocha, Carlos; Wolfrum, Matthias
We investigate heteroclinic orbits between equilibria and rotating waves for scalar semilinear parabolic reaction-advection-diffusion equations with periodic boundary conditions. Using zero number properties of the solutions and the phase shift equivariance of the equation, we establish a necessary and sufficient condition for the existence of a heteroclinic connection between any pair of hyperbolic equilibria or rotating waves.
NASA Astrophysics Data System (ADS)
Pan, Hongjing; Xing, Ruixiang
2008-03-01
In this paper, we derive blow-up rates for higher-order semilinear parabolic equations and systems. Our proof is by contradiction and uses a scaling argument. This procedure reduces the problems of blow-up rate to Fujita-type theorems. In addition, we also give some new Fujita-type theorems for higher-order semilinear parabolic equations and systems with the time variable on . These results are not restricted to positive solutions.
A stability analysis for a semilinear parabolic partial differential equation
NASA Technical Reports Server (NTRS)
Chafee, N.
1973-01-01
The parabolic partial differential equation considered is u sub t = u sub xx + f(u), where minus infinity x plus infinity and o t plus infinity. Under suitable hypotheses pertaining to f, a class of initial data is exhibited: phi(x), minus infinity x plus infinity, for which the corresponding solutions u(x,t) appraoch zero as t approaches the limit of plus infinity. This convergence is uniform with respect to x on any compact subinterval of the real axis.
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.
NASA Astrophysics Data System (ADS)
Needham, D. J.
1992-05-01
In this paper we consider the question of the existence of solutions to an initial-boundary value problem for a singular, semilinear, parabolic equation arising from the study of autocatalytic chemical kinetics of the type A → B at rate k[A][B] P , where A is a reactant, B is the autocatalyst, k>0 the rate constant and 0< p<1 the order of the reaction, King and Needham [1]. A monotone iteration method is adopted in the spirit of Sattinger [2], However the general theory due to Sattinger [2] cannot be applied directly because of the singular nature of the source term in the equation.
An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology
NASA Astrophysics Data System (ADS)
Beretta, Elena; Cavaterra, Cecilia; Cerutti, M. Cristina; Manzoni, Andrea; Ratti, Luca
2017-10-01
In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential in the myocardial tissue. The goal is the detection of an inhomogeneity \
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.
A semilinear parabolic system with a free boundary
NASA Astrophysics Data System (ADS)
Wang, Mingxin; Zhao, Yonggang
2015-12-01
This paper deals with a semilinear parabolic system with reaction terms {v^p, u^q} and a free boundary {x = s(t)} in one space dimension, where {s(t)} evolves according to the free boundary condition {s'(t) = -μ(u_x + ρ v_x)}. The main aim of this paper was to study the existence, uniqueness, regularity and long-time behavior of positive solution (maximal positive solution). Firstly, we prove that this problem has a unique positive solution when {p, q ≥ 1}, and a (unique) maximal positive solution when {p < 1} or {q < 1}. Then, we study the regularity of {(u,v)} and {s}. At last, we discuss the global existence, finite-time blowup of the unique positive solution (maximal positive solution) and long-time behavior of bounded global solution.
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.
On the semilinear elliptic equations of electrostatic NEMS devices
NASA Astrophysics Data System (ADS)
Zhang, Ruifeng; Cai, Liang
2014-12-01
In this paper, we analyze a class of semilinear elliptic equations with boundary value problem based on electrostatic nanoelectromechanical system. First, we will use upper and lower solution method to study the existence of solutions and some properties of minimal solutions for the problem. Then, we will establish the existence of a second solution by variational method in some conditions.
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.
Ground state solutions for semilinear time-harmonic Maxwell equations
NASA Astrophysics Data System (ADS)
Tang, Xianhua; Qin, Dongdong
2016-04-01
This paper is concerned with the time-harmonic semilinear Maxwell equation: ∇ × (∇ × u) + λu = f(x, u) in Ω with the boundary condition ν × u = 0 on ∂Ω, where Ω ⊂ ℝ3 is a simply connected, smooth, bounded domain with connected boundary and ν : ∂Ω → ℝ3 is the exterior normal. Here ∇ × denotes the curl operator in ℝ3 and the boundary condition holds when Ω is surrounded by a perfect conductor. By using the generalized Nehari manifold method due to Szulkin and Weth [Handbook of Nonconvex Analysis and Applications (International Press, Somerville, 2010), pp. 597-632] and some new techniques, existence of ground state solutions for above equation is established under some generic conditions on f.
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.
Well-posedness of semilinear stochastic wave equations with Hölder continuous coefficients
NASA Astrophysics Data System (ADS)
Masiero, Federica; Priola, Enrico
2017-08-01
We prove that semilinear stochastic abstract wave equations, including wave and plate equations, are well-posed in the strong sense with an α-Hölder continuous drift coefficient, if α ∈ (2 / 3 , 1). The uniqueness may fail for the corresponding deterministic PDE and well-posedness is restored by adding an external random forcing of white noise type. This shows a kind of regularization by noise for the semilinear wave equation. To prove the result we introduce an approach based on backward stochastic differential equations. We also establish regularizing properties of the transition semigroup associated to the stochastic wave equation by using control theoretic results.
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.
Orbit Connections in a Parabolic Equation.
1983-04-01
Departamento de Matematica , 13560, Slo Carlos, S.P. Brasil. This research has been supported in part by CAPES-qoordena~io de Aperfeiqoamento de Pessoal...de Nivel Superior , Brasilia, D.F., Brasil under contract Proc. #3056/78. 1k ORBIT CONNECTIONS IN A PARABOLIC EQUATION by Jack K. Hale and Arnaldo S
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
Reverberation Modelling Using a Parabolic Equation Method
2012-10-01
Canada Reverberation Modelling using a Parabolic Equation Method Mr. Craig A. Hamm Dr. Gary H. Brooke Dr. David J. Thomson Mr. Martin L. Taillefer...number: W7707-125517/001/HAL Scientific Authority: Dr. Dale D. Ellis This page intentionally left blank. Reverberation ...model ‘PECan’ is used to determine the feasibility of computing reverberation and target echo fields in various ocean waveguides. Calculations are
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.
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.
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.
Numerical Schemes for Rough Parabolic Equations
Deya, Aurelien
2012-04-15
This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0,1) perturbed by a non-linear rough signal. It is the continuation of Deya (Electron. J. Probab. 16:1489-1518, 2011) and Deya et al. (Probab. Theory Relat. Fields, to appear), where the existence and uniqueness of a solution has been established. The approach combines rough paths methods with standard considerations on discretizing stochastic PDEs. The results apply to a geometric 2-rough path, which covers the case of the multidimensional fractional Brownian motion with Hurst index H>1/3.
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
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.
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.
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.
Spectral Deferred Corrections for Parabolic Partial Differential Equations
2015-06-08
stability properties necessary for the solution of stiff differential equations . Furthermore, for large-scale systems, SDC methods are more...the behavior of these schemes with several numerical examples. Spectral Deferred Corrections for Parabolic Partial Differential Equations Daniel...Approved for public release: distribution is unlimited. Keywords: spectral deferred corrections, parabolic partial differential equations , alternating
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.
NASA Astrophysics Data System (ADS)
Kharibegashvili, S. S.; Jokhadze, O. M.
2014-04-01
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.
Non-local quasi-linear parabolic equations
NASA Astrophysics Data System (ADS)
Amann, H.
2005-12-01
This is a survey of the most common approaches to quasi-linear parabolic evolution equations, a discussion of their advantages and drawbacks, and a presentation of an entirely new approach based on maximal L_p regularity. The general results here apply, above all, to parabolic initial-boundary value problems that are non-local in time. This is illustrated by indicating their relevance for quasi-linear parabolic equations with memory and, in particular, for time-regularized versions of the Perona-Malik equation of image processing.
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.
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)
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.
Differentiability at lateral boundary for fully nonlinear parabolic equations
NASA Astrophysics Data System (ADS)
Ma, Feiyao; Moreira, Diego R.; Wang, Lihe
2017-09-01
For fully nonlinear uniformly parabolic equations, the first derivatives regularity of viscosity solutions at lateral boundary is studied under new Dini type conditions for the boundary, which is called Reifenberg Dini conditions and is weaker than usual Dini conditions.
Kharibegashvili, S. S.; Jokhadze, O. M. E-mail: ojokhadze@yahoo.com
2014-04-30
A mixed problem for a one-dimensional semilinear wave equation with nonlinear boundary conditions is considered. Conditions of this type occur, for example, in the description of the longitudinal oscillations of a spring fastened elastically at one end, but not in accordance with Hooke's linear law. Uniqueness and existence questions are investigated for global and blowup solutions to this problem, in particular how they depend on the nature of the nonlinearities involved in the equation and the boundary conditions. Bibliography: 14 titles. (paper)
On the parallel solution of parabolic equations
NASA Technical Reports Server (NTRS)
Gallopoulos, E.; Saad, Youcef
1989-01-01
Parallel algorithms for the solution of linear parabolic problems are proposed. The first of these methods is based on using polynomial approximation to the exponential. It does not require solving any linear systems and is highly parallelizable. The two other methods proposed are based on Pade and Chebyshev approximations to the matrix exponential. The parallelization of these methods is achieved by using partial fraction decomposition techniques to solve the resulting systems and thus offers the potential for increased time parallelism in time dependent problems. Experimental results from the Alliant FX/8 and the Cray Y-MP/832 vector multiprocessors are also presented.
Real-time optical laboratory solution of parabolic differential equations
NASA Technical Reports Server (NTRS)
Casasent, David; Jackson, James
1988-01-01
An optical laboratory matrix-vector processor is used to solve parabolic differential equations (the transient diffusion equation with two space variables and time) by an explicit algorithm. This includes optical matrix-vector nonbase-2 encoded laboratory data, the combination of nonbase-2 and frequency-multiplexed data on such processors, a high-accuracy optical laboratory solution of a partial differential equation, new data partitioning techniques, and a discussion of a multiprocessor optical matrix-vector architecture.
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.
NASA Astrophysics Data System (ADS)
Galaktionov, V. A.
2009-07-01
Five types of blow-up patterns that can occur for the 4th-order semilinear parabolic equation of the reaction-diffusion type \\[ \\begin{eqnarray*} u_t= -\\Delta^2 u + |u|^{p-1} u\\quad in\\ \\mathbb{R}^N \\times (0,T),\\ p>1,\\\\\\ms\\quad \\lim_{t \\to T^-}\\sup_{x \\in \\mathbb{R}^N} |u(x,t)|= +\\infty, \\end{eqnarray*} \\] are discussed. For the semilinear heat equation ut = Δu + up, various blow-up patterns were under scrutiny since the 1980s, while the case of higher order diffusion was studied much less, regardless of the wide range of its application. The types of blow-up include the following: Type I(ss): patterns of self-similar single point blow-up, including those for which the final time profile |u(·, T-)|N(p-1)/4 is a measure; Type I(log): self-similar non-radial blow-up with angular logarithmic TW swirl; Type I(Her): non-self-similar blow-up close to stable/centre subspaces of Hermitian operators obtained via linearization about constant uniform blow-up pattern; Type II(sing): non-self-similar blow-up on stable/centre manifolds of a singular steady state in the supercritical Sobolev range p >= pS = (N + 4)/(N - 4) for N > 4 and Type II(LN): non-self-similar blow-up along the manifold of stationary generalized Loewner-Nirenberg type explicit solutions in the critical Sobolev case p = pS, when |u(·, T-)|N(p-1)/4 contains a measure as a singular component. There is some evidence that Type I(ss) are structurally stable (generic) patterns. However, justifying this and the existence of other proposed types of blow-up remain difficult open problems, so formal analytic and numerical methods are key in supporting some theoretical judgements.
Highly oscillatory waves in quasilinear hyperbolic-parabolic coupled equations
NASA Astrophysics Data System (ADS)
Meng, Yiping; Wang, Ya-Guang
2017-08-01
In this paper, we study the Cauchy problem for a two-speed quasi-linear hyperbolic-parabolic coupled system in several space variables with highly oscillatory initial data and small viscosity. By means of nonlinear geometric optics, we derive the asymptotic expansions of oscillatory waves and deduce that the leading oscillation profiles satisfy quasilinear hyperbolic-parabolic coupled equations with integral terms, from which we obtain that the oscillations of the solutions to the hyperbolic-parabolic equations are propagated along the characteristics of the hyperbolic operators, and partial profiles of oscillations are dissipated by the parabolic effect of the system. Furthermore, by using the energy method in weighted spaces, we rigorously justify the asymptotic expansion and obtain the existence of the highly oscillatory solutions in a time interval independent of the wavelength. Finally, we use this general result to study the behavior of oscillatory waves in the one dimensional compressible viscous flows and in a two-dimensional hyperbolic-parabolic system.
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.
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.
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.
The blow-up problem for a semilinear parabolic equation with a potential
NASA Astrophysics Data System (ADS)
Cortazar, Carmen; Elgueta, Manuel; Rossi, Julio D.
2007-11-01
Let [Omega] be a bounded smooth domain in . We consider the problem ut=[Delta]u+V(x)up in [Omega]×[0,T), with Dirichlet boundary conditions u=0 on [not partial differential][Omega]×[0,T) and initial datum u(x,0)=M[phi](x) where M[greater-or-equal, slanted]0, [phi] is positive and compatible with the boundary condition. We give estimates for the blow-up time of solutions for large values of M. As a consequence of these estimates we find that, for M large, the blow-up set concentrates near the points where [phi]p-1V attains its maximum.
NASTRAN solutions of problems described by simultaneous parabolic differential equations
NASA Technical Reports Server (NTRS)
Mason, J. B.; Walston, W. H., Jr.
1975-01-01
NASTRAN solution techniques are shown for a numerical analysis of a class of coupled vector flow processes described by simultaneous parabolic differential equations. To define one physical problem type where equations of this form arise, the differential equations describing the coupled transfers of heat and mass in mechanical equilibrium with negligible mass average velocity are presented and discussed. Also shown are the equations describing seepage when both electrokinetic and hydrodynamic forces occur. Based on a variational statement of the general problem type, the concepts of scalar transfer elements and parallel element systems are introduced. It is shown that adoptation of these concepts allows the direct use of NASTRAN's existing Laplace type elements for uncoupled flow (the heat transfer elements) for treating multicomponent coupled transfer. Sample problems are included which demonstrate the application of these techniques for both steady-state and transient problems.
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
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.
Nonlocal operators, parabolic-type equations, and ultrametric random walks
Chacón-Cortes, L. F. Zúñiga-Galindo, W. A.
2013-11-15
In this article, we introduce a new type of nonlocal operators and study the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators. Some of these equations are the p-adic master equations of certain models of complex systems introduced by Avetisov, V. A. and Bikulov, A. Kh., “On the ultrametricity of the fluctuation dynamicmobility of protein molecules,” Proc. Steklov Inst. Math. 265(1), 75–81 (2009) [Tr. Mat. Inst. Steklova 265, 82–89 (2009) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Zubarev, A. P., “First passage time distribution and the number of returns for ultrametric random walks,” J. Phys. A 42(8), 085003 (2009); Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic models of ultrametric diffusion in the conformational dynamics of macromolecules,” Proc. Steklov Inst. Math. 245(2), 48–57 (2004) [Tr. Mat. Inst. Steklova 245, 55–64 (2004) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic description of characteristic relaxation in complex systems,” J. Phys. A 36(15), 4239–4246 (2003); Avetisov, V. A., Bikulov, A. H., Kozyrev, S. V., and Osipov, V. A., “p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes,” J. Phys. A 35(2), 177–189 (2002); Avetisov, V. A., Bikulov, A. Kh., and Kozyrev, S. V., “Description of logarithmic relaxation by a model of a hierarchical random walk,” Dokl. Akad. Nauk 368(2), 164–167 (1999) (in Russian). The fundamental solutions of these parabolic-type equations are transition functions of random walks on the n-dimensional vector space over the field of p-adic numbers. We study some properties of these random walks, including the first passage time.
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
Efficient solution of parabolic equations by Krylov approximation methods
NASA Technical Reports Server (NTRS)
Gallopoulos, E.; Saad, Y.
1990-01-01
Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.
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.
Range-dependent reverberation modeling with the parabolic equation
NASA Astrophysics Data System (ADS)
Ratilal, Purnima; Lee, Sunwoong; Makris, Nicholas C.
2003-10-01
Propagation and scattering are generally convolved in a waveguide. For scatterers small compared to the wavelength, however, the waveguide Green functions to and from the scatterer can be separated from the free space scattering amplitude [Ratilal et al., J. Acoust. Soc. Am. 112, 1797-1816 (2002)]. In this case, waveguide scattering can be modeled using efficient and accurate range-dependent methods such as the parabolic equation (PE) for the waveguide Green function. This approach is implemented for scattering from small particles in the water column and seabed at arbitrary bistatic orientations. Scenarios investigated involving targets of large impedance contrast include scattering from bubbles and fish schools. When the Rayleigh-Born single scatter approximation is valid, PE-based range-dependent scattering can also be used to scatter from elemental water-column and seabed inhomogeneities. This approach is used to model bistatic reverberation from the water column and seabed including returns arising from both diffuse and discrete scattering processes. The former is associated with smoothly decaying reverberation, the latter with clutter. Also, the possibility that internal waves may lead to discrete seafloor scattering returns by focusing energy on the ocean bottom is also investigated with this model.
Caraballo, T. Kloeden, P.E.
2006-11-15
Under a one-sided dissipative Lipschitz condition on its drift, a stochastic evolution equation with additive noise of the reaction-diffusion type is shown to have a unique stochastic stationary solution which pathwise attracts all other solutions. A similar situation holds for each Galerkin approximation and each implicit Euler scheme applied to these Galerkin approximations. Moreover, the stationary solution of the Euler scheme converges pathwise to that of the Galerkin system as the stepsize tends to zero and the stationary solutions of the Galerkin systems converge pathwise to that of the evolution equation as the dimension increases. The analysis is carried out on random partial and ordinary differential equations obtained from their stochastic counterparts by subtraction of appropriate Ornstein-Uhlenbeck stationary solutions.
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
NASA Astrophysics Data System (ADS)
Ashyralyev, Allaberen; Okur, Ulker
2016-08-01
In the present paper, the Crank-Nicolson difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is considered. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, convergence estimates for the solution of difference schemes for the numerical solution of three mixed problems for parabolic equations are obtained. The numerical results are given.
Ashyralyev, Allaberen; Okur, Ulker
2016-08-10
In the present paper, the Crank-Nicolson difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is considered. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, convergence estimates for the solution of difference schemes for the numerical solution of three mixed problems for parabolic equations are obtained. The numerical results are given.
Similarity and generalized finite-difference solutions of parabolic partial differential equations.
NASA Technical Reports Server (NTRS)
Clausing, A. M.
1971-01-01
Techniques are presented for obtaining generalized finite-difference solutions to partial differential equations of the parabolic type. It is shown that the advantages of similarity in the solution of similar problems are generally not lost if the solution to the original partial differential equations is effected in the physical plane by finite-difference methods. The analysis results in a considerable saving in computational effort in the solution of both similar and nonsimilar problems. Several examples, including both the heat-conduction equation and the boundary-layer equations, are given. The analysis also provides a practical means of estimating the accuracy of finite-difference solutions to parabolic equations.
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.
A method for the spatial discretization of parabolic equations in one space variable
Skeel, R.D.; Berzins, M.
1987-02-01
The aim of this paper is to describe and analyze a new spatial discretization method for parabolic equations in one space variable: Ordinary and parabolic partial differential equations in one space variable x often have a singularity due to the use of polar cylindrical or spherical coordinates. The method we propose is a simple piecewise nonlinear Galerkin/Petrov-Galerkin method which is second order accurate in space. (It supersedes the method proposed by Skeel). The case m = 1 involves the use of the logarithm function, which is probably the only accurate way to model the logarithmic singularity present in the solution. A code based on a variant of the proposed method has already been included as part of the SPRINT package of Berzins, Dew, and Furzeland. The method that we propose here will be distributed in the next release of the D03P (parabolic equations) section of the NAG Library. 18 refs.
Two parabolic equations for propagation in layered poro-elastic media.
Metzler, Adam M; Siegmann, William L; Collins, Michael D; Collis, Jon M
2013-07-01
Parabolic equation methods for fluid and elastic media are extended to layered poro-elastic media, including some shallow-water sediments. A previous parabolic equation solution for one model of range-independent poro-elastic media [Collins et al., J. Acoust. Soc. Am. 98, 1645-1656 (1995)] does not produce accurate solutions for environments with multiple poro-elastic layers. First, a dependent-variable formulation for parabolic equations used with elastic media is generalized to layered poro-elastic media. An improvement in accuracy is obtained using a second dependent-variable formulation that conserves dependent variables across interfaces between horizontally stratified layers. Furthermore, this formulation expresses conditions at interfaces using no depth derivatives higher than first order. This feature should aid in treating range dependence because convenient matching across interfaces is possible with discretized derivatives of first order in contrast to second order.
Linear Parabolic Equations with a Singular Lower Order Coefficient.
1982-11-01
J0 21 fL (r (y-z),t-s) - r (Y-z,te-s))s- 1(g(z,g) - g(y,s))dzda0 yy 3 I: IV zotimating these terms, using (2.14), we get II 4 coff Ct-8) -1 .xp(ci -s W...Science Foundation under . Grant No. MCS-7927062, Mod. 2. SIGNIFICANCE AND EXPLANATION This report was motivated by the study of free boundary value...in the conveni-fitoatin of the nonlinear parabolic problem studied in NRC Technical Summary Report #2354. ...’"( II 2;* p ci s_-A:eson _For C , , - C
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.
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].
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.
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.
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.
NASA Astrophysics Data System (ADS)
Fiedler, B.; Grotta-Ragazzo, C.; Rocha, C.
2014-06-01
An explicit Lyapunov function is constructed for scalar parabolic reaction-advection-diffusion equations under periodic boundary conditions. The non-linearity is assumed to be even with respect to the advection term. The method followed was originally suggested by H. Matano for, and limited to, separated boundary conditions. Bibliography: 20 titles.
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.
ɛ-neighbourhoods of orbits of parabolic diffeomorphisms and cohomological equations
NASA Astrophysics Data System (ADS)
Resman, Maja
2014-12-01
In this article, we study the analyticity of (directed) areas of ɛ-neighbourhoods of orbits of parabolic germs. The article is motivated by the question of analytic classification using ɛ-neighbourhoods of orbits in the simplest formal class. We show that the coefficient in front of the ɛ2 term in the asymptotic expansion in ɛ, which we call the principal part of the area, is a sectorially analytic function in the initial point of the orbit. It satisfies a cohomological equation similar to the standard trivialization equation for parabolic diffeomorphisms. We give necessary and sufficient conditions on a diffeomorphism f for the existence of a globally analytic solution of this equation. Furthermore, we introduce a new classification type for diffeomorphisms implied by this new equation and investigate the relative position of its classes with respect to the analytic classes.
NASA Astrophysics Data System (ADS)
Friedlander, Susan; Vicol, Vlad
2012-06-01
Motivated by an equation arising in magnetohydrodynamics, we prove that Hölder continuous weak solutions of a nonlinear parabolic equation with singular drift velocity are classical solutions. The result is proved using the space-time Besov spaces introduced by Chemin and Lerner (J Differ Equ 121(2):314-328, 1995), combined with energy estimates, without any minimality assumption on the Hölder exponent of the weak solutions.
An approximate Riemann solver for real gas parabolized Navier-Stokes equations
Urbano, Annafederica; Nasuti, Francesco
2013-01-15
Under specific assumptions, parabolized Navier-Stokes equations are a suitable mean to study channel flows. A special case is that of high pressure flow of real gases in cooling channels where large crosswise gradients of thermophysical properties occur. To solve the parabolized Navier-Stokes equations by a space marching approach, the hyperbolicity of the system of governing equations is obtained, even for very low Mach number flow, by recasting equations such that the streamwise pressure gradient is considered as a source term. For this system of equations an approximate Roe's Riemann solver is developed as the core of a Godunov type finite volume algorithm. The properties of the approximated Riemann solver, which is a modification of Roe's Riemann solver for the parabolized Navier-Stokes equations, are presented and discussed with emphasis given to its original features introduced to handle fluids governed by a generic real gas EoS. Sample solutions are obtained for low Mach number high compressible flows of transcritical methane, heated in straight long channels, to prove the solver ability to describe flows dominated by complex thermodynamic phenomena.
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.
Controllability of semilinear impulsive nonautonomous systems
NASA Astrophysics Data System (ADS)
Leiva, Hugo
2015-03-01
In this paper we apply Rothe's type fixed-point theorem to prove the controllability of the following semilinear impulsive nonautonomous systems of differential equations ? where ?, ?, A(t), B(t) are continuous matrices of dimension n×n and n×m, respectively, the control function u belongs to ? and ?, ?, k = 1, 2, 3, … , p. Under additional conditions we prove the following statement: if the linear ? is controllable on [0, τ], then the semilinear impulsive system is also controllable on [0, τ]. Moreover, we could exhibit a control steering the nonlinear system from an initial state z0 to a final state z1 at time τ > 0.
A new explicit method for the numerical solution of parabolic differential equations
NASA Technical Reports Server (NTRS)
Satofuka, N.
1983-01-01
A new method is derived for solving parabolic partial differential equations arising in transient heat conduction or in boundary-layer flows. The method is based on a combination of the modified differential quadrature (MDQ) method with the rational Runge-Kutta time-integration scheme. It is fully explicit, requires no matrix inversion, and is stable for any time-step for the heat equations. Burgers equation and the one- and two-dimensional heat equations are solved to demonstrate the accuracy and efficiency of the proposed algorithm. The present method is found to be very accurate and efficient when results are compared with analytic solutions.
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).
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.
Role of secondary instability theory and parabolized stability equations in transition modeling
NASA Technical Reports Server (NTRS)
El-Hady, Nabil M.; Dinavahi, Surya P.; Chang, Chau-Lyan; Zang, Thomas A.
1993-01-01
In modeling the laminar-turbulent transition region, the designer depends largely on benchmark data from experiments and/or direct numerical simulations that are usually extremely expensive. An understanding of the evolution of the Reynolds stresses, turbulent kinetic energy, and quantifies in the transport equations like the dissipation and production is essential in the modeling process. The secondary instability theory and the parabolized stability equations method are used to calculate these quantities, which are then compared with corresponding quantities calculated from available direct numerical simulation data for the incompressible boundary-layer flow of laminar-turbulent transition conditions. The potential of the secondary instability theory and the parabolized stability equations approach in predicting these quantities is discussed; results indicate that inexpensive data that are useful for transition modeling in the early stages of the transition region can be provided by these tools.
Undetermined Coefficient Problems for Quasi-Linear Parabolic Equations
1989-12-18
2.6) where H is a C’ function. This equation is of second kind Volterra type and can be u!uiquely solved for the function 0. Thus k = A- 1 = (I+ lz...2.7) where "Z is the resolvent operator corresponding to the Volterra integral equation (2.6) with smooth kernel H and 0k(0) + I’ ’(r)dr (2.8) We...along these lines was proposed by Lotka . In this treatment one assumes as known, a birth function P and a death function A. 0(a)da and A(a)da are the
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.
Volterra property of an problem of the Frankl type for an parabolic-hyperbolic equation
NASA Astrophysics Data System (ADS)
Dildabek, Gulnara; Saprygina, Marina B.
2017-09-01
In the paper spectral properties of non-local boundary value problem for an equation of the parabolic-hyperbolic type is investigated. The non-local condition binds the solution values at points on boundaries of the parabolic and hyperbolic parts of the domain with each other. This problem was first formulated by T. Sh. Kal'menov and M.A. Sadybekov. They proved the unique strong solvability of the problem. One special case of this problem was investigated in more detail in the work of G. Dildabek. A boundary value problem for the heat equation with conditions of the Samarskii-Ionlin type arises in solving this problem. In this paper, we show in what case this boundary value problem does not have eigenvalues.
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.
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.
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.
2011-01-01
DISTRIBUTION STATEMENT A. Approved for public release: distribution is unlimited. Vertical Structure of Shadow Zone Arrivals: Comparison of...depth of the receivers. The primary objective of this effort was to examine the vertical structure of these " shadow -zone arrivals," and to...SPICEX) were compared with parabolic equation simulations to determine the predictability of the extension of acoustic timefronts into the shadow zone
2008-09-30
Vertical Structure of Shadow Zone Arrivals: Comparison of Parabolic Equation Simulations and Acoustic Data Lora J. Van Uffelen Scripps...particular effort is to examine the vertical structure of these “ shadow -zone arrivals” and to determine the relative roles of different sources of oceanic...and the Basin Acoustic Seamount Scattering EXperiment (BASSEX).) The two closely spaced vertical line arrays (VLAs) together virtually spanned the
2007-09-30
Vertical Structure of Shadow Zone Arrivals: Comparison of Parabolic Equation Simulations and Acoustic Data Lora J. Van Uffelen Scripps...this particular effort is to examine the vertical structure of these “ shadow zone arrivals” and to determine the relative roles of different sources of...LOAPEX) and the Basin Acoustic Seamount Scattering EXperiment (BASSEX).) The two closely spaced vertical line arrays (VLAs) together virtually
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.
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
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.
Parabolic orbit determination. Comparison of the Olbers method and algebraic equations
NASA Astrophysics Data System (ADS)
Kuznetsov, V. B.
2016-05-01
In this paper, the Olbers method for the preliminary parabolic orbit determination (in the Lagrange-Subbotin modification) and the method based on systems of algebraic equations for two or three variables proposed by the author are compared. The maximum number of possible solutions is estimated. The problem of selection of the true solution from the set of solutions obtained both using additional equations and by the problem reduction to finding the objective function minimum is considered. The results of orbit determination of the comets 153P/Ikeya-Zhang and 2007 N3 Lulin are cited as examples.
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.
Doc, Jean-Baptiste; Lihoreau, Bertrand; Félix, Simon; Faure, Cédric; Dubois, Guillaume
2015-01-01
A three-dimensional wide-angle parabolic equation (3DPE) is used to model low frequency sound propagation in irregular urban canyons at low computational cost. This one-way wave equation is solved using the Alternating Direction Implicit method. A finite difference scheme adapted to the geometry of the urban environment is then developed. Abrupt variations of the street width are treated as a single scattering problem using the Kirchhoff approximation. Numerical results are compared with experimental data obtained on a scale model of a street. Comparisons show the ability of the 3DPE model to provide reliable transmitted fields even for large irregularities.
Solving parabolic and hyperbolic equations by the generalized finite difference method
NASA Astrophysics Data System (ADS)
Benito, J. J.; Urena, F.; Gavete, L.
2007-12-01
Classical finite difference schemes are in wide use today for approximately solving partial differential equations of mathematical physics. An evolution of the method of finite differences has been the development of generalized finite difference (GFD) method, that can be applied to irregular grids of points. In this paper the extension of the GFD to the explicit solution of parabolic and hyperbolic equations has been developed for partial differential equations with constant coefficients in the cases of considering one, two or three space dimensions. The convergence of the method has been studied and the truncation errors over irregular grids are given. Different examples have been solved using the explicit finite difference formulae and the criterion of stability. This has been expressed in function of the coefficients of the star equation for irregular clouds of nodes in one, two or three space dimensions. The numerical results show the accuracy obtained over irregular grids. This paper also includes the study of the maximum local error and the global error for different examples of parabolic and hyperbolic time-dependent equations.
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.
A relaxation technique for the parabolized Navier-Stokes (PNS) equations
NASA Technical Reports Server (NTRS)
Kaul, Upender K.
1986-01-01
A rapidly converging relaxation technique for the parabolized Navier-Stokes equations has been devised. The scheme is applicable in both supersonic and subsonic flows, but it is discussed here in the context of supersonic flows. The upstream propagating acoustic influence in the subsonic part of the flow is introduced semi-implicitly through the streamwise momentum equation applied on the body, and through a forward-differencing on the streamwise pressure gradient term in the interior. This procedure yields a new boundary condition on the energy in the total energy equation. The pressure-velocity system in the subsonic layer is coupled, but the positive time-like marching characteristic of the governing equations is still maintained. The relaxation technique is demontrated to work for a three-dimensional flow over a cone-flare in supersonic flight.
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.
Gilbert, Kenneth E
2015-01-01
The original formulation of the Green's function parabolic equation (GFPE) can have numerical accuracy problems for large normalized surface impedances. To solve the accuracy problem, an improved form of the GFPE has been developed. The improved GFPE formulation is similar to the original formulation, but it has the surface-wave pole "subtracted." The improved GFPE is shown to be accurate for surface impedances varying over 2 orders of magnitude, with the largest having a magnitude exceeding 1000. Also, the improved formulation is slightly faster than the original formulation because the surface-wave component does not have to be computed separately.
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.
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.
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.
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
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.
Noniterative three-dimensional grid generation using parabolic partial differential equations
NASA Technical Reports Server (NTRS)
Edwards, T. A.
1985-01-01
A new algorithm for generating three-dimensional grids has been developed and implemented which numerically solves a parabolic partial differential equation (PDE). The solution procedure marches outward in two coordinate directions, and requires inversion of a scalar tridiagonal system in the third. Source terms have been introduced to control the spacing and angle of grid lines near the grid boundaries, and to control the outer boundary point distribution. The method has been found to generate grids about 100 times faster than comparable grids generated via solution of elliptic PDEs, and produces smooth grids for finite-difference flow calculations.
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.
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.
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.
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.
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.
Frank, Scott D; Collis, Jon M; Odom, Robert I
2015-06-01
Oceanic T-waves are earthquake signals that originate when elastic waves interact with the fluid-elastic interface at the ocean bottom and are converted to acoustic waves in the ocean. These waves propagate long distances in the Sound Fixing and Ranging (SOFAR) channel and tend to be the largest observed arrivals from seismic events. Thus, an understanding of their generation is important for event detection, localization, and source-type discrimination. Recently benchmarked seismic self-starting fields are used to generate elastic parabolic equation solutions that demonstrate generation and propagation of oceanic T-waves in range-dependent underwater acoustic environments. Both downward sloping and abyssal ocean range-dependent environments are considered, and results demonstrate conversion of elastic waves into water-borne oceanic T-waves. Examples demonstrating long-range broadband T-wave propagation in range-dependent environments are shown. These results confirm that elastic parabolic equation solutions are valuable for characterization of the relationships between T-wave propagation and variations in range-dependent bathymetry or elastic material parameters, as well as for modeling T-wave receptions at hydrophone arrays or coastal receiving stations.
Elastic parabolic equation solutions for underwater acoustic problems using seismic sources.
Frank, Scott D; Odom, Robert I; Collis, Jon M
2013-03-01
Several problems of current interest involve elastic bottom range-dependent ocean environments with buried or earthquake-type sources, specifically oceanic T-wave propagation studies and interface wave related analyses. Additionally, observed deep shadow-zone arrivals are not predicted by ray theoretic methods, and attempts to model them with fluid-bottom parabolic equation solutions suggest that it may be necessary to account for elastic bottom interactions. In order to study energy conversion between elastic and acoustic waves, current elastic parabolic equation solutions must be modified to allow for seismic starting fields for underwater acoustic propagation environments. Two types of elastic self-starter are presented. An explosive-type source is implemented using a compressional self-starter and the resulting acoustic field is consistent with benchmark solutions. A shear wave self-starter is implemented and shown to generate transmission loss levels consistent with the explosive source. Source fields can be combined to generate starting fields for source types such as explosions, earthquakes, or pile driving. Examples demonstrate the use of source fields for shallow sources or deep ocean-bottom earthquake sources, where down slope conversion, a known T-wave generation mechanism, is modeled. Self-starters are interpreted in the context of the seismic moment tensor.
The numerical solution of the boundary inverse problem for a parabolic equation
NASA Astrophysics Data System (ADS)
Vasil'ev, V. V.; Vasilyeva, M. V.; Kardashevsky, A. M.
2016-10-01
Boundary inverse problems occupy an important place among the inverse problems of mathematical physics. They are connected with the problems of diagnosis, when additional measurements on one of the borders or inside the computational domain are necessary to restore the boundary regime in the other border, inaccessible to direct measurements. The boundary inverse problems belong to a class of conditionally correct problems, and therefore, their numerical solution requires the development of special computational algorithms. The paper deals with the solution of the boundary inverse problem for one-dimensional second-order parabolic equations, consisting in the restoration of boundary regime according to measurements inside the computational domain. For the numerical solution of the inverse problem it is proposed to use an analogue of a computational algorithm, proposed and developed to meet the challenges of identification of the right side of the parabolic equations in the works P.N.Vabishchevich and his students based on a special decomposition of solving the problem at each temporal layer. We present and discuss the results of a computational experiment conducted on model problems with quasi-solutions, including with random errors in the input data.
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.
Geometry of Conservation Laws for a Class of Parabolic Partial Differential Equations
NASA Astrophysics Data System (ADS)
Clelland, Jeanne Nielsen
1996-08-01
I consider the problem of computing the space of conservation laws for a second-order, parabolic partial differential equation for one function of three independent variables. The PDE is formulated as an exterior differential system {cal I} on a 12 -manifold M, and its conservation laws are identified with the vector space of closed 3-forms in the infinite prolongation of {cal I} modulo the so -called "trivial" conservation laws. I use the tools of exterior differential systems and Cartan's method of equivalence to study the structure of the space of conservation laws. My main result is:. Theorem. Any conservation law for a second-order, parabolic PDE for one function of three independent variables can be represented by a closed 3-form in the differential ideal {cal I} on the original 12-manifold M. I show that if a nontrivial conservation law exists, then {cal I} has a deprolongation to an equivalent system {cal J} on a 7-manifold N, and any conservation law for {cal I} can be expressed as a closed 3-form on N which lies in {cal J}. Furthermore, any such system in the real analytic category is locally equivalent to a system generated by a (parabolic) equation of the formA(u _{xx}u_{yy}-u_sp {xy}{2}) + B_1u_{xx }+2B_2u_{xy} +B_3u_ {yy}+C=0crwhere A, B_{i}, C are functions of x, y, t, u, u_{x}, u _{y}, u_{t}. I compute the space of conservation laws for several examples, and I begin the process of analyzing the general case using Cartan's method of equivalence. I show that the non-linearizable equation u_{t} = {1over2}e ^{-u}(u_{xx}+u_ {yy})has an infinite-dimensional space of conservation laws. This stands in contrast to the two-variable case, for which Bryant and Griffiths showed that any equation whose space of conservation laws has dimension 4 or more is locally equivalent to a linear equation, i.e., is linearizable.
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.
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.
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.
Degenerate Regularization of Forward-Backward Parabolic Equations: The Regularized Problem
NASA Astrophysics Data System (ADS)
Smarrazzo, Flavia; Tesei, Alberto
2012-04-01
We study a quasilinear parabolic equation of forward-backward type in one space dimension, under assumptions on the nonlinearity which hold for a number of important mathematical models (for example, the one-dimensional Perona-Malik equation), using a degenerate pseudoparabolic regularization proposed in Barenblatt et al. (SIAM J Math Anal 24:1414-1439, 1993), which takes time delay effects into account. We prove existence and uniqueness of positive solutions of the regularized problem in a space of Radon measures. We also study qualitative properties of such solutions, in particular concerning their decomposition into an absolutely continuous part and a singular part with respect to the Lebesgue measure. In this respect, the existence of a family of viscous entropy inequalities plays an important role.
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
Hasani, Mojtaba H; Gharibzadeh, Shahriar; Farjami, Yaghoub; Tavakkoli, Jahan
2013-09-01
Various numerical algorithms have been developed to solve the Khokhlov-Kuznetsov-Zabolotskaya (KZK) parabolic nonlinear wave equation. In this work, a generalized time-domain numerical algorithm is proposed to solve the diffraction term of the KZK equation. This algorithm solves the transverse Laplacian operator of the KZK equation in three-dimensional (3D) Cartesian coordinates using a finite-difference method based on the five-point implicit backward finite difference and the five-point Crank-Nicolson finite difference discretization techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term. In addition, a new empirical algorithm based on the LU decomposition technique is proposed to solve the system of linear equations obtained from this discretization. The proposed empirical algorithm improves the calculation speed and memory usage, while the order of computational complexity remains linear in calculation of the diffraction term in the KZK equation. For evaluating the accuracy of the proposed algorithm, two previously published algorithms are used as comparison references: the conventional 2D Texas code and its generalization for 3D geometries. The results show that the accuracy/efficiency performance of the proposed algorithm is comparable with the established time-domain methods.
NASA Astrophysics Data System (ADS)
Cohl, H. S.; Volkmer, H.
2012-09-01
A fundamental solution of Laplace’s equation in three dimensions is expanded in harmonic functions that are separated in parabolic or elliptic cylinder coordinates. There are two expansions in each case which reduce to expansions of the Bessel functions J0(kr) or K0(kr), r2 = (x - x0)2 + (y - y0)2, in parabolic and elliptic cylinder harmonics. Advantage is taken of the fact that K0(kr) is a fundamental solution and J0(kr) is the Riemann function of partial differential equations on the Euclidean plane.
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)
Barnett, Mark
This investigation is concerned with calculating strong viscous-inviscid interactions in two-dimensional laminar supersonic flows with and without separation. The equations solved are the so-called parabolized Navier-Stokes equations. The streamwise pressure gradient term is written as a combination of a forward and a backward difference to provide a path for upstream propogation of information. Global iteration is employed to repeatedly update the solution from an initial guess until convergence is achieved. Interacting boundary layer theory is discussed in order to provide some essential background information for the development of the present calculation technique. The numerical scheme used is an alternating direction explicit (ADE) procedure which is adapted from the Saul'yev method. This technique is chosen as an alternative to the more difficult to program multigrid strategy used by other investigators and the slower converging Gauss-Seidel method. Separated flows are computed using the ADE method. Only small or moderate separation bubbles are considered. This restriction permits simple approximations to the convective terms in reversed flow regions without introducing severe error since the reversed flow velocities are small. Results are presented for a number of geometries including compression ramps and humps on flat plates with separation. The present results are compared with those obtained by other investigators using the full Navier-Stokes equations and interacting boundary layer theory. Comparisons were found to be qualitatively good. The quantitative comparisons varied, however mesh refinement studies indicated that the parabolized Navier-Stokes solutions tended towards second-order accurate full Navier-Stokes solutions as well as interacting boundary layer solutions for which mesh refinement studies were also executed.
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}).
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.
Simultaneous determination of time and space-dependent coefficients in a parabolic equation
NASA Astrophysics Data System (ADS)
Hussein, M. S.; Lesnic, D.
2016-04-01
This paper investigates a couple of inverse problems of simultaneously determining time and space dependent coefficients in the parabolic heat equation using initial and boundary conditions of the direct problem and overdetermination conditions. The measurement data represented by these overdetermination conditions ensure that these inverse problems have unique solutions. However, the problems are still ill-posed since small errors in the input data cause large errors in the output solution. To overcome this instability we employ the Tikhonov regularization method. The finite-difference method (FDM) is employed as a direct solver which is fed iteratively in a nonlinear minimization routine. Both exact and noisy data are inverted. Numerical results for a few benchmark test examples are presented, discussed and assessed with respect to the FDM mesh size discretization, the level of noise with which the input data is contaminated, and the chosen regularization parameters.
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)
Kuehl, Joseph
2016-11-01
The parabolized stability equations (PSE) have been developed as an efficient and powerful tool for studying the stability of advection-dominated laminar flows. In this work, a new "wavepacket" formulation of the PSE is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening and results in disturbance saturation amplitudes consistent with experiment. A Mach 6 flared-cone example is presented. Support from the AFOSR Young Investigator Program via Grant FA9550-15-1-0129 is gratefully acknowledges.
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.
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.
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.
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.
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.
NASA Technical Reports Server (NTRS)
Mcaninch, G. L.; Myers, M. K.
1980-01-01
The parabolic approximation for the acoustic equations of motion is applied to the study of the sound field generated by a plane wave at or near grazing incidence to a finite impedance boundary. It is shown how this approximation accounts for effects neglected in the usual plane wave reflection analysis which, at grazing incidence, erroneously predicts complete cancellation of the incident field by the reflected field. Examples are presented which illustrate that the solution obtained by the parabolic approximation contains several of the physical phenomena known to occur in wave propagation near an absorbing boundary.
NASA Astrophysics Data System (ADS)
Cadette, Pierre E.
This thesis develops the theory for solving the parabolic equation (PE) using the Fourier Split-step method for the purpose of modeling tropospheric radiowave propagation over the sea surface. Beginning with Maxwell's equations, the standard parabolic equation (SPE) approximation is derived from a linearly polarized scalar wave equation in Cartesian coordinates. Then, an introduction to the Fourier Split-step method is presented as a solution to the PE equation. Next, we make necessary approximations to the PE formulation to appropriately represented propagation through the troposphere including a conformal transformation of the coordinate system and the inclusion of refractivity profiles to represent evaporation duct conditions. The PE derivation concludes with the incorporation of the effects of finite impedance boundary conditions and sea surface roughness, which has a Split-step solution using the mixed Fourier transform (MFT). Finally, numerical examples are given to compare the field predictions of two well known PE/Split-step propagation models: Tropospheric ElectroMagnetic Parabolic Equation Routine (TEMPER) and Advanced Propagation Model (APM).
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
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.
Analysis of measured broadband acoustic propagation using a parabolic equation approach
NASA Astrophysics Data System (ADS)
Gray, Mason; Knobles, D. P.; Koch, Robert
2003-10-01
A broadband parabolic equation (PE) approach is employed to simulate data taken from two Shallow Water Acoustic Measurement Instrument (SWAMI) bottom mounted horizontal line array (HLA) experiments in shallow water environments off the east coast of the U.S. and in the Gulf of Mexico. In both experiments the HLA was deployed along an isobath. Light bulbs were imploded at known depths and ranges in both the range-independent (array end fire) and range-dependent (array broadside) directions. For the east coast experimental data, the PE model is used to infer a seabed geoacoustic description in both the range-dependent and range-independent directions. Also, comparisons of modeled time series were made for the range-independent case with a broadband normal mode model to validate the PE calculations. In the Gulf of Mexico experiment, the sediment geoacoustic profile is well known from previous inversions and geophysical measurements. This known seabed description was used to simulate the range-dependent data. A broadband energy-conserving coupled mode approach is also employed to model the range-dependent propagation. This allows the physical mechanisms associated with range-dependent propagation to be examined in a quantitative manner for this shallow water environment. [Work supported by ONR.
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.
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
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.
On the homogenization of semilinear elliptic operators in perforated domains
Matevossian, O A; Pikulin, S V
2002-04-30
A second-order semilinear elliptic equation whose lower term has power-like growth at infinity with respect to the unknown function is considered. It is proved that a sequence of its solutions in perforated domains converges to a solution in the non-perforated domain as the diameters of the holes converge to zero with a rate depending on the power exponent of the lower term.
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
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.
Parameter identification in a semilinear hyperbolic system
NASA Astrophysics Data System (ADS)
Egger, H.; Kugler, T.; Strogies, N.
2017-05-01
We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and contraction arguments. We then investigate the inverse problem of recovering the unknown nonlinear damping law from additional boundary measurements of the pressure drop along the pipe. This coefficient inverse problem is shown to be ill-posed and a variational regularization method is considered for its stable solution. We prove existence of minimizers for the Tikhonov functional and discuss the convergence of the regularized solutions under an approximate source condition. The meaning of this condition and some arguments for its validity are discussed in detail and numerical results are presented for illustration of the theoretical findings.
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
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 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)
Hirsh, R. S.
1976-01-01
A numerical method is presented for solving the parabolic-elliptic Navier-Stokes equations. The solution procedure is applied to three-dimensional supersonic laminar jet flow issuing parallel with a supersonic free stream. A coordinate transformation is introduced which maps the boundaries at infinity into a finite computational domain in order to eliminate difficulties associated with the imposition of free-stream boundary conditions. Results are presented for an approximate circular jet, a square jet, varying aspect ratio rectangular jets, and interacting square jets. The solution behavior varies from axisymmetric to nearly two-dimensional in character. For cases where comparisons of the present results with those obtained from shear layer calculations could be made, agreement was good.
A 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 Astrophysics Data System (ADS)
Krylov, N. V.; Priola, E.
2017-09-01
We show, among other things, how knowing Schauder or Sobolev-space estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs for equations with coefficients depending only on the time variable with the same constants as in the case of the one-dimensional heat equation. The method is quite general and is based on using the Poisson stochastic process. It also applies to equations involving non-local operators. It looks like no other methods are available at this time and it is a very challenging problem to find a purely analytical approach to proving such results.
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.
On the existence of Lipschitz solutions to some forward-backward parabolic equations
NASA Astrophysics Data System (ADS)
Kim, Seonghak
In this dissertation we discuss a new approach for studying forward-backward quasilinear diffusion equations. Our main idea is motivated by a reformulation of such equations as non-homogeneous partial differential inclusions and relies on a Baire's category method. In this way the existence of Lipschitz solutions to the initial-boundary value problem of those equations is guaranteed under a certain density condition. Finally we study two important cases of anisotropic diffusion in which such density condition can be realized. The first case is on the Perona-Malik type equations. In 1990, P. Perona and J. Malik [35] proposed an anisotropic diffusion model, called the Perona-Malik model, in image processing ut = div (| Du|/ 1 + Du 2) for denoising and edge enhancement of a computer vision. Since then the dichotomy of numerical stability and theoretical ill-posedness of the model has attracted many interests in the name of the Perona-Malik paradox [28]. Our result in this case provides the model with mathematically rigorous solutions in any dimension that are even reflecting some phenomena observed in numerical simulations. The other case deals with the existence result on the Hollig type equations. In 1983, K. Hollig [20] proved, in dimension n = 1, the existence of infinitely many L2-weak solutions to the initial-boundary value problem of a forward-backward diffusion equation with non-monotone piecewise linear heat flux, and this piecewise linearity was much relaxed later by K. Zhang [45]. The work [20] was initially motivated by the Clausius-Duhem inequality in the second law of thermodynamics, where the negative of the heat flux may violate the monotonicity but should obey the Fourier inequality at least. Our result in this case generalizes [20, 45] to all dimensions.
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.
On a class of inverse problems for a parabolic equation with involution
NASA Astrophysics Data System (ADS)
Sarsenbi, Abdisalam A.
2017-09-01
A class of inverse problems for a heat equation with involution perturbation is considered using four different bound-ary conditions, namely, Dirichlet, Neumann, periodic and anti-periodic boundary conditions. Proved theorems on existence and uniqueness of solutions to these problems are presented. Solutions are obtained in the form of series expansion using a set of appropriate orthogonal basis for each problem. Convergence of the obtained solutions is also discussed.
Application of implicit scheme with AGE iterative method for solving fuzzy parabolic equation
NASA Astrophysics Data System (ADS)
Dahalan, A. A.; Muthuvalu, M. S.; Aruchunan, E.; Sulaiman, J.; Din, W. R. W.
2017-04-01
The objective of this paper is to analyze the application of the Alternating Group Explicit (AGE) iterative method by using central finite approximation equation to solve 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 Gauss-Seidel (GS) iterative method to illustrate their effectiveness and feasibility.
Domínguez, Jorge Bouza; Bérubé-Lauzière, Yves
2011-01-01
We introduce a system of coupled time-dependent parabolic simplified spherical harmonic equations to model the propagation of both excitation and fluorescence light in biological tissues. We resort to a finite element approach to obtain the time-dependent profile of the excitation and the fluorescence light fields in the medium. We present results for cases involving two geometries in three-dimensions: a homogeneous cylinder with an embedded fluorescent inclusion and a realistically-shaped rodent with an embedded inclusion alike an organ filled with a fluorescent probe. For the cylindrical geometry, we show the differences in the time-dependent fluorescence response for a point-like, a spherical, and a spherically Gaussian distributed fluorescent inclusion. From our results, we conclude that the model is able to describe the time-dependent excitation and fluorescent light transfer in small geometries with high absorption coefficients and in nondiffusive domains, as may be found in small animal diffuse optical tomography (DOT) and fluorescence DOT imaging. PMID:21483606
NASA Astrophysics Data System (ADS)
Eibert, Thomas F.
2003-04-01
Fourier split-step (FSS) solutions of the parabolic wave equation (PWE) represent wave fields in terms of plane wave decompositions. However, those field solutions are usually only valid in the air space above built-up terrain, whereas field predictions for modern wireless systems often require knowledge of the fields on a street level. Since FSS PWE solutions with large step sizes are not applicable for field computations between irregular scattering obstacles such as buildings, this problem is overcome by a two-step approach combining the FSS solution of the PWE with ray optical techniques to compute the fields at ground level in wooded and urbanized areas. To account for the great variety of propagation effects in a statistical sense, direct rays, reflected rays, diffracted rays and attenuated rays at typical receiver locations are included into the considerations. Comparisons to a wide variety of measured data show that this two-step approach produces better results than state of the art semiempirical field prediction techniques.
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.
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.
Spectral methods in time for a class of parabolic partial differential equations
Ierley, G. ); Spencer, B. ); Worthing, R. )
1992-09-01
In this paper, we introduce a fully spectral solution for the partial differential equation u[sub t] + uu[sub x] + vu[sub xx] + [mu]u[sub xxx] + [lambda]u[sub xxxx] = O. For periodic boundary conditions in space, the use of a Fourier expansion in x admits of a particularly efficient algorithm with respect to expansion of the time dependence in a Chebyshev series. Boundary conditions other than periodic may still be treated with reasonable, though lesser, efficiency. for all cases, very high accuracy is attainable at moderate computational cost relative to the expense of variable order finite difference methods in time. 14 refs., 9 figs.
Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation
NASA Astrophysics Data System (ADS)
Gomes, S. N.; Kalliadasis, S.; Papageorgiou, D. T.; Pavliotis, G. A.; Pradas, M.
2017-06-01
We present a novel control methodology to control the roughening processes of semilinear parabolic stochastic partial differential equations in one dimension, which we exemplify with the stochastic Kuramoto-Sivashinsky equation. The original equation is split into a linear stochastic and a nonlinear deterministic equation so that we can apply linear feedback control methods. Our control strategy is then based on two steps: first, stabilize the zero solution of the deterministic part and, second, control the roughness of the stochastic linear equation. We consider both periodic controls and point actuated ones, observing in all cases that the second moment of the solution evolves in time according to a power-law until it saturates at the desired controlled value.
Kostin, A B
2013-10-31
We study the inverse problem for a parabolic equation of recovering the source, that is, the right-hand side F(x,t)=h(x,t)f(x), where the function f(x) is unknown. To find f(x), along with the initial and boundary conditions, we also introduce an additional condition of nonlocal observation of the form ∫{sub 0}{sup T}u(x,t) dμ(t)=χ(x). We prove the Fredholm property for the problem stated in this way, and obtain sufficient conditions for the existence and uniqueness of a solution. These conditions are of the form of readily verifiable inequalities and put no restrictions on the value of T>0 or the diameter of the domain Ω under consideration. The proof uses a priori estimates and the qualitative properties of solutions of initial-boundary value problems for parabolic equations. Bibliography: 40 titles.
Numerical 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
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.
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.
NASA Astrophysics Data System (ADS)
Bizhanova, Galina I.
2017-09-01
Studying the solutions of the boundary value problems for the parabolic equations in the Hölder spaces we should require the fulfilment of the compatibility conditions of the initial and boundary data of all necessary orders, they provide the continuity of the solution and its derivatives of all acceptable orders up to the boundary and boundedness of the Hölder constants of the highest derivatives in the closure of a domain. Such problems describe the physical processes which go continuously all the time since the beginning of the processes. If we consider the processes (for instance, heating or cooling), which are not continuous at the initial moment, then compatibility conditions of the initial and boundary data of the problems modeling this processes can not be fulfilled, but processes go, that is the problems with incompatible initial and boundary data have physical sense and they can have the solutions. There is considered a multidimensional first boundary value problem for the parabolic equation with incompatible initial and boundary data of the zero and first orders. It is proved that the solution of the problem may be represented as a sum of a Hölder solution and two singular ones corresponding these two incompatible initial and boundary conditions. The singular solutions belong to the weighted space with parabolic weights and space of the functions, the highest derivatives of which are not continuous, but bounded. These regular and singular solutions are unique, the estimates for them are obtained.
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)
Zampolli, Mario; Haralabus, Georgios; Prior, Mark K.; Heaney, Kevin D.; Campbell, Richard
2014-05-01
Hydrophone stations of the Comprehensive Nuclear-Test-Ban Organisation (CTBTO) International Monitoring System (IMS), with the exception of one in Australia, comprise two triplets of submerged moored hydrophones, one North and one South of the island from which the respective system is deployed. Triplet distances vary approximately between 50 - 100 km from the island, with each triplet connected to the receiving shore equipment by fibre-optic submarine data cables. Once deployed, the systems relay underwater acoustic waveforms in the band 1 - 100 Hz in real time to Vienna via a shore based satellite link. The design life of hydroacoustic stations is at least 20 years, without need for any maintenance of the underwater system. The re-establishment of hydrophone monitoring station HA04 at Crozet (French Southern and Antarctic Territories) in the South-Western Indian Ocean is currently being investigated. In order to determine appropriate locations and depths for the installation of the hydrophones a number of constraints need to be taken into account and balanced against each other. The most important of these are (i) hydrophone depth in a region where the sound-speed profile is mostly upward refracting and the Sound Fixing and Ranging (SOFAR) channel is not well defined, (ii) a safe distance from the surface currents which occupy the first few hundred meters of the water column, (iii) seabed slopes that enable the safe deployment of the hydrophone mooring bases, (iv) avoidance of regions of high internal tide activity, (v) choice of locations to optimize basin and cross-basin scale acoustic coverage of each triplet and (vi) redundancy considerations so that one triplet can partially cover for the other one in case of necessity. A state-of-the-art three-dimensional (3-D) parabolic equation acoustic propagation model was used to model the propagation for a number of potential triplet locations. Criteria for short-listing candidate triplet locations were based on
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.
Apushkinskaya, D.E.; Nazarov, A.I.
1995-12-05
A linear parabolic equation with special singularities is studied. A priori boundary estimates are established for the maximum of the modulus of the gradient of a solution and for the Holder constants as well. These estimates depend linearly on the functions appearing on the right-hand side of the equation.
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 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
NASA Astrophysics Data System (ADS)
Lissy, Pierre
2015-11-01
In this paper, we prove explicit lower bounds for the cost of fast boundary controls for a class of linear equations of parabolic or dispersive type involving the spectral fractional Laplace operator. We notably deduce the following striking result: in the case of the heat equation controlled on the boundary, Miller's conjecture formulated in Miller (2004) [16] is not verified. Moreover, we also give a new lower bound for the minimal time needed to ensure the uniform controllability of the one-dimensional convection-diffusion equation with negative speed controlled on the left boundary, proving that the conjecture formulated in Coron and Guerrero (2005) [2] concerning this problem is also not verified at least for negative speeds. The proof is based on complex analysis, and more precisely on a representation formula for entire functions of exponential type, and is quite related to the moment method.
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.
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.
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 Astrophysics Data System (ADS)
Geiser, Jürgen
2008-07-01
In this paper we design higher-order time integrators for systems of stiff ordinary differential equations. We combine implicit Runge-Kutta and BDF methods with iterative operator-splitting methods to obtain higher-order methods. The idea of decoupling each complicated operator in simpler operators with an adapted time scale allows to solve the problems more efficiently. We compare our new methods with the higher-order fractional-stepping Runge-Kutta methods, developed for stiff ordinary differential equations. The benefit is the individual handling of each operator with adapted standard higher-order time integrators. The methods are applied to equations for convection-diffusion reactions and we obtain higher-order results. Finally we discuss the applications of the iterative operator-splitting methods to multi-dimensional and multi-physical problems.
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.
Runge-Kutta time semidiscretizations of semilinear PDEs with non-smooth data.
Wulff, Claudia; Evans, Chris
2016-01-01
We study semilinear evolution equations [Formula: see text] posed on a Hilbert space [Formula: see text], where A is normal and generates a strongly continuous semigroup, B is a smooth nonlinearity from [Formula: see text] to itself, and [Formula: see text], [Formula: see text], [Formula: see text]. In particular the one-dimensional semilinear wave equation and nonlinear Schrödinger equation with periodic, Neumann and Dirichlet boundary conditions fit into this framework. We discretize the evolution equation with an A-stable Runge-Kutta method in time, retaining continuous space, and prove convergence of order [Formula: see text] for non-smooth initial data [Formula: see text], where [Formula: see text], for a method of classical order p, extending a result by Brenner and Thomée for linear systems. Our approach is to project the semiflow and numerical method to spectral Galerkin approximations, and to balance the projection error with the error of the time discretization of the projected system. Numerical experiments suggest that our estimates are sharp.
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.
On the Existence of Positive Solutions of Semilinear Elliptic Equations.
1981-04-01
after twu inteqratiois by parts : k f uvI dx = k f uv1 dx *’,(I)v I x I dx and this contradicts . A, Nevertheless, something can be said whet (2) is 0t...integrating by parts , this yields N UV1 x = r lf(i V 1 x ) -tX 1V x -5- A! and therefore X < Al anji thus A* < a Remark 1.5: In the case where we have...11.3: The results of [36] show that the last part of the theorem is nearly optimal. We conjecture that the fact solutions of (0.1 - A) distinct from uX
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.
On a generalized Kirchhoff equation with sublinear nonlinearities
NASA Astrophysics Data System (ADS)
Santos Júnior, João R.; Siciliano, Gaetano
2017-07-01
In this paper we consider a generalized Kirchhoff? equation in a bounded domain under the effect of a sublinear nonlinearity. Under suitable assumptions on the data of the problem we show that, with a simple change of variable, the equation can be reduced to a classical semilinear equation and then studied with standard tools.
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)}}.
Parabolic non-diffracting beams: geometrical approach
NASA Astrophysics Data System (ADS)
Sosa-Sánchez, Citlalli Teresa; Silva-Ortigoza, Gilberto; Alejandro Juárez-Reyes, Salvador; de Jesús Cabrera-Rosas, Omar; Espíndola-Ramos, Ernesto; Julián-Macías, Israel; Ortega-Vidals, Paula
2017-08-01
The aim of this work is to present a geometrical characterization of parabolic non-diffracting beams. To this end, we compute the corresponding angular spectrum of the separable non-diffracting parabolic beams in order to determine the one-parameter family of solutions of the eikonal equation associated with this type of beam. Using this information, we compute the corresponding wavefronts and caustic, and find that qualitatively the caustic corresponds to the maximum of the intensity pattern and the wavefronts are deformations of conical surfaces.
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.
GNGA for general regions: Semilinear elliptic PDE and crossing eigenvalues
NASA Astrophysics Data System (ADS)
Hineman, Jay L.; Neuberger, John M.
2007-07-01
We consider the semilinear elliptic PDE Δ u + f( λ, u) = 0 with the zero-Dirichlet boundary condition on a family of regions, namely stadions. Linear problems on such regions have been widely studied in the past. We seek to observe the corresponding phenomena in our nonlinear setting. Using the Gradient Newton Galerkin Algorithm (GNGA) of Neuberger and Swift, we document bifurcation, nodal structure, and symmetry of solutions. This paper provides the first published instance where the GNGA is applied to general regions. Our investigation involves both the dimension of the stadions and the value λ as parameters. We find that the so-called crossings and avoided crossings of eigenvalues as the dimension of the stadions vary influences the symmetry and variational structure of nonlinear solutions in a natural way.
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.
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.
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)
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.
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.
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.
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
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.
Numerical performance of the parabolized ADM formulation of general relativity
Paschalidis, Vasileios; Hansen, Jakob; Khokhlov, Alexei
2008-09-15
In a recent paper [Vasileios Paschalidis, Phys. Rev. D 78, 024002 (2008).], the first coauthor presented a new parabolic extension (PADM) of the standard 3+1 Arnowitt, Deser, Misner (ADM) formulation of the equations of general relativity. By parabolizing first-order ADM in a certain way, the PADM formulation turns it into a well-posed system which resembles the structure of mixed hyperbolic-second-order parabolic partial differential equations. The surface of constraints of PADM becomes a local attractor for all solutions and all possible well-posed gauge conditions. This paper describes a numerical implementation of PADM and studies its accuracy and stability in a series of standard numerical tests. Numerical properties of PADM are compared with those of standard ADM and its hyperbolic Kidder, Scheel, Teukolsky (KST) extension. The PADM scheme is numerically stable, convergent, and second-order accurate. The new formulation has better control of the constraint-violating modes than ADM and KST.
Anisotropic electromagnetic wave propagation modeling using parabolic approximations
NASA Astrophysics Data System (ADS)
Brent, R. I.; Siegmann, W. L.; Jacobson, M. J.; Jacyna, G. M.
1990-12-01
A new method for the investigation of anisotropic electromagnetic wave propagation in the atmosphere is developed using parabolic approximations. Model equations for the electric field components are formulated which include the effects of both the inhomogeneous atmosphere and the static magnetic field of the earth. Application of parabolic-type approximations produces different systems of coupled parabolic equations. Each is valid for different relative magnitudes of components of the electric field. All admissible cases are then synthesized into one system which can be numerically examined, yielding solutions without a priori knowledge of electric field ratios. A specific example is presented and examined to understand static magnetic field effects on electromagnetic wave propagation. The influences of the earth's magnetic field are discussed and displayed in terms of electric components and the Poynting vector. Results demonstrate that the geomagnetic field can significantly influence HF atmospheric propagation.
Strict parabolicity of the multifractal spectrum at the Anderson transition
Suslov, I. M.
2016-11-15
Using the well-known “algebra of multifractality,” we derive the functional equation for anomalous dimensions Δ{sub q}, whose solution Δ = χq(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.
A Parabolic Problem with a Fractional Time Derivative
NASA Astrophysics Data System (ADS)
Allen, Mark; Caffarelli, Luis; Vasseur, Alexis
2016-08-01
We study regularity for a parabolic problem with fractional diffusion in space and a fractional time derivative. Our main result is a De Giorgi-Nash-Moser Hölder regularity theorem for solutions in a divergence form equation. We also prove results regarding existence, uniqueness, and higher regularity in time.
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.
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.
Commercialization of parabolic dish systems
NASA Technical Reports Server (NTRS)
Washom, B.
1982-01-01
The impact of recent federal tax and regulatory legislation on the commercialization of parabolic solar reflector technology is assessed. Specific areas in need of technical or economic improvement are noted.
The planar parabolic optical antenna.
Schoen, David T; Coenen, Toon; García de Abajo, F Javier; Brongersma, Mark L; Polman, Albert
2013-01-09
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.
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.
Non-Parabolic Hydrodynamic Formulations for the Simulation of Inhomogeneous Semiconductor Devices
NASA Technical Reports Server (NTRS)
Smith, A. W.; Brennan, K. F.
1996-01-01
Hydrodynamic models are becoming prevalent design tools for small scale devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band approximation to obtain fairly simple conservation equations. Interest in accounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models cannot fully describe the transport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two different non-parabolic formulations or the hydrodynamic model suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship ((hk)(exp 2)/2m = W(1 + alphaW). The second formulation makes use of a power law ((hk)(exp 2)/2m = xW(exp y)) for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulation readily produces closed form coefficients similar to those obtained using the parabolic band approximation. However, the fitting parameters (x,y) are only valid over a limited energy range. The physical significance of the band non-parabolicity is discussed as well as the advantages/disadvantages and approximations of the two non-parabolic models. A companion paper describes device simulations based on the three dispersion relationships; parabolic, Kane dispersion and power law dispersion.
Parabolic aircraft solidification experiments
NASA Technical Reports Server (NTRS)
Workman, Gary L. (Principal Investigator); Smith, Guy A.; OBrien, Susan
1996-01-01
A number of solidification experiments have been utilized throughout the Materials Processing in Space Program to provide an experimental environment which minimizes variables in solidification experiments. Two techniques of interest are directional solidification and isothermal casting. Because of the wide-spread use of these experimental techniques in space-based research, several MSAD experiments have been manifested for space flight. In addition to the microstructural analysis for interpretation of the experimental results from previous work with parabolic flights, it has become apparent that a better understanding of the phenomena occurring during solidification can be better understood if direct visualization of the solidification interface were possible. Our university has performed in several experimental studies such as this in recent years. The most recent was in visualizing the effect of convective flow phenomena on the KC-135 and prior to that were several successive contracts to perform directional solidification and isothermal casting experiments on the KC-135. Included in this work was the modification and utilization of the Convective Flow Analyzer (CFA), the Aircraft Isothermal Casting Furnace (ICF), and the Three-Zone Directional Solidification Furnace. These studies have contributed heavily to the mission of the Microgravity Science and Applications' Materials Science Program.
Analysis and conceptual design of a lunar radiator parabolic shade
NASA Technical Reports Server (NTRS)
Ewert, Michael K.; Clark, Craig S.
1991-01-01
On the moon, the available heat sink temperature for a vertical unshaded radiator at the equator is 322 K. A method of reducing this heat sink temperature using a parabolic trough shading device was investigated. A steady state heat balance was performed to predict the available heat sink temperature. The effect of optical surface properties on system performance was investigated. Various geometric configurations were also evaluated. A flexible shade conceptual design is presented which greatly reduces the weight and stowed volume of the system. The concept makes use of the natural catenary shape assumed by a flexible material when supported at two points. The catenary shape is very near parabolic. The lunar radiator parabolic shade design presented integrates the energy collection and rejection of a solar dynamic power cycle with the moderate temperature waste heat rejection of a lunar habitat.
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)
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)
Shenandoah parabolic dish solar collector
Kinoshita, G.S.
1985-01-01
The objectives of the Shenandoah, Georgia, Solar Total Energy System are to design, construct, test, and operate a solar energy system to obtain experience with large-scale hardware systems for future applications. This report describes the initial design and testing activities conducted to select and develop a collector that would serve the need of such a solar total energy system. The parabolic dish was selected as the collector most likely to maximize energy collection as required by this specific site. The fabrication, testing, and installation of the parabolic dish collector incorporating improvements identified during the development testing phase are described.
Composite isogrid structures for parabolic surfaces
NASA Technical Reports Server (NTRS)
Silverman, Edward M. (Inventor); Boyd, Jr., William E. (Inventor); Rhodes, Marvin D. (Inventor); Dyer, Jack E. (Inventor)
2000-01-01
The invention relates to high stiffness parabolic structures utilizing integral reinforced grids. The parabolic structures implement the use of isogrid structures which incorporate unique and efficient orthotropic patterns for efficient stiffness and structural stability.
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.
Spectral stability of periodic waves in the generalized reduced Ostrovsky equation
NASA Astrophysics Data System (ADS)
Geyer, Anna; Pelinovsky, Dmitry E.
2017-07-01
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.
Transversal filter for parabolic phase equalization
NASA Technical Reports Server (NTRS)
Kelly, Larry R. (Inventor); Waugh, Geoffrey S. (Inventor)
1993-01-01
An equalizer (10) for removing parabolic phase distortion from an analog signal (3), utilizing a pair of series connected transversal filters. The parabolic phase distortion is cancelled by generating an inverse parabolic approximation using a sinusoidal phase control filter (18). The signal (3) is then passed through an amplitude control filter (21) to remove magnitude ripple components.
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.
Parabolic tapers for overmoded waveguides
Doane, J.L.
1983-11-25
A waveguide taper with a parabolic profile, in which the distance along the taper axis varies as the square of the tapered dimension, provides less mode conversion than equal length linear tapers and is easier to fabricate than other non-linear tapers.
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.
A Quasi-Parabolic technique for computation of three-dimensional viscous flows
NASA Technical Reports Server (NTRS)
Spradley, L. W.; Stalnaker, J. F.; Xiques, K. E.
1981-01-01
A computational technique is presented for obtaining flowfield solutions to a parabolic form of the Navier-Stokes equations. The point of departure is the General Interpolant Method (GIM) which provides a discretization for partial differential equations on arbitrary three-dimensional geometries. The new scheme, termed Quasi-Parabolic, treats the parabolized equations but with 'time-like' terms appended. Addition of these extra terms, which are relaxed by iteration, avoid many of the singularities inherent in classical parabolic Navier-Stokes methods. Streamwise derivatives are approximated by three-point backward differences and the cross plane operators use an alternating forward-backward sweep. A two-step sequence is used to implement the difference scheme in the spatial dimensions and a time-like relaxation converges the quasi-parabolic procedure at each plane. Solutions are presented for flows in two and three dimensions. Inviscid flows are solved for internal and external applications and viscous flows in boundary layers and free shear layers are also computed with the GIM/Quasi-Parabolic scheme.
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.
Curvilinear parabolic approximation for surface wave transformation with wave current interaction
NASA Astrophysics Data System (ADS)
Shi, Fengyan; Kirby, James T.
2005-04-01
The direct coordinate transformation method, which only transforms independent variables and retains Cartesian dependent variables, may not be an appropriate method for the purpose of simplifying the curvilinear parabolic approximation of the vector form of the wave-current equation given by Kirby [Higher-order approximations in the parabolic equation method for water waves, J. Geophys. Res. 91 (1986) 933-952]. In this paper, the covariant-contravariant tensor method is used for the curvilinear parabolic approximation. We use the covariant components of the wave number vector and contravariant components of the current velocity vector so that the derivation of the curvilinear equation closely follows the higher-order approximation in rectangular Cartesian coordinates in Kirby [Higher-order approximations in the parabolic equation method for water waves, J. Geophys. Res. 91 (1986) 933-952]. The resulting curvilinear equation can be easily implemented using the existing model structure and numerical schemes adopted in the Cartesian parabolic wave model [J.T. Kirby, R.A. Dalrymple, F. Shi, Combined Refraction/Diffraction Model REF/DIF 1, Version 2.6. Documentation and User's Manual, Research Report, Center for Applied Coastal Research, Department of Civil and Environmental Engineering, University of Delaware, Newark, 2004]. Several examples of wave simulations in curvilinear coordinate systems, including a case with wave-current interaction, are shown with comparisons to theoretical solutions or measurement data.
Multiplicity results for sign changing bound state solutions of a semilinear equation
NASA Astrophysics Data System (ADS)
Cortázar, Carmen; García-Huidobro, Marta; Herreros, Pilar
2015-12-01
In this paper we give conditions on $f$ so that problem $$ \\Delta u +f(u)=0,\\quad x\\in \\mathbb{R}^N, N\\ge 2, $$ has at least two radial bound state solutions with any prescribed number of zeros, and such that $u(0)$ belongs to a specific subinterval of $(0,\\infty)$. This property will allow us to give conditions on $f$ so that this problem has at least any given number of radial solutions having a prescribed number of zeros.
On the uniqueness of sign changing bound state solutions of a semilinear equation
NASA Astrophysics Data System (ADS)
Cortázar, Carmen; García-Huidobro, Marta; Yarur, Cecilia S.
2011-07-01
We establish the uniqueness of the higher radial bound state solutions of $$ \\Delta u +f(u)=0,\\quad x\\in \\RR^n. \\leqno(P) $$ We assume that the nonlinearity $f\\in C(-\\infty,\\infty)$ is an odd function satisfying some convexity and growth conditions, and either has one zero at $b>0$, is non positive and not identically 0 in $(0,b)$, and is differentiable and positive $[b,\\infty)$, or is positive and differentiable in $[0,\\infty)$.
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
Propagation of hypergeometric laser beams in a medium with a parabolic refractive index
NASA Astrophysics Data System (ADS)
Kotlyar, V. V.; Kovalev, A. A.; Nalimov, A. G.
2013-12-01
An expression to describe the complex amplitude of a family of paraxial hypergeometric laser beams propagating in a parabolic-index fiber is proposed. A particular case of a Gaussian optical vortex propagating in a parabolic-index fiber is studied. Under definite parameters, the Gaussian optical vortices become the modes of the medium. This is a new family of paraxial modes derived for the parabolic-index medium. A wide class of solutions of nonparaxial Helmholtz equations that describe modes in a parabolic refractive index medium is derived in the cylindrical coordinate system. As the solutions derived are proportional to Kummer’s functions, only those of them which are coincident with the nonparaxial Laguerre-Gaussian modes possess a finite energy, meaning that they are physically implementable. A definite length of the graded-index fiber is treated as a parabolic lens, and expressions for the numerical aperture and the focal spot size are deduced. An explicit expression for the radii of the rings of a binary lens approximating a parabolic-index lens is derived. Finite-difference time-domain simulation has shown that using a binary parabolic-index microlens with a refractive index of 1.5, a linearly polarized Gaussian beam can be focused into an elliptic focal spot which is almost devoid of side-lobes and has a smaller full width at half maximum diameter of 0.45 of the incident wavelength.
Shock wave convergence in water with parabolic wall boundaries
Yanuka, D.; Shafer, D.; Krasik, Ya.
2015-04-28
The convergence of shock waves in water, where the cross section of the boundaries between which the shock wave propagates is either straight or parabolic, was studied. The shock wave was generated by underwater electrical explosions of planar Cu wire arrays using a high-current generator with a peak output current of ∼45 kA and rise time of ∼80 ns. The boundaries of the walls between which the shock wave propagates were symmetric along the z axis, which is defined by the direction of the exploding wires. It was shown that with walls having a parabolic cross section, the shock waves converge faster and the pressure in the vicinity of the line of convergence, calculated by two-dimensional hydrodynamic simulations coupled with the equations of state of water and copper, is also larger.
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
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.
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.
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.
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 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
Yanuka, D.; Zinowits, H. E.; Antonov, O.; Efimov, S.; Virozub, A.; Krasik, Ya. E.
2016-07-15
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.
On the solution of the Liouville equation
NASA Astrophysics Data System (ADS)
Menotti, Pietro
2017-09-01
We give a short and rigorous proof of the existence and uniqueness of the solution of the Liouville equation with sources, both elliptic and parabolic, on the sphere and on all higher genus compact Riemann surfaces.
NASA Astrophysics Data System (ADS)
Hazaimeh, Haziem M.
2017-06-01
In this article we study that the linear-implicit Euler method of the solution of nonlinear stochastic wave equation in 2 dimensions has the non-exploding explicit representation and is mean consistent. In [15], we proved that the strong Fourier solution of the semi-linear wave equations exists and is unique on an appropriate Hilbert space. A linear-implicit Euler method is used to discretize the related Fourier coefficients and mean consistency is discussed.
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.
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 .
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.
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
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.
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.
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.
Dynamics Near the Ground State for the Energy Critical Nonlinear Heat Equation in Large Dimensions
NASA Astrophysics Data System (ADS)
Collot, Charles; Merle, Frank; Raphaël, Pierre
2017-05-01
We consider the energy critical semilinear heat equation partial_tu = Δ u + |u|^{4/d-2}u, \\quad x \\in {R}^d and give a complete classification of the flow near the ground state solitary wave Q(x) = 1/(1+{|x|^2{d(d-2)})^{d-2/2}} in dimension {d ≥ 7}, in the energy critical topology and without radial symmetry assumption. Given an initial data {Q + ɛ_0} with {|\
Regularity of the global attractor for the plate equation with nonlocal nonlinearity in ℝn
NASA Astrophysics Data System (ADS)
Yayla, Sema
2017-07-01
This paper deals with the regularity of the global attractor for the semilinear plate equation with nonlocal nonlinearity. We proved the existence of the global attractor in the phase space H2 (ℝn) × L2 (ℝn) in our earlier work. In this study, we show that the global attractor is a bounded subset of H4 (ℝn) × H2 (ℝn).
Energy spectra of a two dimensional parabolic quantum dot in an external field
NASA Astrophysics Data System (ADS)
Rani, Richa; Chand, Fakir
2017-07-01
Here we investigate the electronic energy spectra of a 2-dimensional two electrons parabolic quantum dot which is created by a lateral confining potential. The analytical results are obtained by solving the Schrödinger equation using series expansion method with an ansatz to the wave function. It is observed that, the energy eigenvalues of the parabolic quantum dot increase with increase in magnetic field. The results of this work may have some bearings in growth and development of quantum dot based optoelectronic devices.
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.
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.
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.
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.
Space-time adaptive hierarchical model reduction for parabolic equations.
Perotto, Simona; Zilio, Alessandro
Surrogate solutions and surrogate models for complex problems in many fields of science and engineering represent an important recent research line towards the construction of the best trade-off between modeling reliability and computational efficiency. Among surrogate models, hierarchical model (HiMod) reduction provides an effective approach for phenomena characterized by a dominant direction in their dynamics. HiMod approach obtains 1D models naturally enhanced by the inclusion of the effect of the transverse dynamics. HiMod reduction couples a finite element approximation along the mainstream with a locally tunable modal representation of the transverse dynamics. In particular, we focus on the pointwise HiMod reduction strategy, where the modal tuning is performed on each finite element node. We formalize the pointwise HiMod approach in an unsteady setting, by resorting to a model discontinuous in time, continuous and hierarchically reduced in space (c[M([Formula: see text])G(s)]-dG(q) approximation). The selection of the modal distribution and of the space-time discretization is automatically performed via an adaptive procedure based on an a posteriori analysis of the global error. The final outcome of this procedure is a table, named HiMod lookup diagram, that sets the time partition and, for each time interval, the corresponding 1D finite element mesh together with the associated modal distribution. The results of the numerical verification confirm the robustness of the proposed adaptive procedure in terms of accuracy, sensitivity with respect to the goal quantity and the boundary conditions, and the computational saving. Finally, the validation results in the groundwater experimental setting are promising. The extension of the HiMod reduction to an unsteady framework represents a crucial step with a view to practical engineering applications. Moreover, the results of the validation phase confirm that HiMod approximation is a viable approach.
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.
Elastic Bottom Propagation Mechanisms Investigated by Parabolic Equation Methods
2014-09-30
these waves to the otherwise quiet acoustic field of the deep ocean all require study, in particular as potential sources of unexplained deep shadow ...also been detected by hydrophones near the seafloor[13] well below the SOFAR channel, suggesting these waves could influence deep- shadow zone...channel propagation of oceanic T waves from seismic sources in the presence of intervening seamounts or coral reef barriers is established using elastic PE
Elastic Bottom Propagation Mechanisms Investigated by Parabolic Equation Methods
2013-09-30
potential sources of unexplained deep shadow zone arrivals that have been experimentally observed below the ray-theoretic turning point.[1, 2] APPROACH...that these waves could influence deep- shadow zone arrivals observed during NPAL.[1, 2] Elastic wave theory predicts that the Scholte wave speed is...layered elastic bottom and an intervening seamount . Range-dependence associated with the seamount begins 15 km from the source. Acoustic wave energy
Stable Equilibria in a Scalar Parabolic Equation with Variable Diffusion,
1983-03-25
Universita Degli Studi di Roma, Facolta d’Ingegneria, Istituto di Matematica Applicata, 00161 Roma, Italy. Research supported in part by C.N.R., NATO Senior...that does not vanish in (-1,1]. Thus X0 < 0 is the largest eigenvalue of (13). Therefore, we can state Proposition 1. A necessary and sufficient...a(0,a0,1) = kn. On the other hand Proposition I and the stability of uI imply a(1,ai,I) < 0. Therefore, by continuity there exist 0 <p 1 < p< pk ə
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
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.
Schnider, T W; Minto, C F; Fiset, P; Gregg, K M; Shafer, S L
1996-03-01
The electroencephalographic (EEG) effect of benzodiazepines, and midazolam in particular, has been described using simple measures such as total power in the beta band, waves.s(-1) in the beta band and total power from aperiodic analysis. All these parameters failed to consistently describe the EEG effect of midazolam in a study in which large doses of midazolam were infused, and the effect subsequently reversed with flumazenil. Using a technique called semilinear correlation it is possible to extract a parameter from the EEG that is statistically optimally correlated with the apparent concentration of the benzodiazepine in the effect site. This method has been used to develop new univariate measures of the effects of opioids on the EEG but has not previously been applied to the EEG effects of benzodiazepines. Data from ten subjects who received an infusion of midazolam were analyzed. The data were divided into "learning" and "test" sets. The learning set consisted of ten studies in which the volunteers received an infusion of 2.5 mg.min(-1) midazolam. Semilinear canonical correlation was used to extract an univariate descriptor of the EEG effect by weighting the different frequency bands of the EEG power spectrum. The test set comprised the same subjects on subsequent visits, in which the subjects received a continuous infusion of midazolam to maintain 20% or 80% of the peak drug effect for 3h. Twenty minutes after start of the midazolam infusion, the patient received an infusion of flumazenil to acutely reverse the benzodiazepine drug effect. The weights obtained from the learning set were tested prospectively in the test set, based on the coefficient of multiple determination, R(2), obtained by fitting the EEG effect to a sigmoid Emax model. The canonical univariate parameter of benzodiazepine drug effect on the EEG, when applied to the test set receiving the midazolam infusion with flumazenil reversal, yielded a median R(2) of 0.78. The median R(2) of six
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.
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
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.
Parabolic flight as a spaceflight analog.
Shelhamer, Mark
2016-06-15
Ground-based analog facilities have had wide use in mimicking some of the features of spaceflight in a more-controlled and less-expensive manner. One such analog is parabolic flight, in which an aircraft flies repeated parabolic trajectories that provide short-duration periods of free fall (0 g) alternating with high-g pullout or recovery phases. Parabolic flight is unique in being able to provide true 0 g in a ground-based facility. Accordingly, it lends itself well to the investigation of specific areas of human spaceflight that can benefit from this capability, which predominantly includes neurovestibular effects, but also others such as human factors, locomotion, and medical procedures. Applications to research in artificial gravity and to effects likely to occur in upcoming commercial suborbital flights are also possible. Copyright © 2016 the American Physiological Society.
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.
Semi-parabolic Bifurcations in Complex Dimension Two
NASA Astrophysics Data System (ADS)
Bedford, Eric; Smillie, John; Ueda, Tetsuo
2017-01-01
Parabolic bifurcations in one complex dimension demonstrate a wide variety of interesting dynamical phenomena. In this paper we consider the bifurcations of a holomorphic diffeomorphism in two complex dimensions with a semi-parabolic, semiattracting fixed point.
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.
Rotational Disruption of Comets with Parabolic Orbits
NASA Astrophysics Data System (ADS)
Drahus, Michal
2014-11-01
One of the most fundamental problems in planetary science is the natural lifetime of comets, which is limited by several processes, most notably by spontaneous disruption of the nucleus. While the underlying mechanism is uncertain, rapid rotation is often suspected. To address this problem, I derived the probability of rotational disruption, and investigated it for comets with parabolic orbits as a function of perihelion distance and nucleus size for a range of input parameters. The disruption probability is defined as the ratio of expected change in the rotation rate to the allowable span of the rotation rate, the latter being limited by the critical rotation rate (prograde and retrograde), which I adopted from Davidsson (2001, Icarus 149, 375). The expected change in the rotation rate, resulting from the action of torques generated by mass loss, is calculated following the standard approach (e.g. Drahus et al. 2011, ApJL 734, L4, and ref. therein), but taking into account the suspected decrease of the net torque with an increasing active fraction of the nucleus (Jewitt 1997, EM&P 79, 35; Samarasinha & Mueller 2013, ApJL 775, L10). The sublimation flux is obtained from the standard energy balance equation (e.g. Cowan & A’Hearn 1979, M&P 21, 155), but I also take into account extinction of sunlight in the dust coma. I find that close to the Sun coma transmission steeply decreases with a decreasing heliocentric distance, resulting in the sublimation flux at a remarkably constant level, and also that coma transmission decreases with an increasing nucleus size, both properties being critically important in the calculation of sublimation flux for large sungrazers. The obtained rotational-disruption probability features several interesting properties. It has a well-defined regime occupied by smaller comets closely approaching the Sun, for which rotational disruption is unavoidable regardless of the original rotation state. Moreover, the probability function offers a
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.
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.
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.
Parabolic Dish Concentrator (PDC-2) Development
NASA Technical Reports Server (NTRS)
Rafinejad, D.
1984-01-01
The design of the Parabolic Dish Concentrator (PDC-2) is described. The following five subsystems of the concentrator are discussed: (1) reflective surface subsystem, (2) support structure subsystem, (3) foundation, (4) drive subsystem, and (5) electrical and control subsystem. The status of the PDC-2 development project is assessed.
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
Manufacture of large, lightweight parabolic antennas
NASA Technical Reports Server (NTRS)
Hooper, S. W.
1973-01-01
Antenna was produced in segments. Parabole sections were built up as aluminum foil sandwich with core bonded by film adhesive; whole structure was oven-cured after assembly. Structure was assembled with special tool for splice-bonding segments into complete dish, and inflatable bladder to apply pressure at joints during cure.
The linear regulator problem for parabolic systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Kunisch, K.
1983-01-01
An approximation framework is presented for computation (in finite imensional spaces) of Riccati operators that can be guaranteed to converge to the Riccati operator in feedback controls for abstract evolution systems in a Hilbert space. It is shown how these results may be used in the linear optimal regulator problem for a large class of parabolic systems.
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).
Sampled-Data Fuzzy Control for Nonlinear Coupled Parabolic PDE-ODE Systems.
Wang, Zi-Peng; Wu, Huai-Ning; Li, Han-Xiong
2017-09-01
In this paper, a sampled-data fuzzy control problem is addressed for a class of nonlinear coupled systems, which are described by a parabolic partial differential equation (PDE) and an ordinary differential equation (ODE). Initially, the nonlinear coupled system is accurately represented by the Takagi-Sugeno (T-S) fuzzy coupled parabolic PDE-ODE model. Then, based on the T-S fuzzy model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller such that the closed-loop coupled system is exponentially stable, where the sampled-data fuzzy controller consists of the ODE state feedback and the PDE static output feedback under spatially averaged measurements. The stabilization condition is presented in terms of a set of linear matrix inequalities. Finally, simulation results on the control of a hypersonic rocket car are given to illustrate the effectiveness of the proposed design method.
Bruhn, J; Rehberg, B; Röpcke, H; Bouillon, T; Hoeft, A
2002-10-01
The common parameters of the electroencephalogram quantify a shift of its power spectrum towards lower frequencies with increasing anaesthetic drug concentrations (e.g. spectral-edge frequency 95). These ad hoc parameters are not optimized for the content of information with regard to drug effect. Using semilinear canonical correlation, different frequency ranges (bins) of the power spectrum can be weighted for sensitivity to changes of drug concentration by multiplying their power with iteratively determined coefficients, yielding a new (canonical univariate) electroencephalographic parameter. Electroencephalographic data obtained during application of volatile anaesthetics were used: isoflurane (n = 6), desflurane (7), sevoflurane (7), desflurane during surgical stimulation (12). Volatile anaesthetic end-tidal concentrations varied between 0.5 and 1.6 minimum alveolar concentration (MAC). The canonical univariate parameter and spectral-edge frequency 95 were determined and their correlation with the volatile anaesthetic effect compartment concentration, obtained by simultaneous pharmacokinetic-pharmacodynamic modelling, were compared. The canonical univariate parameter with individually optimized coefficients, but not with mean coefficients, was superior to the spectral-edge frequency 95 as a measure of anaesthetic drug effect. No significant differences of the coefficients were found between the three volatile anaesthetics or between the data with or without surgical stimulus. The coefficients for volatile anaesthetics were similar to the coefficients for opioids, but different from coefficients for propofol and midazolam. The canonical univariate parameter calculated with individually optimized coefficients, but not with mean coefficients, correlates more accurately and consistently with the effect site concentrations of volatile anaesthetics than with spectral-edge frequency 95.
Investigation of a Parabolic Iterative Solver for Three-dimensional Configurations
NASA Technical Reports Server (NTRS)
Nark, Douglas M.; Watson, Willie R.; Mani, Ramani
2007-01-01
A parabolic iterative solution procedure is investigated that seeks to extend the parabolic approximation used within the internal propagation module of the duct noise propagation and radiation code CDUCT-LaRC. The governing convected Helmholtz equation is split into a set of coupled equations governing propagation in the positive and negative directions. The proposed method utilizes an iterative procedure to solve the coupled equations in an attempt to account for possible reflections from internal bifurcations, impedance discontinuities, and duct terminations. A geometry consistent with the NASA Langley Curved Duct Test Rig is considered and the effects of acoustic treatment and non-anechoic termination are included. Two numerical implementations are studied and preliminary results indicate that improved accuracy in predicted amplitude and phase can be obtained for modes at a cut-off ratio of 1.7. Further predictions for modes at a cut-off ratio of 1.1 show improvement in predicted phase at the expense of increased amplitude error. Possible methods of improvement are suggested based on analytic and numerical analysis. It is hoped that coupling the parabolic iterative approach with less efficient, high fidelity finite element approaches will ultimately provide the capability to perform efficient, higher fidelity acoustic calculations within complex 3-D geometries for impedance eduction and noise propagation and radiation predictions.
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.
Prolonging Microgravity on Parabolic Airplane Flights
NASA Technical Reports Server (NTRS)
Robinson, David W.
2003-01-01
Three techniques have been proposed to prolong the intervals of time available for microgravity experiments aboard airplanes flown along parabolic trajectories. Typically, a pilot strives to keep an airplane on such a trajectory during a nominal time interval as long as 25 seconds, and an experimental apparatus is released to float freely in the airplane cabin to take advantage of the microgravitational environment of the trajectory for as long as possible. It is usually not possible to maintain effective microgravity during the entire nominal time interval because random aerodynamic forces and fluctuations in pilot control inputs cause the airplane to deviate slightly from a perfect parabolic trajectory, such that the freely floating apparatus bumps into the ceiling, floor, or a wall of the airplane before the completion of the parabola.
New Parabolic Flight Platform for Microgravity Experiments
NASA Astrophysics Data System (ADS)
Valdatta, M.; Brucas, D.; Tomkus, V.; Ragauskas, U.; Razgunas, M.
2015-09-01
Microgravity experiments are important in field of space development; they give the possibility to simulate near-space conditions to test new kind of systems and subsystems for space or to perform biological researches. The existing platforms, to perform reduced gravity experiments, allow achieving the targets of the researches. Otherwise these platforms are either very expensive or of a very short duration. Another important issue is the repeatability of the experiment for some platforms. Fast repeatability platform (ensuring fast turnaround time), can guarantee only few seconds of microgravity time. For these reason there is the need of platforms for microgravity experiments that will cover the needs of all the experiments that cannot fit into required time, cost and repeatability of any other experiment methodology. The paper explains the mission plan and first scientific data of new family of parabolic unmanned planes. Each of these planes can be used to achieve scientific parabolic flight.
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.
Parabolic dish collectors - A solar option
NASA Technical Reports Server (NTRS)
Truscello, V. C.
1981-01-01
A description is given of several parabolic-dish high temperature solar thermal systems currently undergoing performance trials. A single parabolic dish has the potential for generating 20 to 30 kW of electricity with fluid temperatures from 300 to 1650 C. Each dish is a complete power-producing unit, and may function either independently or as part of a group of linked modules. The two dish designs under consideration are of 11 and 12 meter diameters, yielding receiver operating temperatures of 925 and 815 C, respectively. The receiver designs described include (1) an organic working fluid (toluene) Rankine cycle engine; (2) a Brayton open cycle unit incorporating a hybrid combustion chamber and nozzle and a shaft-coupled permanent magnet alternator; and (3) a modified Stirling cycle device originally designed for automotive use. Also considered are thermal buffer energy storage and thermochemical transport and storage.
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
The second parabolic flight campaign for students.
Ockels, W J
1996-02-01
In conjunction with the European Commission's 'European Week for Scientific and Technological Culture' in November, ESA organised the second parabolic flight campaign for students. Students selected through a competition, were again given the unique opportunity of experiencing weightlessness as they performed their own scientific experiment during a parabolic flight. The experiments covered a wide variety of disciplines. Some illustrated well the effect of microgravity while others may offer new and far-reaching scientific results. The primary goal, however, is to educate and motivate the students rather than to obtain new research. It is hoped that the campaign will stimulate the next generation to think about space and the potential of microgravity. It is in that way that an innovative future user community for the International Space Station Alpha can be built. The great enthusiasm shown by many students and the wide coverage provided by the media also demonstrate the interest in space and the promotional value of the campaign.
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.
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.
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.
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.
Parabolic Trough Organic Rankine Cycle Power Plant
Canada, S.; Cohen, G.; Cable, R.; Brosseau, D.; Price, H.
2005-01-01
Arizona Public Service (APS) is required to generate a portion of its electricity from solar resources in order to satisfy its obligation under the Arizona Environmental Portfolio Standard (EPS). In recent years, APS has installed and operates over 4.5 MWe of fixed, tracking, and concentrating photovoltaic systems to help meet the solar portion of this obligation and to develop an understanding of which solar technologies provide the best cost and performance to meet utility needs. During FY04, APS began construction of a 1-MWe parabolic trough concentrating solar power plant. This plant represents the first parabolic trough plant to begin construction since 1991. The plant will also be the first commercial deployment of the Solargenix parabolic trough collector technology developed under contract to the National Renewable Energy Laboratory (NREL). The plant will use an organic Rankine cycle (ORC) power plant, provided by Ormat. The ORC power plant is much simpler than a conventional steam Rankine cycle power plant and allows unattended operation of the facility.
Simulation of parabolic reflectors for ultraviolet phototherapy
NASA Astrophysics Data System (ADS)
Grimes, David Robert
2016-08-01
Ultraviolet (UVR) phototherapy is widely used to treat an array of skin conditions, including psoriasis, eczema and vitiligo. For such interventions, a quantified dose is vital if the treatment is to be both biologically effective and to avoid the detrimental effects of over-dosing. As dose is absorbed at surface level, the orientation of patient site with respect to the UVR lamps modulates effective dose. Previous investigations have modelled this behaviour, and examined the impact of shaped anodized aluminium reflectors typically placed around lamps in phototherapy cabins. These mirrors are effective but tend to yield complex patterns of reflection around the cabin which can result in substantial dose inhomogeneity. There has been some speculation over whether using the reflective property of parabolic mirrors might improve dose delivery or homogeneity through the treatment cabin. In this work, the effects of parabolic mirrors are simulated and compared with standard shaped mirrors. Simulation results strongly suggest that parabolic reflectors reduce total irradiance relative to standard shaped reflectors, and have a negligible impact on dose homogeneity.
Parabolic resection for mitral valve repair.
Drake, Daniel H; Drake, Charles G; Recchia, Dino
2010-02-01
Parabolic resection, named for the shape of the cut edges of the excised tissue, expands on a common 'trick' used by experienced mitral surgeons to preserve tissue and increase the probability of successful repair. Our objective was to describe and clinically analyze this simple modification of conventional resection. Thirty-six patients with mitral regurgitation underwent valve repair using parabolic resection in combination with other techniques. Institution specific mitral data, Society of Thoracic Surgeons data and preoperative, post-cardiopulmonary bypass (PCPB) and postoperative echocardiography data were collected and analyzed. Preoperative echocardiography demonstrated mitral regurgitation ranging from moderate to severe. PCPB transesophageal echocardiography demonstrated no regurgitation or mild regurgitation in all patients. Thirty-day surgical mortality was 2.8%. Serial echocardiograms demonstrated excellent repair stability. One patient (2.9%) with rheumatic disease progressed to moderate regurgitation 33 months following surgery. Echocardiography on all others demonstrated no or mild regurgitation at a mean follow-up of 22.8+/-12.8 months. No patient required mitral reintervention. Longitudinal analysis demonstrated 80% freedom from cardiac death, reintervention and greater than moderate regurgitation at four years following repair. Parabolic resection is a simple technique that can be very useful during complex mitral reconstruction. Early and intermediate echocardiographic studies demonstrate excellent results.
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.
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.
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.
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.
Hyperbolic type transport equations
NASA Astrophysics Data System (ADS)
García-Colín, L. S.; Olivares-Robles, M. A.
1995-02-01
In recent years hyperbolic type transport equations have acquired a great deal of importance in problems ranging from theoretical physics to biology. In spite of their greater mathematical difficulty as compared with their parabolic type analogs arising from the framework of Linear Irreversible Thermodynamics, they have, in many ways, superseded the latter ones. Although the use of this type of equations is well known since the last century through the telegraphist equation of electromagnetic theory, their use in studying several problems in transport theory is hardly fifty years old. In fact the first appearance of a hyperbolic type transport equation for the problem of heat conduction dates back to Cattaneos' work in 1948. Three years later, in 1951 S. Goldstein showed how in the theory of stochastic processes this type of an equation is obtained in the continuous limit of a one-dimensional persistent random walk problem. After that, other phenomenological derivations have been offered for such equations. The main purpose of this paper is to critically discuss a derivation of a hyperbolic type Fokker-Planck equation recently presented using the same ideas as M.S. Green did in 1952 to provide the stochastic foundations of irreversible statistical mechanics. Arguments are given to show that such an equation as well as transport equations derived from it by taking appropriate averages are at most approximate and that a much more detailed analysis is required before asserting their validity.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Stability of parabolic problems with nonlinear Wentzell boundary conditions
NASA Astrophysics Data System (ADS)
Coclite, Giuseppe M.; Goldstein, Gisèle R.; Goldstein, Jerome A.
Of concern is the nonlinear uniformly parabolic problem u=div(A∇u), u(0,x)=f(x), u+β∂νAu+γ(x,u)-qβΔu=0, for x∈Ω⊂R and t⩾0; the last equation holds on the boundary ∂ Ω. Here A={(x)}ij is a real, hermitian, uniformly positive definite N×N matrix; β∈C(∂Ω) with β>0; γ:∂Ω×R→R; q∈[0,∞), Δ is the Laplace-Beltrami operator on the boundary, and ∂νAu is the conormal derivative of u with respect to A: and everything is sufficiently regular. The solution of this wellposed problem depends continuously on the ingredients of the problem, namely, A,β,γ,q,f. This is shown using semigroup methods in [G.M. Coclite, A. Favini, G.R. Goldstein, J.A. Goldstein, S. Romanelli, Continuous dependence on the boundary parameters for the Wentzell Laplacian, Semigroup Forum 77 (1) (2008) 101-108]. Here we prove explicit stability estimates of the solution u with respect to the coefficients A, β, γ, q, and the initial condition f. Moreover we cover the singular case of a problem with q=0 which is approximated by problems with positive q.
High-order parabolic beam approximation for aero-optics
White, Michael D.
2010-08-01
The parabolic beam equations are solved using high-order compact differences for the Laplacians and Runge-Kutta integration along the beam path. The solution method is verified by comparison to analytical solutions for apertured beams and both constant and complex index of refraction. An adaptive 4th-order Runge-Kutta using an embedded 2nd-order method is presented that has demonstrated itself to be very robust. For apertured beams, the results show that the method fails to capture near aperture effects due to a violation of the paraxial approximation in that region. Initial results indicate that the problem appears to be correctable by successive approximations. A preliminary assessment of the effect of turbulent scales is undertaken using high-order Lagrangian interpolation. The results show that while high fidelity methods are necessary to accurately capture the large scale flow structure, the method may not require the same level of fidelity in sampling the density for the index of refraction. The solution is used to calculate a phase difference that is directly compared with that commonly calculated via the optical path difference. Propagation through a supersonic boundary layer shows that for longer wavelengths, the traditional method to calculate the optical path is less accurate than for shorter wavelengths. While unlikely to supplant more traditional methods for most aero-optics applications, the current method can be used to give a quantitative assessment of the other methods as well as being amenable to the addition of more physics.
NASA Astrophysics Data System (ADS)
Seo, Mansu; Park, Hana; Yoo, DonGyu; Jung, Youngsuk; Jeong, Sangkwon
Gauging the volume or mass of liquid propellant of a rocket vehicle in space is an important issue for its economic feasibility and optimized design of loading mass. Pressure-volume-temperature (PVT) gauging method is one of the most suitable measuring techniques in space due to its simplicity and reliability. This paper presents unique experimental results and analyses of PVT gauging method using liquid nitrogen under microgravity condition by parabolic flight. A vacuum-insulated and cylindrical-shaped liquid nitrogen storage tank with 9.2 L volume is manufactured by observing regulation of parabolic flight. PVT gauging experiments are conducted under low liquid fraction condition from 26% to 32%. Pressure, temperature, and the injected helium mass into the storage tank are measured to obtain the ullage volume by gas state equation. Liquid volume is finally derived by the measured ullage volume and the known total tank volume. Two sets of parabolic flights are conducted and each set is composed of approximately 10 parabolic flights. In the first set of flights, the short initial waiting time (3 ∼ 5 seconds) cannot achieve sufficient thermal equilibrium condition at the beginning. It causes inaccurate gauging results due to insufficient information of the initial helium partial pressure in the tank. The helium injection after 12 second waiting time at microgravity condition with high mass flow rate in the second set of flights achieves successful initial thermal equilibrium states and accurate measurement results of initial helium partial pressure. Liquid volume measurement errors in the second set are within 11%.
THE PARABOLIC JET STRUCTURE IN M87 AS A MAGNETOHYDRODYNAMIC NOZZLE
Nakamura, Masanori; Asada, Keiichi E-mail: asada@asiaa.sinica.edu.tw
2013-10-01
The structure and dynamics of the M87 jet from sub-milliarcsec to arcsecond scales are continuously examined. We analyzed the Very Long Baseline Array archival data taken at 43 and 86 GHz to measure the size of very long baseline interferometry (VLBI) cores. Millimeter/sub-millimeter VLBI cores are considered as innermost jet emissions, which has been originally suggested by Blandford and Königl. Those components fairly follow an extrapolated parabolic streamline in our previous study so that the jet has a single power-law structure with nearly 5 orders of magnitude in the distance starting from the vicinity of the supermassive black hole (SMBH), less than 10 Schwarzschild radius (r{sub s}). We further inspect the jet parabolic structure as a counterpart of the magnetohydrodynamic (MHD) nozzle in order to identify the property of a bulk acceleration. We interpret that the parabolic jet consists of Poynting-flux dominated flows, powered by large-amplitude, nonlinear torsional Alfvén waves. We examine the non-relativistic MHD nozzle equation in a parabolic shape. The nature of trans-fast magnetosonic flow is similar to the one of transonic solution of Parker's hydrodynamic solar wind; the jet becomes super-escape as well as super-fast magnetosonic at around ∼10{sup 3} r{sub s}, while the upstream trans-Alfvénic flow speed increases linearly as a function of the distance at ∼10{sup 2}-10{sup 3} r{sub s}. We here point out that this is the first evidence to identify these features in astrophysical jets. We propose that the M87 jet is magnetically accelerated, but thermally confined by the stratified interstellar medium inside the sphere of gravitational influence of the SMBH potential, which may be a norm in active galactic nucleus jets.
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.
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.
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.
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.
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.
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.
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.
Numerical computation of pyramidal quantum dots with band non-parabolicity
NASA Astrophysics Data System (ADS)
Gong, Liang; Shu, Yong-chun; Xu, Jing-jun; Wang, Zhan-guo
2013-09-01
This paper presents an effective and feasible eigen-energy scanning method to solve polynomial matrix eigenvalues introduced by 3D quantum dots problem with band non-parabolicity. The pyramid-shaped quantum dot is placed in a computational box with uniform mesh in Cartesian coordinates. Its corresponding Schrödinger equation is discretized by the finite difference method. The interface conditions are incorporated into the discretization scheme without explicitly enforcing them. By comparing the eigenvalues from isolated quantum dots and a vertically aligned regular array of them, we investigate the coupling effect for variable distances between the quantum dots and different size.
Nearly Interactive Parabolized Navier-Stokes Solver for High Speed Forebody and Inlet Flows
NASA Technical Reports Server (NTRS)
Benson, Thomas J.; Liou, May-Fun; Jones, William H.; Trefny, Charles J.
2009-01-01
A system of computer programs is being developed for the preliminary design of high speed inlets and forebodies. The system comprises four functions: geometry definition, flow grid generation, flow solver, and graphics post-processor. The system runs on a dedicated personal computer using the Windows operating system and is controlled by graphical user interfaces written in MATLAB (The Mathworks, Inc.). The flow solver uses the Parabolized Navier-Stokes equations to compute millions of mesh points in several minutes. Sample two-dimensional and three-dimensional calculations are demonstrated in the paper.
Entropy solutions for a nonlinear parabolic problems with lower order term in Orlicz spaces
NASA Astrophysics Data System (ADS)
Mabdaoui, M.; Moussa, H.; Rhoudaf, M.
2016-03-01
We shall give the proof of existence results for the entropy solutions of the following nonlinear parabolic problem [Equation not available: see fulltext.]where A is a Leray-Lions operator having a growth not necessarily of polynomial type. The lower order term Φ :Ω × (0,T)× {R}→ {R}^N is a Carathéodory function, for a.e. (x,t)in Q_T and for all sin R , satisfying only a growth condition and the right hand side f belongs to L^1(Q_T).
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.
Investigation of parabolic computational techniques for internal high-speed viscous flows
NASA Technical Reports Server (NTRS)
Anderson, O. L.; Power, G. D.
1985-01-01
A feasibility study was conducted to assess the applicability of an existing parabolic analysis (ADD-Axisymmetric Diffuser Duct), developed previously for subsonic viscous internal flows, to mixed supersonic/subsonic flows with heat addition simulating a SCRAMJET combustor. A study was conducted with the ADD code modified to include additional convection effects in the normal momentum equation when supersonic expansion and compression waves were present. It is concluded from the present study that for the class of problems where strong viscous/inviscid interactions are present a global iteration procedure is required.
Chen, Shihua; Yi, Lin; Guo, Dong-Sheng; Lu, Peixiang
2005-07-01
Three novel types of self-similar solutions, termed parabolic, Hermite-Gaussian, and hybrid pulses, of the generalized nonlinear Schrödinger equation with varying dispersion, nonlinearity, and gain or absorption are obtained. The properties of the self-similar evolutions in various nonlinear media are confirmed by numerical simulations. Despite the diversity of their formations, these self-similar pulses exhibit many universal features which can facilitate significantly the achievement of well-defined linearly chirped output pulses from an optical fiber, an amplifier, or an absorption medium, under certain parametric conditions. The other intrinsic characteristics of each type of self-similar pulses are also discussed.
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.
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.
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.
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.
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
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.
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.
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.
Assessment of simulated surgical skills in parabolic microgravity.
Rafiq, Azhar; Broderick, Timothy J; Williams, David R; Doarn, Charles R; Jones, Jeffrey A; Merrell, Ronald C
2005-04-01
During spaceflight crew health is paramount in the success of flight missions. The delivery of healthcare during flight requires crew readiness for medical and surgical response. There were 20 participants who were evaluated for accurate performance of 4 basic laparoscopic surgical skills (clip applying, cutting, grasping, and suturing) during parabolic weightlessness using an inanimate workstation aboard the NASA KC-135 aircraft. Data indicate that motor skill performance decreased within the parabolic microgravity flight environment. Performance in parabolic microgravity flight included futile effort with an increase in number of tasks attempted and a decrease in tasks completed successfully. There is a decreased frequency of accurate task completion in parabolic microgravity flight, but it is not an obstacle to implementation of effective training for providing in-flight medical care. The data reveal that individuals perform basic laparoscopic surgical simulation with greater effort in microgravity following simulation training.
Antenna cab interior showing waveguide from external parabolic antenna (later ...
Antenna cab interior showing waveguide from external parabolic antenna (later addition), looking north. - Western Union Telegraph Company, Jennerstown Relay, Laurel Summit Road off U.S. 30, Laughlintown, Westmoreland County, PA
Detail, external parabolic antenna (later addition). Note how waveguide was ...
Detail, external parabolic antenna (later addition). Note how waveguide was cut to remove active portion of antenna. - Western Union Telegraph Company, Jennerstown Relay, Laurel Summit Road off U.S. 30, Laughlintown, Westmoreland County, PA
An X-band parabolic antenna based on gradient metasurface
Yao, Wang; Yang, Helin Tian, Ying; Guo, Linyan; Huang, Xiaojun
2016-07-15
We present a novel parabolic antenna by employing reflection gradient metasurface which is composed of a series of circle patches on a grounded dielectric substrate. Similar to the traditional parabolic antenna, the proposed antenna take the metasurface as a “parabolic reflector” and a patch antenna was placed at the focal point of the metasurface as a feed source, then the quasi-spherical wave emitted by the source is reflected and transformed to plane wave with high efficiency. Due to the focus effect of reflection, the beam width of the antenna has been decreased from 85.9° to 13° and the gain has been increased from 6.5 dB to 20.8 dB. Simulation and measurement results of both near and far-field plots demonstrate good focusing properties of the proposed parabolic antenna.
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.
Brain, P; Strimenopoulou, F; Diukova, A; Berry, E; Jolly, A; Hall, J E; Wise, R G; Ivarsson, M; Wilson, F J
2014-12-01
Conventional analysis of clinical resting electroencephalography (EEG) recordings typically involves assessment of spectral power in pre-defined frequency bands at specific electrodes. EEG is a potentially useful technique in drug development for measuring the pharmacodynamic (PD) effects of a centrally acting compound and hence to assess the likelihood of success of a novel drug based on pharmacokinetic-pharmacodynamic (PK-PD) principles. However, the need to define the electrodes and spectral bands to be analysed a priori is limiting where the nature of the drug-induced EEG effects is initially not known. We describe the extension to human EEG data of a generalised semi-linear canonical correlation analysis (GSLCCA), developed for small animal data. GSLCCA uses data from the whole spectrum, the entire recording duration and multiple electrodes. It provides interpretable information on the mechanism of drug action and a PD measure suitable for use in PK-PD modelling. Data from a study with low (analgesic) doses of the μ-opioid agonist, remifentanil, in 12 healthy subjects were analysed using conventional spectral edge analysis and GSLCCA. At this low dose, the conventional analysis was unsuccessful but plausible results consistent with previous observations were obtained using GSLCCA, confirming that GSLCCA can be successfully applied to clinical EEG data.
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.
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.
Solar parabolic dish technology annual evaluation report. Fiscal year 1983
Not Available
1984-04-15
This report summarizes the activities of the JPL Solar Thermal Power Systems Parabolic Dish Project for FY 1983. Included are discussions on designs of module development including their concentrator, receiver, and power conversion subsystem together with a separate discussion of concentrator development. Analyses and test results, along with progress on field tests, Small Community Experiment system development, and tests at the Parabolic Dish Test Site are also included.
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.
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.
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
Solargenix Energy Advanced Parabolic Trough Development
Gee, R. C.; Hale, M. J.
2005-11-01
The Solargenix Advanced Trough Development Project was initiated in the Year 2000 with the support of the DOE CSP Program and, more recently, with the added support of the Nevada Southwest Energy Partnership. Parabolic trough plants are the most mature solar power technology, but no large-scale plants have been built in over a decade. Given this lengthy lull in deployment, our first Project objective was development of improved trough technology for near-term deployment, closely patterned after the best of the prior-generation troughs. The second objective is to develop further improvements in next-generation trough technology that will lead to even larger reductions in the cost of the delivered energy. To date, this Project has successfully developed an advanced trough, which is being deployed on a 1-MW plant in Arizona and will soon be deployed in a 64-MW plant in Nevada. This advanced trough offers a 10% increase in performance and over an 20% decrease in cost, relative to prior-generation troughs.
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.
Thermodynamics and the segmented compound parabolic concentrator
NASA Astrophysics Data System (ADS)
Widyolar, Bennett; Jiang, Lun; Winston, Roland
2017-04-01
Compound parabolic concentrator (CPC) reflector profiles are complex and can be difficult to manufacture using traditional methods. Computer numeric control machines, however, can approximate complex profiles by bending a series of small flat segments. We investigate the relationship between the number of segments and the optical transmission of a CPC approximated by equal length segments whose start and end points lie along the CPC profile. We also investigate a separate method for generating CPC-like profiles by adjusting the angle of each segment to satisfy the edge-ray principle. Three variations of this method are examined where the edge-ray condition is taken from the start, mid, and end points of each segment. A flux efficiency (FE) to compare concentrators, which combines the concentration ratio and optical efficiency, is introduced and directly relates to the maximum achievable flux on the absorber. We demonstrate that the FE defined is another way to look at the compromises one makes for a geometric concentrator designed under real-world constraints.
Affective states and adaptation to parabolic flights
NASA Astrophysics Data System (ADS)
Collado, Aurélie; Langlet, Cécile; Tzanova, Tzvetomira; Hainaut, Jean-Philippe; Monfort, Vincent; Bolmont, Benoît
2017-05-01
This exploratory study investigates (i) inter-individual variations of affective states before a parabolic flight (i.e., PF) on the basis of quality of adaptation to physical demands, and (ii) intra-individual variations of affective states during a PF. Mood-states, state-anxiety and salivary cortisol were assessed in two groups with a different quality of adaptation (an Adaptive Group, i.e., AG, and a Maladaptive Group, i.e., MG) before and during a PF. Before PF, MG scored higher on mood states (Anger-Hostility, Fatigue-Inertia) than AG. During the flight, while AG seemed to present ;normal; affective responses to the demanding environment (e.g., increase in salivary cortisol), MG presented increases in mood states such as Confusion-Bewilderment or Tension-Anxiety. The findings suggest that the psychological states of MG could have disturbed their ability to integrate sensory information from an unusual environment, which led to difficulties in coping with the physical demands of PF.
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.
Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation
Caraballo, Tomas Kloeden, Peter E. Schmalfuss, Bjoern
2004-10-15
We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when zero is not a solution for these equations. We prove the existence of anon-trivial stationary solution which is exponentially stable, where the stationary solution is generated by the composition of a random variable and the Wiener shift. We also construct stationary solutions with the stronger property of attracting bounded sets uniformly. The existence of these stationary solutions follows from the theory of random dynamical systems and their attractors. In addition, we prove some perturbation results and formulate conditions for the existence of stationary solutions for semilinear stochastic partial differential equations with Lipschitz continuous non-linearities.
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.
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.
Nanoscale Heat Transfer using Phonon Boltzmann Transport Equation
2009-10-01
Fourier diffusive equation ( FDE ). The equation can be derived using a conservation law of energy and Fourier’s linear approximation of heat flux...using a temperature gradient. The FDE is a parabolic equation reflecting a diffusive nature of heat transport. An underlying assumption is that...the heat is effectively transferred between localized regions through sufficient scattering events of phonons within a medium. Therefore, the FDE
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
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.
NASA Astrophysics Data System (ADS)
Li, Zhong-xiao; Li, Zhen-chun
2017-08-01
Adaptive multiple subtraction is an important step for successfully conducting surface-related multiple elimination in marine seismic exploration. 2D adaptive multiple subtraction conducted in the parabolic Radon domain has been proposed to better separate primaries and multiples than 2D adaptive multiple subtraction conducted in the time-offset domain. Additionally, the parabolic Radon domain hybrid demultiple method combining parabolic Radon filtering and parabolic Radon domain 2D adaptive multiple subtraction can better remove multiples than the cascaded demultiple method using time-offset domain 2D adaptive multiple subtraction and the parabolic Radon transform method sequentially. To solve the matching filter in the optimization problem with L1 norm minimization constraint of primaries, traditional parabolic Radon domain 2D adaptive multiple subtraction uses the iterative reweighted least squares (IRLS) algorithm, which is computationally expensive for solving a weighted LS inversion in each iteration. In this paper we introduce the fast iterative shrinkage thresholding algorithm (FISTA) as a faster alternative to the IRLS algorithm for parabolic Radon domain 2D adaptive multiple subtraction. FISTA uses the shrinkage-thresholding operator to promote the sparsity of estimated primaries and solves the 2D matching filter with iterative steps. FISTA based parabolic Radon domain 2D adaptive multiple subtraction reduces the computation time effectively while achieving similar accuracy compared with IRLS based parabolic Radon domain 2D adaptive multiple subtraction. Additionally, the provided examples show that FISTA based parabolic Radon domain 2D adaptive multiple subtraction can better separate primaries and multiples than FISTA based time-offset domain 2D adaptive multiple subtraction. Furthermore, we introduce FISTA based parabolic Radon domain 2D adaptive multiple subtraction into the parabolic Radon domain hybrid demultiple method to improve its computation
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.
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.
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.
Molten salt parabolic trough system with synthetic oil preheating
NASA Astrophysics Data System (ADS)
Yuasa, Minoru; Hino, Koichi
2017-06-01
Molten salt parabolic trough system (MSPT), which can heat the heat transfer fluid (HTF) to 550 °C has a better performance than a synthetic oil parabolic trough system (SOPT), which can heat the HTF to 400 °C or less. The utilization of HTF at higher temperature in the parabolic trough system is able to realize the design of a smaller size of storage tank and higher heat to electricity conversion efficiency. However, with MSPT there is a great amount of heat loss at night so it is necessary to circulate the HTF at a high temperature of about 290 °C in order to prevent solidification. A new MSPT concept with SOPT preheating (MSSOPT) has been developed to reduce the heat loss at night. In this paper, the MSSOPT system, its performance by steady state analysis and annual performance analysis are introduced.
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
2017-06-01
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.
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.
Microgravity research during aircraft parabolic flights: the 20 ESA campaigns.
Pletser, V
1995-05-01
Aircraft parabolic flights provide repeated periods of up to 20 seconds of reduced gravity during ballistic flight manoeuvres, preceded and followed by 20 seconds of 1.8 g. Such flights are used to conduct short microgravity investigations in physical and life sciences, to test instrumentation and to train astronauts before a spaceflight. Since 1984, ESA's Microgravity Projects Division has organised 20 parabolic flight campaigns using three different types of aircraft. More than 1700 parabolas have been flown, representing nine and half hours of microgravity in slices of 20 seconds, or equivalently, six low Earth orbits. A total of 235 experiments have been performed using this unique microgravity tool.
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.
An Estimation Theory for Differential Equations and other Problems, with Applications.
1981-11-01
Proposition 5.5). These statements show that each of the sufficient properties for inverse-positivity which are proved in Chapter II can also be used in...Weinberger, H.F.: Invariant sets for weakly coupled parabolic and elliptic systems. Rendiconti di Matematica 8, Serie VI, 295-310 (1975). [8] Lemmert, R...systems of parabolic differential equations. Rendiconti di Matematica (3) Vol. 13, Serie VI, 337-357 (1980). [24] Szeptycki, P.: Existence theorem
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.
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.
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.
Long-term average performance benefits of parabolic trough improvements
Gee, R.; Gaul, H.W.; Kearney, D.; Rabl, A.
1980-03-01
Improved parabolic trough concentrating collectors will result from better design, improved fabrication techniques, and the development and utilization of improved materials. The difficulty of achieving these improvements varies as does their potential for increasing parabolic trough performance. The purpose of this analysis is to quantify the relative merit of various technology advancements in improving the long-term average performance of parabolic trough concentrating collectors. The performance benefits of improvements are determined as a function of operating temperature for north-south, east-west, and polar mounted parabolic troughs. The results are presented graphically to allow a quick determination of the performance merits of particular improvements. Substantial annual energy gains are shown to be attainable. Of the improvements evaluated, the development of stable back-silvered glass reflective surfaces offers the largest performance gain for operating temperatures below 150/sup 0/C. Above 150/sup 0/C, the development of trough receivers that can maintain a vacuum is the most significant potential improvement. The reduction of concentrator slope errors also has a substantial performance benefit at high operating temperatures.
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.
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.
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).
An Application of Calculus: Optimum Parabolic Path Problem
ERIC Educational Resources Information Center
Atasever, Merve; Pakdemirli, Mehmet; Yurtsever, Hasan Ali
2009-01-01
A practical and technological application of calculus problem is posed to motivate freshman students or junior high school students. A variable coefficient of friction is used in modelling air friction. The case in which the coefficient of friction is a decreasing function of altitude is considered. The optimum parabolic path for a flying object…
Orthostatic intolerance and motion sickness after parabolic flight
NASA Technical Reports Server (NTRS)
Schlegel, 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.
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.
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.
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 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
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Arkhipova, A. A.
2017-03-01
The Venttsel' problem in the model statement for quasilinear parabolic systems of equations with nondiagonal principal matrices is considered. It is only assumed that the principal matrices and the boundary condition are bounded with respect to the time variable. The partial smoothness of the weak solutions (Hölder continuity on a set of full measure up to the surface on which the Venttsel' condition is defined) is proved. The proof uses the A( t)-caloric approximation method, which was also used in [1] to investigate the regularity of the solution to the corresponding linear problem.
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.
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.
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.
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.
Pierantozzi, T.; Vazquez, L.
2005-11-01
Through fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D'Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case.
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.
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.
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.
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.
'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.
Secondary concentrators for parabolic dish solar thermal power systems
NASA Technical Reports Server (NTRS)
Jaffe, L. D.; Poon, P. T.
1981-01-01
A variety of different concepts are currently being studied with the objective to lower the cost of parabolic mirrors and to provide alternatives. One of the considered approaches involves the use of compound concentrators. A compound solar concentrator is a concentrator in which the sunlight is reflected or refracted more than once. It consists of a primary mirror or lens, whose aperture determines the amount of sunlight gathered, and a smaller secondary mirror or lens. Additional small optical elements may also be incorporated. The possibilities and problems regarding a use of compound concentrators in parabolic dish systems are discussed. Attention is given to concentrating secondary lenses, secondary imaging and concentrating mirrors, conical secondary mirrors, compound elliptic secondary concentrating mirrors, and hyperbolic trumpet secondary concentrating mirrors.
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.
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.