Optimal linear-quadratic control of coupled parabolic-hyperbolic PDEs

Science.gov (United States)

Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

2017-10-01

This paper focuses on the optimal control design for a system of coupled parabolic-hypebolic partial differential equations by using the infinite-dimensional state-space description and the corresponding operator Riccati equation. Some dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the linear-quadratic (LQ)-optimal control problem. A state LQ-feedback operator is computed by solving the operator Riccati equation, which is converted into a set of algebraic and differential Riccati equations, thanks to the eigenvalues and the eigenvectors of the parabolic operator. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ-optimal controller designed in the early portion of the paper is implemented for the original nonlinear model. Numerical simulations are performed to show the controller performances.

Degenerate parabolic stochastic partial differential equations

Czech Academy of Sciences Publication Activity Database

span class="emphasis">Hofmanová, Martinaspan>

2013-01-01

Roč. 123, č. 12 (2013), s. 4294-4336 ISSN 0304-4149 R&D Projects: GA ČR GAP201/10/0752 Institutional support: RVO:67985556 Keywords : kinetic solutions * degenerate stochastic parabolic equations Subject RIV: BA - General Mathematics Impact factor: 1.046, year: 2013 http://library.utia.cas.cz/separaty/2013/SI/hofmanova-0397241.pdf

Use of fast Fourier transforms for solving partial differential equations in physics

CERN Document Server

Le Bail, R C

1972-01-01

The use of fast Fourier techniques for the direct solution of an important class of elliptic, parabolic, and hyperbolic partial differential equations in two dimensions is described. Extensions to higher-order and higher-dimension equations as well as to integrodifferential equations are presented, and several numerical examples with their resulting precision and timing are reported. (12 refs).

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

International Nuclear Information System (INIS)

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

2015-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

Bakhos, Tania, E-mail: taniab@stanford.edu [Institute for Computational and Mathematical Engineering, Stanford University (United States); Saibaba, Arvind K. [Department of Electrical and Computer Engineering, Tufts University (United States); Kitanidis, Peter K. [Institute for Computational and Mathematical Engineering, Stanford University (United States); Department of Civil and Environmental Engineering, Stanford University (United States)

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.

Cauchy problem for a parabolic equation with Bessel operator and Riemann–Liouville partial derivative

Directory of Open Access Journals (Sweden)

Fatima G. Khushtova

2016-03-01

Full Text Available In this paper Cauchy problem for a parabolic equation with Bessel operator and with Riemann–Liouville partial derivative is considered. The representation of the solution is obtained in terms of integral transform with Wright function in the kernel. It is shown that when this equation becomes the fractional diffusion equation, obtained solution becomes the solution of Cauchy problem for the corresponding equation. The uniqueness of the solution in the class of functions that satisfy the analogue of Tikhonov condition is proved.

Optimal control of coupled parabolic-hyperbolic non-autonomous PDEs: infinite-dimensional state-space approach

Science.gov (United States)

Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

2018-04-01

This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic-hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolic-associated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances.

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

Science.gov (United States)

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.

Chernoff's distribution and parabolic partial differential equations

NARCIS (Netherlands)

P. Groeneboom; S.P. Lalley; N.M. Temme (Nico)

2013-01-01

textabstractWe give an alternative route to the derivation of the distribution of the maximum and the location of the maximum of one-sided and two-sided Brownian motion with a negative parabolic drift, using the Feynman-Kac formula with stopping times. The derivation also uses an interesting

Controllability and stabilization of parabolic equations

CERN Document Server

Barbu, Viorel

2018-01-01

This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems. Starting from foundational questions on Carleman inequalities for linear parabolic equations, the author addresses the controllability of parabolic equations on a variety of domains and the spectral decomposition technique for representing them. This method is, in fact, designed for use in a wider class of parabolic systems that include the heat and diffusion equations. Later chapters develop another process that employs stabilizing feedback controllers with a finite number of unstable modes, with special attention given to its use in the boundary stabilization of Navier–Stokes equations for the motion of viscous fluid. In turn, these applied methods are used to explore related topics like the exact controllability of stochastic parabolic equations with linear multiplicative noise. Intended for graduate students and researchers working on control problems involving nonlinear diff...

Strongly nonlinear parabolic variational inequalities.

Science.gov (United States)

Browder, F E; Brézis, H

1980-02-01

An existence and uniqueness result is established for a general class of variational inequalities for parabolic partial differential equations of the form partial differentialu/ partial differentialt + A(u) + g(u) = f with g nondecreasing but satisfying no growth condition. The proof is based upon a type of compactness result for solutions of variational inequalities that should find a variety of other applications.

Path integral solution of linear second order partial differential equations I: the general construction

International Nuclear Information System (INIS)

LaChapelle, J.

2004-01-01

A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations with boundary conditions. This extends the well-known path integral solution of the Schroedinger/diffusion equation in unbounded space. The construction is based on a framework for functional integration introduced by Cartier/DeWitt-Morette

International Workshop on Elliptic and Parabolic Equations

CERN Document Server

Schrohe, Elmar; Seiler, Jörg; Walker, Christoph

2015-01-01

This volume covers the latest research on elliptic and parabolic equations and originates from the international Workshop on Elliptic and Parabolic Equations, held September 10-12, 2013 at the Leibniz Universität Hannover. It represents a collection of refereed research papers and survey articles written by eminent scientist on advances in different fields of elliptic and parabolic partial differential equations, including singular Riemannian manifolds, spectral analysis on manifolds, nonlinear dispersive equations, Brownian motion and kernel estimates, Euler equations, porous medium type equations, pseudodifferential calculus, free boundary problems, and bifurcation analysis.

An accurate solution of parabolic equations by expansion in ultraspherical polynomials

International Nuclear Information System (INIS)

Doha, E.H.

1986-11-01

An ultraspherical expansion technique is applied to obtain numerically the solution of the third boundary value problem for linear parabolic partial differential equation in one-space variable. The differential equation with its boundary and initial conditions is reduced to a system of ordinary differential equations for the coefficients of the expansion. This system may be solved analytically or numerically in a step-by-step manner. The method in its present form may be considered as a generalization of that of Dew and Scraton. The extension of the method to the polar-type equations is also considered. (author). 12 refs, 1 tab

INERTIAL MANIFOLDS FOR NONAUTONOMOUS SEMILINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH TIME DELAYS

Institute of Scientific and Technical Information of China (English)

无

2006-01-01

The present paper deals with the long-time behavior of a class of nonautonomous retarded semilinear parabolic differential equations. When the time delays are small enough and the spectral gap conditions hold, the inertial manifolds of the nonautonomous retard parabolic equations are constructed by using the Lyapunov-Perron method.

Maximum principles for boundary-degenerate linear parabolic differential operators

OpenAIRE

Feehan, Paul M. N.

2013-01-01

We develop weak and strong maximum principles for boundary-degenerate, linear, parabolic, second-order partial differential operators, $Lu := -u_t-\\tr(aD^2u)-\\langle b, Du\\rangle + cu$, with \\emph{partial} Dirichlet boundary conditions. The coefficient, $a(t,x)$, is assumed to vanish along a non-empty open subset, $\\mydirac_0!\\sQ$, called the \\emph{degenerate boundary portion}, of the parabolic boundary, $\\mydirac!\\sQ$, of the domain $\\sQ\\subset\\RR^{d+1}$, while $a(t,x)$ may be non-zero at po...

Difference method for solving a nonlocal boundary value problem for a degenerating third-order pseudo-parabolic equation with variable coefficients

Science.gov (United States)

Beshtokov, M. Kh.

2016-10-01

A nonlocal boundary value problem for a degenerating third-order pseudo-parabolic equation with variable coefficients is considered. For solving this problem, a priori estimates in the differential and difference forms are obtained. The a priori estimates imply the uniqueness and stability of the solution on a layer with respect to the initial data and the right-hand side and the convergence of the solution of the difference problem to the solution of the differential problem.

Coercive properties of elliptic-parabolic operator

International Nuclear Information System (INIS)

Duong Min Duc.

1987-06-01

Using a generalized Poincare inequality, we study the coercive properties of a class of elliptic-parabolic partial differential equations, which contains many degenerate elliptic equations considered by the other authors. (author). 16 refs

Performance of Infinitely Wide Parabolic and Inclined Slider Bearings Lubricated with Couple Stress or Magnetic Fluids

Science.gov (United States)

Oladeinde, Mobolaji Humphrey; Akpobi, John Ajokpaoghene

2011-10-01

The hydrodynamic and magnetohydrodynamic (MHD) lubrication problem of infinitely wide inclined and parabolic slider bearings is solved numerically using the finite element method. The bearing configurations are discretized into three-node isoparametric quadratic elements. Stiffness integrals obtained from the weak form of the governing equations are solved using Gauss quadrature to obtain a finite number of stiffness matrices. The global system of equations obtained from enforcing nodal continuity of pressure for the bearings are solved using the Gauss-Seidel iterative scheme with a convergence criterion of 10-10. Numerical computations reveal that, when compared for similar profile and couple stress parameters, greater pressure builds up in a parabolic slider compared to an inclined slider, indicating a greater wedge effect in the parabolic slider. The parabolic slider bearing is also shown to develop a greater load capacity when lubricated with magnetic fluids. The superior performance of parabolic slider bearing is more pronounced at greater Hartmann numbers for identical bearing structural parameters. It is also shown that when load carrying capacity is the yardstick for comparison, the parabolic slider bearings are superior to the inclined bearings when lubricated with couple stress or magnetic lubricants.

Coupled, parabolic-marching method for the prediction of three-dimensional viscous incompressible turbomachinery flows. Doctoral thesis

Energy Technology Data Exchange (ETDEWEB)

Kirtley, K.R.

1988-10-01

A new coupled parabolic-marching method was developed to solve the three-dimensional incompressible Navier-Stokes equation for turbulent turbomachinery flows. Earlier space-marching methods were analyzed to determine their global stability during multiple passes of the computational domain. The methods were found to be unconditionally unstable even when an extra equation for the pressure, namely the Poisson equation for the pressure, was used between passes of the domain. Relaxation of one constraint during the solution process was found to be necessary for the successful calculation of a complex flow.Thus, the method of pseudocompressibility was introduced into the partially parabolized Navier-Stokes equation to relax the mass flow constraint during a forward-marching integration as well as globally stable during successive passes of the domain. With consistent discretization, the new method was found to be convergent.

Studies with Parabolic Parabolic Linear Parabolic (PPLP) momentum function in the LHC

CERN Document Server

Solfaroli Camillocci, Matteo; Timko, Helga; Wenninger, Jorg; CERN. Geneva. ATS Department

2018-01-01

Measurements performed with a Parabolic Parabolic Linear Parabolic (PPLP) momentum function in the LHC. Three attempts have been performed with a pilot bunch and one with nominal bunch (1.1x1011 p/bunch).

Sensor for Measuring Hydrogen Partial Pressure in Parabolic Trough Power Plant Expansion Tanks

Energy Technology Data Exchange (ETDEWEB)

Glatzmaier, Greg C.; Cooney, Daniel A.

2017-06-27

The National Renewable Energy Laboratory and Acciona Energy North America are working together to design and implement a process system that provides a permanent solution to the issue of hydrogen buildup at parabolic trough power plants. We are pursuing a method that selectively removes hydrogen from the expansion tanks that serve as reservoirs for the heat transfer fluid (HTF) that circulates in the collector field and power block components. Our modeling shows that removing hydrogen from the expansion tanks at a design rate reduces and maintains dissolved hydrogen in the circulating HTF to a selected target level. Our collaborative work consists of several tasks that are needed to advance this process concept to a development stage, where it is ready for implementation at a commercial power plant. Our main effort is to design and evaluate likely process-unit operations that remove hydrogen from the expansion tanks at a specified rate. Additionally, we designed and demonstrated a method and instrumentation to measure hydrogen partial pressure and concentration in the expansion-tank headspace gas. We measured hydrogen partial pressure in the headspace gas mixture using a palladium-alloy membrane, which is permeable exclusively to hydrogen. The membrane establishes a pure hydrogen gas phase that is in equilibrium with the hydrogen in the gas mixture. We designed and fabricated instrumentation, and demonstrated its effectiveness in measuring hydrogen partial pressures over a range of three orders of magnitude. Our goal is to install this instrument at the Nevada Solar One power plant and to demonstrate its effectiveness in measuring hydrogen levels in the expansion tanks under normal plant operating conditions.

Solving Partial Differential Equations Using a New Differential Evolution Algorithm

Directory of Open Access Journals (Sweden)

Natee Panagant

2014-01-01

Full Text Available This paper proposes an alternative meshless approach to solve partial differential equations (PDEs. With a global approximate function being defined, a partial differential equation problem is converted into an optimisation problem with equality constraints from PDE boundary conditions. An evolutionary algorithm (EA is employed to search for the optimum solution. For this approach, the most difficult task is the low convergence rate of EA which consequently results in poor PDE solution approximation. However, its attractiveness remains due to the nature of a soft computing technique in EA. The algorithm can be used to tackle almost any kind of optimisation problem with simple evolutionary operation, which means it is mathematically simpler to use. A new efficient differential evolution (DE is presented and used to solve a number of the partial differential equations. The results obtained are illustrated and compared with exact solutions. It is shown that the proposed method has a potential to be a future meshless tool provided that the search performance of EA is greatly enhanced.

Convergence of hybrid methods for solving non-linear partial ...

African Journals Online (AJOL)

This paper is concerned with the numerical solution and convergence analysis of non-linear partial differential equations using a hybrid method. The solution technique involves discretizing the non-linear system of PDE to obtain a corresponding non-linear system of algebraic difference equations to be solved at each time ...

EXERGY AND CARBON CREDITS FOR SERIES CONNECTED N PHOTOVOLTAIC THERMAL - COMPOUND PARABOLIC CONCENTRATOR (PVT-CPC) COLLECTOR: AT CONSTANT OUTLET TEMPERATURE

OpenAIRE

Rohit Tripathi 1,*, G. N. Tiwari 2

2017-01-01

In the present study, overall energy and exergy performance of partially covered N photovoltaic thermal - compound parabolic concentrators (PVT-CPC) (25% covered by glass to glass PV module) collector connected in series have been carried out at constant outlet temperature mode. Further, comparison in performance for partially covered N photovoltaic thermal - compound parabolic concentrators (PVT-CPC) [case (i)] and N compound parabolic concentrators (CPC) collector [case (ii)] connected in s...

Optimal control for parabolic-hyperbolic system with time delay

International Nuclear Information System (INIS)

Kowalewski, A.

1985-07-01

In this paper we consider an optimal control problem for a system described by a linear partial differential equation of the parabolic-hyperbolic type with time delay in the state. The right-hand side of this equation and the initial conditions are not continuous functions usually, but they are measurable functions belonging to L 2 or Lsup(infinity) spaces. Therefore, the solution of this equation is given by a certain Sobolev space. The time delay in the state is constant, but it can be also a function of time. The control time T is fixed in our problem. Making use of the Milutin-Dubovicki theorem, necessary and sufficient conditions of optimality with the quadratic performance functional and constrained control are derived for the Dirichlet problem. The flow chart of the algorithm which can be used in the numerical solving of certain optimization problems for distributed systems is also presented. (author)

A New Numerical Technique for Solving Systems Of Nonlinear Fractional Partial Differential Equations

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Mountassir Hamdi Cherif

2017-11-01

Full Text Available In this paper, we apply an efficient method called the Aboodh decomposition method to solve systems of nonlinear fractional partial differential equations. This method is a combined form of Aboodh transform with Adomian decomposition method. The theoretical analysis of this investigated for systems of nonlinear fractional partial differential equations is calculated in the explicit form of a power series with easily computable terms. Some examples are given to shows that this method is very efficient and accurate. This method can be applied to solve others nonlinear systems problems.

Critical spaces for quasilinear parabolic evolution equations and applications

Science.gov (United States)

Prüss, Jan; Simonett, Gieri; Wilke, Mathias

2018-02-01

We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal Lp-regularity in time-weighted function spaces. It is shown that our notion of critical spaces coincides with the concept of scaling invariant spaces in case that the underlying partial differential equation enjoys a scaling invariance. Applications to the vorticity equations for the Navier-Stokes problem, convection-diffusion equations, the Nernst-Planck-Poisson equations in electro-chemistry, chemotaxis equations, the MHD equations, and some other well-known parabolic equations are given.

Computational partial differential equations using Matlab

CERN Document Server

Li, Jichun

2008-01-01

Brief Overview of Partial Differential Equations The parabolic equations The wave equations The elliptic equations Differential equations in broader areasA quick review of numerical methods for PDEsFinite Difference Methods for Parabolic Equations Introduction Theoretical issues: stability, consistence, and convergence 1-D parabolic equations2-D and 3-D parabolic equationsNumerical examples with MATLAB codesFinite Difference Methods for Hyperbolic Equations IntroductionSome basic difference schemes Dissipation and dispersion errors Extensions to conservation lawsThe second-order hyperbolic PDE

An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations

Directory of Open Access Journals (Sweden)

M. Bishehniasar

2017-01-01

Full Text Available The demand of many scientific areas for the usage of fractional partial differential equations (FPDEs to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations (PDEs. The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation (PDE. Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference (NSFD method and standard finite difference (SFD technique, which are popular in the literature for solving engineering problems.

New finite volume methods for approximating partial differential equations on arbitrary meshes

International Nuclear Information System (INIS)

Hermeline, F.

2008-12-01

This dissertation presents some new methods of finite volume type for approximating partial differential equations on arbitrary meshes. The main idea lies in solving twice the problem to be dealt with. One addresses the elliptic equations with variable (anisotropic, antisymmetric, discontinuous) coefficients, the parabolic linear or non linear equations (heat equation, radiative diffusion, magnetic diffusion with Hall effect), the wave type equations (Maxwell, acoustics), the elasticity and Stokes'equations. Numerous numerical experiments show the good behaviour of this type of method. (author)

Higher-order schemes for the Laplace transformation method for parabolic problems

KAUST Repository

Douglas, C.; Kim, I.; Lee, H.; Sheen, D.

2011-01-01

In this paper we solve linear parabolic problems using the three stage noble algorithms. First, the time discretization is approximated using the Laplace transformation method, which is both parallel in time (and can be in space, too) and extremely

A model reduction approach to numerical inversion for a parabolic partial differential equation

International Nuclear Information System (INIS)

Borcea, Liliana; Druskin, Vladimir; Zaslavsky, Mikhail; Mamonov, Alexander V

2014-01-01

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss–Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments. (paper)

A model reduction approach to numerical inversion for a parabolic partial differential equation

Science.gov (United States)

Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail

2014-12-01

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss-Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments.

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

Science.gov (United States)

Fijany, Amir

1993-01-01

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

Maximum principles and sharp constants for solutions of elliptic and parabolic systems

CERN Document Server

Kresin, Gershon

2012-01-01

The main goal of this book is to present results pertaining to various versions of the maximum principle for elliptic and parabolic systems of arbitrary order. In particular, the authors present necessary and sufficient conditions for validity of the classical maximum modulus principles for systems of second order and obtain sharp constants in inequalities of Miranda-Agmon type and in many other inequalities of a similar nature. Somewhat related to this topic are explicit formulas for the norms and the essential norms of boundary integral operators. The proofs are based on a unified approach using, on one hand, representations of the norms of matrix-valued integral operators whose target spaces are linear and finite dimensional, and, on the other hand, on solving certain finite dimensional optimization problems. This book reflects results obtained by the authors, and can be useful to research mathematicians and graduate students interested in partial differential equations.

Cyclotron heating rate in a parabolic mirror

International Nuclear Information System (INIS)

Smith, P.K.

1984-01-01

Cyclotron resonance heating rates are found for a parabolic magnetic mirror. The equation of motion for perpendicular velocity is solved, including the radial magnetic field terms neglected in earlier papers. The expression for heating rate involves an infinite series of Anger's and Weber's functions, compared with a single term of the unrevised expression. The new results show an increase of heating rate compared with previous results. A simple expression is given for the ratio of the heating rates. (author)

Identifying an unknown function in a parabolic equation with overspecified data via He's variational iteration method

International Nuclear Information System (INIS)

Dehghan, Mehdi; Tatari, Mehdi

2008-01-01

In this research, the He's variational iteration technique is used for computing an unknown time-dependent parameter in an inverse quasilinear parabolic partial differential equation. Parabolic partial differential equations with overspecified data play a crucial role in applied mathematics and physics, as they appear in various engineering models. The He's variational iteration method is an analytical procedure for finding solutions of differential equations, is based on the use of Lagrange multipliers for identification of an optimal value of a parameter in a functional. To show the efficiency of the new approach, several test problems are presented for one-, two- and three-dimensional cases

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

Science.gov (United States)

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

Numerical performance of the parabolized ADM formulation of general relativity

International Nuclear Information System (INIS)

Paschalidis, Vasileios; Hansen, Jakob; Khokhlov, Alexei

2008-01-01

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.

Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

Directory of Open Access Journals (Sweden)

Veyis Turut

2013-01-01

Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.

Parabolic Equation Modeling of Propagation over Terrain Using Digital Elevation Model

Directory of Open Access Journals (Sweden)

Xiao-Wei Guan

2018-01-01

Full Text Available The parabolic equation method based on digital elevation model (DEM is applied on propagation predictions over irregular terrains. Starting from a parabolic approximation to the Helmholtz equation, a wide-angle parabolic equation is deduced under the assumption of forward propagation and the split-step Fourier transform algorithm is used to solve it. The application of DEM is extended to the Cartesian coordinate system and expected to provide a precise representation of a three-dimensional surface with high efficiency. In order to validate the accuracy, a perfectly conducting Gaussian terrain profile is simulated and the results are compared with the shift map. As a consequence, a good agreement is observed. Besides, another example is given to provide a theoretical basis and reference for DEM selection. The simulation results demonstrate that the prediction errors will be obvious only when the resolution of the DEM used is much larger than the range step in the PE method.

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

International Nuclear Information System (INIS)

Dvirnyj, Aleksandr I; Slyn'ko, Vitalij I

2013-01-01

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.

Processing of data from innovative parabolic strip telescope.

Science.gov (United States)

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

2015-12-01

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

Iterated Crank-Nicolson method for hyperbolic and parabolic equations in numerical relativity

International Nuclear Information System (INIS)

Leiler, Gregor; Rezzolla, Luciano

2006-01-01

The iterated Crank-Nicolson is a predictor-corrector algorithm commonly used in numerical relativity for the solution of both hyperbolic and parabolic partial differential equations. We here extend the recent work on the stability of this scheme for hyperbolic equations by investigating the properties when the average between the predicted and corrected values is made with unequal weights and when the scheme is applied to a parabolic equation. We also propose a variant of the scheme in which the coefficients in the averages are swapped between two corrections leading to systematically larger amplification factors and to a smaller numerical dispersion

Newton-type methods for the mixed finite element discretization of some degenerate parabolic equations

NARCIS (Netherlands)

Radu, F.A.; Pop, I.S.; Knabner, P.; Bermúdez de Castro, A.; Gómez, D.; Quintela, P.; Salgado, P.

2006-01-01

In this paper we discuss some iterative approaches for solving the nonlinear algebraic systems encountered as fully discrete counterparts of some degenerate (fast diffusion) parabolic problems. After regularization, we combine a mixed finite element discretization with the Euler implicit scheme. For

Higher-order schemes for the Laplace transformation method for parabolic problems

KAUST Repository

Douglas, C.

2011-01-01

In this paper we solve linear parabolic problems using the three stage noble algorithms. First, the time discretization is approximated using the Laplace transformation method, which is both parallel in time (and can be in space, too) and extremely high order convergent. Second, higher-order compact schemes of order four and six are used for the the spatial discretization. Finally, the discretized linear algebraic systems are solved using multigrid to show the actual convergence rate for numerical examples, which are compared to other numerical solution methods. © 2011 Springer-Verlag.

The fundamental solutions for fractional evolution equations of parabolic type

Directory of Open Access Journals (Sweden)

Mahmoud M. El-Borai

2004-01-01

Full Text Available The fundamental solutions for linear fractional evolution equations are obtained. The coefficients of these equations are a family of linear closed operators in the Banach space. Also, the continuous dependence of solutions on the initial conditions is studied. A mixed problem of general parabolic partial differential equations with fractional order is given as an application.

A short proof of increased parabolic regularity

Directory of Open Access Journals (Sweden)

Stephen Pankavich

2015-08-01

Full Text Available We present a short proof of the increased regularity obtained by solutions to uniformly parabolic partial differential equations. Though this setting is fairly introductory, our new method of proof, which uses a priori estimates and an inductive method, can be extended to prove analogous results for problems with time-dependent coefficients, advection-diffusion or reaction diffusion equations, and nonlinear PDEs even when other tools, such as semigroup methods or the use of explicit fundamental solutions, are unavailable.

Inverse source problem and null controllability for multidimensional parabolic operators of Grushin type

International Nuclear Information System (INIS)

Beauchard, K; Cannarsa, P; Yamamoto, M

2014-01-01

The approach to Lipschitz stability for uniformly parabolic equations introduced by Imanuvilov and Yamamoto in 1998 based on Carleman estimates, seems hard to apply to the case of Grushin-type operators of interest to this paper. Indeed, such estimates are still missing for parabolic operators degenerating in the interior of the space domain. Nevertheless, we are able to prove Lipschitz stability results for inverse source problems for such operators, with locally distributed measurements in an arbitrary space dimension. For this purpose, we follow a mixed strategy which combines the approach due to Lebeau and Robbiano, relying on Fourier decomposition and Carleman inequalities for heat equations with non-smooth coefficients (solved by the Fourier modes). As a corollary, we obtain a direct proof of the observability of multidimensional Grushin-type parabolic equations, with locally distributed observations—which is equivalent to null controllability with locally distributed controls. (paper)

Conditional stability in determination of initial data for stochastic parabolic equations

International Nuclear Information System (INIS)

Yuan, Ganghua

2017-01-01

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. (paper)

Conditional stability in determination of initial data for stochastic parabolic equations

Science.gov (United States)

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.

Moving Least Squares Method for a One-Dimensional Parabolic Inverse Problem

Directory of Open Access Journals (Sweden)

Baiyu Wang

2014-01-01

Full Text Available This paper investigates the numerical solution of a class of one-dimensional inverse parabolic problems using the moving least squares approximation; the inverse problem is the determination of an unknown source term depending on time. The collocation method is used for solving the equation; some numerical experiments are presented and discussed to illustrate the stability and high efficiency of the method.

Classical and weak solutions for semilinear parabolic equations with Preisach hysteresis

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Mathias Jais

2008-01-01

Full Text Available We consider the solvability of the semilinear parabolic differential equation \\[\\frac{\\partial u}{\\partial t}(x,t- \\Delta u(x,t + c(x,tu(x,t = \\mathcal{P}(u + \\gamma (x,t\\] in a cylinder \\(D=\\Omega \\times (0,T\\, where \\(\\mathcal{P}\\ is a hysteresis operator of Preisach type. We show that the corresponding initial boundary value problems have unique classical solutions. We further show that using this existence and uniqueness result, one can determine the properties of the Preisach operator \\(\\mathcal{P}\\ from overdetermined boundary data.

Existence and uniqueness to the Cauchy problem for linear and semilinear parabolic equations with local conditions⋆

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Rubio Gerardo

2011-03-01

Full Text Available We consider the Cauchy problem in ℝd for a class of semilinear parabolic partial differential equations that arises in some stochastic control problems. We assume that the coefficients are unbounded and locally Lipschitz, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution by approximation with linear parabolic equations. The linear equations involved can not be solved with the traditional results. Therefore, we construct a classical solution to the linear Cauchy problem under the same hypotheses on the coefficients for the semilinear equation. Our approach is using stochastic differential equations and parabolic differential equations in bounded domains. Finally, we apply the results to a stochastic optimal consumption problem. Nous considérons le problème de Cauchy dans ℝd pour une classe d’équations aux dérivées partielles paraboliques semi linéaires qui se pose dans certains problèmes de contrôle stochastique. Nous supposons que les coefficients ne sont pas bornés et sont localement Lipschitziennes, pas nécessairement différentiables, avec des données continues et ellipticité local uniforme. Nous construisons une solution classique par approximation avec les équations paraboliques linéaires. Les équations linéaires impliquées ne peuvent être résolues avec les résultats traditionnels. Par conséquent, nous construisons une solution classique au problème de Cauchy linéaire sous les mêmes hypothèses sur les coefficients pour l’équation semi-linéaire. Notre approche utilise les équations différentielles stochastiques et les équations différentielles paraboliques dans les domaines bornés. Enfin, nous appliquons les résultats à un problème stochastique de consommation optimale.

Nonlinear parabolic equations with blowing-up coefficients with respect to the unknown and with soft measure data

Directory of Open Access Journals (Sweden)

Khaled Zaki

2016-12-01

Full Text Available We establish the existence of solutions for the nonlinear parabolic problem with Dirichlet homogeneous boundary conditions, $$ \\frac{\\partial u}{\\partial t} - \\sum_{i=1}^N\\frac{\\partial}{\\partial x_i} \\Big( d_i(u\\frac{\\partial u}{\\partial x_i} \\Big =\\mu,\\quad u(t=0=u_0, $$ in a bounded domain. The coefficients $d_i(s$ are continuous on an interval $]-\\infty,m[$, there exists an index p such that $d_p(u$ blows up at a finite value m of the unknown u, and $\\mu$ is a diffuse measure.

A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

Science.gov (United States)

Biala, T A; Jator, S N

2015-01-01

In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

A note on numerical solution of a parabolic-Schrödinger equation

Science.gov (United States)

Ozdemir, Yildirim; Alp, Mustafa

2016-08-01

In the present study, a nonlocal boundary value problem for a parabolic-Schrödinger equation is considered. The stability estimates for the solution of the given problem is established. The first and second order of difference schemes are presented for approximately solving a specific nonlocal boundary problem. The theoretical statements for the solution of these difference schemes are supported by the result of numerical examples.

Solving hyperbolic heat conduction using electrical simulation

International Nuclear Information System (INIS)

Gheitaghy, A. M.; Talaee, M. R.

2013-01-01

In the present study, the electrical network simulation method is proposed to solve the hyperbolic and parabolic heat conduction problem considering Cattaneo-Vernoute (C.V) constitutive relation. Using this new proposed numerical model and the electrical circuit simulation program HSPICE, transient temperature and heat flux profiles at slab can be obtained easily and quickly. To verify the proposed method, the obtained numerical results for cases of one dimensional two-layer slab under periodic boundary temperature with perfect and imperfect thermal contact are compared with the published results. Comparisons show the proposed technique might be considered as a useful tool in the analysis of parabolic and hyperbolic thermal problems.

Role reversal and problem solving in international negotiations: the Partial Nuclear Test Ban case

International Nuclear Information System (INIS)

King, T.D.

1978-01-01

To facilitate finding bargaining space and to reinforce cooperative potential, a number of analysts have promoted the use of role reversal and problem solving. Role reversal involves restating the positions of one's adversary to demonstrate understanding and to develop empathy, while problem solving involves searching for alternatives that promote joint interests. The case of the negotiations in the Eighteen Nation Disarmament Conference from 1962--1963 leading to the Partial Nuclear Test Ban Treaty provided the context for examining bargaining relationships involving role reversal and problem solving. Interactions among the United States, the United Kingdom, and the Soviet Union, as recorded in transcripts of 112 sessions, were coded using Bargaining Process Analysis II, a content analysis instrument used to classify negotiation behaviors. Role reversal was measured by the frequency of paraphrases of the adversary's positions. Problem solving was measured by the frequency of themes promoting the exploration of alternatives and the search for mutually beneficial outcomes. The findings on the use of paraphrasing suggest that it can be used to restrict exploration as well as to promote it. The exploratory focus of problem solving was somewhat limited by its use in association with demands, suggesting that problem solving was interpreted as a sign of weakness

Compressible stability of growing boundary layers using parabolized stability equations

Science.gov (United States)

Chang, Chau-Lyan; Malik, Mujeeb R.; Erlebacher, Gordon; Hussaini, M. Y.

1991-01-01

The parabolized stability equation (PSE) approach is employed to study linear and nonlinear compressible stability with an eye to providing a capability for boundary-layer transition prediction in both 'quiet' and 'disturbed' environments. The governing compressible stability equations are solved by a rational parabolizing approximation in the streamwise direction. Nonparallel flow effects are studied for both the first- and second-mode disturbances. For oblique waves of the first-mode type, the departure from the parallel results is more pronounced as compared to that for the two-dimensional waves. Results for the Mach 4.5 case show that flow nonparallelism has more influence on the first mode than on the second. The disturbance growth rate is shown to be a strong function of the wall-normal distance due to either flow nonparallelism or nonlinear interactions. The subharmonic and fundamental types of breakdown are found to be similar to the ones in incompressible boundary layers.

Fixed point of the parabolic renormalization operator

CERN Document Server

Lanford III, Oscar E

2014-01-01

This monograph grew out of the authors' efforts to provide a natural geometric description for the class of maps invariant under parabolic renormalization and for the Inou-Shishikura fixed point itself as well as to carry out a computer-assisted study of the parabolic renormalization operator. It introduces a renormalization-invariant class of analytic maps with a maximal domain of analyticity and rigid covering properties and presents a numerical scheme for computing parabolic renormalization of a germ, which is used to compute the Inou-Shishikura renormalization fixed point.   Inside, readers will find a detailed introduction into the theory of parabolic bifurcation,  Fatou coordinates, Écalle-Voronin conjugacy invariants of parabolic germs, and the definition and basic properties of parabolic renormalization.   The systematic view of parabolic renormalization developed in the book and the numerical approach to its study will be interesting to both experts in the field as well as graduate students wishi...

On parabolic external maps

DEFF Research Database (Denmark)

Lomonaco, Luna; Petersen, Carsten Lunde; Shen, Weixiao

2017-01-01

We prove that any C1+BV degree d ≥ 2 circle covering h having all periodic orbits weakly expanding, is conjugate by a C1+BV diffeomorphism to a metrically expanding map. We use this to connect the space of parabolic external maps (coming from the theory of parabolic-like maps) to metrically expan...

An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions

Directory of Open Access Journals (Sweden)

A. H. Bhrawy

2014-01-01

Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.

On multilevel RBF collocation to solve nonlinear PDEs arising from endogenous stochastic volatility models

Science.gov (United States)

Bastani, Ali Foroush; Dastgerdi, Maryam Vahid; Mighani, Abolfazl

2018-06-01

The main aim of this paper is the analytical and numerical study of a time-dependent second-order nonlinear partial differential equation (PDE) arising from the endogenous stochastic volatility model, introduced in [Bensoussan, A., Crouhy, M. and Galai, D., Stochastic equity volatility related to the leverage effect (I): equity volatility behavior. Applied Mathematical Finance, 1, 63-85, 1994]. As the first step, we derive a consistent set of initial and boundary conditions to complement the PDE, when the firm is financed by equity and debt. In the sequel, we propose a Newton-based iteration scheme for nonlinear parabolic PDEs which is an extension of a method for solving elliptic partial differential equations introduced in [Fasshauer, G. E., Newton iteration with multiquadrics for the solution of nonlinear PDEs. Computers and Mathematics with Applications, 43, 423-438, 2002]. The scheme is based on multilevel collocation using radial basis functions (RBFs) to solve the resulting locally linearized elliptic PDEs obtained at each level of the Newton iteration. We show the effectiveness of the resulting framework by solving a prototypical example from the field and compare the results with those obtained from three different techniques: (1) a finite difference discretization; (2) a naive RBF collocation and (3) a benchmark approximation, introduced for the first time in this paper. The numerical results confirm the robustness, higher convergence rate and good stability properties of the proposed scheme compared to other alternatives. We also comment on some possible research directions in this field.

Analysis of solar water heater with parabolic dish concentrator and conical absorber

Science.gov (United States)

Rajamohan, G.; Kumar, P.; Anwar, M.; Mohanraj, T.

2017-06-01

This research focuses on developing novel technique for a solar water heating system. The novel solar system comprises a parabolic dish concentrator, conical absorber and water heater. In this system, the conical absorber tube directly absorbs solar radiation from the sun and the parabolic dish concentrator reflects the solar radiations towards the conical absorber tube from all directions, therefore both radiations would significantly improve the thermal collector efficiency. The working fluid water is stored at the bottom of the absorber tubes. The absorber tubes get heated and increases the temperature of the working fluid inside of the absorber tube and causes the working fluid to partially evaporate. The partially vaporized working fluid moves in the upward direction due to buoyancy effect and enters the heat exchanger. When fresh water passes through the heat exchanger, temperature of the vapour decreases through heat exchange. This leads to condensation of the vapour and forms liquid phase. The working fluid returns to the bottom of the collector absorber tube by gravity. Hence, this will continue as a cyclic process inside the system. The proposed investigation shows an improvement of collector efficiency, enhanced heat transfer and a quality water heating system.

Solving Differential Equations in R: Package deSolve

Science.gov (United States)

In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines appr...

Solving Differential Equations in R: Package deSolve

NARCIS (Netherlands)

Soetaert, K.E.R.; Petzoldt, T.; Setzer, R.W.

2010-01-01

In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines approach. The

Self-accelerating parabolic cylinder waves in 1-D

Energy Technology Data Exchange (ETDEWEB)

Yuce, C., E-mail: cyuce@anadolu.edu.tr

2016-11-25

Highlights: • We find a new class of self-accelerating waves. • We show that parabolic cylinder waves self-accelerates in a parabolic potential. • We discuss that truncated parabolic cylinder waves propagates large distance without almost being non-diffracted in free space. - Abstract: We introduce a new self-accelerating wave packet solution of the Schrodinger equation in one dimension. We obtain an exact analytical parabolic cylinder wave for the inverted harmonic potential. We show that truncated parabolic cylinder waves exhibits their accelerating feature.

The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces

KAUST Repository

Piret, Cé cile

2012-01-01

Much work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper

Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative

Directory of Open Access Journals (Sweden)

Ai-Min Yang

2014-01-01

Full Text Available The local fractional Laplace variational iteration method was applied to solve the linear local fractional partial differential equations. The local fractional Laplace variational iteration method is coupled by the local fractional variational iteration method and Laplace transform. The nondifferentiable approximate solutions are obtained and their graphs are also shown.

Local Properties of Solutions to Non-Autonomous Parabolic PDEs with State-Dependent Delays

Czech Academy of Sciences Publication Activity Database

Rezunenko, Oleksandr

2012-01-01

Roč. 2, č. 2 (2012), s. 56-71 ISSN 2158-611X R&D Projects: GA ČR(CZ) GAP103/12/2431 Institutional support: RVO:67985556 Keywords : partial differential equations * state-dependent delay * invariance principle Subject RIV: BC - Control Systems Theory http://library.utia.cas.cz/separaty/2012/AS/rezunenko- local properties of solutions to non-autonomous parabolic PDEs with state-dependent delay s.pdf

Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential

Directory of Open Access Journals (Sweden)

K. Atifi

2017-01-01

Full Text Available A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with singular potential. This problem can be formulated in a least-squares framework, an iterative procedure which minimizes the difference between the given measurements and the value at sensor locations of a reconstructed field. The mathematical model leads to a nonconvex minimization problem. To solve it, we prove the existence of at least one solution of problem and we propose two approaches: the first is based on a Tikhonov regularization, while the second approach is based on a hybrid genetic algorithm (married genetic with descent method type gradient. Some numerical experiments are given.

A parabolic model for dimple potentials

International Nuclear Information System (INIS)

Aydin, Melike Cibik; Uncu, Haydar; Deniz, Coskun

2013-01-01

We study the truncated parabolic function and demonstrate that it is a representation of the Dirac δ function. We also show that the truncated parabolic function, used as a potential in the Schrödinger equation, has the same bound state spectrum, tunneling and reflection amplitudes as the Dirac δ potential, as the width of the parabola approximates to zero. Dirac δ potential is used to model dimple potentials which are utilized to increase the phase-space density of a Bose–Einstein condensate in a harmonic trap. We show that a harmonic trap with a δ function at the origin is a limiting case of the harmonic trap with a symmetric truncated parabolic potential around the origin. Hence, the truncated parabolic is a better candidate for modeling the dimple potentials. (paper)

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

Energy Technology Data Exchange (ETDEWEB)

Angstmann, C.N.; Donnelly, I.C. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Henry, B.I., E-mail: B.Henry@unsw.edu.au [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Jacobs, B.A. [School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050 (South Africa); DST–NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) (South Africa); Langlands, T.A.M. [Department of Mathematics and Computing, University of Southern Queensland, Toowoomba QLD 4350 (Australia); Nichols, J.A. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia)

2016-02-15

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.

Non-local quasi-linear parabolic equations

International Nuclear Information System (INIS)

Amann, H

2005-01-01

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

Partial differential equations

CERN Document Server

Evans, Lawrence C

2010-01-01

This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...

A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations

International Nuclear Information System (INIS)

Feng Qing-Hua

2014-01-01

In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space-time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained. (general)

Gradient-type methods in inverse parabolic problems

International Nuclear Information System (INIS)

Kabanikhin, Sergey; Penenko, Aleksey

2008-01-01

This article is devoted to gradient-based methods for inverse parabolic problems. In the first part, we present a priori convergence theorems based on the conditional stability estimates for linear inverse problems. These theorems are applied to backwards parabolic problem and sideways parabolic problem. The convergence conditions obtained coincide with sourcewise representability in the self-adjoint backwards parabolic case but they differ in the sideways case. In the second part, a variational approach is formulated for a coefficient identification problem. Using adjoint equations, a formal gradient of an objective functional is constructed. A numerical test illustrates the performance of conjugate gradient algorithm with the formal gradient.

F John's stability conditions versus A Carasso's SECB constraint for backward parabolic problems

International Nuclear Information System (INIS)

Lee, Jinwoo; Sheen, Dongwoo

2009-01-01

In order to solve backward parabolic problems John (1960 Commun. Pure. Appl. Math.13 551–85) introduced the two constraints ||u(T)|| ≤ M and ||u(0) − g|| ≤ δ where u(t) satisfies the backward heat equation for t in (0, T) with the initial data u(0). The slow evolution from the continuation boundary (SECB) constraint was introduced by Carasso (1994 SIAM J. Numer. Anal. 31 1535–57) to attain continuous dependence on data for backward parabolic problems even at the continuation boundary t = T. The additional 'SECB constraint' guarantees a significant improvement in stability up to t = T. In this paper, we prove that the same type of stability can be obtained by using only two constraints among the three. More precisely, we show that the a priori boundedness condition ||u(T)|| ≤ M is redundant. This implies that Carasso's SECB condition can be used to replace the a priori boundedness condition of John with an improved stability estimate. Also, a new class of regularized solutions is introduced for backward parabolic problems with an SECB constraint. The new regularized solutions are optimally stable and we also provide a constructive scheme to compute. Finally, numerical examples are provided

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

Science.gov (United States)

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.

Thermal behaviour of solar air heater with compound parabolic concentrator

International Nuclear Information System (INIS)

Tchinda, Rene

2008-01-01

A mathematical model for computing the thermal performance of an air heater with a truncated compound parabolic concentrator having a flat one-sided absorber is presented. A computer code that employs an iterative solution procedure is constructed to solve the governing energy equations and to estimate the performance parameters of the collector. The effects of the air mass flow rate, the wind speed and the collector length on the thermal performance of the present air heater are investigated. Predictions for the performance of the solar heater also exhibit reasonable agreement, with experimental data with an average error of 7%

The Adomian decomposition method for solving partial differential equations of fractal order in finite domains

Energy Technology Data Exchange (ETDEWEB)

El-Sayed, A.M.A. [Faculty of Science University of Alexandria (Egypt)]. E-mail: amasyed@hotmail.com; Gaber, M. [Faculty of Education Al-Arish, Suez Canal University (Egypt)]. E-mail: mghf408@hotmail.com

2006-11-20

The Adomian decomposition method has been successively used to find the explicit and numerical solutions of the time fractional partial differential equations. A different examples of special interest with fractional time and space derivatives of order {alpha}, 0<{alpha}=<1 are considered and solved by means of Adomian decomposition method. The behaviour of Adomian solutions and the effects of different values of {alpha} are shown graphically for some examples.

The parabolic equation method for outdoor sound propagation

DEFF Research Database (Denmark)

Arranz, Marta Galindo

The parabolic equation method is a versatile tool for outdoor sound propagation. The present study has focused on the Cranck-Nicolson type Parabolic Equation method (CNPE). Three different applications of the CNPE method have been investigated. The first two applications study variations of the g......The parabolic equation method is a versatile tool for outdoor sound propagation. The present study has focused on the Cranck-Nicolson type Parabolic Equation method (CNPE). Three different applications of the CNPE method have been investigated. The first two applications study variations...

Stability analysis of impulsive parabolic complex networks

Energy Technology Data Exchange (ETDEWEB)

Wang Jinliang, E-mail: wangjinliang1984@yahoo.com.cn [Science and Technology on Aircraft Control Laboratory, School of Automation Science and Electrical Engineering, Beihang University, XueYuan Road, No. 37, HaiDian District, Beijing 100191 (China); Wu Huaining [Science and Technology on Aircraft Control Laboratory, School of Automation Science and Electrical Engineering, Beihang University, XueYuan Road, No. 37, HaiDian District, Beijing 100191 (China)

2011-11-15

Highlights: > Two impulsive parabolic complex network models are proposed. > The global exponential stability of impulsive parabolic complex networks are considered. > The robust global exponential stability of impulsive parabolic complex networks are considered. - Abstract: In the present paper, two kinds of impulsive parabolic complex networks (IPCNs) are considered. In the first one, all nodes have the same time-varying delay. In the second one, different nodes have different time-varying delays. Using the Lyapunov functional method combined with the inequality techniques, some global exponential stability criteria are derived for the IPCNs. Furthermore, several robust global exponential stability conditions are proposed to take uncertainties in the parameters of the IPCNs into account. Finally, numerical simulations are presented to illustrate the effectiveness of the results obtained here.

Stability analysis of impulsive parabolic complex networks

International Nuclear Information System (INIS)

Wang Jinliang; Wu Huaining

2011-01-01

Highlights: → Two impulsive parabolic complex network models are proposed. → The global exponential stability of impulsive parabolic complex networks are considered. → The robust global exponential stability of impulsive parabolic complex networks are considered. - Abstract: In the present paper, two kinds of impulsive parabolic complex networks (IPCNs) are considered. In the first one, all nodes have the same time-varying delay. In the second one, different nodes have different time-varying delays. Using the Lyapunov functional method combined with the inequality techniques, some global exponential stability criteria are derived for the IPCNs. Furthermore, several robust global exponential stability conditions are proposed to take uncertainties in the parameters of the IPCNs into account. Finally, numerical simulations are presented to illustrate the effectiveness of the results obtained here.

Numerical simulation of solar parabolic trough collector performance in the Algeria Saharan region

International Nuclear Information System (INIS)

Marif, Yacine; Benmoussa, Hocine; Bouguettaia, Hamza; Belhadj, Mohamed M.; Zerrouki, Moussa

2014-01-01

Highlights: • The parabolic trough collector performance is examined. • The finite difference method is proposed and validated. • Two fluids are considered water and TherminolVP-1™. - Abstract: In order to determine the optical and thermal performance of a solar parabolic trough collector under the climate conditions of Algerian Sahara, a computer program based on one dimensional implicit finite difference method with energy balance approach has been developed. The absorber pipe, glass envelope and fluid were divided into several segments and the partial derivation in the differential equations was replaced by the backward finite difference terms in each segment. Two fluids were considered, liquid water and TherminolVP-1™ synthetic oil. Furthermore, the intensity of the direct solar radiation was estimated by monthly average values of the atmospheric Linke turbidity factor for different tracking systems. According to the simulation findings, the one axis polar East–West and horizontal East–West tracking systems were most desirable for a parabolic trough collector throughout the whole year. In addition, it is found that the thermal efficiency was about 69.73–72.24%, which decreases with the high synthetic oil fluid temperatures and increases in the lower water temperature by 2%

Solar parabolic dish technology evaluation report

Science.gov (United States)

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.

Radio wave propagation and parabolic equation modeling

CERN Document Server

Apaydin, Gokhan

2018-01-01

A thorough understanding of electromagnetic wave propagation is fundamental to the development of sophisticated communication and detection technologies. The powerful numerical methods described in this book represent a major step forward in our ability to accurately model electromagnetic wave propagation in order to establish and maintain reliable communication links, to detect targets in radar systems, and to maintain robust mobile phone and broadcasting networks. The first new book on guided wave propagation modeling and simulation to appear in nearly two decades, Radio Wave Propagation and Parabolic Equation Modeling addresses the fundamentals of electromagnetic wave propagation generally, with a specific focus on radio wave propagation through various media. The authors explore an array of new applications, and detail various v rtual electromagnetic tools for solving several frequent electromagnetic propagation problems. All of the methods described are presented within the context of real-world scenari...

Model and control scheme for recirculation mode direct steam generation parabolic trough solar power plants

International Nuclear Information System (INIS)

Guo, Su; Liu, Deyou; Chen, Xingying; Chu, Yinghao; Xu, Chang; Liu, Qunming; Zhou, Ling

2017-01-01

Highlights: •A nonlinear dynamic model of recirculation DSG parabolic trough is developed. •Collector row, water separator and spray attemperator are modeled, respectively. •The dynamic behaviors of the collector field are simulated and analyzed. •Transfer functions of water level and outlet fluid temperature are derived. •Multi-model switching generalized predictive control strategy is developed. -- Abstract: This work describes and evaluates a new nonlinear dynamic model, and a new generalized predictive control scheme for a collector field of direct steam generation parabolic troughs in recirculation mode. Modeling the dynamic behaviors of collector fields is essential to design, testing and validation of automatic control systems for direct steam generation parabolic troughs. However, the behaviors of two-phase heat transfer fluids impose challenges to simulating and developing process control schemes. In this work, a new nonlinear dynamic model is proposed, based on the nonlinear distributed parameter and the nonlinear lumped parameter methods. The proposed model is used to simulate and analyze the dynamic behaviors of the entire collector field for recirculation mode direct steam generation parabolic troughs under different weather conditions, without excessive computational costs. Based on the proposed model, transfer functions for both the water level of the separator and outlet steam temperatures are derived, and a new multi-model switching generalized predictive control scheme is developed for simulated control of the plant behaviors for a wide region of operational conditions. The proposed control scheme achieves excellent control performance and robustness for systems with long delay, large inertia and time-varying parameters, and efficiently solves the model mismatching problem in direct steam generation parabolic troughs. The performances of the model and control scheme are validated with design data from the project of Integration of Direct

Parabolic features and the erosion rate on Venus

Science.gov (United States)

Strom, Robert G.

1993-01-01

The impact cratering record on Venus consists of 919 craters covering 98 percent of the surface. These craters are remarkably well preserved, and most show pristine structures including fresh ejecta blankets. Only 35 craters (3.8 percent) have had their ejecta blankets embayed by lava and most of these occur in the Atla-Beta Regio region; an area thought to be recently active. parabolic features are associated with 66 of the 919 craters. These craters range in size from 6 to 105 km diameter. The parabolic features are thought to be the result of the deposition of fine-grained ejecta by winds in the dense venusian atmosphere. The deposits cover about 9 percent of the surface and none appear to be embayed by younger volcanic materials. However, there appears to be a paucity of these deposits in the Atla-Beta Regio region, and this may be due to the more recent volcanism in this area of Venus. Since parabolic features are probably fine-grain, wind-deposited ejecta, then all impact craters on Venus probably had these deposits at some time in the past. The older deposits have probably been either eroded or buried by eolian processes. Therefore, the present population of these features is probably associated with the most recent impact craters on the planet. Furthermore, the size/frequency distribution of craters with parabolic features is virtually identical to that of the total crater population. This suggests that there has been little loss of small parabolic features compared to large ones, otherwise there should be a significant and systematic paucity of craters with parabolic features with decreasing size compared to the total crater population. Whatever is erasing the parabolic features apparently does so uniformly regardless of the areal extent of the deposit. The lifetime of parabolic features and the eolian erosion rate on Venus can be estimated from the average age of the surface and the present population of parabolic features.

Semilinear Kolmogorov Equations and Applications to Stochastic Optimal Control

International Nuclear Information System (INIS)

Masiero, Federica

2005-01-01

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

An evolution infinity Laplace equation modelling dynamic elasto-plastic torsion

Science.gov (United States)

Messelmi, Farid

2017-12-01

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.

Heat transfer analysis of parabolic trough solar receiver

International Nuclear Information System (INIS)

Padilla, Ricardo Vasquez; Demirkaya, Gokmen; Goswami, D. Yogi; Stefanakos, Elias; Rahman, Muhammad M.

2011-01-01

Highlights: → In this paper a detailed one dimensional numerical heat transfer analysis of a PTC is performed. → The receiver and envelope were divided into several segments and mass and energy balance were applied in each segment. → Improvements either in the heat transfer correlations or radiative heat transfer analysis are presented. → The proposed heat transfer model was validated with experimental data obtained from Sandia National Laboratory. → Our results showed a better agreement with experimental data compared to other models. -- Abstract: Solar Parabolic Trough Collectors (PTCs) are currently used for the production of electricity and applications with relatively higher temperatures. A heat transfer fluid circulates through a metal tube (receiver) with an external selective surface that absorbs solar radiation reflected from the mirror surfaces of the PTC. In order to reduce the heat losses, the receiver is covered by an envelope and the enclosure is usually kept under vacuum pressure. The heat transfer and optical analysis of the PTC is essential to optimize and understand its performance under different operating conditions. In this paper a detailed one dimensional numerical heat transfer analysis of a PTC is performed. The receiver and envelope were divided into several segments and mass and energy balance were applied in each segment. Improvements either in the heat transfer correlations or radiative heat transfer analysis are presented as well. The partial differential equations were discretized and the nonlinear algebraic equations were solved simultaneously. Finally, to validate the numerical results, the model was compared with experimental data obtained from Sandia National Laboratory (SNL) and other one dimensional heat transfer models. Our results showed a better agreement with experimental data compared to other models.

Manufacturing parabolic mirrors

CERN Multimedia

CERN PhotoLab

1975-01-01

The photo shows the construction of a vertical centrifuge mounted on an air cushion, with a precision of 1/10000 during rotation, used for the manufacture of very high=precision parabolic mirrors. (See Annual Report 1974.)

Photovoltaic applications of Compound Parabolic Concentrator (CPC)

Science.gov (United States)

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.

Thermal behaviour of a solar air heater with a compound parabolic concentrator

International Nuclear Information System (INIS)

Tchinda, R.

2005-11-01

A mathematical model for computing the thermal performance of an air heater with a truncated compound parabolic concentrator having a flat one-sided absorber is presented. A computed code that employs an iterative solution procedure is constructed to solve the governing energy equations and to estimate the performance parameters of the collector. The effects of the air mass flow rate, the wind speed and the collector length on the thermal performance of the present air heater are investigated. Prediction for the performance of the solar heater also exhibits reasonable agreement with experimental data with an average error of 7%. (author)

Implementation of compact finite-difference method to parabolized Navier-Stokes equations

International Nuclear Information System (INIS)

Esfahanian, V.; Hejranfar, K.; Darian, H.M.

2005-01-01

The numerical simulation of the Parabolized Navier-Stokes (PNS) equations for supersonic/hypersonic flow field is obtained by using the fourth-order compact finite-difference method. The PNS equations in the general curvilinear coordinates are solved by using the implicit finite-difference algorithm of Beam and Warming. A shock fitting procedure is utilized to obtain the accurate solution in the vicinity of the shock. The computations are performed for hypersonic axisymmetric flow over a blunt cone. The present results for the flow field along with those of the second-order method are presented and accuracy analysis is performed to insure the fourth-order accuracy of the method. (author)

Two new designs of parabolic solar collectors

Directory of Open Access Journals (Sweden)

Karimi Sadaghiyani Omid

2014-01-01

Full Text Available In this work, two new compound parabolic trough and dish solar collectors are presented with their working principles. First, the curves of mirrors are defined and the mathematical formulation as one analytical method is used to trace the sun rays and recognize the focus point. As a result of the ray tracing, the distribution of heat flux around the inner wall can be reached. Next, the heat fluxes are calculated versus several absorption coefficients. These heat flux distributions around absorber tube are functions of angle in polar coordinate system. Considering, the achieved heat flux distribution are used as a thermal boundary condition. After that, Finite Volume Methods (FVM are applied for simulation of absorber tube. The validation of solving method is done by comparing with Dudley's results at Sandia National Research Laboratory. Also, in order to have a good comparison between LS-2 and two new designed collectors, some of their parameters are considered equal with together. These parameters are consist of: the aperture area, the measures of tube geometry, the thermal properties of absorber tube, the working fluid, the solar radiation intensity and the mass flow rate of LS-2 collector are applied for simulation of the new presented collectors. After the validation of the used numerical models, this method is applied to simulation of the new designed models. Finally, the outlet results of new designed collector are compared with LS-2 classic collector. Obviously, the obtained results from the comparison show the improving of the new designed parabolic collectors efficiency. In the best case-study, the improving of efficiency are about 10% and 20% for linear and convoluted models respectively.

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

Science.gov (United States)

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.

The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: II. Numerical Treatment

OpenAIRE

Scheidsteger, T.; Urbschat, H.; Griffiths, R. B.; Schellnhuber, H. J.

1997-01-01

A procedure is described for efficiently finding the ground state energy and configuration for a Frenkel-Kontorova model in a periodic potential, consisting of N parabolic segments of identical curvature in each period, through a numerical solution of the convex minimization problem described in the preceding paper. The key elements are the use of subdifferentials to describe the structure of the minimization problem; an intuitive picture of how to solve it, based on motion of quasiparticles;...

A new efficient analytical method for a system of vibration. Structural analysis using a new technique of partially solving method

International Nuclear Information System (INIS)

Gunyasu, Kenzo; Hiramoto, Tsuneyuki; Tanimoto, Mitsumori; Osano, Minetada

2002-01-01

We describe a new method for solving large-scale system of linear equations resulting from discretization of ordinary differential equation and partial differential equation directly. This new method effectively reduces the memory capacity requirements and computing time problems for analyses using finite difference method and finite element method. In this paper we have tried to solve one-million linear equations directly for the case that initial displacement and boundary displacement are known about the finite difference scheme of second order inhomogeneous differential equation for vibration of a 10 story structure. Excellent results were got. (author)

European parabolic flight campaigns with Airbus ZERO-G: Looking back at the A300 and looking forward to the A310

Science.gov (United States)

Pletser, Vladimir; Rouquette, Sebastien; Friedrich, Ulrike; Clervoy, Jean-Francois; Gharib, Thierry; Gai, Frederic; Mora, Christophe

2015-09-01

Aircraft parabolic flights repetitively provide up to 23 s of reduced gravity during ballistic flight manoeuvres. Parabolic flights are used to conduct short microgravity investigations in Physical and Life Sciences and in Technology, to test instrumentation prior to space flights and to train astronauts before a space mission. The use of parabolic flights is complementary to other microgravity carriers (drop towers, sounding rockets), and preparatory to manned space missions on board the International Space Station and other manned spacecraft, such as Shenzhou and the Chinese Space Station CSS. The European Space Agency (ESA), the 'Centre National d'Etudes Spatiales' (CNES, French Space Agency) and the 'Deutsches Zentrum für Luft- und Raumfahrt e.V.' (DLR, the German Aerospace Centre) have used the Airbus A300 ZERO-G for research experiments in microgravity, and at Moon and Mars gravity levels, from 1997 until October 2014. The French company Novespace, a subsidiary of CNES, based in Bordeaux, France, is in charge of the organisation of Airbus A300 ZERO-G flights. A total of 104 parabolic flight campaigns have been organised by ESA, CNES and DLR since 1997, including 38 ESA, 34 CNES and 23 DLR microgravity campaigns, two Joint European ESA-CNES-DLR Partial-g Parabolic Flight Campaigns, and seven ESA Student campaigns. After 17 years of good and loyal services, this European workhorse for microgravity research in parabolic flights has been retired. The successor aircraft, the Airbus A310 ZERO-G, is being prepared for a first ESA-CNES-DLR cooperative campaign in Spring 2015. This paper looks back over 17 years of microgravity research in parabolic flights with the A300 ZERO-G, and introduces the new A310 ZERO-G that will be used from 2015 onwards.

Federal technology alert. Parabolic-trough solar water heating

Energy Technology Data Exchange (ETDEWEB)

NONE

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.

Adaptive distributed parameter and input estimation in linear parabolic PDEs

KAUST Repository

Mechhoud, Sarra

2016-01-01

In this paper, we discuss the on-line estimation of distributed source term, diffusion, and reaction coefficients of a linear parabolic partial differential equation using both distributed and interior-point measurements. First, new sufficient identifiability conditions of the input and the parameter simultaneous estimation are stated. Then, by means of Lyapunov-based design, an adaptive estimator is derived in the infinite-dimensional framework. It consists of a state observer and gradient-based parameter and input adaptation laws. The parameter convergence depends on the plant signal richness assumption, whereas the state convergence is established using a Lyapunov approach. The results of the paper are illustrated by simulation on tokamak plasma heat transport model using simulated data.

The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces

KAUST Repository

Piret, Cécile

2012-05-01

Much work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper, we investigate methods to solve PDEs on arbitrary stationary surfaces embedded in . R3 using the RBF method. We present three RBF-based methods that easily discretize surface differential operators. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent the most complex geometries in any dimension. Two out of the three methods, which we call the orthogonal gradients (OGr) methods are the result of our work and are hereby presented for the first time. © 2012 Elsevier Inc.

Mixed hyperbolic-second-order-parabolic formulations of general relativity

International Nuclear Information System (INIS)

Paschalidis, Vasileios

2008-01-01

Two new formulations of general relativity are introduced. The first one is a parabolization of the Arnowitt-Deser-Misner formulation and is derived by the addition of combinations of the constraints and their derivatives to the right-hand side of the Arnowitt-Deser-Misner evolution equations. The desirable property of this modification is that it turns the surface of constraints into a local attractor because the constraint propagation equations become second-order parabolic independently of the gauge conditions employed. This system may be classified as mixed hyperbolic--second-order parabolic. The second formulation is a parabolization of the Kidder-Scheel-Teukolsky formulation and is a manifestly mixed strongly hyperbolic--second-order-parabolic set of equations, bearing thus resemblance to the compressible Navier-Stokes equations. As a first test, a stability analysis of flat space is carried out and it is shown that the first modification exponentially damps and smoothes all constraint-violating modes. These systems provide a new basis for constructing schemes for long-term and stable numerical integration of the Einstein field equations.

Moduli of Parabolic Higgs Bundles and Atiyah Algebroids

DEFF Research Database (Denmark)

Logares, Marina; Martens, Johan

2010-01-01

In this paper we study the geometry of the moduli space of (non-strongly) parabolic Higgs bundles over a Riemann surface with marked points. We show that this space possesses a Poisson structure, extending the one on the dual of an Atiyah algebroid over the moduli space of parabolic vector bundle...

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

International Nuclear Information System (INIS)

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 s 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 useful

Solving variational problems and partial differential equations that map between manifolds via the closest point method

Science.gov (United States)

King, Nathan D.; Ruuth, Steven J.

2017-05-01

Maps from a source manifold M to a target manifold N appear in liquid crystals, color image enhancement, texture mapping, brain mapping, and many other areas. A numerical framework to solve variational problems and partial differential equations (PDEs) that map between manifolds is introduced within this paper. Our approach, the closest point method for manifold mapping, reduces the problem of solving a constrained PDE between manifolds M and N to the simpler problems of solving a PDE on M and projecting to the closest points on N. In our approach, an embedding PDE is formulated in the embedding space using closest point representations of M and N. This enables the use of standard Cartesian numerics for general manifolds that are open or closed, with or without orientation, and of any codimension. An algorithm is presented for the important example of harmonic maps and generalized to a broader class of PDEs, which includes p-harmonic maps. Improved efficiency and robustness are observed in convergence studies relative to the level set embedding methods. Harmonic and p-harmonic maps are computed for a variety of numerical examples. In these examples, we denoise texture maps, diffuse random maps between general manifolds, and enhance color images.

Moduli space of Parabolic vector bundles over hyperelliptic curves

Indian Academy of Sciences (India)

27

This has been generalized for higher dimensional varieties by Maruyama ... Key words and phrases. Parabolic structure .... Let E be a vector bundle of rank r on X. Recall that a parabolic ..... Let us understand this picture geometrically. Let ω1 ...

Numerical and experimental investigation on a new type of compound parabolic concentrator solar collector

International Nuclear Information System (INIS)

Zheng, Wandong; Yang, Lin; Zhang, Huan; You, Shijun; Zhu, Chunguang

2016-01-01

Highlights: • A serpentine compound parabolic concentrator solar collector is proposed. • A mathematical model for the new collector is developed and verified by experiments. • The thermal efficiency of the collector can be up to 60.5% during the experiments. • The effects of key parameters on the thermal performance are mathematically studied. - Abstract: In order to improve the thermal efficiency, reduce the heat losses and achieve high freezing resistance of the solar device for space heating in cold regions, a new type of serpentine compound parabolic concentrator solar collector is presented in this paper, which is a combination of a compound parabolic concentrator solar collector and a flat plate solar collector. A detailed mathematical model for the new collector based on the analysis of heat transfer is developed and then solved by the software tool Matlab. The numerical results are compared with the experimental data and the maximum deviation is 8.07%, which shows a good agreement with each other. The experimental results show that the thermal efficiency of the collector can be as high as 60.5%. The model is used to predict the thermal performance of the new collector. The effects of structure and operating parameters on the thermal performance are mathematically discussed. The numerical and experimental results show that the new collector is more suitable to provide low temperature hot water for space heating in cold regions and the mathematical model will be much helpful in the designing and optimizing of the solar collectors.

Study on the optical properties of the off-axis parabolic collimator with eccentric pupil

Science.gov (United States)

Li, Gang; Gao, Xin; Duan, Jing; Zhang, Henjin

2017-02-01

The off-axis parabolic collimator with eccentric pupil has the advantages of wide spectrum, simple structure, easy assembly and adjustment, high performance price ratio. So, it is widely used for parameters testing and image quality calibration of ground-based and space-based cameras. In addition to the Strehl ratio, resolution, wavefront aberration, modulation transfer function, the general evaluation criteria on the imaging quality of the optical system, the beam parallelism characterize the collimator angle resolving capability and collimation condition of the collimator with the target board, can be measured easily ,quickly and operation process is simple, but the study mainly focus on how to measure it so far. In order to solve Quantitative calculation of this problem, firstly, the discussion of aberration condition of the off- axis parabolic is carried out based on the primary aberration theory. Secondly, analysis on the influencing factor on collimator optical properties is given, including the geometrical aberrations of spherical aberration, coma, astigmatism , the relation between the position of the eccentric pupil and the aberration and optical element surface wavefront aberration, after that, according to the basis of diffraction and wavefront aberration theory, the paper deduced calculation method of the beam parallelism, at last, an example of a 400mm diameter off-axis parabolic collimator with eccentric pupil is given to calculate, the practical results shows that calculation data is well in accordance with actual measurement data and results can meet the demand and has a guiding significance to the actual project manufacture and the theory analysis.

A compact representation of drawing movements with sequences of parabolic primitives.

Directory of Open Access Journals (Sweden)

Felix Polyakov

2009-07-01

Full Text Available Some studies suggest that complex arm movements in humans and monkeys may optimize several objective functions, while others claim that arm movements satisfy geometric constraints and are composed of elementary components. However, the ability to unify different constraints has remained an open question. The criterion for a maximally smooth (minimizing jerk motion is satisfied for parabolic trajectories having constant equi-affine speed, which thus comply with the geometric constraint known as the two-thirds power law. Here we empirically test the hypothesis that parabolic segments provide a compact representation of spontaneous drawing movements. Monkey scribblings performed during a period of practice were recorded. Practiced hand paths could be approximated well by relatively long parabolic segments. Following practice, the orientations and spatial locations of the fitted parabolic segments could be drawn from only 2-4 clusters, and there was less discrepancy between the fitted parabolic segments and the executed paths. This enabled us to show that well-practiced spontaneous scribbling movements can be represented as sequences ("words" of a small number of elementary parabolic primitives ("letters". A movement primitive can be defined as a movement entity that cannot be intentionally stopped before its completion. We found that in a well-trained monkey a movement was usually decelerated after receiving a reward, but it stopped only after the completion of a sequence composed of several parabolic segments. Piece-wise parabolic segments can be generated by applying affine geometric transformations to a single parabolic template. Thus, complex movements might be constructed by applying sequences of suitable geometric transformations to a few templates. Our findings therefore suggest that the motor system aims at achieving more parsimonious internal representations through practice, that parabolas serve as geometric primitives and that non

Upwind algorithm for the parabolized Navier-Stokes equations

Science.gov (United States)

Lawrence, Scott L.; Tannehill, John C.; Chausee, Denny S.

1989-01-01

A new upwind algorithm based on Roe's scheme has been developed to solve the two-dimensional parabolized Navier-Stokes equations. This method does not require the addition of user-specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming (1978) scheme in terms of accuracy, stability, computer time and storage requirements, and programming effort. The new algorithm has been validated by applying it to three laminar test cases, including flat-plate boundary-layer flow, hypersonic flow past a 15-deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with results obtained using the conventional Beam-Warming algorithm.

A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

Science.gov (United States)

Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

2018-06-01

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

Parabolized stability equations

Science.gov (United States)

Herbert, Thorwald

1994-01-01

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

A comparative Thermal Analysis of conventional parabolic receiver tube and Cavity model tube in a Solar Parabolic Concentrator

Science.gov (United States)

Arumugam, S.; Ramakrishna, P.; Sangavi, S.

2018-02-01

Improvements in heating technology with solar energy is gaining focus, especially solar parabolic collectors. Solar heating in conventional parabolic collectors is done with the help of radiation concentration on receiver tubes. Conventional receiver tubes are open to atmosphere and loose heat by ambient air currents. In order to reduce the convection losses and also to improve the aperture area, we designed a tube with cavity. This study is a comparative performance behaviour of conventional tube and cavity model tube. The performance formulae were derived for the cavity model based on conventional model. Reduction in overall heat loss coefficient was observed for cavity model, though collector heat removal factor and collector efficiency were nearly same for both models. Improvement in efficiency was also observed in the cavity model’s performance. The approach towards the design of a cavity model tube as the receiver tube in solar parabolic collectors gave improved results and proved as a good consideration.

Analytic perturbation theory for screened Coulomb potential: full continuum wave function

International Nuclear Information System (INIS)

Bechler, A.; Ennan, Mc J.; Pratt, R.H.

1979-01-01

An analytic perturbation theory developed previously is used to find a continuum screened-Coulomb wave function characterized by definite asymptotic momentum. This wave function satisfies an inhomogeneous partial differential equation which is solved in parabolic coordinates; the solution depends on both parabolic variables. We calculate partial wave projections of this solution and show that we can choose to add a solution of the homogeneous equation such that the partial wave projections become equal to the normalized continuum radial function found previously. However, finding the unique solution with given asymptotic linear momentum will require either using boundary conditions to determine the unique needed solution of the homogeneous equation or equivalently specifying the screened-Coulomb phase-shifts. (author)

Environmental Controls and Eco-geomorphic Interactions of the Barchan-to-parabolic Dune Stabilisation and the Parabolic-to-barchan Dune Reactivation

Science.gov (United States)

Yan, Na; Baas, Andreas

2015-04-01

Parabolic dunes are one of a few common aeolian landforms which are highly controlled by eco-geomorphic interactions. Parabolic dunes, on the one hand, can be developed from highly mobile dune landforms, barchans for instance, in an ameliorated vegetation condition; or on the other hand, they can be reactivated and transformed back into mobile dunes due to vegetation deterioration. The fundamental mechanisms and eco-geomorphic interactions controlling both dune transformations remain poorly understood. To bridge the gap between complex processes involved in dune transformations on a relatively long temporal scale and real world monitoring records on a very limited temporal scale, this research has extended the DECAL model to incorporate 'dynamic' growth functions and the different 'growth' of perennial shrubs between growing and non-growing seasons, informed by field measurements and remote sensing analysis, to explore environmental controls and eco-geomorphic interactions of both types of dune transformation. A non-dimensional 'dune stabilising index' is proposed to capture the interactions between environmental controls (i.e. the capabilities of vegetation to withstand wind erosion and sand burial, the sandy substratum thickness, the height of the initial dune, and the sand transport potential), and establish the linkage between these controls and the geometry of a stabilising dune. An example demonstrates how to use the power-law relationship between the dune stabilising index and the normalised migration distance to assist in extrapolating the historical trajectories of transforming dunes. The modelling results also show that a slight increase in vegetation cover of an initial parabolic dune can significantly increase the reactivation threshold of climatic impact (both drought stress and wind strength) required to reactivate a stabilising parabolic dune into a barchan. Four eco-geomorphic interaction zones that govern a barchan-to-parabolic dune transformation

Finite-time blow-up for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type

Science.gov (United States)

Hashira, Takahiro; Ishida, Sachiko; Yokota, Tomomi

2018-05-01

This paper deals with the quasilinear degenerate Keller-Segel systems of parabolic-parabolic type in a ball of RN (N ≥ 2). In the case of non-degenerate diffusion, Cieślak-Stinner [3,4] proved that if q > m + 2/N, where m denotes the intensity of diffusion and q denotes the nonlinearity, then there exist initial data such that the corresponding solution blows up in finite time. As to the case of degenerate diffusion, it is known that a solution blows up if q > m + 2/N (see Ishida-Yokota [13]); however, whether the blow-up time is finite or infinite has been unknown. This paper gives an answer to the unsolved problem. Indeed, the finite-time blow-up of energy solutions is established when q > m + 2/N.

Flux form Semi-Lagrangian methods for parabolic problems

Directory of Open Access Journals (Sweden)

Bonaventura Luca

2016-09-01

Full Text Available A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and stability analysis is proposed. Numerical examples validate the proposed method and display its potential for consistent semi-Lagrangian discretization of advection diffusion and nonlinear parabolic problems.

Magnetization of a parabolic quantum dot in the presence of Rashba and Dresselhaus spin-orbit interactions

Energy Technology Data Exchange (ETDEWEB)

Kumar, D. Sanjeev, E-mail: sanjeevchs@gmail.com; Chatterjee, Ashok [School of Physics, University of Hyderabad, Hyderabad 500046 (India); Mukhopadhyay, Soma [Department of Physics, DVR College of Engineering and Technology, Kashipur, Sangareddy Mandal, Hyderabad 502 285 (India)

2015-05-15

The magnetization of a parabolic quantum dot has been studied as a function of temperature and external magnetic field in the presence of Rashba, Dresselhaus Spin Orbit Interactions (SOI) and the electron-electron interactions. By the introduction of a simple and physically reasonable model potential, the problem has been solved exactly up to second order in both the SOI terms. Both the SOI found to be showing considerable effects on the magnetization of the quantum dot. The effect of electron-electron interaction on the magnetization also has been studied.

Magnetization of a parabolic quantum dot in the presence of Rashba and Dresselhaus spin-orbit interactions

International Nuclear Information System (INIS)

Kumar, D. Sanjeev; Chatterjee, Ashok; Mukhopadhyay, Soma

2015-01-01

The magnetization of a parabolic quantum dot has been studied as a function of temperature and external magnetic field in the presence of Rashba, Dresselhaus Spin Orbit Interactions (SOI) and the electron-electron interactions. By the introduction of a simple and physically reasonable model potential, the problem has been solved exactly up to second order in both the SOI terms. Both the SOI found to be showing considerable effects on the magnetization of the quantum dot. The effect of electron-electron interaction on the magnetization also has been studied

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

Science.gov (United States)

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.

Handbook of Nonlinear Partial Differential Equations

CERN Document Server

Polyanin, Andrei D

2011-01-01

New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear PDEs with Maple(t), Mathematica(R), and MATLAB(R) Many new illustrative examples and tables A large list of references consisting of over 1,300 sources To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology. They

Performance Analysis of Fractional-Order PID Controller for a Parabolic Distributed Solar Collector

KAUST Repository

Elmetennani, Shahrazed

2017-09-01

This paper studies the performance of a fractional-order proportional integral derivative (FOPID) controller designed for parabolic distributed solar collectors. The control problem addressed in concentrated solar collectors aims at forcing the produced heat to follow a desired reference despite the unevenly varying solar irradiance. In addition to the unpredictable variations of the energy source, the parabolic solar collectors are subject to inhomogeneous distributed efficiency parameters affecting the heat production. The FOPID controller is well known for its simplicity with better tuning flexibility along with robustness with respect to disturbances. Thus, we propose a control strategy based on FOPID to achieve the control objectives. First, the FOPID controller is designed based on a linear approximate model describing the system dynamics under nominal working conditions. Then, the FOPID gains and differentiation orders are optimally tuned in order to fulfill the robustness design specifications by solving a nonlinear optimization problem. Numerical simulations are carried out to evaluate the performance of the proposed FOPID controller. A comparison to the robust integer order PID is also provided. Robustness tests are performed for the nominal model to show the effectiveness of the FOPID. Furthermore, the proposed FOPID is numerically tested to control the distributed solar collector under real working conditions.

Parabolic-trough technology roadmap: A pathway for sustained commercial development and deployment of parabolic-trough technology

International Nuclear Information System (INIS)

David Kearney; Hank Price

1999-01-01

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

Photoionization cross section in a spherical quantum dot: Effects of some parabolic confining electric potentials

Directory of Open Access Journals (Sweden)

M. Tshipa

2017-12-01

Full Text Available A theoretical investigation of the effects of spatial variation of confining electric potential on photoionization cross section (PCS in a spherical quantum dot is presented. The potential profiles considered here are the shifted parabolic potential and the inverse lateral shifted parabolic potential compared with the well-studied parabolic potential. The primary findings are that parabolic potential and the inverse lateral shifted parabolic potential blue shift the peaks of the PCS while the shifted parabolic potential causes a red shift.

Hermitian-Einstein metrics on parabolic stable bundles

International Nuclear Information System (INIS)

Li Jiayu; Narasimhan, M.S.

1995-12-01

Let M-bar be a compact complex manifold of complex dimension two with a smooth Kaehler metric and D a smooth divisor on M-bar. If E is a rank 2 holomorphic vector bundle on M-bar with a stable parabolic structure along D, we prove the existence of a metric on E' = E module MbarD (compatible with the parabolic structure) which is Hermitian-Einstein with respect to the restriction of Kaehler metric of M-barD. A converse is also proved. (author). 24 refs

An air-based corrugated cavity-receiver for solar parabolic trough concentrators

International Nuclear Information System (INIS)

Bader, Roman; Pedretti, Andrea; Barbato, Maurizio; Steinfeld, Aldo

2015-01-01

Highlights: • We analyze a novel tubular cavity-receiver for solar parabolic trough collectors. • Four-fold solar concentration ratio is reached compared to conventional receivers. • Efficient operation at up to 500 °C is possible. • The pumping power requirement is found to be acceptably low. - Abstract: A tubular cavity-receiver that uses air as the heat transfer fluid is evaluated numerically using a validated heat transfer model. The receiver is designed for use on a large-span (9 m net concentrator aperture width) solar parabolic trough concentrator. Through the combination of a parabolic primary concentrator with a nonimaging secondary concentrator, the collector reaches a solar concentration ratio of 97.5. Four different receiver configurations are considered, with smooth or V-corrugated absorber tube and single- or double-glazed aperture window. The collector’s performance is characterized by its optical efficiency and heat loss. The optical efficiency is determined with the Monte Carlo ray-tracing method. Radiative heat exchange inside the receiver is calculated with the net radiation method. The 2D steady-state energy equation, which couples conductive, convective, and radiative heat transfer, is solved for the solid domains of the receiver cross-section, using finite-volume techniques. Simulations for Sevilla/Spain at the summer solstice at solar noon (direct normal solar irradiance: 847 W m −2 , solar incidence angle: 13.9°) yield collector efficiencies between 60% and 65% at a heat transfer fluid temperature of 125 °C and between 37% and 42% at 500 °C, depending on the receiver configuration. The optical losses amount to more than 30% of the incident solar radiation and constitute the largest source of energy loss. For a 200 m long collector module operated between 300 and 500 °C, the isentropic pumping power required to pump the HTF through the receiver is between 11 and 17 kW

PARALLEL SOLUTION METHODS OF PARTIAL DIFFERENTIAL EQUATIONS

Directory of Open Access Journals (Sweden)

Korhan KARABULUT

1998-03-01

Full Text Available Partial differential equations arise in almost all fields of science and engineering. Computer time spent in solving partial differential equations is much more than that of in any other problem class. For this reason, partial differential equations are suitable to be solved on parallel computers that offer great computation power. In this study, parallel solution to partial differential equations with Jacobi, Gauss-Siedel, SOR (Succesive OverRelaxation and SSOR (Symmetric SOR algorithms is studied.

Linear and quasi-linear equations of parabolic type

CERN Document Server

Ladyženskaja, O A; Ural′ceva, N N; Uralceva, N N

1968-01-01

Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.

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

Science.gov (United States)

Dinar, N.

1978-01-01

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

Describing Quadratic Cremer Point Polynomials by Parabolic Perturbations

DEFF Research Database (Denmark)

Sørensen, Dan Erik Krarup

1996-01-01

We describe two infinite order parabolic perturbation proceduresyielding quadratic polynomials having a Cremer fixed point. The main ideais to obtain the polynomial as the limit of repeated parabolic perturbations.The basic tool at each step is to control the behaviour of certain externalrays.......Polynomials of the Cremer type correspond to parameters at the boundary of ahyperbolic component of the Mandelbrot set. In this paper we concentrate onthe main cardioid component. We investigate the differences between two-sided(i.e. alternating) and one-sided parabolic perturbations.In the two-sided case, we prove...... the existence of polynomials having an explicitlygiven external ray accumulating both at the Cremer point and at its non-periodicpreimage. We think of the Julia set as containing a "topologists double comb".In the one-sided case we prove a weaker result: the existence of polynomials havingan explicitly given...

An upwind algorithm for the parabolized Navier-Stokes equations

Science.gov (United States)

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

1986-01-01

A new upwind algorithm based on Roe's scheme has been developed to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method does not require the addition of user specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming scheme in terms of accuracy, stability, computer time and storage, and programming effort. The new algorithm has been validated by applying it to three laminar test cases including flat plate boundary-layer flow, hypersonic flow past a 15 deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with the results obtained using the conventional Beam-Warming algorithm.

Efficient solution of parabolic equations by Krylov approximation methods

Science.gov (United States)

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.

Mechatronic Prototype of Parabolic Solar Tracker.

Science.gov (United States)

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.

Numerical performance of the parabolized ADM (PADM) formulation of General Relativity

OpenAIRE

Paschalidis, Vasileios; Hansen, Jakob; Khokhlov, Alexei

2007-01-01

In a recent paper the first coauthor presented a new parabolic extension (PADM) of the standard 3+1 Arnowitt, Deser, Misner formulation of the equations of general relativity. By parabolizing first-order ADM in a certain way, the PADM formulation turns it into a mixed hyperbolic - second-order parabolic, well-posed system. 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...

Spectral methods for time dependent partial differential equations

Science.gov (United States)

Gottlieb, D.; Turkel, E.

1983-01-01

The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.

Changes in Gene Expression of Arabidopsis Thaliana Cell Cultures Upon Exposure to Real and Simulated Partial- g Forces

Science.gov (United States)

Fengler, Svenja; Spirer, Ina; Neef, Maren; Ecke, Margret; Hauslage, Jens; Hampp, Rüdiger

2016-06-01

Cell cultures of the plant model organism Arabidopsis thaliana were exposed to partial- g forces during parabolic flight and clinostat experiments (0.16 g, 0.38 g and 0.5 g were tested). In order to investigate gravity-dependent alterations in gene expression, samples were metabolically quenched by the fixative RNA later Ⓡ to stabilize nucleic acids and used for whole-genome microarray analysis. An attempt to identify the potential threshold acceleration for the gravity-dependent response showed that the smaller the experienced g-force, the greater was the susceptibility of the cell cultures. Compared to short-term μ g during a parabolic flight, the number of differentially expressed genes under partial- g was lower. In addition, the effect on the alteration of amounts of transcripts decreased during partial- g parabolic flight due to the sequence of the different parabolas (0.38 g, 0.16 g and μ g). A time-dependent analysis under simulated 0.5 g indicates that adaptation occurs within minutes. Differentially expressed genes (at least 2-fold up- or down-regulated in expression) under real flight conditions were to some extent identical with those affected by clinorotation. The highest number of homologuous genes was detected within seconds of exposure to 0.38 g (both flight and clinorotation). To a considerable part, these genes deal with cell wall properties. Additionally, responses specific for clinorotation were observed.

Solving Differential Equations in R: Package deSolve

Directory of Open Access Journals (Sweden)

Karline Soetaert

2010-02-01

Full Text Available In this paper we present the R package deSolve to solve initial value problems (IVP written as ordinary differential equations (ODE, differential algebraic equations (DAE of index 0 or 1 and partial differential equations (PDE, the latter solved using the method of lines approach. The differential equations can be represented in R code or as compiled code. In the latter case, R is used as a tool to trigger the integration and post-process the results, which facilitates model development and application, whilst the compiled code significantly increases simulation speed. The methods implemented are efficient, robust, and well documented public-domain Fortran routines. They include four integrators from the ODEPACK package (LSODE, LSODES, LSODA, LSODAR, DVODE and DASPK2.0. In addition, a suite of Runge-Kutta integrators and special-purpose solvers to efficiently integrate 1-, 2- and 3-dimensional partial differential equations are available. The routines solve both stiff and non-stiff systems, and include many options, e.g., to deal in an efficient way with the sparsity of the Jacobian matrix, or finding the root of equations. In this article, our objectives are threefold: (1 to demonstrate the potential of using R for dynamic modeling, (2 to highlight typical uses of the different methods implemented and (3 to compare the performance of models specified in R code and in compiled code for a number of test cases. These comparisons demonstrate that, if the use of loops is avoided, R code can efficiently integrate problems comprising several thousands of state variables. Nevertheless, the same problem may be solved from 2 to more than 50 times faster by using compiled code compared to an implementation using only R code. Still, amongst the benefits of R are a more flexible and interactive implementation, better readability of the code, and access to R’s high-level procedures. deSolve is the successor of package odesolve which will be deprecated in

Pramana – Journal of Physics | Indian Academy of Sciences

Indian Academy of Sciences (India)

Through such preformed plasma channel, when a delayed pulse propagates, the phenomena of diffraction, refraction and self-phase modulation come into play. We have solved the nonlinear parabolic partial differential equation governing the propagation characteristics for an approximate analytical solution using ...

Determination of source terms in a degenerate parabolic equation

International Nuclear Information System (INIS)

Cannarsa, P; Tort, J; Yamamoto, M

2010-01-01

In this paper, we prove Lipschitz stability results for inverse source problems relative to parabolic equations. We use the method introduced by Imanuvilov and Yamamoto in 1998 based on Carleman estimates. What is new here is that we study a class of one-dimensional degenerate parabolic equations. In our model, the diffusion coefficient vanishes at one extreme point of the domain. Instead of the classical Carleman estimates obtained by Fursikov and Imanuvilov for non degenerate equations, we use and extend some recent Carleman estimates for degenerate equations obtained by Cannarsa, Martinez and Vancostenoble. Finally, we obtain Lipschitz stability results in inverse source problems for our class of degenerate parabolic equations both in the case of a boundary observation and in the case of a locally distributed observation

Interaction Potential between Parabolic Rotator and an Outside Particle

Directory of Open Access Journals (Sweden)

Dan Wang

2014-01-01

Full Text Available At micro/nanoscale, the interaction potential between parabolic rotator and a particle located outside the rotator is studied on the basis of the negative exponential pair potential 1/Rn between particles. Similar to two-dimensional curved surfaces, we confirm that the potential of the three-dimensional parabolic rotator and outside particle can also be expressed as a unified form of curvatures; that is, it can be written as the function of curvatures. Furthermore, we verify that the driving forces acting on the particle may be induced by the highly curved micro/nano-parabolic rotator. Curvatures and the gradient of curvatures are the essential elements forming the driving forces. Through the idealized numerical experiments, the accuracy of the curvature-based potential is preliminarily proved.

Numerical Analysis of Partial Differential Equations

CERN Document Server

Lui, S H

2011-01-01

A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis

Numerical Methods for Partial Differential Equations

CERN Document Server

Guo, Ben-yu

1987-01-01

These Proceedings of the first Chinese Conference on Numerical Methods for Partial Differential Equations covers topics such as difference methods, finite element methods, spectral methods, splitting methods, parallel algorithm etc., their theoretical foundation and applications to engineering. Numerical methods both for boundary value problems of elliptic equations and for initial-boundary value problems of evolution equations, such as hyperbolic systems and parabolic equations, are involved. The 16 papers of this volume present recent or new unpublished results and provide a good overview of current research being done in this field in China.

Mechatronic Prototype of Parabolic Solar Tracker

Directory of Open Access Journals (Sweden)

Carlos Morón

2016-06-01

Full Text Available 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.

Nanofocusing parabolic refractive x-ray lenses

International Nuclear Information System (INIS)

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

2003-01-01

Parabolic refractive x-ray lenses with short focal distance can generate intensive hard x-ray microbeams with lateral extensions in the 100 nm range even at a short distance from a synchrotron radiation source. We have fabricated planar parabolic lenses made of silicon that have a focal distance in the range of a few millimeters at hard x-ray energies. In a crossed geometry, two lenses were used to generate a microbeam with a lateral size of 380 nm by 210 nm at 25 keV in a distance of 42 m from the synchrotron radiation source. Using diamond as the lens material, microbeams with a lateral size down to 20 nm and below are conceivable in the energy range from 10 to 100 keV

The uniqueness of the solution for the definite problem of a parabolic variational inequality

Directory of Open Access Journals (Sweden)

Liping Song

2016-12-01

Full Text Available Abstract The uniqueness of the solution for the definite problem of a parabolic variational inequality is proved. The problem comes from the study of the optimal exercise strategies for the perpetual executive stock options with unrestricted exercise in financial market. Because the variational inequality is degenerate and the obstacle condition contains the partial derivative of an unknown function, it makes the theoretical study of the definite problem of the variational inequality problem very difficult. Firstly, the property which the value function satisfies is derived by applying the Jensen inequality. Then the uniqueness of the solution is proved by using this property and maximum principles.

Computer aided FEA simulation of EN45A parabolic leaf spring

Directory of Open Access Journals (Sweden)

Krishan Kumar

2013-04-01

Full Text Available This paper describes computer aided finite element analysis of parabolic leaf spring. The present work is an improvement in design of EN45A parabolic leaf spring used by a light commercial automotive vehicle. Development of a leaf spring is a long process which requires lots of test to validate the design and manufacturing variables. A three-layer parabolic leaf spring of EN45A has been taken for this work. The thickness of leaves varies from center to the outer side following a parabolic pattern. These leaf springs are designed to become lighter, but also provide a much improved ride to the vehicle through a reduction on interleaf friction. The CAD modeling of parabolic leaf spring has been done in CATIA V5 and for analysis the model is imported in ANSYS-11 workbench. The finite element analysis (FEA of the leaf spring has been carried out by initially discretizing the model into finite number of elements and nodes and then applying the necessary boundary conditions. Maximum displacement, directional displacement, equivalent stress and weight of the assembly are the output targets of this analysis for comparison & validation of the work.

Well-posedness of nonlocal parabolic differential problems with dependent operators.

Science.gov (United States)

Ashyralyev, Allaberen; Hanalyev, Asker

2014-01-01

The nonlocal boundary value problem for the parabolic differential equation v'(t) + A(t)v(t) = f(t) (0 ≤ t ≤ T), v(0) = v(λ) + φ, 0 exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.

The adaptive CCCG({eta}) method for efficient solution of time dependent partial differential equations

Energy Technology Data Exchange (ETDEWEB)

Campos, F.F. [Universidade Federal de Minas Gerais, Belo Horizonte (Brazil); Birkett, N.R.C. [Oxford Univ. Computing Lab. (United Kingdom)

1996-12-31

The Controlled Cholesky factorisation has been shown to be a robust preconditioner for the Conjugate Gradient method. In this scheme the amount of fill-in is defined in terms of a parameter {eta}, the number of extra elements allowed per column. It is demonstrated how an optimum value of {eta} can be automatically determined when solving time dependent p.d.e.`s using an implicit time step method. A comparison between CCCG({eta}) and the standard ICCG solving parabolic problems on general grids shows CCCG({eta}) to be an efficient general purpose solver.

DISPL-1, 2. Order Nonlinear Partial Differential Equation System Solution for Kinetics Diffusion Problems

International Nuclear Information System (INIS)

Leaf, G.K.; Minkoff, M.

1982-01-01

1 - Description of problem or function: DISPL1 is a software package for solving second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types. The package is designed primarily for chemical kinetics- diffusion problems, although not limited to these problems. Fairly general nonlinear boundary conditions are allowed as well as inter- face conditions for problems in an inhomogeneous medium. The spatial domain is one- or two-dimensional with rectangular Cartesian, cylindrical, or spherical (in one dimension only) geometry. 2 - Method of solution: The numerical method is based on the use of Galerkin's procedure combined with the use of B-Splines (C.W.R. de-Boor's B-spline package) to generate a system of ordinary differential equations. These equations are solved by a sophisticated ODE software package which is a modified version of Hindmarsh's GEAR package, NESC Abstract 592. 3 - Restrictions on the complexity of the problem: The spatial domain must be rectangular with sides parallel to the coordinate geometry. Cross derivative terms are not permitted in the PDE. The order of the B-Splines is at most 12. Other parameters such as the number of mesh points in each coordinate direction, the number of PDE's etc. are set in a macro table used by the MORTRAn2 preprocessor in generating the object code

Parabolic Trough Solar Power for Competitive U.S. Markets

International Nuclear Information System (INIS)

Price, Henry W.

1998-01-01

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

Use of a Parabolic Microphone to Detect Hidden Subjects in Search and Rescue.

Science.gov (United States)

Bowditch, Nathaniel L; Searing, Stanley K; Thomas, Jeffrey A; Thompson, Peggy K; Tubis, Jacqueline N; Bowditch, Sylvia P

2018-03-01

This study compares a parabolic microphone to unaided hearing in detecting and comprehending hidden callers at ranges of 322 to 2510 m. Eight subjects were placed 322 to 2510 m away from a central listening point. The subjects were concealed, and their calling volume was calibrated. In random order, subjects were asked to call the name of a state for 5 minutes. Listeners with parabolic microphones and others with unaided hearing recorded the direction of the call (detection) and name of the state (comprehension). The parabolic microphone was superior to unaided hearing in both detecting subjects and comprehending their calls, with an effect size (Cohen's d) of 1.58 for detection and 1.55 for comprehension. For each of the 8 hidden subjects, there were 24 detection attempts with the parabolic microphone and 54 to 60 attempts by unaided listeners. At the longer distances (1529-2510 m), the parabolic microphone was better at detecting callers (83% vs 51%; P<0.00001 by χ 2 ) and comprehension (57% vs 12%; P<0.00001). At the shorter distances (322-1190 m), the parabolic microphone offered advantages in detection (100% vs 83%; P=0.000023) and comprehension (86% vs 51%; P<0.00001), although not as pronounced as at the longer distances. Use of a 66-cm (26-inch) parabolic microphone significantly improved detection and comprehension of hidden calling subjects at distances between 322 and 2510 m when compared with unaided hearing. This study supports the use of a parabolic microphone in search and rescue to locate responsive subjects in favorable weather and terrain. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

Identifying the principal coefficient of parabolic equations with non-divergent form

International Nuclear Information System (INIS)

Jiang, L S; Bian, B J

2005-01-01

We deal with an inverse problem of determining a coefficient a(x, t) of principal part for second order parabolic equations with non-divergent form when the solution is known. Such a problem has important applications in a large fields of applied science. We propose a well-posed approximate algorithm to identify the coefficient. The existence, uniqueness and stability of such solutions a(x, t) are proved. A necessary condition which is a couple system of a parabolic equation and a parabolic variational inequality is deduced. Our numerical simulations show that the coefficient is recovered very well

Identifying the principal coefficient of parabolic equations with non-divergent form

Science.gov (United States)

Jiang, L. S.; Bian, B. J.

2005-01-01

We deal with an inverse problem of determining a coefficient a(x, t) of principal part for second order parabolic equations with non-divergent form when the solution is known. Such a problem has important applications in a large fields of applied science. We propose a well-posed approximate algorithm to identify the coefficient. The existence, uniqueness and stability of such solutions a(x, t) are proved. A necessary condition which is a couple system of a parabolic equation and a parabolic variational inequality is deduced. Our numerical simulations show that the coefficient is recovered very well.

Sasakian and Parabolic Higgs Bundles

Science.gov (United States)

Biswas, Indranil; Mj, Mahan

2018-03-01

Let M be a quasi-regular compact connected Sasakian manifold, and let N = M/ S 1 be the base projective variety. We establish an equivalence between the class of Sasakian G-Higgs bundles over M and the class of parabolic (or equivalently, ramified) G-Higgs bundles over the base N.

A Two-Species Cooperative Lotka-Volterra System of Degenerate Parabolic Equations

Directory of Open Access Journals (Sweden)

Jiebao Sun

2011-01-01

parabolic equations. We are interested in the coexistence of the species in a bounded domain. We establish the existence of global generalized solutions of the initial boundary value problem by means of parabolic regularization and also consider the existence of the nontrivial time-periodic solution for this system.

Nanofocusing Parabolic Refractive X-Ray Lenses

International Nuclear Information System (INIS)

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

2004-01-01

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

Improved stochastic approximation methods for discretized parabolic partial differential equations

Science.gov (United States)

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).

Unconditionally stable difference methods for delay partial differential equations

OpenAIRE

Huang, Chengming; Vandewalle, Stefan

2012-01-01

This paper is concerned with the numerical solution of parabolic partial differential equations with time-delay. We focus in particular on the delay dependent stability analysis of difference methods that use a non-constrained mesh, i.e., the time step-size is not required to be a submultiple of the delay. We prove that the fully discrete system unconditionally preserves the delay dependent asymptotic stability of the linear test problem under consideration, when the following discretizati...

Parallel Algorithm Solves Coupled Differential Equations

Science.gov (United States)

Hayashi, A.

1987-01-01

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

Quasilinear parabolic variational inequalities with multi-valued lower-order terms

Science.gov (United States)

Carl, Siegfried; Le, Vy K.

2014-10-01

In this paper, we provide an analytical frame work for the following multi-valued parabolic variational inequality in a cylindrical domain : Find and an such that where is some closed and convex subset, A is a time-dependent quasilinear elliptic operator, and the multi-valued function is assumed to be upper semicontinuous only, so that Clarke's generalized gradient is included as a special case. Thus, parabolic variational-hemivariational inequalities are special cases of the problem considered here. The extension of parabolic variational-hemivariational inequalities to the general class of multi-valued problems considered in this paper is not only of disciplinary interest, but is motivated by the need in applications. The main goals are as follows. First, we provide an existence theory for the above-stated problem under coercivity assumptions. Second, in the noncoercive case, we establish an appropriate sub-supersolution method that allows us to get existence, comparison, and enclosure results. Third, the order structure of the solution set enclosed by sub-supersolutions is revealed. In particular, it is shown that the solution set within the sector of sub-supersolutions is a directed set. As an application, a multi-valued parabolic obstacle problem is treated.

4th Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE’s

CERN Document Server

Ishige, Kazuhiro; Nitsch, Carlo; Salani, Paolo

2016-01-01

This book collects recent research papers by respected specialists in the field. It presents advances in the field of geometric properties for parabolic and elliptic partial differential equations, an area that has always attracted great attention. It settles the basic issues (existence, uniqueness, stability and regularity of solutions of initial/boundary value problems) before focusing on the topological and/or geometric aspects. These topics interact with many other areas of research and rely on a wide range of mathematical tools and techniques, both analytic and geometric. The Italian and Japanese mathematical schools have a long history of research on PDEs and have numerous active groups collaborating in the study of the geometric properties of their solutions. .

Explicit nonlinear finite element geometric analysis of parabolic leaf springs under various loads.

Science.gov (United States)

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

2013-01-01

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

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

Directory of Open Access Journals (Sweden)

Y. S. Kong

2013-01-01

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

Effects of parabolic motion on an isothermal vertical plate with constant mass flux

Directory of Open Access Journals (Sweden)

R. Muthucumaraswamy

2014-12-01

Full Text Available An analytical study of free convection flow near a parabolic started infinite vertical plate with isothermal in the presence of uniform mass flux was considered. The mathematical model is reduced to a system of linear partial differential equations for the velocity, the concentration and the temperature; the closed form exact solutions were obtained by the Laplace transform technique. The velocity, temperature and concentration profiles for the different parameters as thermal Grashof number Gr, mass Grashof number Gc, Prandtl number Pr, Schmidt number Sc and time t were graphed and the numerical values for the skin friction were as tabulated. It is observed that the velocity is enhanced as the time increased and the velocity is decreased as the Prandtl number increased.

An introduction to geometric theory of fully nonlinear parabolic equations

International Nuclear Information System (INIS)

Lunardi, A.

1991-01-01

We study a class of nonlinear evolution equations in general Banach space being an abstract version of fully nonlinear parabolic equations. In addition to results of existence, uniqueness and continuous dependence on the data, we give some qualitative results about stability of the stationary solutions, existence and stability of the periodic orbits. We apply such results to some parabolic problems arising from combustion theory. (author). 24 refs

Nonimaging secondary concentrators for large rim angle parabolic troughs with tubular absorbers.

Science.gov (United States)

Ries, H; Spirkl, W

1996-05-01

For parabolic trough solar collectors with tubular absorbers, we design new tailored secondary concentrators. The design is applicable for any rim angle of a parabolic reflector. With the secondary, the concentration can be increased by a factor of more than 2 with a compact secondary reflector consisting of a single piece, even for the important case of a rim angle of 90 deg. The parabolic reflector can be used without changes; the reduced absorber is still tubular but smaller than the original absorber and slightly displaced toward the primary.

Canonical generators of the cohomology of moduli of parabolic bundles on curves

International Nuclear Information System (INIS)

Biswas, I.; Raghavendra, N.

1994-11-01

We determine generators of the rational cohomology algebras of moduli spaces of parabolic vector bundles on a curve, under some 'primality' conditions on the parabolic datum. These generators are canonical in a precise sense. Our results are new even for usual vector bundles (i.e., vector bundles without parabolic structure) whose rank is greater than 2 and is coprime to the degree; in this case, they are generalizations of a theorem of Newstead on the moduli of vector bundles of rank 2 and odd degree. (author). 11 refs

On the behaviour of solutions of parabolic equations for large values of time

International Nuclear Information System (INIS)

Denisov, V N

2005-01-01

This paper is a survey of classical and new results on stabilization of solutions of the Cauchy problem and mixed problems for second-order linear parabolic equations. Proofs are given for some new results about exact sufficient conditions on the behaviour of lower-order coefficients of the parabolic equation; these conditions ensure stabilization of a solution of the Cauchy problem for the parabolic equation in the class of bounded or increasing initial functions

Artificial neural networks approach on solar parabolic dish cooker

International Nuclear Information System (INIS)

Lokeswaran, S.; Eswaramoorthy, M.

2011-01-01

This paper presents heat transfer analysis of solar parabolic dish cooker using Artificial Neural Network (ANN). The objective of this study to envisage thermal performance parameters such as receiver plate and pot water temperatures of the solar parabolic dish cooker by using the ANN for experimental data. An experiment is conducted under two cases (1) cooker with plain receiver and (2) cooker with porous receiver. The Back Propagation (BP) algorithm is used to train and test networks and ANN predictions are compared with experimental results. Different network configurations are studied by the aid of searching a relatively better network for prediction. The results showed a good regression analysis with the correlation coefficients in the range of 0.9968-0.9992 and mean relative errors (MREs) in the range of 1.2586-4.0346% for the test data set. Thus ANN model can successfully be used for the prediction of the thermal performance parameters of parabolic dish cooker with reasonable degree of accuracy. (authors)

Parabolic dish collectors - A solar option

Science.gov (United States)

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.

Spheroidal corrections to the spherical and parabolic bases of the hydrogen atom

International Nuclear Information System (INIS)

Mardyan, L.G.; Pogosyan, G.S.; Sisakyan, A.N.

1986-01-01

This paper introduces the bases of the hydrogen atom and obtains recursion relations that determine the expansion of the spheroidal basis with respect to its parabolic basis. The leading spheroidal corrections to the spherical and parabolic bases are calculated by perturbation theory

Some integral representations and limits for (products of) the parabolic cylinder function

NARCIS (Netherlands)

Veestraeten, D.

2016-01-01

Recently, [Veestraeten D. On the inverse transform of Laplace transforms that contain (products of) the parabolic cylinder function. Integr Transf Spec F 2015;26:859-871] derived inverse Laplace transforms for Laplace transforms that contain products of two parabolic cylinder functions by exploiting

Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions

KAUST Repository

Ruggeri, Fabrizio; Sawlan, Zaid A; Scavino, Marco; Tempone, Raul

2016-01-01

In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.

Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions

KAUST Repository

Ruggeri, Fabrizio

2015-01-07

In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.

Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions

KAUST Repository

Ruggeri, Fabrizio

2016-01-06

In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.

Irreversible thermodynamics, parabolic law and self-similar state in grain growth

International Nuclear Information System (INIS)

Rios, P.R.

2004-01-01

The formalism of the thermodynamic theory of irreversible processes is applied to grain growth to investigate the nature of the self-similar state and its corresponding parabolic law. Grain growth does not reach a steady state in the sense that the entropy production remains constant. However, the entropy production can be written as a product of two factors: a scale factor that tends to zero for long times and a scaled entropy production. It is suggested that the parabolic law and the self-similar state may be associated with the minimum of this scaled entropy production. This result implies that the parabolic law and the self-similar state have a sound irreversible thermodynamical basis

Controllability of partial differential equations governed by multiplicative controls

CERN Document Server

Khapalov, Alexander Y

2010-01-01

The goal of this monograph is to address the issue of the global controllability of partial differential equations in the context of multiplicative (or bilinear) controls, which enter the model equations as coefficients. The mathematical models we examine include the linear and nonlinear parabolic and hyperbolic PDE's, the Schrödinger equation, and coupled hybrid nonlinear distributed parameter systems modeling the swimming phenomenon. The book offers a new, high-quality and intrinsically nonlinear methodology to approach the aforementioned highly nonlinear controllability problems.

A Two-Species Cooperative Lotka-Volterra System of Degenerate Parabolic Equations

OpenAIRE

Sun, Jiebao; Zhang, Dazhi; Wu, Boying

2011-01-01

We consider a cooperating two-species Lotka-Volterra model of degenerate parabolic equations. We are interested in the coexistence of the species in a bounded domain. We establish the existence of global generalized solutions of the initial boundary value problem by means of parabolic regularization and also consider the existence of the nontrivial time-periodic solution for this system.

Recovering the source and initial value simultaneously in a parabolic equation

International Nuclear Information System (INIS)

Zheng, Guang-Hui; Wei, Ting

2014-01-01

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. (papers)

Parabolic solar cooker: Cooking with heat pipe vs direct spiral copper tubes

Science.gov (United States)

Craig, Omotoyosi O.; Dobson, Robert T.

2016-05-01

Cooking with solar energy has been seen by many researchers as a solution to the challenges of poverty and hunger in the world. This is no exception in Africa, as solar coking is viewed as an avenue to eliminate the problem of food insecurity, insufficient energy supply for household and industrial cooking. There are several types of solar cookers that have been manufactured and highlighted in literature. The parabolic types of solar cookers are known to reach higher temperatures and therefore cook faster. These cookers are currently being developed for indoor cooking. This technology has however suffered low cooking efficiency and thus leads to underutilization of the high heat energy captured from the sun in the cooking. This has made parabolic solar cookers unable to compete with other conventional types of cookers. Several methods to maximize heat from the sun for indirect cooking has been developed, and the need to improve on them of utmost urgency. This paper investigates how to optimize the heat collected from the concentrating types of cookers by proposing and comparing two types of cooking sections: the spiral hot plate copper tube and the heat pipe plate. The system uses the concentrating solar parabolic dish technology to focus the sun on a conical cavity of copper tubes and the heat is stored inside an insulated tank which acts both as storage and cooking plate. The use of heat pipes to transfer heat between the oil storage and the cooking pot was compared to the use of a direct natural syphon principle which is achieved using copper tubes in spiral form like electric stove. An accurate theoretical analysis for the heat pipe cooker was achieved by solving the boiling and vaporization in the evaporator side and then balancing it with the condensation and liquid-vapour interaction in the condenser part while correct heat transfer, pressure and height balancing was calculated in the second experiment. The results show and compare the cooking time, boiling

The dynamics of parabolic flight: Flight characteristics and passenger percepts

Science.gov (United States)

Karmali, Faisal; Shelhamer, Mark

2008-09-01

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

A note on Hermitian-Einstein metrics on parabolic stable bundles

International Nuclear Information System (INIS)

Li Jiayu; Narasimhan, M.S.

2000-01-01

Let M-bar be a compact complex manifold of complex dimension two with a smooth Kaehler metric and D a smooth divisor on M-bar. If E is a rank 2 holomorphic vector bundle on M-bar with a stable parabolic structure along D, we prove that there exists a Hermitian-Einstein metric on E' = E-vertical bar M-barbackslashD compatible with the parabolic structure, and whose curvature is square integrable. (author)

Solutions to variational inequalities of parabolic type

Science.gov (United States)

Zhu, Yuanguo

2006-09-01

The existence of strong solutions to a kind of variational inequality of parabolic type is investigated by the theory of semigroups of linear operators. As an application, an abstract semi permeable media problem is studied.

Convergence of shock waves between conical and parabolic boundaries

Energy Technology Data Exchange (ETDEWEB)

Yanuka, D.; Zinowits, H. E.; Antonov, O.; Efimov, S.; Virozub, A.; Krasik, Ya. E. [Physics Department, Technion, Haifa 32000 (Israel)

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.

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

Science.gov (United States)

Banks, H. T.; Kunisch, K.

1982-01-01

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

Integrated parabolic nanolenses on MicroLED color pixels

Science.gov (United States)

Demory, Brandon; Chung, Kunook; Katcher, Adam; Sui, Jingyang; Deng, Hui; Ku, Pei-Cheng

2018-04-01

A parabolic nanolens array coupled to the emission of a nanopillar micro-light emitting diode (LED) color pixel is shown to reduce the far field divergence. For a blue wavelength LED, the total emission is 95% collimated within a 0.5 numerical aperture zone, a 3.5x improvement over the same LED without a lens structure. This corresponds to a half-width at half-maximum (HWHM) line width reduction of 2.85 times. Using a resist reflow and etchback procedure, the nanolens array dimensions and parabolic shape are formed. Experimental measurement of the far field emission shows a HWHM linewidth reduction by a factor of 2x, reducing the divergence over the original LED.

Human Health Countermeasures - Partial-Gravity Analogs Workshop

Science.gov (United States)

Barr, Yael; Clement, Gilles; Norsk, Peter

2016-01-01

The experimental conditions that were deemed the most interesting by the HHC Element lead scientists are those permitting studies of the long-term effects of exposure to (a) chronic rotation when supine or in head down tilt (ground-based); and (b) long-radius centrifugation (space based). It is interesting to note that chronic ground based slow rotation room studies have not been performed since the 1960's, when the USA and USSR were investigating the potential use of AG for long-duration space missions. On the other hand, the other partial gravity analogs, i.e., parabolic flight, HUT, suspension, and short-radius centrifugation, have been regularly used in the last three decades (see review in Clément et al. 2015). Based on the workshop evaluations and the scores by the HHC scientific disciplines indicated in tables 3 and 4, simulation of partial G between 0 and 1 should be prioritized as follows: Priority 1. Chronic space-based partial-G analogs: a. Chronic space-based long-radius centrifugation. The ideal scenario would be chronic long-radius centrifugation of cells, animals and humans in a translational research approach - ideally beyond low earth orbit under deep space environmental effects and at various rotations - to obtain different G-effects. In this scenario, all physiological systems could be evaluated and the relationship between physiological response and G level established. This would be the most integrative way of defining, for the first time ever, G-thresholds for each physiological system. b. Chronic space-based centrifugation of animals. Chronic centrifugation of rodents at various G levels in space would allow for determination of AG thresholds of protection for each physiological system. In this case, all physiological systems will be of interest. Intermittent centrifugation will be of secondary interest. c. Chronic space-based centrifugation of cell cultures (RWV). Bioreactor studies of cells and cell cultures of various tissues at various G

Nonlinear anisotropic parabolic equations in Lm

Directory of Open Access Journals (Sweden)

Fares Mokhtari

2014-01-01

Full Text Available In this paper, we give a result of regularity of weak solutions for a class of nonlinear anisotropic parabolic equations with lower-order term when the right-hand side is an Lm function, with m being ”small”. This work generalizes some results given in [2] and [3].

Solving of some Problems with On-Line Mode Measurement of Partial Discharges

Directory of Open Access Journals (Sweden)

Karel Zalis

2004-01-01

Full Text Available This paper deals with the problems discussing the transition from off-line diagnostic methods to on-line ones. Based on the experience with commercial partial discharge measuring equipment a new digital system for the evaluation of partial discharge measurement including software and hardware facilities has been developed at the Czech Technical University in Prague. Two expert systems work in this complex evaluating system: a rule-based expert system performing an amplitude analysis of partial discharge impulses for determining the damage of the insulation system, and a neural network which is used for a phase analysis of partial discharge impulses to determine the kind of partial discharge activity. Problem of the elimination of disturbances is also discussed.

Global Carleman estimates for degenerate parabolic operators with applications

CERN Document Server

Cannarsa, P; Vancostenoble, J

2016-01-01

Degenerate parabolic operators have received increasing attention in recent years because they are associated with both important theoretical analysis, such as stochastic diffusion processes, and interesting applications to engineering, physics, biology, and economics. This manuscript has been conceived to introduce the reader to global Carleman estimates for a class of parabolic operators which may degenerate at the boundary of the space domain, in the normal direction to the boundary. Such a kind of degeneracy is relevant to study the invariance of a domain with respect to a given stochastic diffusion flow, and appears naturally in climatology models.

Mobile point sensors and actuators in the controllability theory of partial differential equations

CERN Document Server

Khapalov, Alexander Y

2017-01-01

This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time. Based on the author’s extensive research in the area of controllability theory, this monograph specifically focuses on the issues of controllability, observability, and stabilizability for parabolic and hyperbolic partial differential equations. The topics in this book also cover related applied questions such as the problem of localization of unknown pollution sources based on information obtained from point sensors that arise in environmental monitoring. Researchers and graduate students interested in controllability theory of partial differential equations and its applications will find this book to be an invaluable resource to their studies.

First Middle East Aircraft Parabolic Flights for ISU Participant Experiments

Science.gov (United States)

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.

Temperature Performance Evaluation of Parabolic Dishes Covered ...

African Journals Online (AJOL)

Aweda

The parabolic dish with glass material gave the highest temperature of .... 3: Second day variation temperature and time using different materials. 8. 10 .... the sun rays at that particular time. ... especially between 11:00 am and 3:00 pm when.

Solving binary-state multi-objective reliability redundancy allocation series-parallel problem using efficient epsilon-constraint, multi-start partial bound enumeration algorithm, and DEA

International Nuclear Information System (INIS)

Khalili-Damghani, Kaveh; Amiri, Maghsoud

2012-01-01

In this paper, a procedure based on efficient epsilon-constraint method and data envelopment analysis (DEA) is proposed for solving binary-state multi-objective reliability redundancy allocation series-parallel problem (MORAP). In first module, a set of qualified non-dominated solutions on Pareto front of binary-state MORAP is generated using an efficient epsilon-constraint method. In order to test the quality of generated non-dominated solutions in this module, a multi-start partial bound enumeration algorithm is also proposed for MORAP. The performance of both procedures is compared using different metrics on well-known benchmark instance. The statistical analysis represents that not only the proposed efficient epsilon-constraint method outperform the multi-start partial bound enumeration algorithm but also it improves the founded upper bound of benchmark instance. Then, in second module, a DEA model is supplied to prune the generated non-dominated solutions of efficient epsilon-constraint method. This helps reduction of non-dominated solutions in a systematic manner and eases the decision making process for practical implementations. - Highlights: ► A procedure based on efficient epsilon-constraint method and DEA was proposed for solving MORAP. ► The performance of proposed procedure was compared with a multi-start PBEA. ► Methods were statistically compared using multi-objective metrics.

Spike-adding in parabolic bursters: The role of folded-saddle canards

Science.gov (United States)

Desroches, Mathieu; Krupa, Martin; Rodrigues, Serafim

2016-09-01

The present work develops a new approach to studying parabolic bursting, and also proposes a novel four-dimensional canonical and polynomial-based parabolic burster. In addition to this new polynomial system, we also consider the conductance-based model of the Aplysia R15 neuron known as the Plant model, and a reduction of this prototypical biophysical parabolic burster to three variables, including one phase variable, namely the Baer-Rinzel-Carillo (BRC) phase model. Revisiting these models from the perspective of slow-fast dynamics reveals that the number of spikes per burst may vary upon parameter changes, however the spike-adding process occurs in an explosive fashion that involves special solutions called canards. This spike-adding canard explosion phenomenon is analysed by using tools from geometric singular perturbation theory in tandem with numerical bifurcation techniques. We find that the bifurcation structure persists across all considered systems, that is, spikes within the burst are incremented via the crossing of an excitability threshold given by a particular type of canard orbit, namely the true canard of a folded-saddle singularity. However there can be a difference in the spike-adding transitions in parameter space from one case to another, according to whether the process is continuous or discontinuous, which depends upon the geometry of the folded-saddle canard. Using these findings, we construct a new polynomial approximation of the Plant model, which retains all the key elements for parabolic bursting, including the spike-adding transitions mediated by folded-saddle canards. Finally, we briefly investigate the presence of spike-adding via canards in planar phase models of parabolic bursting, namely the theta model by Ermentrout and Kopell.

A parabolic mirror x-ray collimator

Science.gov (United States)

Franks, A.; Jackson, K.; Yacoot, A.

2000-05-01

A robust and stable x-ray collimator has been developed to produce a parallel beam of x-rays by total external reflection from a parabolic mirror. The width of the gold-coated silica mirror varies along its length, which allows it to be bent from a plane surface into a parabolic form by application of unequal bending forces at its ends. A family of parabolas of near constant focal length can be formed by changing the screw-applied bending force, thus allowing the collimator to cater for a range of wavelengths by the turning of a screw. Even with radiation with a wavelength as short as that as Mo Kicons/Journals/Common/alpha" ALT="alpha" ALIGN="TOP"/> 1 (icons/Journals/Common/lambda" ALT="lambda" ALIGN="TOP"/> = 0.07 nm), a gain in flux by a factor of 5.5 was achieved. The potential gain increases with wavelength, e.g. for Cu Kicons/Journals/Common/alpha" ALT="alpha" ALIGN="TOP"/> 1 radiation this amounts to over a factor of ten.

Moving interfaces and quasilinear parabolic evolution equations

CERN Document Server

Prüss, Jan

2016-01-01

In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions...

Wind load design methods for ground-based heliostats and parabolic dish collectors

Energy Technology Data Exchange (ETDEWEB)

Peterka, J A; Derickson, R G [Colorado State Univ., Fort Collins, CO (United States). Fluid Dynamics and Diffusion Lab.

1992-09-01

The purpose of this design method is to define wind loads on flat heliostat and parabolic dish collectors in a simplified form. Wind loads are defined for both mean and peak loads accounting for the protective influence of upwind collectors, wind protective fences, or other wind-blockage elements. The method used to define wind loads was to generalize wind load data obtained during tests on model collectors, heliostats or parabolic dishes, placed in a modeled atmospheric wind in a boundary-layer wind-tunnel at Colorado State University. For both heliostats and parabolic dishes, loads are reported for solitary collectors and for collectors as elements of a field. All collectors were solid with negligible porosity; thus the effects of porosity in the collectors is not addressed.

Gas Turbine/Solar Parabolic Trough Hybrid Designs: Preprint

Energy Technology Data Exchange (ETDEWEB)

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

2011-03-01

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

Improvement Design of Parabolic Trough

Science.gov (United States)

Ihsan, S. I.; Safian, M. A. I. M.; Taufek, M. A. M.; Mohiuddin, A. K. M.

2017-03-01

The performance of parabolic trough solar collector (PTSC) has been evaluated using different heat transfer working fluids; namely water and SAE20 W50 engine oil. New and slightly improved PTSC was developed to run the experimental study. Under the meteorological conditions of Malaysia, authors found that PTSC can operate at a higher temperature than water collector but the performance efficiency of collector using engine oil is much lower than the water collector.

A gradient estimate for solutions to parabolic equations with discontinuous coefficients

Directory of Open Access Journals (Sweden)

Jishan Fan

2013-04-01

Full Text Available Li-Vogelius and Li-Nirenberg gave a gradient estimate for solutions of strongly elliptic equations and systems of divergence forms with piecewise smooth coefficients, respectively. The discontinuities of the coefficients are assumed to be given by manifolds of codimension 1, which we called them emph{manifolds of discontinuities}. Their gradient estimate is independent of the distances between manifolds of discontinuities. In this paper, we gave a parabolic version of their results. That is, we gave a gradient estimate for parabolic equations of divergence forms with piecewise smooth coefficients. The coefficients are assumed to be independent of time and their discontinuities are likewise the previous elliptic equations. As an application of this estimate, we also gave a pointwise gradient estimate for the fundamental solution of a parabolic operator with piecewise smooth coefficients. Both gradient estimates are independent of the distances between manifolds of discontinuities.

Analysis of the stress-deformed condition of the disassembly parabolic antenna

Science.gov (United States)

Odinets, M. N.; Kaygorodtseva, N. V.; Krysova, I. V.

2018-01-01

Active development of satellite communications and computer-aided design systems raises the problem of designing parabolic antennas on a new round of development. The aim of the work was to investigate the influence of the design of the mirror of a parabolic antenna on its endurance under wind load. The research task was an automated analysis of the stress-deformed condition of various designs of computer models of a paraboloid mirror (segmented or holistic) at modeling the exploitation conditions. The peculiarity of the research was that the assembly model of the antenna’s mirror was subjected to rigid connections on the contacting surfaces of the segments and only then the finite element grid was generated. The analysis showed the advantage of the design of the demountable antenna, which consists of cyclic segments, in front of the construction of the holistic antenna. Calculation of the stress-deformed condition of the antennas allows us to conclude that dividing the design of the antenna’s mirror on parabolic and cyclic segments increases it strength and rigidity. In the future, this can be used to minimize the mass of antenna and the dimensions of the disassembled antenna. The presented way of modeling a mirror of a parabolic antenna using to the method of the finite-element analysis can be used in the production of antennas.

Some blow-up problems for a semilinear parabolic equation with a potential

Science.gov (United States)

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].

Domain decomposition methods for solving an image problem

Energy Technology Data Exchange (ETDEWEB)

Tsui, W.K.; Tong, C.S. [Hong Kong Baptist College (Hong Kong)

1994-12-31

The domain decomposition method is a technique to break up a problem so that ensuing sub-problems can be solved on a parallel computer. In order to improve the convergence rate of the capacitance systems, pre-conditioned conjugate gradient methods are commonly used. In the last decade, most of the efficient preconditioners are based on elliptic partial differential equations which are particularly useful for solving elliptic partial differential equations. In this paper, the authors apply the so called covering preconditioner, which is based on the information of the operator under investigation. Therefore, it is good for various kinds of applications, specifically, they shall apply the preconditioned domain decomposition method for solving an image restoration problem. The image restoration problem is to extract an original image which has been degraded by a known convolution process and additive Gaussian noise.

Polarization properties of linearly polarized parabolic scaling Bessel beams

Energy Technology Data Exchange (ETDEWEB)

Guo, Mengwen; Zhao, Daomu, E-mail: zhaodaomu@yahoo.com

2016-10-07

The intensity profiles for the dominant polarization, cross polarization, and longitudinal components of modified parabolic scaling Bessel beams with linear polarization are investigated theoretically. The transverse intensity distributions of the three electric components are intimately connected to the topological charge. In particular, the intensity patterns of the cross polarization and longitudinal components near the apodization plane reflect the sign of the topological charge. - Highlights: • We investigated the polarization properties of modified parabolic scaling Bessel beams with linear polarization. • We studied the evolution of transverse intensity profiles for the three components of these beams. • The intensity patterns of the cross polarization and longitudinal components can reflect the sign of the topological charge.

Parabolic approximation method for fast magnetosonic wave propagation in tokamaks

International Nuclear Information System (INIS)

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

1985-07-01

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

Convergence of method of lines approximations to partial differential equations

International Nuclear Information System (INIS)

Verwer, J.G.; Sanz-Serna, J.M.

1984-01-01

Many existing numerical schemes for evolutionary problems in partial differential equations (PDEs) can be viewed as method of lines (MOL) schemes. This paper treats the convergence of one-step MOL schemes. The main purpose is to set up a general framework for a convergence analysis applicable to nonlinear problems. The stability materials for this framework are taken from the field of nonlinear stiff ODEs. In this connection, important concepts are the logarithmic matrix norm and C-stability. A nonlinear parabolic equation and the cubic Schroedinger equation are used for illustrating the ideas. (Auth.)

The Parabolic Variational Inequalities for Variably Saturated Water Flow in Heterogeneous Fracture Networks

Directory of Open Access Journals (Sweden)

Zuyang Ye

2018-01-01

Full Text Available Fractures are ubiquitous in geological formations and have a substantial influence on water seepage flow in unsaturated fractured rocks. While the matrix permeability is small enough to be ignored during the partially saturated flow process, water seepage in heterogeneous fracture systems may occur in a non-volume-average manner as distinguished from a macroscale continuum model. This paper presents a systematic numerical method which aims to provide a better understanding of the effect of fracture distribution on the water seepage behavior in such media. Based on the partial differential equation (PDE formulations with a Signorini-type complementary condition on the variably saturated water flow in heterogeneous fracture networks, the equivalent parabolic variational inequality (PVI formulations are proposed and the related numerical algorithm in the context of the finite element scheme is established. With the application to the continuum porous media, the results of the numerical simulation for one-dimensional infiltration fracture are compared to the analytical solutions and good agreements are obtained. From the application to intricate fracture systems, it is found that water seepage flow can move rapidly along preferential pathways in a nonuniform fashion and the variably saturated seepage behavior is intimately related to the geometrical characteristics orientation of fractures.

Temperature Performance Evaluation of Parabolic Dishes Covered ...

African Journals Online (AJOL)

Solar radiation reaching the earth is considered to be affected by some parameters like diffusion. This radiation is reflected or scattered by air molecules, cloud and aerosols (dust). Parabolic dishes made of different materials (glass, foil and painted surface) were used to concentrate energy on a copper calorimeter filled with ...

DISPL: a software package for one and two spatially dimensioned kinetics-diffusion problems. [FORTRAN for IBM computers

Energy Technology Data Exchange (ETDEWEB)

Leaf, G K; Minkoff, M; Byrne, G D; Sorensen, D; Bleakney, T; Saltzman, J

1978-11-01

DISPL is a software package for solving some second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types such as parabolic--elliptic equations. Fairly general nonlinear boundary conditions are allowed as well as interface conditions for problems in an inhomogeneous media. The spatial domain is one- or two-dimensional with Cartesian, cylindrical, or spherical (in one dimension only) geometry. The numerical method is based on the use of Galerkin's procedure combined with the use of B-splines in order to reduce the system of PDE's to a system of ODE's. The latter system is then solved with a sophisticated ODE software package. Software features include extensive dump/restart facilities, free format input, moderate printed output capability, dynamic storage allocation, and three graphics packages. 17 figures, 9 tables.

Solving the Coupled System Improves Computational Efficiency of the Bidomain Equations

KAUST Repository

Southern, J.A.

2009-10-01

The bidomain equations are frequently used to model the propagation of cardiac action potentials across cardiac tissue. At the whole organ level, the size of the computational mesh required makes their solution a significant computational challenge. As the accuracy of the numerical solution cannot be compromised, efficiency of the solution technique is important to ensure that the results of the simulation can be obtained in a reasonable time while still encapsulating the complexities of the system. In an attempt to increase efficiency of the solver, the bidomain equations are often decoupled into one parabolic equation that is computationally very cheap to solve and an elliptic equation that is much more expensive to solve. In this study, the performance of this uncoupled solution method is compared with an alternative strategy in which the bidomain equations are solved as a coupled system. This seems counterintuitive as the alternative method requires the solution of a much larger linear system at each time step. However, in tests on two 3-D rabbit ventricle benchmarks, it is shown that the coupled method is up to 80% faster than the conventional uncoupled method-and that parallel performance is better for the larger coupled problem.

Solving the Coupled System Improves Computational Efficiency of the Bidomain Equations

KAUST Repository

Southern, J.A.; Plank, G.; Vigmond, E.J.; Whiteley, J.P.

2009-01-01

The bidomain equations are frequently used to model the propagation of cardiac action potentials across cardiac tissue. At the whole organ level, the size of the computational mesh required makes their solution a significant computational challenge. As the accuracy of the numerical solution cannot be compromised, efficiency of the solution technique is important to ensure that the results of the simulation can be obtained in a reasonable time while still encapsulating the complexities of the system. In an attempt to increase efficiency of the solver, the bidomain equations are often decoupled into one parabolic equation that is computationally very cheap to solve and an elliptic equation that is much more expensive to solve. In this study, the performance of this uncoupled solution method is compared with an alternative strategy in which the bidomain equations are solved as a coupled system. This seems counterintuitive as the alternative method requires the solution of a much larger linear system at each time step. However, in tests on two 3-D rabbit ventricle benchmarks, it is shown that the coupled method is up to 80% faster than the conventional uncoupled method-and that parallel performance is better for the larger coupled problem.

Introduction to partial differential equations

CERN Document Server

Greenspan, Donald

2000-01-01

Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.

Elliptic and parabolic equations for measures

Energy Technology Data Exchange (ETDEWEB)

Bogachev, Vladimir I [M. V. Lomonosov Moscow State University, Moscow (Russian Federation); Krylov, Nikolai V [University of Minnesota, Minneapolis, MN (United States); Roeckner, Michael [Universitat Bielefeld, Bielefeld (Germany)

2009-12-31

This article gives a detailed account of recent investigations of weak elliptic and parabolic equations for measures with unbounded and possibly singular coefficients. The existence and differentiability of densities are studied, and lower and upper bounds for them are discussed. Semigroups associated with second-order elliptic operators acting in L{sup p}-spaces with respect to infinitesimally invariant measures are investigated. Bibliography: 181 titles.

Beginning partial differential equations

CERN Document Server

O'Neil, Peter V

2014-01-01

A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or

Schottky diode model for non-parabolic dispersion in narrow-gap semiconductor and few-layer graphene

Science.gov (United States)

Ang, Yee Sin; Ang, L. K.; Zubair, M.

Despite the fact that the energy dispersions are highly non-parabolic in many Schottky interfaces made up of 2D material, experimental results are often interpreted using the conventional Schottky diode equation which, contradictorily, assumes a parabolic energy dispersion. In this work, the Schottky diode equation is derived for narrow-gap semiconductor and few-layer graphene where the energy dispersions are highly non-parabolic. Based on Kane's non-parabolic band model, we obtained a more general Kane-Schottky scaling relation of J (T2 + γkBT3) which connects the contrasting J T2 in the conventional Schottky interface and the J T3 scaling in graphene-based Schottky interface via a non-parabolicity parameter, γ. For N-layer graphene of ABC -stacking and of ABA -stacking, the scaling relation follows J T 2 / N + 1 and J T3 respectively. Intriguingly, the Richardson constant extracted from the experimental data using an incorrect scaling can differ with the actual value by more than two orders of magnitude. Our results highlights the importance of using the correct scaling relation in order to accurately extract important physical properties, such as the Richardson constant and the Schottky barrier's height.

Parabolic dune development modes according to shape at the southern fringes of the Hobq Desert, Inner Mongolia, China

Science.gov (United States)

Guan, Chao; Hasi, Eerdun; Zhang, Ping; Tao, Binbin; Liu, Dan; Zhou, Yanguang

2017-10-01

Since the 1970s, parabolic dunes at the southern fringe of the Hobq Desert, Inner Mongolia, China have exhibited many different shapes (V-shaped, U-shaped, and palmate) each with a unique mode of development. In the study area, parabolic dunes are mainly distributed in Regions A, B, and C with an intermittent river running from the south to the north. We used high-resolution remote-sensing images from 1970 to 2014 and RTK-GPS measurements to study the development modes of different dune shapes; the modes are characterized by the relationship between the intermittent river and dunes, formation of the incipient dune patterns, the predominant source supply of dunes, and the primary formation of different shapes (V-shaped, U-shaped, and palmate). Most parabolic dunes in Region A are V-shaped and closer to the bank of the river. The original barchans in this region exhibit "disconnected arms" behavior. With the sand blown out of the riverbed through gullies, the nebkhas on the disconnected arms acquire the external sand source through the "fertile island effect", thereby developing into triangular sand patches and further developing into V-shaped parabolic dunes. Most parabolic dunes in Regions B and C are palmate. The residual dunes cut by the re-channelization of river from transverse dune fields on the west bank are the main sand source of Region B. The parabolic dunes in Region C are the original barchans having then been transformed. The stoss slopes of V-shaped parabolic dunes along the riverbank are gradual and the dunes are flat in shape. The dune crest of V-shaped parabolic dune is the deposition area, which forms the "arc-shaped sand ridge". Their two arms are non-parallel; the lateral airflow of the arms jointly transport sand to the middle part of dunes, resulting in a narrower triangle that gradually becomes V-shaped. Palmate parabolic dunes have a steeper stoss slope and height. The dune crest of the palmate parabolic dune is the erosion area, which forms

Gradient remediability in linear distributed parabolic systems ...

African Journals Online (AJOL)

The aim of this paper is the introduction of a new concept that concerned the analysis of a large class of distributed parabolic systems. It is the general concept of gradient remediability. More precisely, we study with respect to the gradient observation, the existence of an input operator (gradient efficient actuators) ensuring ...

Auxiliary equation method for solving nonlinear partial differential equations

International Nuclear Information System (INIS)

Sirendaoreji,; Jiong, Sun

2003-01-01

By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation

Modeling mode interactions in boundary layer flows via the Parabolized Floquet Equations

OpenAIRE

Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanović, Mihailo R.

2017-01-01

In this paper, we develop a linear model to study interactions between different modes in slowly-growing boundary layer flows. Our method consists of two steps. First, we augment the Blasius boundary layer profile with a disturbance field resulting from the linear Parabolized Stability Equations (PSE) to obtain the modified base flow; and, second, we combine Floquet analysis with the linear PSE to capture the spatial evolution of flow fluctuations. This procedure yields the Parabolized Floque...

CIME course on Control of Partial Differential Equations

CERN Document Server

Alabau-Boussouira, Fatiha; Glass, Olivier; Le Rousseau, Jérôme; Zuazua, Enrique

2012-01-01

The term “control theory” refers to the body of results - theoretical, numerical and algorithmic - which have been developed to influence the evolution of the state of a given system in order to meet a prescribed performance criterion. Systems of interest to control theory may be of very different natures. This monograph is concerned with models that can be described by partial differential equations of evolution. It contains five major contributions and is connected to the CIME Course on Control of Partial Differential Equations that took place in Cetraro (CS, Italy), July 19 - 23, 2010.  Specifically, it covers the stabilization of evolution equations, control of the Liouville equation, control in fluid mechanics, control and numerics for the wave equation, and Carleman estimates for elliptic and parabolic equations with application to control. We are confident this work will provide an authoritative reference work for all scientists who are interested in this field, representing at the same time a fri...

Packing of equal discs on a parabolic spiral lattice

International Nuclear Information System (INIS)

Xudong, F.; Bursill, L.A.; Julin, P.

1989-01-01

A contact disc model is investigated to determine the most closely-packed parabolic spiral lattice. The most space-efficient packings have divergence angles in agreement with the priority ranking of natural spiral structures

Exp-function method for solving fractional partial differential equations.

Science.gov (United States)

Zheng, Bin

2013-01-01

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

"Real-Time Optical Laboratory Linear Algebra Solution Of Partial Differential Equations"

Science.gov (United States)

Casasent, David; Jackson, James

1986-03-01

A Space Integrating (SI) Optical Linear Algebra Processor (OLAP) employing space and frequency-multiplexing, new partitioning and data flow, and achieving high accuracy performance with a non base-2 number system is described. Laboratory data on the performance of this system and the solution of parabolic Partial Differential Equations (PDEs) is provided. A multi-processor OLAP system is also described for the first time. It use in the solution of multiple banded matrices that frequently arise is then discussed. The utility and flexibility of this processor compared to digital systolic architectures should be apparent.

Modeling, Simulation and Performance Evaluation of Parabolic Trough

African Journals Online (AJOL)

Mekuannint

Mekuannint Mesfin and Abebayehu Assefa. Department of Mechanical Engineering. Addis Ababa University ... off design weather conditions as well. Keywords: Parabolic Trough Collector (PTC);. Heat Transfer ... of a conventional Rankine cycle power plant with solar fields that are used to increase the temperature of heat ...

Modeling, Simulation and Performance Evaluation of Parabolic Trough

African Journals Online (AJOL)

Mekuannint

Heat Transfer Fluid (HTF); TRNSYS power plant model; STEC library; Solar Advisor Model (SAM);. TRNSYS solar field model; Solar Electric. Generation System (SEGS). INTRODUCTION. Parabolic troughs are currently most used means of power generation option of solar sources. Solar electric generation systems (SEGs) ...

Solving Nonlinear Partial Differential Equations with Maple and Mathematica

CERN Document Server

Shingareva, Inna K

2011-01-01

The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple an

Rothe's method for parabolic equations on non-cylindrical domains

Czech Academy of Sciences Publication Activity Database

Dasht, J.; Engström, J.; Kufner, Alois; Persson, L.E.

2006-01-01

Roč. 1, č. 1 (2006), s. 59-80 ISSN 0973-2306 Institutional research plan: CEZ:AV0Z10190503 Keywords : parabolic equations * non-cylindrical domains * Rothe's method * time-discretization Subject RIV: BA - General Mathematics

Physiologic Pressure and Flow Changes During Parabolic Flight (Pilot Study)

Science.gov (United States)

Pantalos, George; Sharp, M. Keith; Mathias, John R.; Hargens, Alan R.; Watenpaugh, Donald E.; Buckey, Jay C.

1999-01-01

The objective of this study was to obtain measurement of cutaneous tissue perfusion central and peripheral venous pressure, and esophageal and abdominal pressure in human test subjects during parabolic flight. Hemodynamic data recorded during SLS-I and SLS-2 missions have resulted in the paradoxical finding of increased cardiac stroke volume in the presence of a decreased central venous pressure (CVP) following entry in weightlessness. The investigators have proposed that in the absence of gravity, acceleration-induced peripheral vascular compression is relieved, increasing peripheral vascular capacity and flow while reducing central and peripheral venous pressure, This pilot study seeks to measure blood pressure and flow in human test subjects during parabolic flight for different postures.

A parabolic-hyperbolic system modelling a moving cell

Directory of Open Access Journals (Sweden)

Fabiana Cardetti

2009-08-01

Full Text Available In this article, we study the existence and uniqueness of local solutions for a moving boundary problem governed by a coupled parabolic-hyperbolic system. The results can be applied to cell movement, extending a result obtained by Choi, Groulx, and Lui in 2005.

Effect of Rashba and Dresselhaus interactions on the energy spectrum, chemical potential, addition energy and spin-splitting in a many-electron parabolic GaAs quantum dot in a magnetic field

Energy Technology Data Exchange (ETDEWEB)

Kumar, D. Sanjeev [School of Physics, University of Hyderabad, Hyderabad 500046 (India); Mukhopadhyay, Soma [H & S Department of Physics, CMR College of Engineering and Technology, Kandlakoya, Medchal Road, Hyderabad 501 401 (India); Chatterjee, Ashok [School of Physics, University of Hyderabad, Hyderabad 500046 (India)

2016-11-15

The effect of electron–electron interaction and the Rashba and Dresselhaus spin–orbit interactions on the electronic properties of a many-electron system in a parabolically confined quantum dot placed in an external magnetic field is studied. With a simple and physically reasonable model potential for electron–electron interaction term, the problem is solved exactly to second-order in the spin–orbit coupling constants to obtain the energy spectrum, the chemical potential, addition energy and the spin-splitting energy.

Effect of Rashba and Dresselhaus interactions on the energy spectrum, chemical potential, addition energy and spin-splitting in a many-electron parabolic GaAs quantum dot in a magnetic field

International Nuclear Information System (INIS)

Kumar, D. Sanjeev; Mukhopadhyay, Soma; Chatterjee, Ashok

2016-01-01

The effect of electron–electron interaction and the Rashba and Dresselhaus spin–orbit interactions on the electronic properties of a many-electron system in a parabolically confined quantum dot placed in an external magnetic field is studied. With a simple and physically reasonable model potential for electron–electron interaction term, the problem is solved exactly to second-order in the spin–orbit coupling constants to obtain the energy spectrum, the chemical potential, addition energy and the spin-splitting energy.

Modeling of the pyrolysis of biomass under parabolic and exponential temperature increases using the Distributed Activation Energy Model

International Nuclear Information System (INIS)

Soria-Verdugo, Antonio; Goos, Elke; Arrieta-Sanagustín, Jorge; García-Hernando, Nestor

2016-01-01

Highlights: • Pyrolysis of biomass under parabolic and exponential temperature profiles is modeled. • The model is based on a simplified Distributed Activation Energy Model. • 4 biomasses are analyzed in TGA with parabolic and exponential temperature increases. • Deviations between the model prediction and TGA measurements are under 5 °C. - Abstract: A modification of the simplified Distributed Activation Energy Model is proposed to simulate the pyrolysis of biomass under parabolic and exponential temperature increases. The pyrolysis of pine wood, olive kernel, thistle flower and corncob was experimentally studied in a TGA Q500 thermogravimetric analyzer. The results of the measurements of nine different parabolic and exponential temperature increases for each sample were employed to validate the models proposed. The deviation between the experimental TGA measurements and the estimation of the reacted fraction during the pyrolysis of the four samples under parabolic and exponential temperature increases was lower than 5 °C for all the cases studied. The models derived in this work to describe the pyrolysis of biomass with parabolic and exponential temperature increases were found to be in good agreement with the experiments conducted in a thermogravimetric analyzer.

Generalized Second Law of Thermodynamics in Parabolic LTB Inhomogeneous Cosmology

International Nuclear Information System (INIS)

Sheykhi, A.; Moradpour, H.; Sarab, K. Rezazadeh; Wang, B.

2015-01-01

We study thermodynamics of the parabolic Lemaitre–Tolman–Bondi (LTB) cosmology supported by a perfect fluid source. This model is the natural generalization of the flat Friedmann–Robertson–Walker (FRW) universe, and describes an inhomogeneous universe with spherical symmetry. After reviewing some basic equations in the parabolic LTB cosmology, we obtain a relation for the deceleration parameter in this model. We also obtain a condition for which the universe undergoes an accelerating phase at the present time. We use the first law of thermodynamics on the apparent horizon together with the Einstein field equations to get a relation for the apparent horizon entropy in LTB cosmology. We find out that in LTB model of cosmology, the apparent horizon's entropy could be feeded by a term, which incorporates the effects of the inhomogeneity. We consider this result and get a relation for the total entropy evolution, which is used to examine the generalized second law of thermodynamics for an accelerating universe. We also verify the validity of the second law and the generalized second law of thermodynamics for a universe filled with some kinds of matters bounded by the event horizon in the framework of the parabolic LTB model. (paper)

Design and experimental investigation of a stretched parabolic linear Fresnel reflector collecting system

International Nuclear Information System (INIS)

Zhu, Yanqing; Shi, Jifu; Li, Yujian; Wang, Leilei; Huang, Qizhang; Xu, Gang

2016-01-01

Highlights: • A parabolic primary mirror field is designed to reduce the gap between adjacent mirrors. • The movable receiver can reduce the end losses. • The thermal efficiency of 66% is achieved at Guangzhou in winter. - Abstract: This paper proposes a stretched parabolic linear Fresnel reflector (SPLFR) collecting system. The primary optical mirror field of the SPLFR collecting system and the second-stage concentrator of compound parabolic collector are designed. The mirrors located at the parabolic line are close to each other, which effectively reduce the gap between the adjacent mirrors. The end losses of the receiver are very important, especially in a small-scale collecting system. A movable receiver is introduced for the reduction of the end losses. Moreover, a stretched structure of SPLFR is designed for wind resistance. Finally, the thermal performance of the SPLFR collecting system with fixed and movable receiver located in Guangzhou is tested. The maximum thermal efficiency obtained by this collecting system with movable receiver is 66% which avoid the end losses effectively, and the solar collector thermal loss coefficient is 1.32 W/m"2 °C. The results show that the SPLFR collecting system has excellent thermal performance and a promising application future. Meanwhile, this system will provide a valuable reference for concentrating solar power technology.

Piecewise parabolic negative magnetoresistance of two-dimensional electron gas with triangular antidot lattice

International Nuclear Information System (INIS)

Budantsev, M. V.; Lavrov, R. A.; Pogosov, A. G.; Zhdanov, E. Yu.; Pokhabov, D. A.

2011-01-01

Extraordinary piecewise parabolic behavior of the magnetoresistance has been experimentally detected in the two-dimensional electron gas with a dense triangular lattice of antidots, where commensurability magnetoresistance oscillations are suppressed. The magnetic field range of 0–0.6 T can be divided into three wide regions, in each of which the magnetoresistance is described by parabolic dependences with high accuracy (comparable to the experimental accuracy) and the transition regions between adjacent regions are much narrower than the regions themselves. In the region corresponding to the weakest magnetic fields, the parabolic behavior becomes almost linear. The observed behavior is reproducible as the electron gas density changes, which results in a change in the resistance by more than an order of magnitude. Possible physical mechanisms responsible for the observed behavior, including so-called “memory effects,” are discussed.

Shock wave convergence in water with parabolic wall boundaries

International Nuclear Information System (INIS)

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

2015-01-01

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

Quantum crystal growing: adiabatic preparation of a bosonic antiferromagnet in the presence of a parabolic inhomogeneity

DEFF Research Database (Denmark)

Gammelmark, Søren; Eckardt, André

2013-01-01

felt by the two species. Using numerical simulations we predict that a finite parabolic potential can assist the adiabatic preparation of the antiferromagnet. The optimal strength of the parabolic inhomogeneity depends sensitively on the number imbalance between the two species. We also find...

Hydrostatic pressure and conduction band non-parabolicity effects on the impurity binding energy in a spherical quantum dot

International Nuclear Information System (INIS)

Sivakami, A.; Mahendran, M.

2010-01-01

The binding energy of a shallow hydrogenic impurity in a spherical quantum dot under hydrostatic pressure with square well potential is calculated using a variational approach within the effective mass approximation. The effect of conduction band non-parabolicity on these energies is also estimated. The binding energy is computed for GaAs spherical quantum dot as a function of dot size, hydrostatic pressure both in the presence and absence of the band non-parabolicity effect. Our results show that (i) the hydrostatic pressure increases the impurity binding energy when dot radius increases for a given pressure, (ii) the hydrostatic pressure with the band non-parabolicity effect effectively increases the binding energy such that the variation is large for smaller dots and (iii) the maximum contribution by the non-parabolicity effect is about 15% for narrow dots. Our results are in good agreement with Perez-Merchancano et al. [J. Phys. Condens. Matter 19 (2007) 026225] who have not considered the conduction band non-parabolicity effect.

Distribution-valued weak solutions to a parabolic problem arising in financial mathematics

Directory of Open Access Journals (Sweden)

Michael Eydenberg

2009-07-01

Full Text Available We study distribution-valued solutions to a parabolic problem that arises from a model of the Black-Scholes equation in option pricing. We give a minor generalization of known existence and uniqueness results for solutions in bounded domains $Omega subset mathbb{R}^{n+1}$ to give existence of solutions for certain classes of distributions $fin mathcal{D}'(Omega$. We also study growth conditions for smooth solutions of certain parabolic equations on $mathbb{R}^nimes (0,T$ that have initial values in the space of distributions.

Classification of conformal representations induced from the maximal cuspidal parabolic

Energy Technology Data Exchange (ETDEWEB)

Dobrev, V. K., E-mail: dobrev@inrne.bas.bg [Scuola Internazionale Superiore di Studi Avanzati (Italy)

2017-03-15

In the present paper we continue the project of systematic construction of invariant differential operators on the example of representations of the conformal algebra induced from the maximal cuspidal parabolic.

Almost monotonicity formulas for elliptic and parabolic operators with variable coefficients

KAUST Repository

Matevosyan, Norayr

2010-10-21

In this paper we extend the results of Caffarelli, Jerison, and Kenig [Ann. of Math. (2)155 (2002)] and Caffarelli and Kenig [Amer. J. Math.120 (1998)] by establishing an almost monotonicity estimate for pairs of continuous functions satisfying u± ≥ 0 Lu± ≥ -1, u+ · u_ = 0 ;in an infinite strip (global version) or a finite parabolic cylinder (localized version), where L is a uniformly parabolic operator Lu = LA,b,cu := div(A(x, s)∇u) + b(x,s) · ∇u + c(x,s)u - δsu with double Dini continuous A and uniformly bounded b and c. We also prove the elliptic counterpart of this estimate.This closes the gap between the known conditions in the literature (both in the elliptic and parabolic case) imposed on u± in order to obtain an almost monotonicity estimate.At the end of the paper, we demonstrate how to use this new almost monotonicity formula to prove the optimal C1,1-regularity in a fairly general class of quasi-linear obstacle-type free boundary problems. © 2010 Wiley Periodicals, Inc.

Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators

Directory of Open Access Journals (Sweden)

Allaberen Ashyralyev

2014-01-01

Full Text Available The nonlocal boundary value problem for the parabolic differential equation v'(t+A(tv(t=f(t  (0≤t≤T,  v(0=v(λ+φ,  0<λ≤T in an arbitrary Banach space E with the dependent linear positive operator A(t is investigated. The well-posedness of this problem is established in Banach spaces C0β,γ(Eα-β of all Eα-β-valued continuous functions φ(t on [0,T] satisfying a Hölder condition with a weight (t+τγ. New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.

Parabolic dune reactivation and migration at Napeague, NY, USA: Insights from aerial and GPR imagery

Science.gov (United States)

Girardi, James D.; Davis, Dan M.

2010-02-01

Observations from mapping since the 19th century and aerial imagery since 1930 have been used to study changes in the aeolian geomorphology of coastal parabolic dunes over the last ~ 170 years in the Walking Dune Field, Napeague, NY. The five large parabolic dunes of the Walking Dune Field have all migrated across, or are presently interacting with, a variably forested area that has affected their migration, stabilization and morphology. This study has concentrated on a dune with a particularly complex history of stabilization, reactivation and migration. We have correlated that dune's surface evolution, as revealed by aerial imagery, with its internal structures imaged using 200 MHz and 500 MHz Ground Penetrating Radar (GPR) surveys. Both 2D (transect) and high-resolution 3D GPR imagery image downwind dipping bedding planes which can be grouped by apparent dip angle into several discrete packages of beds that reflect distinct decadal-scale episodes of dune reactivation and growth. From aerial and high resolution GPR imagery, we document a unique mode of reactivation and migration linked to upwind dune formation and parabolic dune interactions with forest trees. This study documents how dune-dune and dune-vegetation interactions have influenced a unique mode of blowout deposition that has alternated on a decadal scale between opposite sides of a parabolic dune during reactivation and migration. The pattern of recent parabolic dune reactivation and migration in the Walking Dune Field appears to be somewhat more complex, and perhaps more sensitive to subtle environmental pressures, than an idealized growth model with uniform deposition and purely on-axis migration. This pattern, believed to be prevalent among other parabolic dunes in the Walking Dune Field, may occur also in many other places where similar observational constraints are unavailable.

OPTIMAL ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA

KAUST Repository

GOSWAMI, DEEPJYOTI; PANI, AMIYA K.; YADAV, SANGITA

2014-01-01

AWe propose and analyse an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time-dependent parabolic integro-differential equation with nonsmooth initial data. The method is based on energy arguments combined with repeated use of time integration, but without using parabolic-type duality techniques. An optimal L2-error estimate is derived for the semidiscrete approximation when the initial data is in L2. A superconvergence result is obtained and then used to prove a maximum norm estimate for parabolic integro-differential equations defined on a two-dimensional bounded domain. © 2014 Australian Mathematical Society.

Structured inverse modeling in parabolic diffusion processess

OpenAIRE

Schulz, Volker; Siebenborn, Martin; Welker, Kathrin

2014-01-01

Often, the unknown diffusivity in diffusive processes is structured by piecewise constant patches. This paper is devoted to efficient methods for the determination of such structured diffusion parameters by exploiting shape calculus. A novel shape gradient is derived in parabolic processes. Furthermore quasi-Newton techniques are used in order to accelerate shape gradient based iterations in shape space. Numerical investigations support the theoretical results.

A parabolic analogue of the higher-order comparison theorem of De Silva and Savin

Science.gov (United States)

Banerjee, Agnid; Garofalo, Nicola

2016-01-01

We show that the quotient of two caloric functions which vanish on a portion of the lateral boundary of a H k + α domain is H k + α up to the boundary for k ≥ 2. In the case k = 1, we show that the quotient is in H 1 + α if the domain is assumed to be space-time C 1 , α regular. This can be thought of as a parabolic analogue of a recent important result in [8], and we closely follow the ideas in that paper. We also give counterexamples to the fact that analogous results are not true at points on the parabolic boundary which are not on the lateral boundary, i.e., points which are at the corner and base of the parabolic boundary.

The First European Parabolic Flight Campaign with the Airbus A310 ZERO-G

Science.gov (United States)

Pletser, Vladimir; Rouquette, Sebastien; Friedrich, Ulrike; Clervoy, Jean-Francois; Gharib, Thierry; Gai, Frederic; Mora, Christophe

2016-12-01

Aircraft parabolic flights repetitively provide up to 23 seconds of reduced gravity during ballistic flight manoeuvres. Parabolic flights are used to conduct short microgravity investigations in Physical and Life Sciences and in Technology, to test instrumentation prior to space flights and to train astronauts before a space mission. The use of parabolic flights is complementary to other microgravity carriers (drop towers, sounding rockets), and preparatory to manned space missions on board the International Space Station and other manned spacecraft, such as Shenzhou and the future Chinese Space Station. After 17 years of using the Airbus A300 ZERO-G, the French company Novespace, a subsidiary of the ' Centre National d'Etudes Spatiales' (CNES, French Space Agency), based in Bordeaux, France, purchased a new aircraft, an Airbus A310, to perform parabolic flights for microgravity research in Europe. Since April 2015, the European Space Agency (ESA), CNES and the ` Deutsches Zentrum für Luft- und Raumfahrt e.V.' (DLR, the German Aerospace Center) use this new aircraft, the Airbus A310 ZERO-G, for research experiments in microgravity. The first campaign was a Cooperative campaign shared by the three agencies, followed by respectively a CNES, an ESA and a DLR campaign. This paper presents the new Airbus A310 ZERO-G and its main characteristics and interfaces for scientific experiments. The experiments conducted during the first European campaign are presented.

Building a parabolic solar concentrator prototype

International Nuclear Information System (INIS)

Escobar-Romero, J F M; Montiel, S Vazquez y; Granados-AgustIn, F; Rodriguez-Rivera, E; Martinez-Yanez, L; Cruz-Martinez, V M

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.

Humidification dehumidification desalination system using parabolic trough solar air collector

International Nuclear Information System (INIS)

Al-Sulaiman, Fahad A.; Zubair, M. Ifras; Atif, Maimoon; Gandhidasan, Palanichamy; Al-Dini, Salem A.; Antar, Mohamed A.

2015-01-01

This paper deals with a detailed thermodynamic analysis to assess the performance of an HDH system with an integrated parabolic trough solar collector (PTSC). The HDH system considered is an open air, open water, air heated system that uses a PTSC as an air heater. Two different configurations were considered of the HDH system. In the first configuration, the solar air heater was placed before the humidifier whereas in the second configuration the solar air heater was placed between the humidifier and the dehumidifier. The current study revealed that PTSCs are well suited for air heated HDH systems for high radiation location, such as Dhahran, Saudi Arabia. The comparison between the two HDH configurations demonstrates that the gained output ratio (GOR) of the first configuration is, on average, about 1.5 whereas for the second configuration the GOR increases up to an average value of 4.7. The study demonstrates that the HDH configuration with the air heater placed between the humidifier and the dehumidifier has a better performance and a higher productivity. - Highlights: • Thermodynamic analysis of an HDH system driven by a parabolic trough solar collector was conducted. • The first configuration reveals a GOR of 1.5 while the second configuration reveals a GOR of 4.7. • Effective heating of the HDH system was obtained through parabolic trough solar collector

A Review of Psycho-Physiological Responses to Parabolic Flight

Science.gov (United States)

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

2008-06-01

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

Laser propagation and compton scattering in parabolic plasma channel

CERN Document Server

Dongguo, L; Yokoya, K; Hirose, T

2003-01-01

A Gaussian laser beam propagating in a parabolic plasma channel is discussed in this paper. For a weak laser, plasma density perturbation induced by interaction between the laser field and plasma is very small, the refractive index can be assumed to be constant with respect to time variable. For a parabolic plasma channel, through the static propagation equation, we obtain an analytical solution of the profile function of the Gaussian laser beam for an unmatched case and give the general condition for the matched case. As the laser intensity increases, an effect due to strong laser fields is included. We discuss how to design and select the distribution of plasma density for a certain experiment in which a plasma channel is utilized to guide a laser beam. The number of scattered photons (X-rays) generated through Compton backscattering in a plasma channel is discussed. (author)

Stopping test of iterative methods for solving PDE

International Nuclear Information System (INIS)

Wang Bangrong

1991-01-01

In order to assure the accuracy of the numerical solution of the iterative method for solving PDE (partial differential equation), the stopping test is very important. If the coefficient matrix of the system of linear algebraic equations is strictly diagonal dominant or irreducible weakly diagonal dominant, the stopping test formulas of the iterative method for solving PDE is proposed. Several numerical examples are given to illustrate the applications of the stopping test formulas

Classical behavior of few-electron parabolic quantum dots

International Nuclear Information System (INIS)

Ciftja, O.

2009-01-01

Quantum dots are intricate and fascinating systems to study novel phenomena of great theoretical and practical interest because low dimensionality coupled with the interplay between strong correlations, quantum confinement and magnetic field creates unique conditions for emergence of fundamentally new physics. In this work we consider two-dimensional semiconductor quantum dot systems consisting of few interacting electrons confined in an isotropic parabolic potential. We study the many-electron quantum ground state properties of such systems in presence of a perpendicular magnetic field as the number of electrons is varied using exact numerical diagonalizations and other approaches. The results derived from the calculations of the quantum model are then compared to corresponding results for a classical model of parabolically confined point charges who interact with a Coulomb potential. We find that, for a wide range of parameters and magnetic fields considered in this work, the quantum ground state energy is very close to the classical energy of the most stable classical configuration under the condition that the classical energy is properly adjusted to incorporate the quantum zero point motion.

Teaching Modeling with Partial Differential Equations: Several Successful Approaches

Science.gov (United States)

Myers, Joseph; Trubatch, David; Winkel, Brian

2008-01-01

We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

Parallel SOR methods with a parabolic-diffusion acceleration technique for solving an unstructured-grid Poisson equation on 3D arbitrary geometries

Science.gov (United States)

Zapata, M. A. Uh; Van Bang, D. Pham; Nguyen, K. D.

2016-05-01

This paper presents a parallel algorithm for the finite-volume discretisation of the Poisson equation on three-dimensional arbitrary geometries. The proposed method is formulated by using a 2D horizontal block domain decomposition and interprocessor data communication techniques with message passing interface. The horizontal unstructured-grid cells are reordered according to the neighbouring relations and decomposed into blocks using a load-balanced distribution to give all processors an equal amount of elements. In this algorithm, two parallel successive over-relaxation methods are presented: a multi-colour ordering technique for unstructured grids based on distributed memory and a block method using reordering index following similar ideas of the partitioning for structured grids. In all cases, the parallel algorithms are implemented with a combination of an acceleration iterative solver. This solver is based on a parabolic-diffusion equation introduced to obtain faster solutions of the linear systems arising from the discretisation. Numerical results are given to evaluate the performances of the methods showing speedups better than linear.

Absorber Alignment Measurement Tool for Solar Parabolic Trough Collectors: Preprint

Energy Technology Data Exchange (ETDEWEB)

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.

Automatic Fourier transform and self-Fourier beams due to parabolic potential

Energy Technology Data Exchange (ETDEWEB)

Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Liu, Xing [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu [Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Zhong, Weiping [Department of Electronic and Information Engineering, Shunde Polytechnic, Shunde 528300 (China); Petrović, Milan S. [Institute of Physics, P.O. Box 68, 11001 Belgrade (Serbia); Zhang, Yanpeng, E-mail: ypzhang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)

2015-12-15

We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fourier transforms are the beams themselves.

Viscosity solutions of fully nonlinear functional parabolic PDE

Directory of Open Access Journals (Sweden)

Liu Wei-an

2005-01-01

Full Text Available By the technique of coupled solutions, the notion of viscosity solutions is extended to fully nonlinear retarded parabolic equations. Such equations involve many models arising from optimal control theory, economy and finance, biology, and so forth. The comparison principle is shown. Then the existence and uniqueness are established by the fixed point theory.

Almost periodic solutions to systems of parabolic equations

Directory of Open Access Journals (Sweden)

Janpou Nee

1994-01-01

Full Text Available In this paper we show that the second-order differential solution is 2-almost periodic, provided it is 2-bounded, and the growth of the components of a non-linear function of a system of parabolic equation is bounded by any pair of con-secutive eigenvalues of the associated Dirichlet boundary value problems.

Spherical and plane integral operators for PDEs construction, analysis, and applications

CERN Document Server

Sabelfeld, Karl K

2013-01-01

The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.

Optical analysis and performance evaluation of a solar parabolic dish concentrator

Directory of Open Access Journals (Sweden)

Pavlović Saša R.

2016-01-01

Full Text Available In this study, the optical design of a solar parabolic dish concentrator is presented. The parabolic dish concentrator consists from 11 curvilinear trapezoidal reflective petals made of polymethyl methacrylate with special reflective coating. The dish diameter is equal to 3.8 m and the theoretical focal point distance is 2.26 m. Numerical simulations are made with the commercial software TracePro from Lambda Research, USA, and the final optimum position between absorber and reflector was calculated to 2.075 m; lower than focus distance. This paper presents results for the optimum position and the optimum diameter of the receiver. The decision for selecting these parameters is based on the calculation of the total flux over the flat and corrugated pipe receiver surface; in its central region and in the peripheral region. The simulation results could be useful reference for designing and optimizing of solar parabolic dish concentrators as for as for CFD analysis, heat transfer and fluid flow analysis in corrugated spiral heat absorbers. [Projekat Ministarstva nauke Republike Srbije, br. III42006: Research and development of energy and environmentally highly effective polygeneration systems based on renewable energy resources i br. III45016: Fabrication and characterization of nanophotonic functional structures in biomedicine and informatics

A Concentrator Photovoltaic System Based on a Combination of Prism-Compound Parabolic Concentrators

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Ngoc Hai Vu

2016-08-01

Full Text Available We present a cost-effective concentrating photovoltaic system composed of a prism and a compound parabolic concentrator (P-CPC. In this approach, the primary collector consists of a prism, a solid compound parabolic concentrator (CPC, and a slab waveguide. The prism, which is placed on the input aperture of CPC, directs the incoming sunlight beam to be parallel with the main axes of parabolic rims of CPC. Then, the sunlight is reflected at the parabolic rims and concentrated at the focal point of these parabolas. A slab waveguide is coupled at the output aperture of the CPC to collect focused sunlight beams and to guide them to the solar cell. The optical system was modeled and simulated with commercial ray tracing software (LightTools™. Simulation results show that the optical efficiency of a P-CPC can achieve up to 89%. when the concentration ratio of the P-CPC is fixed at 50. We also determine an optimal geometric structure of P-CPC based on simulation. Because of the simplicity of the P-CPC structure, a lower-cost mass production process is possible. A simulation based on optimal structure of P-CPC was performed and the results also shown that P-CPC has high angular tolerance for input sunlight. The high tolerance of the input angle of sunlight allows P-CPC solar concentrator utilize a single sun tracking system instead of a highly precise dual suntracking system as cost effective solution.

An inverse problem in a parabolic equation

Directory of Open Access Journals (Sweden)

Zhilin Li

1998-11-01

Full Text Available In this paper, an inverse problem in a parabolic equation is studied. An unknown function in the equation is related to two integral equations in terms of heat kernel. One of the integral equations is well-posed while another is ill-posed. A regularization approach for constructing an approximate solution to the ill-posed integral equation is proposed. Theoretical analysis and numerical experiment are provided to support the method.

Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

Science.gov (United States)

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

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.

A compactness lemma of Aubin type and its application to degenerate parabolic equations

Directory of Open Access Journals (Sweden)

Anvarbek Meirmanov

2014-10-01

Full Text Available Let $\\Omega\\subset \\mathbb{R}^{n}$ be a regular domain and $\\Phi(s\\in C_{\\rm loc}(\\mathbb{R}$ be a given function. If $\\mathfrak{M}\\subset L_2(0,T;W^1_2(\\Omega \\cap L_{\\infty}(\\Omega\\times (0,T$ is bounded and the set $\\{\\partial_t\\Phi(v|\\,v\\in \\mathfrak{M}\\}$ is bounded in $L_2(0,T;W^{-1}_2(\\Omega$, then there is a sequence $\\{v_k\\}\\in \\mathfrak{M}$ such that $v_k\\rightharpoonup v \\in L^2(0,T;W^1_2(\\Omega$, and $v_k\\to v$, $\\Phi(v_k\\to \\Phi(v$ a.e. in $\\Omega_T=\\Omega\\times (0,T$. This assertion is applied to prove solvability of the one-dimensional initial and boundary-value problem for a degenerate parabolic equation arising in the Buckley-Leverett model of two-phase filtration. We prove existence and uniqueness of a weak solution, establish the property of finite speed of propagation and construct a self-similar solution.

Bilinear reduced order approximate model of parabolic distributed solar collectors

KAUST Repository

Elmetennani, Shahrazed; Laleg-Kirati, Taous-Meriem

2015-01-01

This paper proposes a novel, low dimensional and accurate approximate model for the distributed parabolic solar collector, by means of a modified gaussian interpolation along the spatial domain. The proposed reduced model, taking the form of a low

Solar parabolic dish Stirling engine system design, simulation, and thermal analysis

International Nuclear Information System (INIS)

Hafez, A.Z.; Soliman, Ahmed; El-Metwally, K.A.; Ismail, I.M.

2016-01-01

Highlights: • Modeling and simulation for different parabolic dish Stirling engine designs using Matlab®. • The effect of solar dish design features and factors had been taken. • Estimation of output power from the solar dish using Matlab®. • The present analysis provides a theoretical guidance for designing and operating solar parabolic dish system. - Abstract: Modeling and simulation for different parabolic dish Stirling engine designs have been carried out using Matlab®. The effect of solar dish design features and factors such as material of the reflector concentrators, the shape of the reflector concentrators and the receiver, solar radiation at the concentrator, diameter of the parabolic dish concentrator, sizing the aperture area of concentrator, focal Length of the parabolic dish, the focal point diameter, sizing the aperture area of receiver, geometric concentration ratio, and rim angle have been studied. The study provides a theoretical guidance for designing and operating solar parabolic dish Stirling engines system. At Zewail city of Science and Technology, Egypt, for a 10 kW Stirling engine; The maximum solar dish Stirling engine output power estimation is 9707 W at 12:00 PM where the maximum beam solar radiation applied in solar dish concentrator is 990 W/m"2 at 12:00 PM. The performance of engine can be improved by increasing the precision of the engine parts and the heat source efficiency. The engine performance could be further increased if a better receiver working fluid is used. We can conclude that where the best time for heating the fluid and fasting the processing, the time required to heat the receiver to reach the minimum temperature for operating the Solar-powered Stirling engine for different heat transfer fluids; this will lead to more economic solar dish systems. Power output of the solar dish system is one of the most important targets in the design that show effectiveness of the system, and this has achieved when we take

A parabolic singular perturbation problem with an internal layer

NARCIS (Netherlands)

Grasman, J.; Shih, S.D.

2004-01-01

A method is presented to approximate with singular perturbation methods a parabolic differential equation for the quarter plane with a discontinuity at the corner. This discontinuity gives rise to an internal layer. It is necessary to match the local solution in this layer with the one in a corner

Strain effect on graphene nanoribbon carrier statistic in the presence of non-parabolic band structure

International Nuclear Information System (INIS)

Izuani Che Rosid, N A; Ahmadi, M T; Ismail, Razali

2016-01-01

The effect of tensile uniaxial strain on the non-parabolic electronic band structure of armchair graphene nanoribbon (AGNR) is investigated. In addition, the density of states and the carrier statistic based on the tight-binding Hamiltonian are modeled analytically. It is found that the property of AGNR in the non-parabolic band region is varied by the strain. The tunable energy band gap in AGNR upon strain at the minimum energy is described for each of n-AGNR families in the non-parabolic approximation. The behavior of AGNR in the presence of strain is attributed to the breakable AGNR electronic band structure, which varies the physical properties from its normality. The linear relation between the energy gap and the electrical properties is featured to further explain the characteristic of the deformed AGNR upon strain. (paper)

ε-neighbourhoods of orbits of parabolic diffeomorphisms and cohomological equations

International Nuclear Information System (INIS)

Resman, Maja

2014-01-01

In this article, we study the analyticity of (directed) areas of ε-neighbourhoods of orbits of parabolic germs. The article is motivated by the question of analytic classification using ε-neighbourhoods of orbits in the simplest formal class. We show that the coefficient in front of the ε 2 term in the asymptotic expansion in ε, 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. (paper)

Achieving uniform efficient illumination with multiple asymmetric compound parabolic luminaires

Science.gov (United States)

Gordon, Jeffrey M.; Kashin, Peter

1994-01-01

Luminaire designs based on multiple asymmetric nonimaging compound parabolic reflectors are proposed for 2-D illumination applications that require highly uniform far-field illuminance, while ensuring maximal lighting efficiency and sharp angular cutoffs. The new designs derive from recent advances in nonimaging secondary concentrators for line-focus solar collectors. The light source is not treated as a single entity, but rather is divided into two or more separate adjoining sources. An asymmetric compound parabolic luminaire is then designed around each half-source. Attaining sharp cutoffs requires relatively large reflectors. However, severe truncation of the reflectors renders these devices as compact as many conventional luminaires, at the penalty of a small fraction of the radiation being emitted outside the nominal cutoff. The configurations that maximize the uniformity of far-field illuminance offer significant improvements in flux homogeneity relative to alternative designs to date.

Non-linear partial differential equations an algebraic view of generalized solutions

CERN Document Server

Rosinger, Elemer E

1990-01-01

A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomen

Persona-Based Journaling: Striving for Authenticity in Representing the Problem-Solving Process

Science.gov (United States)

Liljedahl, Peter

2007-01-01

Students' mathematical problem-solving experiences are fraught with failed attempts, wrong turns, and partial successes that move in fits and jerks, oscillating between periods of inactivity, stalled progress, rapid advancement, and epiphanies. Students' problem-solving journals, however, do not always reflect this rather organic process. Without…

Methods for partial differential equations qualitative properties of solutions, phase space analysis, semilinear models

CERN Document Server

Ebert, Marcelo R

2018-01-01

This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the “research project for beginners” proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area. The book is organized in five parts: In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation. Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes...

Differential equation analysis in biomedical science and engineering partial differential equation applications with R

CERN Document Server

Schiesser, William E

2014-01-01

Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fields With a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the com

HEAT AND MASS TRANSFER EFFECTS ON FLOW PAST PARABOLIC STARTING MOTION OF ISOTHERMAL VERTICAL PLATE IN THE PRESENCE OF FIRST ORDER CHEMICAL REACTION

Directory of Open Access Journals (Sweden)

R. Muthucumaraswamy

2013-06-01

Full Text Available An exact solution of unsteady flow past a parabolic starting motion of the infinite isothermal vertical plate with uniform mass diffusion, in the presence of a homogeneous chemical reaction of the first order, has been studied. The plate temperature and the concentration level near the plate are raised uniformly. The dimensionless governing equations are solved using the Laplace transform technique. The effect of velocity profiles are studied for different physical parameters, such as chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number, and time. It is observed that velocity increases with increasing values of thermal Grashof number or mass Grashof number. The trend is reversed with respect to the chemical reaction parameter.

Parabolic cyclinder functions : examples of error bounds for asymptotic expansions

NARCIS (Netherlands)

R. Vidunas; N.M. Temme (Nico)

2002-01-01

textabstractSeveral asymptotic expansions of parabolic cylinder functions are discussedand error bounds for remainders in the expansions are presented. Inparticular Poincaré-type expansions for large values of the argument$z$ and uniform expansions for large values of the parameter areconsidered.

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

Science.gov (United States)

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.

Investigation on the dynamic behaviour of a parabolic trough power plant during strongly cloudy days

International Nuclear Information System (INIS)

Al-Maliki, Wisam Abed Kattea; Alobaid, Falah; Starkloff, Ralf; Kez, Vitali; Epple, Bernd

2016-01-01

Highlights: • A detailed dynamic model of a parabolic trough solar thermal power plant is done. • Simulated results are compared to the experimental data from the real power plant. • Discrepancy between model result and real data is caused by operation strategy. • The model strategy increased the operating hours of power plant by around 2.5–3 h. - Abstract: The objective of this study is the development of a full scale dynamic model of a parabolic trough power plant with a thermal storage system, operated by the Actividades de Construcción y Servicios Group in Spain. The model includes solar field, thermal storage system and the power block and describes the heat transfer fluid and steam/water paths in detail. The parabolic trough power plant is modelled using Advanced Process Simulation Software (APROS). To validate the model, the numerical results are compared to the measured data, obtained from “Andasol II” during strongly cloudy periods in the summer days. The comparisons show a qualitative agreement between the dynamic simulation model and the measurements. The results confirm that the thermal storage enables the parabolic trough power plant to provide a constant power rate when the storage energy discharge is available, despite significant oscillations in the solar radiation.

Extending the Utility of the Parabolic Approximation in Medical Ultrasound Using Wide-Angle Diffraction Modeling.

Science.gov (United States)

Soneson, Joshua E

2017-04-01

Wide-angle parabolic models are commonly used in geophysics and underwater acoustics but have seen little application in medical ultrasound. Here, a wide-angle model for continuous-wave high-intensity ultrasound beams is derived, which approximates the diffraction process more accurately than the commonly used Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation without increasing implementation complexity or computing time. A method for preventing the high spatial frequencies often present in source boundary conditions from corrupting the solution is presented. Simulations of shallowly focused axisymmetric beams using both the wide-angle and standard parabolic models are compared to assess the accuracy with which they model diffraction effects. The wide-angle model proposed here offers improved focusing accuracy and less error throughout the computational domain than the standard parabolic model, offering a facile method for extending the utility of existing KZK codes.

L^p-continuity of solutions to parabolic free boundary problems

Directory of Open Access Journals (Sweden)

Abdeslem Lyaghfouri

2015-07-01

Full Text Available In this article, we consider a class of parabolic free boundary problems. We establish some properties of the solutions, including L^infinity-regularity in time and a monotonicity property, from which we deduce strong L^p-continuity in time.

Interior Gradient Estimates for Nonuniformly Parabolic Equations II

Directory of Open Access Journals (Sweden)

Lieberman Gary M

2007-01-01

Full Text Available We prove interior gradient estimates for a large class of parabolic equations in divergence form. Using some simple ideas, we prove these estimates for several types of equations that are not amenable to previous methods. In particular, we have no restrictions on the maximum eigenvalue of the coefficient matrix and we obtain interior gradient estimates for so-called false mean curvature equation.

Verification of the Microgravity Active Vibration Isolation System based on Parabolic Flight

Science.gov (United States)

Zhang, Yong-kang; Dong, Wen-bo; Liu, Wei; Li, Zong-feng; Lv, Shi-meng; Sang, Xiao-ru; Yang, Yang

2017-12-01

The Microgravity active vibration isolation system (MAIS) is a device to reduce on-orbit vibration and to provide a lower gravity level for certain scientific experiments. MAIS system is made up of a stator and a floater, the stator is fixed on the spacecraft, and the floater is suspended by electromagnetic force so as to reduce the vibration from the stator. The system has 3 position sensors, 3 accelerometers, 8 Lorentz actuators, signal processing circuits and a central controller embedded in the operating software and control algorithms. For the experiments on parabolic flights, a laptop is added to MAIS for monitoring and operation, and a power module is for electric power converting. The principle of MAIS is as follows: the system samples the vibration acceleration of the floater from accelerometers, measures the displacement between stator and floater from position sensitive detectors, and computes Lorentz force current for each actuator so as to eliminate the vibration of the scientific payload, and meanwhile to avoid crashing between the stator and the floater. This is a motion control technic in 6 degrees of freedom (6-DOF) and its function could only be verified in a microgravity environment. Thanks for DLR and Novespace, we get a chance to take the DLR 27th parabolic flight campaign to make experiments to verify the 6-DOF control technic. The experiment results validate that the 6-DOF motion control technique is effective, and vibration isolation performance perfectly matches what we expected based on theoretical analysis and simulation. The MAIS has been planned on Chinese manned spacecraft for many microgravity scientific experiments, and the verification on parabolic flights is very important for its following mission. Additionally, we also test some additional function by microgravity electromagnetic suspension, such as automatic catching and locking and working in fault mode. The parabolic flight produces much useful data for these experiments.

On formation of a partially coherent beam in a stable-resonator laser

International Nuclear Information System (INIS)

Suvorov, A A

2010-01-01

A new method involving the expansion of the field coherence function in partially coherent modes - the eigensolutions of the problem for the second-order coherence function in a stable resonator - is proposed for the theoretical description of the process of multimode laser beam formation. The method for solving the problem for arbitrary partially coherent modes is formulated and the expressions for these modes are derived in the general form. The characteristics of the fundamental partially coherent mode, which coincides with the coherence function of a Gaussian partially coherent beam, are analysed in detail. The partially coherent modes are shown to possess two spatial scales - the effective radius and the coherence radius, which makes them a convenient tool for solving the problem of generation of a partially coherent beam. It is found that the unambiguous relation between the characteristics of partially coherent modes and the stable-resonator parameters is achieved by involving into consideration not only the process of the beam formation by the resonator mirrors but also the process of interaction of radiation with the active laser medium. (laser beams and resonators)

Conversion of solar radiation using parabolic mirrors

Directory of Open Access Journals (Sweden)

Jolanta Fieducik

2017-08-01

Full Text Available The use of solar energy is a promising source of renewable energy to cover the energy needs of our society. The aim of the study will be to analyze the possibility of converting solar energy using parabolic reflectors to the heat energy needed to meet the needs of hot water for a family of 4 people. This study presents simulations of the use of solar radiation using radiant concentration systems. The parabolic mirror directs the concentrated beam of sunlight onto a tube located in the focal plane, which is filled with water that under the influence of solar radiation heats up. This article assumes constant mirror geometry and tube cross section, while simulation is performed for different coefficients. For calculations it was assumed that the reflection coefficient of sunlight from the mirror r is variable and an analysis of its effect on the amount of heated liquid is made. The radiation absorption coefficient across the tube surface was determined by a, the thermal surface emissivity coefficient was determined as e and the simulations were performed at variable values for the amount of heated liquid. The calculations and their analysis show that, with appropriately chosen coefficients, it is possible to meet the needs of a 4-person family in warm water using the proposed installation in Poland.

Solving Two -Dimensional Diffusion Equations with Nonlocal Boundary Conditions by a Special Class of Padé Approximants

Directory of Open Access Journals (Sweden)

Mohammad Siddique

2010-08-01

Full Text Available Parabolic partial differential equations with nonlocal boundary conditions arise in modeling of a wide range of important application areas such as chemical diffusion, thermoelasticity, heat conduction process, control theory and medicine science. In this paper, we present the implementation of positivity- preserving Padé numerical schemes to the two-dimensional diffusion equation with nonlocal time dependent boundary condition. We successfully implemented these numerical schemes for both Homogeneous and Inhomogeneous cases. The numerical results show that these Padé approximation based numerical schemes are quite accurate and easily implemented.

Barrelet zeros and elastic π+p partial waves

International Nuclear Information System (INIS)

Chew, D.M.; Urban, M.

1976-06-01

A procedure is proposed for constructing low-order partial-wave amplitudes from a knowledge of Barrelet zeros near the physical region. The method is applied to the zeros already obtained for elastic π + p scattering data between 1.2 and 2.2 GeV cm energies. The partial waves emerge with errors that are straight-forwardly related to the accuracy of the data and satisfy unitarity without any constraint being imposed. There are significant differences from the partial waves obtained by other methods; this can be partially explained by the fact that no previous partial-wave analysis has been able to solve the discrete ambiguity. The cost of the analysis is much less

Monotone difference schemes for weakly coupled elliptic and parabolic systems

NARCIS (Netherlands)

P. Matus (Piotr); F.J. Gaspar Lorenz (Franscisco); L. M. Hieu (Le Minh); V.T.K. Tuyen (Vo Thi Kim)

2017-01-01

textabstractThe present paper is devoted to the development of the theory of monotone difference schemes, approximating the so-called weakly coupled system of linear elliptic and quasilinear parabolic equations. Similarly to the scalar case, the canonical form of the vector-difference schemes is

Current-voltage relation for thin tunnel barriers: Parabolic barrier model

DEFF Research Database (Denmark)

Hansen, Kim; Brandbyge, Mads

2004-01-01

We derive a simple analytic result for the current-voltage curve for tunneling of electrons through a thin uniform insulating layer modeled by a parabolic barrier. Our model, which goes beyond the Wentzel–Kramers–Brillouin approximation, is applicable also in the limit of highly transparant...

Numerical Schemes for Rough Parabolic Equations

Energy Technology Data Exchange (ETDEWEB)

Deya, Aurelien, E-mail: deya@iecn.u-nancy.fr [Universite de Nancy 1, Institut Elie Cartan Nancy (France)

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.

Light absorption in thin quantizing semiconductor wires with non-parabolic law of dispersion of charge carriers

International Nuclear Information System (INIS)

Djotian, A.P.; Kazarian, E.M.; Karakashinian, Y.V.

1993-01-01

Interband absorption of light in a quantizing wire with non-parabolic dispersion law of charge carries, as well as energy spectrum and state densities are studied. The effect of Coulomb interaction between particles on the spectral curve of interband absorption is considered. Non-parabolic dispersion law of charge carries leads to an essential displacement of absorption line to ground state of one-dimensional exciton. 7 refs

Neuronal Activity in the Subthalamic Cerebrovasodilator Area under Partial-Gravity Conditions in Rats

Directory of Open Access Journals (Sweden)

Zeredo L Zeredo

2014-03-01

Full Text Available The reduced-gravity environment in space is known to cause an upward shift in body fluids and thus require cardiovascular adaptations in astronauts. In this study, we recorded in rats the neuronal activity in the subthalamic cerebrovasodilator area (SVA, a key area that controls cerebral blood flow (CBF, in response to partial gravity. “Partial gravity” is the term that defines the reduced-gravity levels between 1 g (the unit gravity acceleration on Earth and 0 g (complete weightlessness in space. Neuronal activity was recorded telemetrically through chronically implanted microelectrodes in freely moving rats. Graded levels of partial gravity from 0.4 g to 0.01 g were generated by customized parabolic-flight maneuvers. Electrophysiological signals in each partial-gravity phase were compared to those of the preceding 1 g level-flight. As a result, SVA neuronal activity was significantly inhibited by the partial-gravity levels of 0.15 g and lower, but not by 0.2 g and higher. Gravity levels between 0.2–0.15 g could represent a critical threshold for the inhibition of neurons in the rat SVA. The lunar gravity (0.16 g might thus trigger neurogenic mechanisms of CBF control. This is the first study to examine brain electrophysiology with partial gravity as an experimental parameter.

Effects of an electric field on the confined hydrogen atom in a parabolic potential well

International Nuclear Information System (INIS)

Xie Wenfang

2009-01-01

Using the perturbation method, the confined hydrogen atom by a parabolic potential well is investigated. The binding energy of the confined hydrogen atom in a parabolic potential well is calculated as a function of the confined potential radius and as a function of the intensity of an applied electric field. It is shown that the binding energy of the confined hydrogen atom is highly dependent on the confined potential radius and the intensity of an applied electric field.

An Alternate Approach to Optimal L 2 -Error Analysis of Semidiscrete Galerkin Methods for Linear Parabolic Problems with Nonsmooth Initial Data

KAUST Repository

Goswami, Deepjyoti

2011-09-01

In this article, we propose and analyze an alternate proof of a priori error estimates for semidiscrete Galerkin approximations to a general second order linear parabolic initial and boundary value problem with rough initial data. Our analysis is based on energy arguments without using parabolic duality. Further, it follows the spirit of the proof technique used for deriving optimal error estimates for finite element approximations to parabolic problems with smooth initial data and hence, it unifies both theories, that is, one for smooth initial data and other for nonsmooth data. Moreover, the proposed technique is also extended to a semidiscrete mixed method for linear parabolic problems. In both cases, optimal L2-error estimates are derived, when the initial data is in L2. A superconvergence phenomenon is also observed, which is then used to prove L∞-estimates for linear parabolic problems defined on two-dimensional spatial domain again with rough initial data. Copyright © Taylor & Francis Group, LLC.

Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients

KAUST Repository

Nobile, Fabio; Tempone, Raul

2009-01-01

We consider the problem of numerically approximating statistical moments of the solution of a time- dependent linear parabolic partial differential equation (PDE), whose coefficients and/or forcing terms are spatially correlated random fields. The stochastic coefficients of the PDE are approximated by truncated Karhunen-Loève expansions driven by a finite number of uncorrelated random variables. After approxi- mating the stochastic coefficients, the original stochastic PDE turns into a new deterministic parametric PDE of the same type, the dimension of the parameter set being equal to the number of random variables introduced. After proving that the solution of the parametric PDE problem is analytic with respect to the parameters, we consider global polynomial approximations based on tensor product, total degree or sparse polynomial spaces and constructed by either a Stochastic Galerkin or a Stochastic Collocation approach. We derive convergence rates for the different cases and present numerical results that show how these approaches are a valid alternative to the more traditional Monte Carlo Method for this class of problems. © 2009 John Wiley & Sons, Ltd.

Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients

KAUST Repository

Nobile, Fabio

2009-11-05

We consider the problem of numerically approximating statistical moments of the solution of a time- dependent linear parabolic partial differential equation (PDE), whose coefficients and/or forcing terms are spatially correlated random fields. The stochastic coefficients of the PDE are approximated by truncated Karhunen-Loève expansions driven by a finite number of uncorrelated random variables. After approxi- mating the stochastic coefficients, the original stochastic PDE turns into a new deterministic parametric PDE of the same type, the dimension of the parameter set being equal to the number of random variables introduced. After proving that the solution of the parametric PDE problem is analytic with respect to the parameters, we consider global polynomial approximations based on tensor product, total degree or sparse polynomial spaces and constructed by either a Stochastic Galerkin or a Stochastic Collocation approach. We derive convergence rates for the different cases and present numerical results that show how these approaches are a valid alternative to the more traditional Monte Carlo Method for this class of problems. © 2009 John Wiley & Sons, Ltd.

Output Feedback-Based Boundary Control of Uncertain Coupled Semilinear Parabolic PDE Using Neurodynamic Programming.

Science.gov (United States)

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

In this paper, neurodynamic programming-based output feedback boundary control of distributed parameter systems governed by uncertain coupled semilinear parabolic partial differential equations (PDEs) under Neumann or Dirichlet boundary control conditions is introduced. First, Hamilton-Jacobi-Bellman (HJB) equation is formulated in the original PDE domain and the optimal control policy is derived using the value functional as the solution of the HJB equation. Subsequently, a novel observer is developed to estimate the system states given the uncertain nonlinearity in PDE dynamics and measured outputs. Consequently, the suboptimal boundary control policy is obtained by forward-in-time estimation of the value functional using a neural network (NN)-based online approximator and estimated state vector obtained from the NN observer. Novel adaptive tuning laws in continuous time are proposed for learning the value functional online to satisfy the HJB equation along system trajectories while ensuring the closed-loop stability. Local uniformly ultimate boundedness of the closed-loop system is verified by using Lyapunov theory. The performance of the proposed controller is verified via simulation on an unstable coupled diffusion reaction process.

Attractors for a class of doubly nonlinear parabolic systems

Directory of Open Access Journals (Sweden)

Hamid El Ouardi

2006-03-01

Full Text Available In this paper, we establish the existence and boundedness of solutions of a doubly nonlinear parabolic system. We also obtain the existence of a global attractor and the regularity property for this attractor in $\\left[ L^{\\infty }(\\Omega \\right] ^{2}$ and ${\\prod_{i=1}^{2}}{B_{\\infty }^{1+\\sigma_{i},p_{i}}( \\Omega } $.

On the Schauder estimates of solutions to parabolic equations

International Nuclear Information System (INIS)

Han Qing

1998-01-01

This paper gives a priori estimates on asymptotic polynomials of solutions to parabolic differential equations at any points. This leads to a pointwise version of Schauder estimates. The result improves the classical Schauder estimates in a way that the estimates of solutions and their derivatives at one point depend on the coefficient and nonhomogeneous terms at this particular point

On some perturbation techniques for quasi-linear parabolic equations

Directory of Open Access Journals (Sweden)

Igor Malyshev

1990-01-01

Full Text Available We study a nonhomogeneous quasi-linear parabolic equation and introduce a method that allows us to find the solution of a nonlinear boundary value problem in “explicit” form. This task is accomplished by perturbing the original equation with a source function, which is then found as a solution of some nonlinear operator equation.

Bilinear Approximate Model-Based Robust Lyapunov Control for Parabolic Distributed Collectors

KAUST Repository

Elmetennani, Shahrazed; Laleg-Kirati, Taous-Meriem

2016-01-01

This brief addresses the control problem of distributed parabolic solar collectors in order to maintain the field outlet temperature around a desired level. The objective is to design an efficient controller to force the outlet fluid temperature

On the Approximate Controllability of Some Semilinear Parabolic Boundary-Value Problems

International Nuclear Information System (INIS)

Diaz, J. I.; Henry, J.; Ramos, A. M.

1998-01-01

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

The Cousin problems in the viewpoint of partial differential equations

International Nuclear Information System (INIS)

Le Hung Son.

1990-01-01

In this paper we consider the Cousin problems for overdetermined systems of partial differential equations, which are generalizations of the Cauchy-Riemann system. The general methods for solving these problems are given. Applying the given methods we can solve the Cousin problems for many important systems in theoretical physics. (author). 19 refs

Characterization of a focusing parabolic guide using neutron radiography method

International Nuclear Information System (INIS)

Kardjilov, Nikolay; Boeni, Peter; Hilger, Andre; Strobl, Markus; Treimer, Wolfgang

2005-01-01

The aim of the investigation was to test the focusing properties of a new type of focusing neutron guide (trumpet) with parabolically shaped walls. The guide has a length of 431mm with an entrance area of 16x16mm 2 and an output area of 4x4mm 2 . The interior surfaces were coated with a supermirror-surface m=3 and due to their parabolic shape it was expected that an incident parallel beam can be focused in the focal point of the parabolas. To prove this statement the neutron intensity distribution at different distances behind the guide was recorded by means of a standard, high-resolution radiography detector. The experiments were performed at the V12b instrument at HMI with different levels of beam monochromatization demonstrating maximum intensity gains of about 25. The consideration for using the focusing guide for the purposes of cold neutron radiography will be presented

Experimental study on a parabolic concentrator assisted solar desalting system

International Nuclear Information System (INIS)

Arunkumar, T.; Denkenberger, David; Velraj, R.; Sathyamurthy, Ravishankar; Tanaka, Hiroshi; Vinothkumar, K.

2015-01-01

Highlights: • We optimized the augmentation of condense by enhanced desalination methodology. • Parabolic concentrator has been integrated with solar distillation systems. • We measured ambient together with solar radiation intensity. - Abstract: This paper presents a modification of parabolic concentrator (PC) – solar still with continuous water circulation using a storage tank to enhance the productivity. Four modes of operation were studied experimentally: (i) PC-solar still without top cover cooling; (ii) PC-solar still with top cover cooling, PC-solar still integrated with phase change material (PCM) without top cover cooling and PC-solar still integrated PCM with cooling. The experiments were carried out for the cooling water flow rates of 40 ml/min; 50 ml/min, 60 ml/min, 80 ml/min and 100 ml/min. Diurnal variations of water temperature (T_w), ambient air temperature (T_a), top cover temperature (T_o_c) and production rate are measured with frequent time intervals. Water cooling was not cost effective, but adding PCM was.

Tails and bridges in the parabolic restricted three-body problem

Science.gov (United States)

Barrabés, Esther; Cors, Josep M.; Garcia-Taberner, Laura; Ollé, Mercè

2017-12-01

After a close encounter of two galaxies, bridges and tails can be seen between or around them. A bridge would be a spiral arm between a galaxy and its companion, whereas a tail would correspond to a long and curving set of debris escaping from the galaxy. The goal of this paper is to present a mechanism, applying techniques of dynamical systems theory, that explains the formation of tails and bridges between galaxies in a simple model, the so-called parabolic restricted three-body problem, i.e. we study the motion of a particle under the gravitational influence of two primaries describing parabolic orbits. The equilibrium points and the final evolutions in this problem are recalled,and we show that the invariant manifolds of the collinear equilibrium points and the ones of the collision manifold explain the formation of bridges and tails. Massive numerical simulations are carried out and their application to recover previous results are also analysed.

Finite element simulation of cracks formation in parabolic flume above fixed service live

Science.gov (United States)

Bandurin, M. A.; Volosukhin, V. A.; Mikheev, A. V.; Volosukhin, Y. V.; Bandurina, I. P.

2018-03-01

In the article, digital simulation data on influence of defect different characteristics on cracks formation in a parabolic flume are presented. The finite element method is based on general hypotheses of the theory of elasticity. The studies showed that the values of absolute movements satisfy the standards of design. The results of the digital simulation of stresses and strains for cracks formation in concrete parabolic flumes after long-term service above the fixed service life are described. Stressed and strained state of reinforced concrete bearing elements under different load combinations is considered. Intensive threshold of danger to form longitudinal cracks in reinforced concrete elements is determined.

Piecewise-parabolic methods for astrophysical fluid dynamics

International Nuclear Information System (INIS)

Woodward, P.R.

1983-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2008-05-01

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

Survey of the status of finite element methods for partial differential equations

Science.gov (United States)

Temam, Roger

1986-01-01

The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.

Parabolic transformation cloaks for unbounded and bounded cloaking of matter waves

Science.gov (United States)

Chang, Yu-Hsuan; Lin, De-Hone

2014-01-01

Parabolic quantum cloaks with unbounded and bounded invisible regions are presented with the method of transformation design. The mass parameters of particles for perfect cloaking are shown to be constant along the parabolic coordinate axes of the cloaking shells. The invisibility performance of the cloaks is inspected from the viewpoints of waves and probability currents. The latter shows the controllable characteristic of a probability current by a quantum cloak. It also provides us with a simpler and more efficient way of exhibiting the performance of a quantum cloak without the solutions of the transformed wave equation. Through quantitative analysis of streamline structures in the cloaking shell, one defines the efficiency of the presented quantum cloak in the situation of oblique incidence. The cloaking models presented here give us more choices for testing and applying quantum cloaking.

Shock unsteadiness in a thrust optimized parabolic nozzle

Science.gov (United States)

Verma, S. B.

2009-07-01

This paper discusses the nature of shock unsteadiness, in an overexpanded thrust optimized parabolic nozzle, prevalent in various flow separation modes experienced during start up {(δ P0 /δ t > 0)} and shut down {(δ P0/δ t The results are based on simultaneously acquired data from real-time wall pressure measurements using Kulite pressure transducers, high-speed schlieren (2 kHz) of the exhaust flow-field and from strain-gauges installed on the nozzle bending tube. Shock unsteadiness in the separation region is seen to increase significantly just before the onset of each flow transition, even during steady nozzle operation. The intensity of this measure ( rms level) is seen to be strongly influenced by relative locations of normal and overexpansion shock, the decrease in radial size of re-circulation zone in the back-flow region, and finally, the local nozzle wall contour. During restricted shock separation, the pressure fluctuations in separation region exhibit periodic characteristics rather than the usually observed characteristics of intermittent separation. The possible physical mechanisms responsible for the generation of flow unsteadiness in various separation modes are discussed. The results are from an experimental study conducted in P6.2 cold-gas subscale test facility using a thrust optimized parabolic nozzle of area-ratio 30.

A parabolic velocity-decomposition method for wind turbines

Science.gov (United States)

Mittal, Anshul; Briley, W. Roger; Sreenivas, Kidambi; Taylor, Lafayette K.

2017-02-01

An economical parabolized Navier-Stokes approximation for steady incompressible flow is combined with a compatible wind turbine model to simulate wind turbine flows, both upstream of the turbine and in downstream wake regions. The inviscid parabolizing approximation is based on a Helmholtz decomposition of the secondary velocity vector and physical order-of-magnitude estimates, rather than an axial pressure gradient approximation. The wind turbine is modeled by distributed source-term forces incorporating time-averaged aerodynamic forces generated by a blade-element momentum turbine model. A solution algorithm is given whose dependent variables are streamwise velocity, streamwise vorticity, and pressure, with secondary velocity determined by two-dimensional scalar and vector potentials. In addition to laminar and turbulent boundary-layer test cases, solutions for a streamwise vortex-convection test problem are assessed by mesh refinement and comparison with Navier-Stokes solutions using the same grid. Computed results for a single turbine and a three-turbine array are presented using the NREL offshore 5-MW baseline wind turbine. These are also compared with an unsteady Reynolds-averaged Navier-Stokes solution computed with full rotor resolution. On balance, the agreement in turbine wake predictions for these test cases is very encouraging given the substantial differences in physical modeling fidelity and computer resources required.

Effect of Phonon Drag on the Thermopower in a Parabolic Quantum Well

Energy Technology Data Exchange (ETDEWEB)

Hasanov, Kh. A., E-mail: xanlarhasanli@rambler.ru; Huseynov, J. I. [Azerbaijan State Pedagogical University (Azerbaijan); Dadashova, V. V. [Baku State University (Azerbaijan); Aliyev, F. F. [National Academy of Sciences of Azerbaijan, Abdullaev Institute of Physics (Azerbaijan)

2016-03-15

The theory of phonon-drag thermopower resulting from a temperature gradient in the plane of a two-dimensional electron gas layer in a parabolic quantum well is developed. The interaction mechanisms between electrons and acoustic phonons are considered, taking into account potential screening of the interaction. It is found that the effect of electron drag by phonons makes a significant contribution to the thermopower of the two-dimensional electron gas. It is shown that the consideration of screening has a significant effect on the drag thermopower. For the temperature dependence of the thermopower in a parabolic GaAs/AlGaAs quantum well in the temperature range of 1–10 K, good agreement between the obtained theoretical results and experiments is shown.

Excitons in undoped AlGaAs/GaAs wide parabolic quantum wells

Energy Technology Data Exchange (ETDEWEB)

Tabata, A; Oliveira, J B B [Departamento de Fisica, Universidade Estadual Paulista, 17033-360, Bauru (Brazil); Silva, E C F da; Lamas, T E; Duarte, C A; Gusev, G M, E-mail: tabata@fc.unesp.b [Instituto de Fisica, Universidade de Sao Paulo, 05315-970, Sao Paulo (Brazil)

2010-02-01

In this work the electronic structure of undoped AlGaAs/GaAs wide parabolic quantum wells (PQWs) with different well widths (1000 A and 3000 A) were investigated by means of photoluminescence (PL) measurements. Due to the particular potential shape, the sample structure confines photocreated carriers with almost three-dimensional characteristics. Our data show that depending on the well width thickness it is possible to observe very narrow structures in the PL spectra, which were ascribed to emissions associated to the recombination of confined 1s-excitons of the parabolic potential wells. From our measurements, the exciton binding energies (of a few meV) were estimated. Besides the exciton emission, we have also observed PL emissions associated to electrons in the excited subbands of the PQWs.

Real parabolic vector bundles over a real curve

Indian Academy of Sciences (India)

Abstract. We define real parabolic structures on real vector bundles over a real curve. Let (X,σX ) be a real curve, and let S ⊂ X be a non-empty finite subset of X such that σX (S) = S. Let N ≥ 2 be an integer. We construct an N-fold cyclic cover p : Y → X in the category of real curves, ramified precisely over each point of S, ...

Femtosecond laser micromachining of compound parabolic concentrator fiber tipped glucose sensors

DEFF Research Database (Denmark)

Hassan, Hafeez Ul; Lacraz, Amédée; Kalli, Kyriacos

2017-01-01

We report on highly accurate femtosecond (fs) laser micromachining of a compound parabolic concentrator (CPC) fiber tip on a polymer optical fiber (POF). The accuracy is reflected in an unprecedented correspondence between the numerically predicted and experimentally found improvement in fluoresc...

Numerical solutions of a general coupled nonlinear system of parabolic and hyperbolic equations of thermoelasticity

Science.gov (United States)

Sweilam, N. H.; Abou Hasan, M. M.

2017-05-01

In this paper, the weighted-average non-standard finite-difference (WANSFD) method is used to study numerically the general time-fractional nonlinear, one-dimensional problem of thermoelasticity. This model contains the standard system arising in thermoelasticity as a special case. The stability of the proposed method is analyzed by a procedure akin to the standard John von Neumann technique. Moreover, the accuracy of the proposed scheme is proved. Numerical results are presented graphically, which reveal that the WANSFD method is easy to implement, effective and convenient for solving the proposed system. The proposed method could also be easily extended to solve other systems of fractional partial differential equations.

Partial regularity of weak solutions to a PDE system with cubic nonlinearity

Science.gov (United States)

Liu, Jian-Guo; Xu, Xiangsheng

2018-04-01

In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly singular elliptic equation for the scalar pressure of the underlying biological network coupled to a diffusion equation for the conductance vector of the network. There are several different types of nonlinearities in the system. Of particular mathematical interest is a term that is a polynomial function of solutions and their partial derivatives and this polynomial function has degree three. That is, the system contains a cubic nonlinearity. Only weak solutions to the system have been shown to exist. The regularity theory for the system remains fundamentally incomplete. In particular, it is not known whether or not weak solutions develop singularities. In this paper we obtain a partial regularity theorem, which gives an estimate for the parabolic Hausdorff dimension of the set of possible singular points.

Optimal Wentzell Boundary Control of Parabolic Equations

International Nuclear Information System (INIS)

Luo, Yousong

2017-01-01

This paper deals with a class of optimal control problems governed by an initial-boundary value problem of a parabolic equation. The case of semi-linear boundary control is studied where the control is applied to the system via the Wentzell boundary condition. The differentiability of the state variable with respect to the control is established and hence a necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained convex problems. A second order condition is also derived.

Optimal Wentzell Boundary Control of Parabolic Equations

Energy Technology Data Exchange (ETDEWEB)

Luo, Yousong, E-mail: yousong.luo@rmit.edu.au [RMIT University, School of Mathematical and Geospatial Sciences (Australia)

2017-04-15

This paper deals with a class of optimal control problems governed by an initial-boundary value problem of a parabolic equation. The case of semi-linear boundary control is studied where the control is applied to the system via the Wentzell boundary condition. The differentiability of the state variable with respect to the control is established and hence a necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained convex problems. A second order condition is also derived.

Essential partial differential equations analytical and computational aspects

CERN Document Server

Griffiths, David F; Silvester, David J

2015-01-01

This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods.   Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems.   The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test unde...

Numerical Solution of Parabolic Equations

DEFF Research Database (Denmark)

Østerby, Ole

These lecture notes are designed for a one-semester course on finite-difference methods for parabolic equations. These equations which traditionally are used for describing diffusion and heat-conduction problems in Geology, Physics, and Chemistry have recently found applications in Finance Theory...... ? and how do boundary value approximations affect the overall order of the method. Knowledge of a reliable order and error estimate enables us to determine (near-)optimal step sizes to meet a prescribed error tolerance, and possibly to extrapolate to get (higher order and) better accuracy at a minimal...... expense. Problems in two space dimensions are effectively handled using the Alternating Direction Implicit (ADI) technique. We present a systematic way of incorporating inhomogeneous terms and derivative boundary conditions in ADI methods as well as mixed derivative terms....

Pressure-volume-temperature gauging method experiment using liquid nitrogen under microgravity condition of parabolic flight

Energy Technology Data Exchange (ETDEWEB)

Seo, Man Su; Park, Hana; Yoo, Don Gyu; Jeong, Sang Kwon [Cryogenic Engineering Laboratory, Department of Mechanical Engineering, KAIST, Daejeon (Korea, Republic of); Jung, Young Suk [Launcher Systems Development Team, Korea Aerospace Research Institute, Daejeon (Korea, Republic of)

2014-06-15

Measuring an exact amount of remaining cryogenic liquid propellant under microgravity condition is one of the important issues of rocket vehicle. A Pressure-Volume-Temperature (PVT) gauging method is attractive due to its minimal additional hardware and simple gauging process. In this paper, PVT gauging method using liquid nitrogen is investigated under microgravity condition with parabolic flight. A 9.2 litre metal cryogenic liquid storage tank containing approximately 30% of liquid nitrogen is pressurized by ambient temperature helium gas. During microgravity condition, the inside of the liquid tank becomes near-isothermal condition within 1 K difference indicated by 6 silicon diode sensors vertically distributed in the middle of the liquid tank. Helium injection with higher mass flow rate after 10 seconds of the waiting time results in successful measurements of helium partial pressure in the tank. Average liquid volume measurement error is within 11% of the whole liquid tank volume and standard deviation of errors is 11.9. As a result, the applicability of PVT gauging method to liquid.

Pressure-volume-temperature gauging method experiment using liquid nitrogen under microgravity condition of parabolic flight

International Nuclear Information System (INIS)

Seo, Man Su; Park, Hana; Yoo, Don Gyu; Jeong, Sang Kwon; Jung, Young Suk

2014-01-01

Measuring an exact amount of remaining cryogenic liquid propellant under microgravity condition is one of the important issues of rocket vehicle. A Pressure-Volume-Temperature (PVT) gauging method is attractive due to its minimal additional hardware and simple gauging process. In this paper, PVT gauging method using liquid nitrogen is investigated under microgravity condition with parabolic flight. A 9.2 litre metal cryogenic liquid storage tank containing approximately 30% of liquid nitrogen is pressurized by ambient temperature helium gas. During microgravity condition, the inside of the liquid tank becomes near-isothermal condition within 1 K difference indicated by 6 silicon diode sensors vertically distributed in the middle of the liquid tank. Helium injection with higher mass flow rate after 10 seconds of the waiting time results in successful measurements of helium partial pressure in the tank. Average liquid volume measurement error is within 11% of the whole liquid tank volume and standard deviation of errors is 11.9. As a result, the applicability of PVT gauging method to liquid

Asynchronous and corrected-asynchronous numerical solutions of parabolic PDES on MIMD multiprocessors

Science.gov (United States)

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.

ICM: an Integrated Compartment Method for numerically solving partial differential equations

Energy Technology Data Exchange (ETDEWEB)

Yeh, G.T.

1981-05-01

An integrated compartment method (ICM) is proposed to construct a set of algebraic equations from a system of partial differential equations. The ICM combines the utility of integral formulation of finite element approach, the simplicity of interpolation of finite difference approximation, and the flexibility of compartment analyses. The integral formulation eases the treatment of boundary conditions, in particular, the Neumann-type boundary conditions. The simplicity of interpolation provides great economy in computation. The flexibility of discretization with irregular compartments of various shapes and sizes offers advantages in resolving complex boundaries enclosing compound regions of interest. The basic procedures of ICM are first to discretize the region of interest into compartments, then to apply three integral theorems of vectors to transform the volume integral to the surface integral, and finally to use interpolation to relate the interfacial values in terms of compartment values to close the system. The Navier-Stokes equations are used as an example of how to derive the corresponding ICM alogrithm for a given set of partial differential equations. Because of the structure of the algorithm, the basic computer program remains the same for cases in one-, two-, or three-dimensional problems.

New method for solving three-dimensional Schroedinger equation

International Nuclear Information System (INIS)

Melezhik, V.S.

1992-01-01

A new method is developed for solving the multidimensional Schroedinger equation without the variable separation. To solve the Schroedinger equation in a multidimensional coordinate space X, a difference grid Ω i (i=1,2,...,N) for some of variables, Ω, from X={R,Ω} is introduced and the initial partial-differential equation is reduced to a system of N differential-difference equations in terms of one of the variables R. The arising multi-channel scattering (or eigenvalue) problem is solved by the algorithm based on a continuous analog of the Newton method. The approach has been successfully tested for several two-dimensional problems (scattering on a nonspherical potential well and 'dipole' scatterer, a hydrogen atom in a homogenous magnetic field) and for a three-dimensional problem of the helium-atom bound states. (author)

Branch and bound algorithms to solve semiring constraint satisfaction problems

CSIR Research Space (South Africa)

Leenen, L

2008-12-01

Full Text Available The Semiring Constraint Satisfaction Problem (SCSP) framework is a popular approach for the representation of partial constraint satisfaction problems. Considerable research has been done in solving SCSPs, but limited work has been done in building...

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

Science.gov (United States)

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.

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

Directory of Open Access Journals (Sweden)

S. S. Motsa

2014-01-01

Full Text Available 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.

An Improved Heaviside Approach to Partial Fraction Expansion and Its Applications

Science.gov (United States)

Man, Yiu-Kwong

2009-01-01

In this note, we present an improved Heaviside approach to compute the partial fraction expansions of proper rational functions. This method uses synthetic divisions to determine the unknown partial fraction coefficients successively, without the need to use differentiation or to solve a system of linear equations. Examples of its applications in…

On purpose simulation model for molten salt CSP parabolic trough

Science.gov (United States)

Caranese, Carlo; Matino, Francesca; Maccari, Augusto

2017-06-01

The utilization of computer codes and simulation software is one of the fundamental aspects for the development of any kind of technology and, in particular, in CSP sector for researchers, energy institutions, EPC and others stakeholders. In that extent, several models for the simulation of CSP plant have been developed with different main objectives (dynamic simulation, productivity analysis, techno economic optimization, etc.), each of which has shown its own validity and suitability. Some of those models have been designed to study several plant configurations taking into account different CSP plant technologies (Parabolic trough, Linear Fresnel, Solar Tower or Dish) and different settings for the heat transfer fluid, the thermal storage systems and for the overall plant operating logic. Due to a lack of direct experience of Molten Salt Parabolic Trough (MSPT) commercial plant operation, most of the simulation tools do not foresee a suitable management of the thermal energy storage logic and of the solar field freeze protection system, but follow standard schemes. ASSALT, Ase Software for SALT csp plants, has been developed to improve MSPT plant's simulations, by exploiting the most correct operational strategies in order to provide more accurate technical and economical results. In particular, ASSALT applies MSPT specific control logics for the electric energy production and delivery strategy as well as the operation modes of the Solar Field in off-normal sunshine condition. With this approach, the estimated plant efficiency is increased and the electricity consumptions required for the plant operation and management is drastically reduced. Here we present a first comparative study on a real case 55 MWe Molten Salt Parabolic Trough CSP plant placed in the Tibetan highlands, using ASSALT and SAM (System Advisor Model), which is a commercially available simulation tool.

Rotating Parabolic-Reflector Antenna Target in SAR Data: Model, Characteristics, and Parameter Estimation

Directory of Open Access Journals (Sweden)

Bin Deng

2013-01-01

Full Text Available Parabolic-reflector antennas (PRAs, usually possessing rotation, are a particular type of targets of potential interest to the synthetic aperture radar (SAR community. This paper is aimed to investigate PRA’s scattering characteristics and then to extract PRA’s parameters from SAR returns, for supporting image interpretation and target recognition. We at first obtain both closed-form and numeric solutions to PRA’s backscattering by geometrical optics (GO, physical optics, and graphical electromagnetic computation, respectively. Based on the GO solution, a migratory scattering center model is at first presented for representing the movement of the specular point with aspect angle, and then a hybrid model, named the migratory/micromotion scattering center (MMSC model, is proposed for characterizing a rotating PRA in the SAR geometry, which incorporates PRA’s rotation into its migratory scattering center model. Additionally, we in detail analyze PRA’s radar characteristics on radar cross-section, high-resolution range profiles, time-frequency distribution, and 2D images, which also confirm the models proposed. A maximal likelihood estimator is developed for jointly solving the MMSC model for PRA’s multiple parameters by optimization. By exploiting the aforementioned characteristics, the coarse parameter estimation guarantees convergency upon global minima. The signatures recovered can be favorably utilized for SAR image interpretation and target recognition.

The cost of integration of parabolic trough CSP plants in isolated Mediterranean power systems

International Nuclear Information System (INIS)

Poullikkas, Andreas; Hadjipaschalis, Ioannis; Kourtis, George

2010-01-01

In this work, a technical and economic analysis concerning the integration of parabolic trough concentrated solar power (CSP) technologies, with or without thermal storage capability, in an existing typical small isolated Mediterranean power generation system, in the absence of a feed-in tariff scheme, is carried out. In addition to the business as usual (BAU) scenario, five more scenarios are examined in the analysis in order to assess the electricity unit cost with the penetration of parabolic trough CSP plants of 50 MWe or 100 MWe, with or without thermal storage capability. Based on the input data and assumptions made, the simulations indicated that the scenario with the utilization of a single parabolic trough CSP plant (either 50 MWe or 100 MWe and with or without thermal storage capability) in combination with BAU will effect an insignificant change in the electricity unit cost of the generation system compared to the BAU scenario. In addition, a sensitivity analysis on natural gas price, showed that increasing fuel prices and the existence of thermal storage capability in the CSP plant make this scenario marginally more economically attractive compared to the BAU scenario. (author)

Evaluation of the optical quality of compound parabolic concentrator solar collectors; Avaliacao da qualidade otica de coletores solares concentradores parabolicos compostos

Energy Technology Data Exchange (ETDEWEB)

Beyer, P.O.; Krenzinger, A. [Rio Grande do Sul Univ., Porto Alegre, RS (Brazil). Programa de Pos-graduacao em Engenharia Mecanica

1990-12-31

This work presents a simulation of solar compound parabolic concentrators using the ray tracing technique. The program can be used as a computer aided design and quality control applications for parabolic mirrors. (author). 4 refs., 8 figs.

Boundary value problems and partial differential equations

CERN Document Server

Powers, David L

2005-01-01

Boundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, (Clarkson) has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering.* CD with animations and graphics of solutions, additional exercises and chapter review questions* Nearly 900 exercises ranging in difficulty* Many fully worked examples

Binding energy of impurity states in an inverse parabolic quantum well under magnetic field

International Nuclear Information System (INIS)

Kasapoglu, E.; Sari, H.; Soekmen, I.

2007-01-01

We have investigated the effects of the magnetic field which is directed perpendicular to the well on the binding energy of the hydrogenic impurities in an inverse parabolic quantum well (IPQW) with different widths as well as different Al concentrations at the well center. The Al concentration at the barriers was always x max =0.3. The calculations were performed within the effective mass approximation, using a variational method. We observe that IPQW structure turns into parabolic quantum well with the inversion effect of the magnetic field and donor impurity binding energy in IPQW strongly depends on the magnetic field, Al concentration at the well center and well dimensions

a numerical analysis of the energy behavior of a parabolic trough ...

African Journals Online (AJOL)

M. Ghodbane

A computer program was developed in Matlab after discretization equations. For the calculation of energy balance was asks these assumptions: The heat transfer fluid is incompressible;. The parabolic shape is symmetrical;. The ambient temperature around the concentrator is uniform;. The effect of the shadow of ...

A 40 W cw Nd:YAG solar laser pumped through a heliostat: a parabolic mirror system

International Nuclear Information System (INIS)

Almeida, J; Liang, D; Guillot, E; Abdel-Hadi, Y

2013-01-01

Solar-pumped solid-state lasers are promising for renewable extreme-temperature material processing. Here, we report a significant improvement in solar laser collection efficiency by pumping the most widely used Nd:YAG single-crystal rod through a heliostat–parabolic mirror system. A conical-shaped fused silica light guide with 3D-CPC output end is used to both transmit and compress the concentrated solar radiation from the focal zone of a 2 m diameter parabolic mirror to a 5 mm diameter Nd:YAG rod within a conical pump cavity, which enables multi-pass pumping through the laser rod. 40 W cw laser power is measured, corresponding to 13.9 W m −2 record-high collection efficiency for the solar laser pumped through a heliostat–parabolic mirror system. 2.9% slope efficiency is fitted, corresponding to 132% enhancement over that of our previous pumping scheme. A 209% reduction in threshold pump power is also registered. (paper)

A two-stage compound parabolic concentrator system with a large entrance over the exit aperture ratio

International Nuclear Information System (INIS)

Angelescu, Tatiana; Radu, A. A.

2000-01-01

Certain optical designs in the field of high energy gamma ray astronomy components of the Cherenkov light, collected by the mirror of telescope, be concentrated on the photo-cathodes of the photomultiplier tubes, with the help of the light collectors having large entrance and small exit apertures. Mathematical restrictions imposed by the design of the compound parabolic concentrator (CPC) implied that for a given cut-off angle and an entrance aperture, the exit aperture of the CPC should not exceed a limit value. If this value is larger than the active diameter of the photocathode, an additional concentrator must be added to the system in order to transfer the light collected, from the exit aperture of the compound parabolic concentrator to the photocathode of the photomultiplier tube. Different designs of a two-stage system composed by a a hollow compound parabolic concentrator and a solid, dielectric filled concentrator are evaluated in this paper, from the point of view of optical efficiency and manufacturability. (authors)

Design and Realisation of a Parabolic Solar Cooker

International Nuclear Information System (INIS)

Ouannene, M; Chaouachi, B; Gabsi, S

2009-01-01

The sun s energy is really powerful. Solar energy is renewable and it s free. We can use it to make electricity, to heat buildings and to cook. The field of cooking consumes many fossil fuels such as gas and wood. Million people cannot find enough gas and/or wood to cook, so using solar cookers is a good idea. During this work, we designed, built and studied a parabolic solar cooker. The characteristic equations and the experimental results are given

DEVELOPMENT AND PRELIMINARY TESTING OF A PARABOLIC TROUGH SOLAR WATER HEATER

Directory of Open Access Journals (Sweden)

O. A. Lasode

2011-06-01

Full Text Available Solar energy is a high-temperature, high-energy radiant energy source, with tremendous advantages over other alternative energy sources. It is a reliable, robust renewable resource which is largely undeveloped. The design and fabrication of parabolic trough solar water heater for water heating was executed. The procedure employed includes the design, construction and testing stages. The equipment which is made up of the reflector surface (curved mirror, reflector support, absorber pipe and a stand was fabricated using locally sourced materials. The results obtained. compared favourably with other research works in the literature. It depicts that employing a suitable design, selection of time of heating and proper focusing of the reflected rays to the focal spot region, solar radiation can efficiently be utilized for water heating in a tropical environment. This work presents a parabolic trough solar water heater as a suitable renewable energy technology for reducing water-heating costs.

A numerical method for solving singular De`s

Energy Technology Data Exchange (ETDEWEB)

Mahaver, W.T.

1996-12-31

A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.

Space-DRUMS trade mark sign experimental development using parabolic reduced gravity flights

International Nuclear Information System (INIS)

Guigne, J.Y.; Millan, D.; Davidson, R.

2000-01-01

Space-DRUMS trade mark sign is a microgravity containerless-processing facility that uses acoustic beams to position large diameter liquid or solid samples within a gas-filled chamber. Its capacity to control the position of large diameter (6 cm) low density solid materials was successfully demonstrated on NASA's DC-9 parabolic aircraft in July 1996; two subsequent flights occurred in 1998 using the KC-135 and A-300 aircraft to further refine the technology used in the system. The working environment for the Space-DRUMS trade mark sign facility is the Space Shuttle/Space Station where long duration microgravity experimentation can take place. Since the reduced gravity environment of an A-300 or a KC-135 parabolic flight is much harsher than that of the Space Shuttle in terms of residual acceleration magnitudes experienced by the samples to be held in position; this more extreme environment allows for most Space-DRUMS trade mark sign technical payload functionality tests to be conducted. In addition to flight hardware shakedowns, parabolic flights continue to be extensively used to study and evaluate the behavior of candidate-advanced materials proposed for ISS Space-DRUMS trade mark sign campaigns. The first samples to be processed in 2001 involve combustion synthesis (also known as SHS - Self-propagating High Temperature Synthesis) of large glass-ceramic and of porous ceramic spheres. Upmassing Space-DRUMS trade mark sign for the International Space Station is scheduled for early 2001

American lookback option with fixed strike price—2-D parabolic variational inequality

Science.gov (United States)

Chen, Xiaoshan; Yi, Fahuai; Wang, Lihe

In this paper we study a 2-dimensional parabolic variational inequality with financial background. We define a suitable weak formula and obtain existence and uniqueness of the problem. Moreover we analyze the behaviors of the free boundary surface.

Study of the parabolic-spherical shape on the energy resolution in gamma spectrometry

International Nuclear Information System (INIS)

Silva, Joao Carlos Pereira da

1997-01-01

In gamma spectrometry, the energy resolution is an important parameter. This parameter measures the capability of the system to separate two photopeaks that are together. Scintillation systems have various factors that affect the energy resolution: energy deposition, light emission, light collection and electric signal processing. Light collection depended on the mechanisms of light transport until light strikes on the photocathode. In this trajectory the light losses energy by attenuation and refractions on the surfaces. In order to minimize these effects, a parabolic-spherical shape is proposed. The energy resolutions of hemispherical and parabolic-spherical shapes were measured. The results show a better resolution for the new shape, about 33% for Compton edge due to a 137 Cs radioactive source. (author)

Alignment method for parabolic trough solar concentrators

Science.gov (United States)

Diver, Richard B [Albuquerque, NM

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.

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

Science.gov (United States)

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.

Performance Analysis of Fractional-Order PID Controller for a Parabolic Distributed Solar Collector

KAUST Repository

Elmetennani, Shahrazed; N'Doye, Ibrahima; Salama, Khaled N.; Laleg-Kirati, Taous-Meriem

2017-01-01

This paper studies the performance of a fractional-order proportional integral derivative (FOPID) controller designed for parabolic distributed solar collectors. The control problem addressed in concentrated solar collectors aims at forcing

Iterative Splitting Methods for Differential Equations

CERN Document Server

Geiser, Juergen

2011-01-01

Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential

Computational modeling for fluid flow and interfacial transport

CERN Document Server

Shyy, Wei

2006-01-01

Practical applications and examples highlight this treatment of computational modeling for handling complex flowfields. A reference for researchers and graduate students of many different backgrounds, it also functions as a text for learning essential computation elements.Drawing upon his own research, the author addresses both macroscopic and microscopic features. He begins his three-part treatment with a survey of the basic concepts of finite difference schemes for solving parabolic, elliptic, and hyperbolic partial differential equations. The second part concerns issues related to computati

Partially specified physics problems: university students' attitudes and performance

International Nuclear Information System (INIS)

Marusic, M; Erceg, N; Slisko, J

2011-01-01

In this research we asked the fourth year students (N = 50) of a technical faculty of the University of Split (Republic of Croatia) to solve a partially specified physics problem related to gravitational force. The task for the students was to decide whether the situation described in the problem is feasible or not. Nevertheless, the formulation of the problem is such that it does not give students any explicit advice regarding what to calculate or how to judge the feasibility of the given situation in the real world. The research was carried out using a structured written exam method. The worksheet was structured in order to assess explicitly a few elements of the students' problem-solving performance. Based on their results, the examinees were classified into four categories, depending on what they could or could not accomplish during problem solving. A majority of students were not able to solve the given physical problem completely. A selection of students' and professors' observations is also included. Our results show that traditionally formulated numerical exercises, which are mostly used in physics teaching, do not develop students' abilities in higher-order thinking (i.e. planning, decision making or result evaluation) to a desirable extent. We suggest that partially specified problems should be given to students, both in problem-solving sessions and exams, in order to prepare them for dealing with ill-structured tasks in real life.

Time-optimal control of infinite order distributed parabolic systems involving time lags

Directory of Open Access Journals (Sweden)

G.M. Bahaa

2014-06-01

Full Text Available A time-optimal control problem for linear infinite order distributed parabolic systems involving constant time lags appear both in the state equation and in the boundary condition is presented. Some particular properties of the optimal control are discussed.

Sound field computations in the Bay of Bengal using parabolic equation method

Digital Repository Service at National Institute of Oceanography (India)

Navelkar, G.S.; Somayajulu, Y.K.; Murty, C.S.

Effect of the cold core eddy in the Bay of Bengal on acoustic propagation was analysed by parabolic equation (PE) method. Source depth, frequency and propagation range considered respectively for the two numerical experiments are 150 m, 400 Hz, 650...

Multi-parameter optimization design of parabolic trough solar receiver

International Nuclear Information System (INIS)

Guo, Jiangfeng; Huai, Xiulan

2016-01-01

Highlights: • The optimal condition can be obtained by multi-parameter optimization. • Exergy and thermal efficiencies are employed as objective function. • Exergy efficiency increases at the expense of heat losses. • The heat obtained by working fluid increases as thermal efficiency grows. - Abstract: The design parameters of parabolic trough solar receiver are interrelated and interact with one another, so the optimal performance of solar receiver cannot be obtained by the convectional single-parameter optimization. To overcome the shortcoming of single-parameter optimization, a multi-parameter optimization of parabolic trough solar receiver is employed based on genetic algorithm in the present work. When the thermal efficiency is taken as the objective function, the heat obtained by working fluid increases while the average temperature of working fluid and wall temperatures of solar receiver decrease. The average temperature of working fluid and the wall temperatures of solar receiver increase while the heat obtained by working fluid decreases generally by taking the exergy efficiency as an objective function. Assuming that the solar radiation intensity remains constant, the exergy obtained by working fluid increases by taking exergy efficiency as the objective function, which comes at the expense of heat losses of solar receiver.

A problem-solving routine for improving hospital operations.

Science.gov (United States)

Ghosh, Manimay; Sobek Ii, Durward K

2015-01-01

The purpose of this paper is to examine empirically why a systematic problem-solving routine can play an important role in the process improvement efforts of hospitals. Data on 18 process improvement cases were collected through semi-structured interviews, reports and other documents, and artifacts associated with the cases. The data were analyzed using a grounded theory approach. Adherence to all the steps of the problem-solving routine correlated to greater degrees of improvement across the sample. Analysis resulted in two models. The first partially explains why hospital workers tended to enact short-term solutions when faced with process-related problems; and tended not seek longer-term solutions that prevent problems from recurring. The second model highlights a set of self-reinforcing behaviors that are more likely to address problem recurrence and result in sustained process improvement. The study was conducted in one hospital setting. Hospital managers can improve patient care and increase operational efficiency by adopting and diffusing problem-solving routines that embody three key characteristics. This paper offers new insights on why caregivers adopt short-term approaches to problem solving. Three characteristics of an effective problem-solving routine in a healthcare setting are proposed.

Parabolic solar concentrator

Science.gov (United States)

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

2006-08-01

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

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).

Science.gov (United States)

Murase, Kenya

2016-01-01

Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.

Solving dominance and potential optimality in imprecise multi-attribute additive problems

International Nuclear Information System (INIS)

Mateos, Alfonso; Jimenez, Antonio; Rios-Insua, Sixto

2003-01-01

We consider the multicriteria decision-making problem where there is partial information on decision maker preferences, represented by means of an imprecise multiattribute additive utility function, and where the consequences of the alternatives or strategies are also possibly imprecise. Under these circumstances we consider how useful problem-solving concepts, namely nondominated, potentially optimal, adjacent potentially optimal alternatives, can be analytically computed. Thus, the problem can be solved much more efficiently using the classical methodology of linear programming

A Systematic Approach to Higher-Order Parabolic Propagation in a Weakly Range-Dependent Duct

National Research Council Canada - National Science Library

Gragg, Robert F

2005-01-01

Energy-conserving transformations are exploited to split a monochromatic field in a weakly inhomogeneous waveguide into a pair of components that undergo uncoupled parabolic propagation in opposite...

Introduction to partial differential equations and Hilbert space methods

CERN Document Server

Gustafson, Karl E

1997-01-01

Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.

Performance and durability testing of parabolic trough receivers

Science.gov (United States)

Lei, Dongqiang; Fu, Xuqiang; Zhao, Dongming; Yuan, Guofeng; Wang, Zhifeng; Guo, Minghuan

2017-06-01

The paper describes the key performance and durability testing facilities of the parabolic trough receiver developed by Institute of Electrical Engineering, Chinese Academy of Sciences. The indoor heat loss test can be applied at 4-7 different temperature levels within 200-550 on receivers. The optical efficiency test bench consists of 12 metal halide lamps as the solar simulator and a 5 m length half-elliptical cylinder reflector with flat end reflectors. 3 ultra-precision temperature sensors are used in receiver each end to get the temperature difference. The residual gas analysis test bench is applied to analyze and predict the vacuum lifetime of the receiver. It can test the variations of composition and partial pressure of residual gases with temperature and time in the receiver annulus space by a high sensitivity quadrupole mass spectrometer gas analyzer. A coating accelerated ageing test bench, which is also used to test the thermal cycle, has been developed. This test bench uses the absorber tube of the recevier as the resistance heater to heat up the whole receiver. The coating lifetime can be predicted by the Arrhenius parameters. For the cycling test, the compressed air is used to directly cool the inner surface of the absorber tube. The thermal cycling test is performed with temperature cycles from 150 °C to 450 °C for 160 cycles. The maximum thermal cycling frequency is 8 cycles per day. The mechanical fatigue test bench is used to test the bellows and the glass-to-metal seals durability at the same time. Both bellows are expanded and compressed to 6.5 mm in turn with 10,000 cycles. A new rotating test bench was also developed to test the thermal efficiency of the receiver.

Numerical solution of fully developed heat transfer problem with constant wall temperature and application to isosceles triangle and parabolic ducts

International Nuclear Information System (INIS)

Karabulut, Halit; Ipci, Duygu; Cinar, Can

2016-01-01

Highlights: • A numerical method has been developed for fully developed flows with constant wall temperature. • The governing equations were transformed to boundary fitted coordinates. • The Nusselt number of parabolic duct has been investigated. • Validation of the numerical method has been made by comparing published data. - Abstract: In motor-vehicles the use of more compact radiators have several advantages such as; improving the aerodynamic form of cars, reducing the weight and volume of the cars, reducing the material consumption and environmental pollutions, and enabling faster increase of the engine coolant temperature after starting to run and thereby improving the thermal efficiency. For the design of efficient and compact radiators, the robust determination of the heat transfer coefficient becomes imperative. In this study the external heat transfer coefficient of the radiator has been investigated for hydrodynamically and thermally fully developed flows in channels with constant wall temperature. In such situation the numerical treatment of the problem results in a trivial solution. To find a non-trivial solution the problem is treated either as an eigenvalue problem or as a thermally developing flow problem. In this study a numerical solution procedure has been developed and the heat transfer coefficients of the fully developed flow in triangular and parabolic air channels were investigated. The governing equations were transformed to boundary fitted coordinates and numerically solved. The non-trivial solution was obtained by means of guessing the temperature of any grid point within the solution domain. The correction of the guessed temperature was performed via smoothing the temperature profile on a line passing through the mentioned grid point. Results were compared with literature data and found to be consistent.

A numerical analysis of the energy behavior of a parabolic trough ...

African Journals Online (AJOL)

The solar power is a clean and a durable energy; there are several techniques for using them. When necessary to elevated temperatures of heat transfer fluid, this energy must concentration. This paper presents the efficiencies study of a linear solar concentrator of a parabolic trough type. This study was conducted on the ...

Analytic expressions for mode conversion in a plasma with a parabolic density profile: Generalized results

International Nuclear Information System (INIS)

Hinkel-Lipsker, D.E.; Fried, B.D.; Morales, G.J.

1993-01-01

This study provides an analytic solution to the general problem of mode conversion in an unmagnetized plasma. Specifically, an electromagnetic wave of frequency ω propagating through a plasma with a parabolic density profile of scale length L p is examined. The mode conversion points are located a distance Δ 0 from the peak of the profile, where the electron plasma frequency ω p (z) matches the wave frequency ω. The corresponding reflection, transmission, and mode conversion coefficients are expressed analytically in terms of parabolic cylinder functions for all values of Δ 0 . The method of solution is based on a source approximation technique that is valid when the electromagnetic and electrostatic scale lengths are well separated. For large Δ 0 , i.e., (cL p /ω) 1/2 much-lt Δ 0 p , the appropriately scaled result [D. E. Hinkel-Lipsker et al., Phys. Fluids B 4, 559 (1992)] for a linear density profile is recovered as the parabolic cylinder functions asymptotically become Airy functions. When Δ 0 →0, the special case of conversion at the peak of the profile [D. E. Hinkel-Lipsker et al., Phys. Fluids B 4, 1772 (1992)] is obtained

A semi-parabolic wake model for large offshore wind farms based on the open source CFD solver OpenFOAM

Directory of Open Access Journals (Sweden)

Cabezón D.

2014-01-01

Full Text Available Wake effect represents one of the main sources of energy loss and uncertainty when designing offshore wind farms. Traditionally analytical models have been used to optimize and estimate power deficits. However these models have shown to underestimate wake effect and consequently overestimate output power [1, 2]. This means that analytical models can be very helpful at optimizing preliminary layouts but not as accurate as needed for an ultimate fine design. Different techniques can be found in the literature to study wind turbine wakes that include simplified kinematic models and more advanced field models, that solve flow equations with different turbulence closure schemes. See the review papers of Crespo et al. [3], Vermeer et al. [4], and Sanderse et al. [5]. Purely elliptic Computational Fluid Dynamics (CFD models based on the actuator disk technique have been developed during the last years [6–8]. They consider wind turbine rotor as a disk where a distribution of axial forces act over the incoming air. It is a fair approach but it can still be computationally expensive for big wind farms in an operative mode. With this technique still active, an alternative approach inspired on the parabolic wake models [9, 10] is proposed. Wind turbine rotors continue to be represented as actuator disks but now the domain is split into subdomains containing one or more wind turbines. The output of each subdomain is mapped onto the input boundary of the next one until the end of the domain is reached, getting a considerable decrease on computational time, by a factor of order 10. As the model is based on the open source CFD solver OpenFOAM, it can be parallelized to speed-up convergence. The near wake is calculated so no initial wind speed deficit profiles have to be supposed as in totally parabolic models and alternative turbulence models, such as the anisotropic Reynolds Stress Model (RSM can be used. Traditional problems of elliptic models related to

Harnack's Inequality for Degenerate and Singular Parabolic Equations

CERN Document Server

DiBenedetto, Emmanuele; Vespri, Vincenzo

2012-01-01

Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years. Despite important achievements, the issue of the Harnack inequality for non-negative solutions to these equations, both of p-Laplacian and porous medium type, while raised by several authors, has remained basically open. Recently considerable progress has been made on this issue, to the point that, except for the singular sub-critical range, both for the p-laplacian and the porous medium equations, the theory is reasonably complete. It seemed therefore timely to trace a comprehensive

Analytic semigroups and optimal regularity in parabolic problems

CERN Document Server

Lunardi, Alessandra

2012-01-01

The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones. Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived. The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in p

Tracking local control of a parabolic trough collector

International Nuclear Information System (INIS)

Ajona, J.I.; Alberdi, J.; Gamero, E.; Blanco, J.

1992-01-01

In the local control, the sun position related to the trough collector is measured by two photo-resistors. The provided electronic signal is then compared with reference levels in order to get a set of B logical signals which form a byte. This byte and the commands issued by a programmable controller are connected to the inputs of o P.R.O.M. memory which is programmed with the logical equations of the control system. The memory output lines give the control command of the parabolic trough collector motor. (Author)

Behaviour of Human Hemodynamics under Microcavity –a Proposal for the 7th German Parabolic Flight Campaign

Directory of Open Access Journals (Sweden)

Vladimir Blazek

2005-01-01

Full Text Available All astronauts often feel uncomfortable during first encounter microgravity because of fluid shifts from the lower extremities to the head caused by weightlessness. Parabolic flights offer a great possibility for research of this phenomenon under “zero gravity”. With a combination of the optoelectronic sensor concepts PPG and PPGI and an ultrasound device it should be possible to measure all relevant parameters for description and further explanation of rapid fluid shifts along the body axis in humans during parabolic flights. A research team of the RWTH Aachen University and the Charité University Berlin will participate in the 7th German Parabolic Flight Campaign in September 2005 and perform the experiments under micro gravitation. A combination of used non-invasive strategies will reveal new insights into the human hemodynamics under microgravity conditions. The optoelectronic part of this interdisciplinary research experiment, details from the measuring setup, data collecting and post processing will be discussed.

Highly efficient end-side-pumped Nd:YAG solar laser by a heliostat-parabolic mirror system.

Science.gov (United States)

Almeida, J; Liang, D; Vistas, C R; Guillot, E

2015-03-10

We report a large improvement in the collection and slope efficiency of an Nd:YAG solar laser pumped by a heliostat-parabolic mirror system. A conical fused silica lens was used to further concentrate the solar radiation from the focal zone of a 2 m diameter primary concentrator to a Nd:YAG single-crystal rod within a conical pump cavity, which enabled multipass pumping to the active medium. A 56 W cw laser power was measured, corresponding to 21.1  W/m2 record-high solar laser collection efficiency with the heliostat-parabolic mirror system. 4.9% slope efficiency was calculated, corresponding to 175% enhancement over our previous result.

Theoretical Study of the Compound Parabolic Trough Solar Collector

OpenAIRE

Dr. Subhi S. Mahammed; Dr. Hameed J. Khalaf; Tadahmun A. Yassen

2012-01-01

Theoretical design of compound parabolic trough solar collector (CPC) without tracking is presented in this work. The thermal efficiency is obtained by using FORTRAN 90 program. The thermal efficiency is between (60-67)% at mass flow rate between (0.02-0.03) kg/s at concentration ratio of (3.8) without need to tracking system.The total and diffused radiation is calculated for Tikrit city by using theoretical equations. Good agreement between present work and the previous work.

A Novel Partial Differential Algebraic Equation (PDAE) Solver

DEFF Research Database (Denmark)

Lim, Young-il; Chang, Sin-Chung; Jørgensen, Sten Bay

2004-01-01

For solving partial differential algebraic equations (PDAEs), the space-time conservation element/solution element (CE/SE) method is addressed in this study. The method of lines (MOL) using an implicit time integrator is compared with the CE/SE method in terms of computational efficiency, solution...... or nonlinear adsorption isotherm are solved by the two methods. The CE/SE method enforces both local and global flux conservation in space and time, and uses a simple stencil structure (two points at the previous time level and one point at the present time level). Thus, accurate and computationally...

Some characteristics of heat production by stationary parabolic, cylindrical solar concentrator

Energy Technology Data Exchange (ETDEWEB)

Bojic, M.; Marjanovic, N.; Miletic, I.; Mitic, A. [Kragujevac Univ., Kragujevac (Serbia). Faculty of Mechanical Engineering; Stefanovic, V. [Nis Univ., Nis (Serbia). Faculty of Mechanical Engineering

2009-07-01

The use of solar energy for heating, cooling and electricity production was discussed with particular reference to the use of a stationary, asymmetric solar concentrator for conversion of solar energy to heat using a reflector and absorber. The infinite length CP-0A type stationary parabolic, cylindrical solar concentrator for heat production consists of the absorber (with water pipes) and parabolic, cylindrical reflector (with a metal surface). It has a geometrical concentration ratio of up to 4. This paper reported on a study that used the CATIA computer software to investigate how direct solar radiation approaches the concentrator aperture and the concentrator reflector. The propagation of light rays inside the concentrator to reach the absorber surface was examined. The study showed that the solar ray either hits the absorber directly or it bounces one or several time from the concentrator reflector. The efficiency of light rays was also calculated as a function of angles of incident of solar rays and type of reflector surface. 5 refs., 8 figs.

Within Your Control? When Problem Solving May Be Most Helpful.

Science.gov (United States)

Sarfan, Laurel D; Gooch, Peter; Clerkin, Elise M

2017-08-01

Emotion regulation strategies have been conceptualized as adaptive or maladaptive, but recent evidence suggests emotion regulation outcomes may be context-dependent. The present study tested whether the adaptiveness of a putatively adaptive emotion regulation strategy-problem solving-varied across contexts of high and low controllability. The present study also tested rumination, suggested to be one of the most putatively maladaptive strategies, which was expected to be associated with negative outcomes regardless of context. Participants completed an in vivo speech task, in which they were randomly assigned to a controllable ( n = 65) or an uncontrollable ( n = 63) condition. Using moderation analyses, we tested whether controllability interacted with emotion regulation use to predict negative affect, avoidance, and perception of performance. Partially consistent with hypotheses, problem solving was associated with certain positive outcomes (i.e., reduced behavioral avoidance) in the controllable (vs. uncontrollable) condition. Consistent with predictions, rumination was associated with negative outcomes (i.e., desired avoidance, negative affect, negative perception of performance) in both conditions. Overall, findings partially support contextual models of emotion regulation, insofar as the data suggest that the effects of problem solving may be more adaptive in controllable contexts for certain outcomes, whereas rumination may be maladaptive regardless of context.

Two-stage solar concentrators based on parabolic troughs: asymmetric versus symmetric designs.

Science.gov (United States)

Schmitz, Max; Cooper, Thomas; Ambrosetti, Gianluca; Steinfeld, Aldo

2015-11-20

While nonimaging concentrators can approach the thermodynamic limit of concentration, they generally suffer from poor compactness when designed for small acceptance angles, e.g., to capture direct solar irradiation. Symmetric two-stage systems utilizing an image-forming primary parabolic concentrator in tandem with a nonimaging secondary concentrator partially overcome this compactness problem, but their achievable concentration ratio is ultimately limited by the central obstruction caused by the secondary. Significant improvements can be realized by two-stage systems having asymmetric cross-sections, particularly for 2D line-focus trough designs. We therefore present a detailed analysis of two-stage line-focus asymmetric concentrators for flat receiver geometries and compare them to their symmetric counterparts. Exemplary designs are examined in terms of the key optical performance metrics, namely, geometric concentration ratio, acceptance angle, concentration-acceptance product, aspect ratio, active area fraction, and average number of reflections. Notably, we show that asymmetric designs can achieve significantly higher overall concentrations and are always more compact than symmetric systems designed for the same concentration ratio. Using this analysis as a basis, we develop novel asymmetric designs, including two-wing and nested configurations, which surpass the optical performance of two-mirror aplanats and are comparable with the best reported 2D simultaneous multiple surface designs for both hollow and dielectric-filled secondaries.

Parabolic trough solar concentrators: a technology which can contribute towards pakistan's energy future

International Nuclear Information System (INIS)

Masood, R.

2013-01-01

The utilization of solar thermal energy has got prime importance in Pakistan due to the current energy scarcity and escalating cost scenario in the country. Parabolic Trough Solar Concentrator is one of the most reliable technologies for utilization of solar thermal energy. In solar thermal power generation, Parabolic Trough Solar Concentrators are most successful as almost 96 percent of total solar thermal power is generated across the world by utilizing this technology. Its high reliability, operational compatibility, comparative low cost and high efficiency adds to its high value among other resources. Fortunately, Pakistan lies in the high Solar Insolation Zone; thus, a huge potential exists to benefit from this technology. This technology may cater to the Pakistan's seasonal increased electricity demand. Apart from electric power generation, this technology may also have cost-effective solutions for Pakistan's other industries, like steam generation, preheating of boiler make-up water, air-conditioning, and hot water production for food, textile, dairy and leather industries. However, economic justification of such projects would be possible only on accomplishing an indigenous technology base. Globally, this is a proven technology, but in Pakistan there is hardly any development in this field. In this study, an effort has been made by designing and fabricating an experimental Parabolic Trough Solar Water Heater by utilizing locally available materials and manufacturing capabilities. On achieving encouraging results, a solar boiler (steam generator) is proposed to be manufactured locally. (author)

Vector-valued Lizorkin-Triebel spaces and sharp trace theory for functions in Sobolev spaces with mixed \\pmb{L_p}-norm for parabolic problems

Science.gov (United States)

Weidemaier, P.

2005-06-01

The trace problem on the hypersurface y_n=0 is investigated for a function u=u(y,t) \\in L_q(0,T;W_{\\underline p}^{\\underline m}(\\mathbb R_+^n)) with \\partial_t u \\in L_q(0,T; L_{\\underline p}(\\mathbb R_+^n)), that is, Sobolev spaces with mixed Lebesgue norm L_{\\underline p,q}(\\mathbb R^n_+\\times(0,T))=L_q(0,T;L_{\\underline p}(\\mathbb R_+^n)) are considered; here \\underline p=(p_1,\\dots,p_n) is a vector and \\mathbb R^n_+=\\mathbb R^{n-1} \\times (0,\\infty). Such function spaces are useful in the context of parabolic equations. They allow, in particular, different exponents of summability in space and time. It is shown that the sharp regularity of the trace in the time variable is characterized by the Lizorkin-Triebel space F_{q,p_n}^{1-1/(p_nm_n)}(0,T;L_{\\widetilde{\\underline p}}(\\mathbb R^{n-1})), \\underline p=(\\widetilde{\\underline p},p_n). A similar result is established for first order spatial derivatives of u. These results allow one to determine the exact spaces for the data in the inhomogeneous Dirichlet and Neumann problems for parabolic equations of the second order if the solution is in the space L_q(0,T; W_p^2(\\Omega)) \\cap W_q^1(0,T;L_p(\\Omega)) with p \\le q.

Summary assessment of solar thermal parabolic dish technology for electrical power generation

Science.gov (United States)

Penda, P. L.; Fujita, T.; Lucas, J. W.

1985-01-01

An assessment is provided of solar thermal parabolic dish technology for electrical power generation. The assessment is based on the development program undertaken by the Jet Propulsion Laboratory for the U.S. Department of Energy and covers the period from the initiation of the program in 1976 through mid-1984. The program was founded on developing components and subsystems that are integrated into parabolic dish power modules for test and evaluation. The status of the project is summarized in terms of results obtained through testing of modules, and the implications of these findings are assessed in terms of techno-economic projections and market potential. The techno-economic projections are based on continuation of an evolutionary technological development program and are related to the accomplishments of the program as of mid-1984. The accomplishments of the development effort are summarized for each major subsystem including concentrators, receivers, and engines. The ramifications of these accomplishments are assessed in the context of developmental objectives and strategies.

Incompressible Navier-Stokes and parabolized Navier-Stokes solution procedures and computational techniques

Science.gov (United States)

Rubin, S. G.

1982-01-01

Recent developments with finite-difference techniques are emphasized. The quotation marks reflect the fact that any finite discretization procedure can be included in this category. Many so-called finite element collocation and galerkin methods can be reproduced by appropriate forms of the differential equations and discretization formulas. Many of the difficulties encountered in early Navier-Stokes calculations were inherent not only in the choice of the different equations (accuracy), but also in the method of solution or choice of algorithm (convergence and stability, in the manner in which the dependent variables or discretized equations are related (coupling), in the manner that boundary conditions are applied, in the manner that the coordinate mesh is specified (grid generation), and finally, in recognizing that for many high Reynolds number flows not all contributions to the Navier-Stokes equations are necessarily of equal importance (parabolization, preferred direction, pressure interaction, asymptotic and mathematical character). It is these elements that are reviewed. Several Navier-Stokes and parabolized Navier-Stokes formulations are also presented.

Heat Loss Testing of Schott's 2008 PTR70 Parabolic Trough Receiver

Energy Technology Data Exchange (ETDEWEB)

Burkholder, Frank [National Renewable Energy Lab. (NREL), Golden, CO (United States); Kutscher, Chuck [National Renewable Energy Lab. (NREL), Golden, CO (United States)

2009-05-01

Two Schott 2008 model year PTR70 HCEs were tested on NREL's heat loss test stand from 100 - 500 deg C in 50 deg C increments. Absorber emittance was determined from the laboratory testing so that the performance of the HCEs could be modeled in a parabolic trough collector. Collector/HCE simulation results for many different field operation conditions were used to create heat loss correlationcoefficients for Excelergy and SAM. SAM estimates that the decreased emittance of the 2008 PTR70 will decrease the LCOE for parabolic trough power plants by 0.5 cents/kWh and increase the electricity generated by 5% relative to previous PTR70s. These conclusions assume that the 2008 PTR70 is supplied at the same cost and with the same optical performance as earlier PTR70 models.

Partially specified physics problems: university students' attitudes and performance

Energy Technology Data Exchange (ETDEWEB)

Marusic, M [Prva Gimnazija, Teslina 10, 21000 Split (Croatia); Erceg, N [Department of Physics, University of Rijeka, Omladinska 14, 51000 Rijeka (Croatia); Slisko, J, E-mail: mirko@marusic.inf, E-mail: nerceg@phy.uniri.hr, E-mail: jslisko@fcfm.buap.mx [Benemerita Universidad Autonoma de Puebla, Apartado Postal 1152, Puebla, Puebla CP 72000 (Mexico)

2011-05-15

In this research we asked the fourth year students (N = 50) of a technical faculty of the University of Split (Republic of Croatia) to solve a partially specified physics problem related to gravitational force. The task for the students was to decide whether the situation described in the problem is feasible or not. Nevertheless, the formulation of the problem is such that it does not give students any explicit advice regarding what to calculate or how to judge the feasibility of the given situation in the real world. The research was carried out using a structured written exam method. The worksheet was structured in order to assess explicitly a few elements of the students' problem-solving performance. Based on their results, the examinees were classified into four categories, depending on what they could or could not accomplish during problem solving. A majority of students were not able to solve the given physical problem completely. A selection of students' and professors' observations is also included. Our results show that traditionally formulated numerical exercises, which are mostly used in physics teaching, do not develop students' abilities in higher-order thinking (i.e. planning, decision making or result evaluation) to a desirable extent. We suggest that partially specified problems should be given to students, both in problem-solving sessions and exams, in order to prepare them for dealing with ill-structured tasks in real life.

Effect of non-parabolicity on the binding energy of a hydrogenic donor in quantum well with a magnetic field

International Nuclear Information System (INIS)

Jayakumar, K.; Balasubramanian, S.; Tomak, M.

1985-08-01

A hydrogenic donor in a quantum well in the presence of a magnetic field perpendicular to the barrier is considered in the effective mass approximation. The non-parabolicity of the subband is included in the Hamiltonian by an energy-dependent effective mass. The donor binding energy is calculated variationally for different well widths and the effect of non-parabolicity is discussed in the light of recent experimental results. (author)

A self-applicable online partial evaluator for recursive flowchart languages

DEFF Research Database (Denmark)

Glück, Robert

2012-01-01

This paper describes a self-applicable online partial evaluator for a ¿owchart language with recursive calls. Self-application of the partial evaluator yields generating extensions that are as ef¿cient as those reported in the literature for of¿ine partial evaluation. This result is remarkable...... because it has been assumed that online partial evaluation techniques unavoidably lead to inef¿cient and overgeneralized generating extensions. The purpose of this paper is not to determine which kind of partial evaluation is better, but to show how the problem can be solved by recursive polyvariant...... specialization. The design of the self-applicable online partial evaluator is based on a number of known techniques, but by combining them in a new way this result can be produced. The partial evaluator, its techniques, and its implementation are presented in full. Self-application according to all three...

Study of weak solutions for parabolic variational inequalities with nonstandard growth conditions.

Science.gov (United States)

Dong, Yan

2018-01-01

In this paper, we study the degenerate parabolic variational inequality problem in a bounded domain. First, the weak solutions of the variational inequality are defined. Second, the existence and uniqueness of the solutions in the weak sense are proved by using the penalty method and the reduction method.

Theoretical Study of the Compound Parabolic Trough Solar Collector

Directory of Open Access Journals (Sweden)

Dr. Subhi S. Mahammed

2012-06-01

Full Text Available Theoretical design of compound parabolic trough solar collector (CPC without tracking is presented in this work. The thermal efficiency is obtained by using FORTRAN 90 program. The thermal efficiency is between (60-67% at mass flow rate between (0.02-0.03 kg/s at concentration ratio of (3.8 without need to tracking system.The total and diffused radiation is calculated for Tikrit city by using theoretical equations. Good agreement between present work and the previous work.

Analytic convergence of harmonic metrics for parabolic Higgs bundles

Science.gov (United States)

Kim, Semin; Wilkin, Graeme

2018-04-01

In this paper we investigate the moduli space of parabolic Higgs bundles over a punctured Riemann surface with varying weights at the punctures. We show that the harmonic metric depends analytically on the weights and the stable Higgs bundle. This gives a Higgs bundle generalisation of a theorem of McOwen on the existence of hyperbolic cone metrics on a punctured surface within a given conformal class, and a generalisation of a theorem of Judge on the analytic parametrisation of these metrics.

Integral transform method for solving time fractional systems and fractional heat equation

Directory of Open Access Journals (Sweden)

Arman Aghili

2014-01-01

Full Text Available In the present paper, time fractional partial differential equation is considered, where the fractional derivative is defined in the Caputo sense. Laplace transform method has been applied to obtain an exact solution. The authors solved certain homogeneous and nonhomogeneous time fractional heat equations using integral transform. Transform method is a powerful tool for solving fractional singular Integro - differential equations and PDEs. The result reveals that the transform method is very convenient and effective.

RECTC/RECTCF, 2. Order Elliptical Partial Differential Equation, Arbitrary Boundary Conditions

International Nuclear Information System (INIS)

Hackbusch, W.

1983-01-01

1 - Description of problem or function: A general linear elliptical second order partial differential equation on a rectangle with arbitrary boundary conditions is solved. 2 - Method of solution: Multi-grid iteration

Mass flow and velocity profiles in Neurospora hyphae: partial plug flow dominates intra-hyphal transport.

Science.gov (United States)

Abadeh, Aryan; Lew, Roger R

2013-11-01

Movement of nuclei, mitochondria and vacuoles through hyphal trunks of Neurospora crassa were vector-mapped using fluorescent markers and green fluorescent protein tags. The vectorial movements of all three were strongly correlated, indicating the central role of mass (bulk) flow in cytoplasm movements in N. crassa. Profiles of velocity versus distance from the hyphal wall did not match the parabolic shape predicted by the ideal Hagen-Poiseuille model of flow at low Reynolds number. Instead, the profiles were flat, consistent with a model of partial plug flow due to the high concentration of organelles in the flowing cytosol. The intra-hyphal pressure gradients were manipulated by localized external osmotic treatments to demonstrate the dependence of velocity (and direction) on pressure gradients within the hyphae. The data support the concept that mass transport, driven by pressure gradients, dominates intra-hyphal transport. The transport occurs by partial plug flow due to the organelles in the cytosol.

Annual measured and simulated thermal performance analysis of a hybrid solar district heating plant with flat plate collectors and parabolic trough collectors in series

DEFF Research Database (Denmark)

Tian, Zhiyong; Perers, Bengt; Furbo, Simon

2017-01-01

Flat plate collectors have relatively low efficiency at the typical supply temperatures of district heating networks (70–95 °C). Parabolic trough collectors retain their high efficiency at these temperatures. To maximize the advantages of flat plate collectors and parabolic trough collectors in l...... for this type of hybrid solar district heating plants with flat plate collectors and parabolic trough collectors in the Nordic region, but also introduce a novel design concept of solar district heating plants to other high solar radiation areas....... in large solar heating plants for a district heating network, a hybrid solar collector field with 5960 m2 flat plate collectors and 4039 m2 parabolic trough collectors in series was constructed in Taars, Denmark. The design principle is that the flat plate collectors preheat the return water from...

Solving a robust airline crew pairing problem with column generation

NARCIS (Netherlands)

Muter, I.; Birbil, S.I.; Bülbül, K.; Sahin, G.; Yenigün, H.; Tas, D.; Tüzün, D.

2013-01-01

In this study, we solve a robust version of the airline crew pairing problem. Our concept of robustness was partially shaped during our discussions with small local airlines in Turkey which may have to add a set of extra flights into their schedule at short notice during operation. Thus, robustness

A Fovea Localization Scheme Using Vessel Origin-Based Parabolic Model

Directory of Open Access Journals (Sweden)

Chun-Yuan Yu

2014-09-01

Full Text Available At the center of the macula, fovea plays an important role in computer-aided diagnosis. To locate the fovea, this paper proposes a vessel origin (VO-based parabolic model, which takes the VO as the vertex of the parabola-like vasculature. Image processing steps are applied to accurately locate the fovea on retinal images. Firstly, morphological gradient and the circular Hough transform are used to find the optic disc. The structure of the vessel is then segmented with the line detector. Based on the characteristics of the VO, four features of VO are extracted, following the Bayesian classification procedure. Once the VO is identified, the VO-based parabolic model will locate the fovea. To find the fittest parabola and the symmetry axis of the retinal vessel, an Shift and Rotation (SR-Hough transform that combines the Hough transform with the shift and rotation of coordinates is presented. Two public databases of retinal images, DRIVE and STARE, are used to evaluate the proposed method. The experiment results show that the average Euclidean distances between the located fovea and the fovea marked by experts in two databases are 9.8 pixels and 30.7 pixels, respectively. The results are stronger than other methods and thus provide a better macular detection for further disease discovery.

Analysis of the Efficacy of an Intervention to Improve Parent-Adolescent Problem Solving

OpenAIRE

Semeniuk, Yulia Yuriyivna; Brown, Roger L.; Riesch, Susan K.

2016-01-01

We conducted a two-group longitudinal partially nested randomized controlled trial to examine whether young adolescent youth-parent dyads participating in Mission Possible: Parents and Kids Who Listen, in contrast to a comparison group, would demonstrate improved problem solving skill. The intervention is based on the Circumplex Model and Social Problem Solving Theory. The Circumplex Model posits that families who are balanced, that is characterized by high cohesion and flexibility and open c...

ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION

KAUST Repository

MARKOWICH, P. A.

2009-10-01

We discuss existence and uniqueness of solutions for a one-dimensional parabolic evolution equation with a free boundary. This problem was introduced by Lasry and Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in-time-extension of the local solution which is closely related to the regularity of the free boundary. We also present numerical results. © 2009 World Scientific Publishing Company.

ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION

KAUST Repository

MARKOWICH, P. A.; MATEVOSYAN, N.; PIETSCHMANN, J.-F.; WOLFRAM, M.-T.

2009-01-01

We discuss existence and uniqueness of solutions for a one-dimensional parabolic evolution equation with a free boundary. This problem was introduced by Lasry and Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in-time-extension of the local solution which is closely related to the regularity of the free boundary. We also present numerical results. © 2009 World Scientific Publishing Company.

Adaptive Energy-based Bilinear Control of First-Order 1-D Hyperbolic PDEs: Application to a One-Loop Parabolic Solar Collector Trough

KAUST Repository

Mechhoud, Sarra; Laleg-Kirati, Taous-Meriem

2017-01-01

In this paper, the adaptive bilinear control of a first-order 1-D hyperbolic partial differential equation (PDE) with an unknown time-varying source term is investigated where only boundary measurements are available. By means of boundary injection, the bilinear adaptive law is developed in the Lyapunov approach. It consists of a state observer and an input adaptation law combined with a bilinear control method derived using an energy-like principle. Both global asymptotic practical convergence of the tracking error and input-to-state stability of the system are guaranteed. A potential application of this control strategy is the one-loop solar collector parabolic trough where the solar irradiance is the unknown input (source term) and the flow rate is the control variable. The objective is to drive the boundary temperature at the outlet to track a desired profile. Simulation results are provided to illustrate the performance of the proposed method.

Adaptive Energy-based Bilinear Control of First-Order 1-D Hyperbolic PDEs: Application to a One-Loop Parabolic Solar Collector Trough

KAUST Repository

Mechhoud, Sarra

2017-12-14

In this paper, the adaptive bilinear control of a first-order 1-D hyperbolic partial differential equation (PDE) with an unknown time-varying source term is investigated where only boundary measurements are available. By means of boundary injection, the bilinear adaptive law is developed in the Lyapunov approach. It consists of a state observer and an input adaptation law combined with a bilinear control method derived using an energy-like principle. Both global asymptotic practical convergence of the tracking error and input-to-state stability of the system are guaranteed. A potential application of this control strategy is the one-loop solar collector parabolic trough where the solar irradiance is the unknown input (source term) and the flow rate is the control variable. The objective is to drive the boundary temperature at the outlet to track a desired profile. Simulation results are provided to illustrate the performance of the proposed method.

Inverse Problems for a Parabolic Integrodifferential Equation in a Convolutional Weak Form

Directory of Open Access Journals (Sweden)

Kairi Kasemets

2013-01-01

Full Text Available We deduce formulas for the Fréchet derivatives of cost functionals of several inverse problems for a parabolic integrodifferential equation in a weak formulation. The method consists in the application of an integrated convolutional form of the weak problem and all computations are implemented in regular Sobolev spaces.

On the Ext algebras of parabolic Verma modules and A infinity-structures

DEFF Research Database (Denmark)

Klamt, Angela; Stroppel, Catharina

2012-01-01

We study the Ext-algebra of the direct sum of all parabolic Verma modules in the principal block of the Bernstein–Gelfand–Gelfand category O for the Hermitian symmetric pair (gln+m,gln¿glm) and present the corresponding quiver with relations for the cases n=1,2. The Kazhdan–Lusztig combinatorics ...

Admissible solutions for a class of nonlinear parabolic problem with non-negative data

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Petzeltová, Hana; Simondon, F.

2001-01-01

Roč. 131, č. 5 (2001), s. 857-883 ISSN 0308-2105 R&D Projects: GA AV ČR IAA1019703 Keywords : admissible solutions%nonlinear parabolic problem * admissible solutions * comparison principle * non-negative data Subject RIV: BA - General Mathematics Impact factor: 0.441, year: 2001

Smart reconfigurable parabolic space antenna for variable electromagnetic patterns

Science.gov (United States)

Kalra, Sahil; Datta, Rituparna; Munjal, B. S.; Bhattacharya, Bishakh

2018-02-01

An application of reconfigurable parabolic space antenna for satellite is discussed in this paper. The present study focuses on shape morphing of flexible parabolic antenna actuated with Shape Memory Alloy (SMA) wires. The antenna is able to transmit the signals to the desired footprint on earth with a desired gain value. SMA wire based actuation with a locking device is developed for a precise control of Antenna shape. The locking device is efficient to hold the structure in deformed configuration during power cutoff from the system. The maximum controllable deflection at any point using such actuation system is about 25mm with a precision of ±100 m. In order to control the shape of the antenna in a closed feedback loop, a Proportional, Integral and Derivative (PID) based controller is developed using LabVIEW (NI) and experiments are performed. Numerical modeling and analysis of the structure is carried out using finite element software ABAQUS. For data reduction and fast computation, stiffness matrix generated by ABAQUS is condensed by Guyan Reduction technique and shape optimization is performed using Non-dominated Sorting Genetic Algorithm (NSGA-II). The matching in comparative study between numerical and experimental set-up shows efficacy of our method. Thereafter, Electro-Magnetic (EM) simulations of the deformed shape is carried out using electromagnetic field simulation, High Frequency Structure Simulator (HFSS). The proposed design is envisaged to be very effective for multipurpose application of satellite system in the future missions of Indian Space Research Organization (ISRO).

Economic analysis of power generation from parabolic trough solar thermal plants for the Mediterranean region. A case study for the island of Cyprus

International Nuclear Information System (INIS)

Poullikkas, Andreas

2009-01-01

In this work a feasibility study is carried out in order to investigate whether the installation of a parabolic trough solar thermal technology for power generation in the Mediterranean region is economically feasible. The case study takes into account the available solar potential for Cyprus, as well as all available data concerning current renewable energy sources policy of the Cyprus Government, including the relevant feed-in tariff. In order to identify the least cost feasible option for the installation of the parabolic trough solar thermal plant a parametric cost-benefit analysis is carried out by varying parameters, such as, parabolic trough solar thermal plant capacity, parabolic trough solar thermal capital investment, operating hours, carbon dioxide emission trading system price, etc. For all above cases the electricity unit cost or benefit before tax, as well as after tax cash flow, net present value, internal rate of return and payback period are calculated. The results indicate that under certain conditions such projects can be profitable. (author)

Designing High-Efficiency Thin Silicon Solar Cells Using Parabolic-Pore Photonic Crystals

Science.gov (United States)

Bhattacharya, Sayak; John, Sajeev

2018-04-01

We demonstrate the efficacy of wave-interference-based light trapping and carrier transport in parabolic-pore photonic-crystal, thin-crystalline silicon (c -Si) solar cells to achieve above 29% power conversion efficiencies. Using a rigorous solution of Maxwell's equations through a standard finite-difference time domain scheme, we optimize the design of the vertical-parabolic-pore photonic crystal (PhC) on a 10 -μ m -thick c -Si solar cell to obtain a maximum achievable photocurrent density (MAPD) of 40.6 mA /cm2 beyond the ray-optical, Lambertian light-trapping limit. For a slanted-parabolic-pore PhC that breaks x -y symmetry, improved light trapping occurs due to better coupling into parallel-to-interface refraction modes. We achieve the optimum MAPD of 41.6 mA /cm2 for a tilt angle of 10° with respect to the vertical axis of the pores. This MAPD is further improved to 41.72 mA /cm2 by introducing a 75-nm SiO2 antireflective coating on top of the solar cell. We use this MAPD and the associated charge-carrier generation profile as input for a numerical solution of Poisson's equation coupled with semiconductor drift-diffusion equations using a Shockley-Read-Hall and Auger recombination model. Using experimentally achieved surface recombination velocities of 10 cm /s , we identify semiconductor doping profiles that yield power conversion efficiencies over 29%. Practical considerations of additional upper-contact losses suggest efficiencies close to 28%. This improvement beyond the current world record is largely due to an open-circuit voltage approaching 0.8 V enabled by reduced bulk recombination in our thin silicon architecture while maintaining a high short-circuit current through wave-interference-based light trapping.

Ultraprecise parabolic interpolator for numerically controlled machine tools. [Digital differential analyzer circuit

Energy Technology Data Exchange (ETDEWEB)

Davenport, C. M.

1977-02-01

The mathematical basis for an ultraprecise digital differential analyzer circuit for use as a parabolic interpolator on numerically controlled machines has been established, and scaling and other error-reduction techniques have been developed. An exact computer model is included, along with typical results showing tracking to within an accuracy of one part per million.

Annealed asymptotics for the parabolic Anderson model with a moving catalyst

NARCIS (Netherlands)

Gärtner, J.; Heydenreich, M.O.

2006-01-01

This paper deals with the solution u to the parabolic Anderson equation ¿u/¿t=¿¿u+¿u on the lattice . We consider the case where the potential ¿ is time-dependent and has the form ¿(t,x)=d0(x-Yt) with Yt being a simple random walk with jump rate 2d. The solution u may be interpreted as the

Pressure Distribution on Inner Wall of Parabolic Nozzle in Laser Propulsion with Single Pulse

Science.gov (United States)

Cui, Cunyan; Hong, Yanji; Wen, Ming; Song, Junling; Fang, Juan

2011-11-01

A system based of dynamic pressure sensors was established to study the time resolved pressure distribution on the inner wall of a parabolic nozzle in laser propulsion. Dynamic calibration and static calibration of the test system were made and the results showed that frequency response was up to 412 kHz and linear error was less than 10%. Experimental model was a parabolic nozzle and three test points were preset along one generating line. This study showed that experimental results agreed well with those obtained by numerical calculation way in pressure evolution tendency. The peak value of the calculation was higher than that of the experiment at each tested orifice because of the limitation of the numerical models. The results of this study were very useful for analyzing the energy deposition in laser propulsion and modifying numerical models.

Gas Turbine/Solar Parabolic Trough Hybrid Design Using Molten Salt Heat Transfer Fluid: Preprint

Energy Technology Data Exchange (ETDEWEB)

Turchi, C. S.; Ma, Z.

2011-08-01

Parabolic trough power plants can provide reliable power by incorporating either thermal energy storage (TES) or backup heat from fossil fuels. This paper describes a gas turbine / parabolic trough hybrid design that combines a solar contribution greater than 50% with gas heat rates that rival those of natural gas combined-cycle plants. Previous work illustrated benefits of integrating gas turbines with conventional oil heat-transfer-fluid (HTF) troughs running at 390?C. This work extends that analysis to examine the integration of gas turbines with salt-HTF troughs running at 450 degrees C and including TES. Using gas turbine waste heat to supplement the TES system provides greater operating flexibility while enhancing the efficiency of gas utilization. The analysis indicates that the hybrid plant design produces solar-derived electricity and gas-derived electricity at lower cost than either system operating alone.

A compound parabolic concentrator as an ultracold neutron spectrometer

Energy Technology Data Exchange (ETDEWEB)

Hickerson, K.P., E-mail: hickerson@gmail.com; Filippone, B.W., E-mail: bradf@caltech.edu

2013-09-01

The design principles of nonimaging optics are applied to ultracold neutrons (UCN). In particular a vertical compound parabolic concentrator (CPC) that efficiently redirects UCN vertically into a bounded spatial volume where they have a maximum energy mga that depends only on the initial phase space cross sectional area πa{sup 2} creates a spectrometer which can be applied to neutron lifetime and gravitational quantum state experiments. -- Highlights: • Nonimaging optics is applied to ultracold neutrons. • A novel ultracold neutron spectrometer is discussed. • New uses may include a neutron lifetime experiment.

A compound parabolic concentrator as an ultracold neutron spectrometer

International Nuclear Information System (INIS)

Hickerson, K.P.; Filippone, B.W.

2013-01-01

The design principles of nonimaging optics are applied to ultracold neutrons (UCN). In particular a vertical compound parabolic concentrator (CPC) that efficiently redirects UCN vertically into a bounded spatial volume where they have a maximum energy mga that depends only on the initial phase space cross sectional area πa 2 creates a spectrometer which can be applied to neutron lifetime and gravitational quantum state experiments. -- Highlights: • Nonimaging optics is applied to ultracold neutrons. • A novel ultracold neutron spectrometer is discussed. • New uses may include a neutron lifetime experiment

Tunneling of an energy eigenstate through a parabolic barrier viewed from Wigner phase space

DEFF Research Database (Denmark)

Heim, D.M.; Schleich, W.P.; Alsing, P.M.

2013-01-01

We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential equations in phase space determining the Wigner function...... of an energy eigenstate of the inverted oscillator. The reflection or transmission coefficients R or T are then given by the total weight of all classical phase-space trajectories corresponding to energies below, or above the top of the barrier given by the Wigner function....

Performance and Simulation of a Stand-alone Parabolic Trough Solar Thermal Power Plant

Science.gov (United States)

Mohammad, S. T.; Al-Kayiem, H. H.; Assadi, M. K.; Gilani, S. I. U. H.; Khlief, A. K.

2018-05-01

In this paper, a Simulink® Thermolib Model has been established for simulation performance evaluation of Stand-alone Parabolic Trough Solar Thermal Power Plant in Universiti Teknologi PETRONAS, Malaysia. This paper proposes a design of 1.2 kW parabolic trough power plant. The model is capable to predict temperatures at any system outlet in the plant, as well as the power output produced. The conditions that are taken into account as input to the model are: local solar radiation and ambient temperatures, which have been measured during the year. Other parameters that have been input to the model are the collector’s sizes, location in terms of latitude and altitude. Lastly, the results are presented in graphical manner to describe the analysed variations of various outputs of the solar fields obtained, and help to predict the performance of the plant. The developed model allows an initial evaluation of the viability and technical feasibility of any similar solar thermal power plant.

System Entropy Measurement of Stochastic Partial Differential Systems

Directory of Open Access Journals (Sweden)

Bor-Sen Chen

2016-03-01

Full Text Available System entropy describes the dispersal of a system’s energy and is an indication of the disorder of a physical system. Several system entropy measurement methods have been developed for dynamic systems. However, most real physical systems are always modeled using stochastic partial differential dynamic equations in the spatio-temporal domain. No efficient method currently exists that can calculate the system entropy of stochastic partial differential systems (SPDSs in consideration of the effects of intrinsic random fluctuation and compartment diffusion. In this study, a novel indirect measurement method is proposed for calculating of system entropy of SPDSs using a Hamilton–Jacobi integral inequality (HJII-constrained optimization method. In other words, we solve a nonlinear HJII-constrained optimization problem for measuring the system entropy of nonlinear stochastic partial differential systems (NSPDSs. To simplify the system entropy measurement of NSPDSs, the global linearization technique and finite difference scheme were employed to approximate the nonlinear stochastic spatial state space system. This allows the nonlinear HJII-constrained optimization problem for the system entropy measurement to be transformed to an equivalent linear matrix inequalities (LMIs-constrained optimization problem, which can be easily solved using the MATLAB LMI-toolbox (MATLAB R2014a, version 8.3. Finally, several examples are presented to illustrate the system entropy measurement of SPDSs.

Life science experiments during parabolic flight: The McGill experience

Science.gov (United States)

Watt, D. G. D.

1988-01-01

Over the past twelve years, members of the Aerospace Medical Research Unit of McGill University have carried out a wide variety of tests and experiments in the weightless condition created by parabolic flight. This paper discusses the pros and cons of that environment for the life scientist, and uses examples from the McGill program of the types of activities which can be carried out in a transport aircraft such as the NASA KC-135.

Nonlinear partial differential equations of second order

CERN Document Server

Dong, Guangchang

1991-01-01

This book addresses a class of equations central to many areas of mathematics and its applications. Although there is no routine way of solving nonlinear partial differential equations, effective approaches that apply to a wide variety of problems are available. This book addresses a general approach that consists of the following: Choose an appropriate function space, define a family of mappings, prove this family has a fixed point, and study various properties of the solution. The author emphasizes the derivation of various estimates, including a priori estimates. By focusing on a particular approach that has proven useful in solving a broad range of equations, this book makes a useful contribution to the literature.

Development and validation of a physics problem-solving assessment rubric

Science.gov (United States)

Docktor, Jennifer Lynn

Problem solving is a complex process that is important for everyday life and crucial for learning physics. Although there is a great deal of effort to improve student problem solving throughout the educational system, there is no standard way to evaluate written problem solving that is valid, reliable, and easy to use. Most tests of problem solving performance given in the classroom focus on the correctness of the end result or partial results rather than the quality of the procedures and reasoning leading to the result, which gives an inadequate description of a student's skills. A more detailed and meaningful measure is necessary if different curricular materials or pedagogies are to be compared. This measurement tool could also allow instructors to diagnose student difficulties and focus their coaching. It is important that the instrument be applicable to any problem solving format used by a student and to a range of problem types and topics typically used by instructors. Typically complex processes such as problem solving are assessed by using a rubric, which divides a skill into multiple quasi-independent categories and defines criteria to attain a score in each. This dissertation describes the development of a problem solving rubric for the purpose of assessing written solutions to physics problems and presents evidence for the validity, reliability, and utility of score interpretations on the instrument.

An improved partial bundle method for linearly constrained minimax problems

Directory of Open Access Journals (Sweden)

Chunming Tang

2016-02-01

Full Text Available In this paper, we propose an improved partial bundle method for solving linearly constrained minimax problems. In order to reduce the number of component function evaluations, we utilize a partial cutting-planes model to substitute for the traditional one. At each iteration, only one quadratic programming subproblem needs to be solved to obtain a new trial point. An improved descent test criterion is introduced to simplify the algorithm. The method produces a sequence of feasible trial points, and ensures that the objective function is monotonically decreasing on the sequence of stability centers. Global convergence of the algorithm is established. Moreover, we utilize the subgradient aggregation strategy to control the size of the bundle and therefore overcome the difficulty of computation and storage. Finally, some preliminary numerical results show that the proposed method is effective.

An error estimate for Tremolieres method for the discretization of parabolic variational inequalities

International Nuclear Information System (INIS)

Uko, L.U.

1990-02-01

We study a scheme for the time-discretization of parabolic variational inequalities that is often easier to use than the classical method of Rothe. We show that if the data are compatible in a certain sense, then this scheme is of order ≥1/2. (author). 10 refs

A new desalination system using a combination of heat pipe, evacuated tube and parabolic trough collector

International Nuclear Information System (INIS)

Jafari Mosleh, H.; Jahangiri Mamouri, S.; Shafii, M.B.; Hakim Sima, A.

2015-01-01

Highlights: • A new desalination uses a combination of heat pipe and parabolic trough collector. • A twin-glass evacuated tube is used to decrease the thermal losses from heat pipe. • Adding oil into the space between heat pipe and tube collector enhances the yield. • The yield and efficiency reach up to 0.933 kg/(m 2 h) and 65.2%, respectively. - Abstract: The solar collectors have been commonly used in desalination systems. Recent investigations show that the use of a linear parabolic trough collector in solar stills can improve the efficiency of a desalination system. In this work, a combination of a heat pipe and a twin-glass evacuated tube collector is utilized with a parabolic trough collector. Results show that the rate of production and efficiency can reach to 0.27 kg/(m 2 h) and 22.1% when aluminum conducting foils are used in the space between the heat pipe and the twin-glass evacuated tube collector to transfer heat from the tube collector to the heat pipe. When oil is used as a medium for the transfer of heat, filling the space between heat pipe and twin-glass evacuated tube collector, the production and efficiency can increase to 0.933 kg/(m 2 h) and 65.2%, respectively

An ansatz for solving nonlinear partial differential equations in mathematical physics.

Science.gov (United States)

Akbar, M Ali; Ali, Norhashidah Hj Mohd

2016-01-01

In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.

Partial differential equations & boundary value problems with Maple

CERN Document Server

Articolo, George A

2009-01-01

Partial Differential Equations and Boundary Value Problems with Maple presents all of the material normally covered in a standard course on partial differential equations, while focusing on the natural union between this material and the powerful computational software, Maple. The Maple commands are so intuitive and easy to learn, students can learn what they need to know about the software in a matter of hours- an investment that provides substantial returns. Maple''s animation capabilities allow students and practitioners to see real-time displays of the solutions of partial differential equations.  Maple files can be found on the books website. Ancillary list: Maple files- http://www.elsevierdirect.com/companion.jsp?ISBN=9780123747327  Provides a quick overview of the software w/simple commands needed to get startedIncludes review material on linear algebra and Ordinary Differential equations, and their contribution in solving partial differential equationsIncorporates an early introduction to Sturm-L...

Modeling of a Parabolic Trough Solar Field for Acceptance Testing: A Case Study

Energy Technology Data Exchange (ETDEWEB)

Wagner, M. J.; Mehos, M. S.; Kearney, D. W.; McMahan, A. C.

2011-01-01

As deployment of parabolic trough concentrating solar power (CSP) systems ramps up, the need for reliable and robust performance acceptance test guidelines for the solar field is also amplified. Project owners and/or EPC contractors often require extensive solar field performance testing as part of the plant commissioning process in order to ensure that actual solar field performance satisfies both technical specifications and performance guaranties between the involved parties. Performance test code work is currently underway at the National Renewable Energy Laboratory (NREL) in collaboration with the SolarPACES Task-I activity, and within the ASME PTC-52 committee. One important aspect of acceptance testing is the selection of a robust technology performance model. NREL1 has developed a detailed parabolic trough performance model within the SAM software tool. This model is capable of predicting solar field, sub-system, and component performance. It has further been modified for this work to support calculation at subhourly time steps. This paper presents the methodology and results of a case study comparing actual performance data for a parabolic trough solar field to the predicted results using the modified SAM trough model. Due to data limitations, the methodology is applied to a single collector loop, though it applies to larger subfields and entire solar fields. Special consideration is provided for the model formulation, improvements to the model formulation based on comparison with the collected data, and uncertainty associated with the measured data. Additionally, this paper identifies modeling considerations that are of particular importance in the solar field acceptance testing process and uses the model to provide preliminary recommendations regarding acceptable steady-state testing conditions at the single-loop level.

Ground Reaction Forces During Reduced Gravity Running in Parabolic Flight.

Science.gov (United States)

Cavanagh, Peter; Rice, Andrea; Glauberman, Molly; Sudduth, Amanda; Cherones, Arien; Davis, Shane; Lewis, Michael; Hanson, Andrea; Wilt, Grier

2017-08-01

Treadmills have been employed as both a form of exercise and a countermeasure to prevent changes in the musculoskeletal system on almost all NASA missions and many Russian missions since the early Space Shuttle flights. It is possible that treadmills may also be part of exercise programs on future Mars missions and that they may be a component of exercise facilities in lunar or Martian habitats. In order to determine if the ambient gravity on these destinations will provide osteogenic effects while performing exercise on a treadmill, ground reactions forces (GRFs) were measured on eight subjects (six women and two men) running at 6 mph during parabolic flight in Martian and lunar gravity conditions. On average, stride length increased as gravity decreased. The first and second peaks of the GRFs decreased by 0.156 and 0.196 bodyweights, respectively, per 1/10 g change in ambient gravity. Based on comparisons with previously measured GRF during loaded treadmill running on the International Space Station, we conclude that unloaded treadmill running under lunar and Martian conditions during exploration missions is not likely to be an osteo-protective exercise.Cavanagh P, Rice A, Glauberman M, Sudduth A, Cherones A, Davis S, Lewis M, Hanson A, Wilt G. Ground reaction forces during reduced gravity running in parabolic flight. Aerosp Med Hum Perform. 2017; 88(8):730-736.

Existence of the Optimal Control for Stochastic Boundary Control Problems Governed by Semilinear Parabolic Equations

Directory of Open Access Journals (Sweden)

Weifeng Wang

2014-01-01

Full Text Available We study an optimal control problem governed by a semilinear parabolic equation, whose control variable is contained only in the boundary condition. An existence theorem for the optimal control is obtained.

Reduced differential transform method for partial differential equations within local fractional derivative operators

Directory of Open Access Journals (Sweden)

Hossein Jafari

2016-04-01

Full Text Available The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations.

Numerical solution of the problems for plates on partial internal supports of complicated configurations

International Nuclear Information System (INIS)

Quang A, Dang; Hai, Truong Ha

2014-01-01

Very recently in the work S imple Iterative Method for Solving Problems for Plates with Partial Internal Supports, Journal of Engineering Mathematics, DOI: 10.1007/s10665-013-9652-7 (in press) , we proposed a numerical method for solving some problems of plates on one and two line partial internal supports (LPIS). In the essence they are problems with strongly mixed boundary conditions for biharmonic equation. Using this method we reduced the problems to a sequence of boundary value problems for the Poisson equation with weakly mixed boundary conditions, which are easily solved numerically. The advantages of the method over other ones were shown. In this paper we apply the method to plates on internal supports of more complicated configurations. Namely, we consider the case of three LPIS and the case of the cross support. The convergence of the method is established theoretically and its efficiency is confirmed on numerical experiments

A "feasible direction" search for Lineal Programming problem solving

Directory of Open Access Journals (Sweden)

Jaime U Malpica Angarita

2003-07-01

Full Text Available The study presents an approach to solve linear programming problems with no artificial variables. A primal linear minimization problem is standard form and its associated dual linear maximization problem are used. Initially, the dual (or a partial dual program is solved by a "feasible direction" search, where the Karush-Kuhn-Tucker conditions help to verify its optimality and then its feasibility. The "feasible direction" search exploits the characteristics of the convex polyhedron (or prototype formed by the dual program constraints to find a starting point and then follows line segments, whose directions are found in afine subspaces defined by boundary hyperplanes of polyhedral faces, to find next points up to the (an optimal one. Them, the remaining dual constraints not satisfaced at that optimal dual point, if there are any, are handled as nonbasic variables of the primal program, which is to be solved by such "feasible direction" search.

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II

Science.gov (United States)

Shertzer, J.; Temkin, A.

2003-01-01

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE) can be reduced to a 2d partial differential equation (pde), and was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation. The resultant equation can be reduced to a pair of coupled pde's, to which the finite element method can still be applied. The resultant scattering amplitudes, both singlet and triplet, as a function of angle can be calculated for various energies. The results are in excellent agreement with converged partial wave results.

Stability and instability of stationary solutions for sublinear parabolic equations

Science.gov (United States)

Kajikiya, Ryuji

2018-01-01

In the present paper, we study the initial boundary value problem of the sublinear parabolic equation. We prove the existence of solutions and investigate the stability and instability of stationary solutions. We show that a unique positive and a unique negative stationary solutions are exponentially stable and give the exact exponent. We prove that small stationary solutions are unstable. For one space dimensional autonomous equations, we elucidate the structure of stationary solutions and study the stability of all stationary solutions.

Perturbation of parabolic kinetics resulting from the accumulation of stress in protective oxide layers

International Nuclear Information System (INIS)

Evans, H.E.; Norfolk, D.J.; Swan, T.

1978-01-01

A frequent observation in metal oxidation is the development of subparabolic kinetics, variously described as cubic or quartic. Although a number of detailed mechanisms have been proposed to account for this effect, none seem generally applicable. A model is presented of the oxidation process which is divorced from such restrictions. It is argued that deviations from parabolic behavior occur as a result of the concurrent development of stresses within the oxide. It is shown that the presence of stress fields can influence significantly the rate of transport of vacancy defects within the oxide such that tensile stresses produce positive deviations and compressive stresses, negative deviations from parabolic behavior. The model is applied in detail to Zircaloy-2 oxidation at 773 0 K. It is predicted that the kinetics should be insensitive to the oxygen potential of the environment and this has been confirmed by previous experimental work. 31 refs

Finite-dimensional global attractors for parabolic nonlinear equations with state-dependent delay

Czech Academy of Sciences Publication Activity Database

Chueshov, I.; Rezunenko, Oleksandr

2015-01-01

Roč. 14, č. 5 (2015), s. 1685-1704 ISSN 1534-0392 R&D Projects: GA ČR GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Parabolic evolution equations * state-dependent delay * global attractor * finite-dimension * exponential attractor Subject RIV: BC - Control Systems Theory Impact factor: 0.926, year: 2015 http://library.utia.cas.cz/separaty/2015/AS/rezunenko-0444705.pdf

Multigrid methods for partial differential equations - a short introduction

International Nuclear Information System (INIS)

Linden, J.; Stueben, K.

1993-01-01

These notes summarize the multigrid methods and emphasis is laid on the algorithmic concepts of multigrid for solving linear and non-linear partial differential equations. In this paper there is brief description of the basic structure of multigrid methods. Detailed introduction is also contained with applications to VLSI process simulation. (A.B.)

On a non classical oblique derivative problem for parabolic singular integro-differential operators

International Nuclear Information System (INIS)

Nguyen Minh Chuong; Le Quang Trung

1989-10-01

In this paper an oblique derivative problem for parabolic singular integro-differential operators was studied. In this problem the direction of the derivative may be tangent to the boundary of the domain. By the large parameter method theorems of existence and uniqueness of solutions of the problem were obtained. (author). 10 refs

Roy-Steiner equations for {pi}N scattering - The Muskhelishvili-Omnes problem for the t-channel partial waves

Energy Technology Data Exchange (ETDEWEB)

Ditsche, Christoph; Hoferichter, Martin; Kubis, Bastian [Helmholtz-Institut fuer Strahlen- und Kernphysik (Theorie), Universitaet Bonn (Germany); Bethe Center for Theoretical Physics, Bonn (Germany); Meissner, Ulf G. [Helmholtz-Institut fuer Strahlen- und Kernphysik (Theorie), Universitaet Bonn (Germany); Institut fuer Kernphysik (Theorie), Institute for Advanced Simulations, and Juelich Center for Hadron Physics, Forschungszentrum Juelich, D-52425 Juelich (Germany); Bethe Center for Theoretical Physics, Bonn (Germany)

2011-07-01

Starting from (subtracted) hyperbolic dispersion relations for {pi}N scattering, which are based on the general principles of Lorentz invariance, unitarity, crossing and analyticity as well as isospin symmetry, we propose a closed system of (subtracted) hyperbolic partial wave dispersion relations for the partial waves f{sup I}{sub l{+-}}({radical}(s)) of the s-channel reaction {pi}N{yields}{pi}N and the partial waves f{sup J}{sub {+-}}(t) of the t-channel reaction {pi}{pi}{yields} anti NN in the spirit of Roy and Steiner. A key step to the ultimate goal of solving this Roy-Steiner system is to first solve the corresponding (subtracted) Muskhelishvili-Omnes problem with inelasticities and a finite matching point for the lowest t-channel partial waves f{sup 0}{sub +}(t), f{sup 1}{sub {+-}}(t). The recent status of this ongoing effort is presented.

Lagrange-Noether method for solving second-order differential equations

Institute of Scientific and Technical Information of China (English)

Wu Hui-Bin; Wu Run-Heng

2009-01-01

The purpose of this paper is to provide a new method called the Lagrange-Noether method for solving second-order differential equations. The method is,firstly,to write the second-order differential equations completely or partially in the form of Lagrange equations,and secondly,to obtain the integrals of the equations by using the Noether theory of the Lagrange system. An example is given to illustrate the application of the result.

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II: Inclusion of Exchange

Science.gov (United States)

Shertzer, Janine; Temkin, A.

2003-01-01

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE), which can be reduced to a 2d partial differential equation (pde), was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation, which is reducible to a pair of coupled pde's. The resultant scattering amplitudes, both singlet and triplet, calculated as a function of energy are in excellent agreement with converged partial wave results.

A gradient estimate for solutions to parabolic equations with discontinuous coefficients

OpenAIRE

Fan, Jishan; Kim, Kyoungsun; Nagayasu, Sei; Nakamura, Gen

2011-01-01

Li-Vogelius and Li-Nirenberg gave a gradient estimate for solutions of strongly elliptic equations and systems of divergence forms with piecewise smooth coefficients, respectively. The discontinuities of the coefficients are assumed to be given by manifolds of codimension 1, which we called them emph{manifolds of discontinuities}. Their gradient estimate is independent of the distances between manifolds of discontinuities. In this paper, we gave a parabolic version of their results. T...

The effect and contribution of wind generated rotation on outlet temperature and heat gain of LS-2 parabolic trough solar collector

Directory of Open Access Journals (Sweden)

Sadaghiyani Omid Karimi

2013-01-01

Full Text Available The Monte Carlo ray tracing method is applied and coupled with finite volume numerical methods to study effect of rotation on outlet temperature and heat gain of LS-2 parabolic trough concentrator (PTC. Based on effect of sunshape, curve of mirror and use of MCRT, heat flux distribution around of inner wall of evacuated tube is calculated. After calculation of heat flux, the geometry of LS-2 Luz collector is created and finite volume method is applied to simulate. The obtained results are compared with Dudley et al test results for irrotational cases to validate these numerical solving models. Consider that, for rotational models ,the solving method separately with K.S. Ball's results. In this work, according to the structure of mentioned collector, we use plug as a flow restriction. In the rotational case studies, the inner wall rotates with different angular speeds. We compare results of rotational collector with irrotational. Also for these two main states, the location of plug changed then outlet temperature and heat gain of collector are studied. The results show that rotation have positive role on heat transfer processing and the rotational plug in bottom half of tube have better effectual than upper half of tube. Also the contribution of rotation is calculated in the all of case studies. Working fluid of these study is one of the oil derivatives namely Syltherm-800. The power of wind can be used to rotate tube of collector.

Solving Optimal Control Problem of Monodomain Model Using Hybrid Conjugate Gradient Methods

Directory of Open Access Journals (Sweden)

Kin Wei Ng

2012-01-01

Full Text Available We present the numerical solutions for the PDE-constrained optimization problem arising in cardiac electrophysiology, that is, the optimal control problem of monodomain model. The optimal control problem of monodomain model is a nonlinear optimization problem that is constrained by the monodomain model. The monodomain model consists of a parabolic partial differential equation coupled to a system of nonlinear ordinary differential equations, which has been widely used for simulating cardiac electrical activity. Our control objective is to dampen the excitation wavefront using optimal applied extracellular current. Two hybrid conjugate gradient methods are employed for computing the optimal applied extracellular current, namely, the Hestenes-Stiefel-Dai-Yuan (HS-DY method and the Liu-Storey-Conjugate-Descent (LS-CD method. Our experiment results show that the excitation wavefronts are successfully dampened out when these methods are used. Our experiment results also show that the hybrid conjugate gradient methods are superior to the classical conjugate gradient methods when Armijo line search is used.

Parabolic Trough Solar Collector Initial Trials

Directory of Open Access Journals (Sweden)

Ghalya Pikra

2012-03-01

Full Text Available This paper discusses initial trials of parabolic trough solar collector (PTSC in Bandung. PTSC model consists of concentrator, absorber and tracking system. Concentrator designs are made with 2m aperture width, 6m length and 0.75m focal distance. The design is equipped with an automatic tracking system which is driven using 12V and 24Watt DC motor with 0.0125rpm rotational speed. Absorber/receiver is designed with evacuated tube type, with 1 inch core diameter and tube made of AISI304 and coated with black oxide, the outer tube is borosilicate glass with a 70 mm diameter and 1.5 m length. Working fluid stored in single type of thermal storage tank, a single phase with 37.7 liter volume. PTSC model testing carried out for 2 hours and 10 minutes produces heat output and input of 11.5 kW and 0.64 kW respectively. 

Beryllium parabolic refractive x-ray lenses

International Nuclear Information System (INIS)

Lengeler, B.; Schroer, C.G.; Kuhlmann, M.; Benner, B.; Guenzler, T.F.; Kurapova, O.; Somogyi, A.; Snigirev, A.; Snigireva, I.

2004-01-01

Parabolic refractive x-ray lenses are novel optical components for the hard x-ray range from about 5 keV to about 120 keV. They focus in both directions. They are compact, robust, and easy to align and to operate. They can be used like glass lenses are used for visible light, the main difference being that the numerical aperture N.A. is much smaller than 1 (of order 10-4 to 10-3). Their main applications are in micro- and nanofocusing, in imaging by absorption and phase contrast and in fluorescence mode. In combination with tomography they allow for 3-dimensional imaging of opaque media with submicrometer resolution. Finally, they can be used in speckle spectroscopy by means of coherent x-ray scattering. Beryllium as lens material strongly enhances the transmission and the field of view as compared to aluminium. With increased N.A. the lateral resolution is also considerably improved with Be lenses. References to a number of applications are given

Stability of mixing layers

Science.gov (United States)

Tam, Christopher; Krothapalli, A

1993-01-01

The research program for the first year of this project (see the original research proposal) consists of developing an explicit marching scheme for solving the parabolized stability equations (PSE). Performing mathematical analysis of the computational algorithm including numerical stability analysis and the determination of the proper boundary conditions needed at the boundary of the computation domain are implicit in the task. Before one can solve the parabolized stability equations for high-speed mixing layers, the mean flow must first be found. In the past, instability analysis of high-speed mixing layer has mostly been performed on mean flow profiles calculated by the boundary layer equations. In carrying out this project, it is believed that the boundary layer equations might not give an accurate enough nonparallel, nonlinear mean flow needed for parabolized stability analysis. A more accurate mean flow can, however, be found by solving the parabolized Navier-Stokes equations. The advantage of the parabolized Navier-Stokes equations is that its accuracy is consistent with the PSE method. Furthermore, the method of solution is similar. Hence, the major part of the effort of the work of this year has been devoted to the development of an explicit numerical marching scheme for the solution of the Parabolized Navier-Stokes equation as applied to the high-seed mixing layer problem.

Chosen interval methods for solving linear interval systems with special type of matrix

Science.gov (United States)

Szyszka, Barbara

2013-10-01

The paper is devoted to chosen direct interval methods for solving linear interval systems with special type of matrix. This kind of matrix: band matrix with a parameter, from finite difference problem is obtained. Such linear systems occur while solving one dimensional wave equation (Partial Differential Equations of hyperbolic type) by using the central difference interval method of the second order. Interval methods are constructed so as the errors of method are enclosed in obtained results, therefore presented linear interval systems contain elements that determining the errors of difference method. The chosen direct algorithms have been applied for solving linear systems because they have no errors of method. All calculations were performed in floating-point interval arithmetic.

Impurity magnetopolaron in a parabolic quantum dot: the squeezed-state variational approach

International Nuclear Information System (INIS)

Kandemir, B S; Cetin, A

2005-01-01

We present a calculation of the ground-state binding energy of an impurity magnetopolaron confined in a three-dimensional (3D) parabolic quantum dot potential, in the framework of a variational approach based on two successive canonical transformations. First, we apply a displaced-oscillator type unitary transformation to diagonalize the relevant Froehlich Hamiltonian. Second, a single-mode squeezed-state transformation is introduced to deal with bilinear terms arising from the first transformation. Finally, the parameters of these transformations together with the parameters included in the electronic trial wavefunction are determined variationally to obtain the ground-state binding energy of an impurity magnetopolaron confined in a 3D parabolic quantum dot potential. Our approach has two advantages: first, the displaced-oscillator transformation allows one to obtain results valid for whole range of electron-phonon coupling strength since it is a special combination of Lee-Low-Pines and Huybrechts (LLP-H) canonical transformations, and second, the later transformation improves all-coupling results. It has been shown that the effects of quadratic terms arising from the all-coupling approach are very important and should be taken into account in studying the size-dependent physical properties of nanostructured materials

Analysis of the Efficacy of an Intervention to Improve Parent-Adolescent Problem Solving.

Science.gov (United States)

Semeniuk, Yulia Yuriyivna; Brown, Roger L; Riesch, Susan K

2016-07-01

We conducted a two-group longitudinal partially nested randomized controlled trial to examine whether young adolescent youth-parent dyads participating in Mission Possible: Parents and Kids Who Listen, in contrast to a comparison group, would demonstrate improved problem-solving skill. The intervention is based on the Circumplex Model and Social Problem-Solving Theory. The Circumplex Model posits that families who are balanced, that is characterized by high cohesion and flexibility and open communication, function best. Social Problem-Solving Theory informs the process and skills of problem solving. The Conditional Latent Growth Modeling analysis revealed no statistically significant differences in problem solving among the final sample of 127 dyads in the intervention and comparison groups. Analyses of effect sizes indicated large magnitude group effects for selected scales for youth and dyads portraying a potential for efficacy and identifying for whom the intervention may be efficacious if study limitations and lessons learned were addressed. © The Author(s) 2016.

A parabolic model of drag coefficient for storm surge simulation in the South China Sea

Science.gov (United States)

Peng, Shiqiu; Li, Yineng

2015-01-01

Drag coefficient (Cd) is an essential metric in the calculation of momentum exchange over the air-sea interface and thus has large impacts on the simulation or forecast of the upper ocean state associated with sea surface winds such as storm surges. Generally, Cd is a function of wind speed. However, the exact relationship between Cd and wind speed is still in dispute, and the widely-used formula that is a linear function of wind speed in an ocean model could lead to large bias at high wind speed. Here we establish a parabolic model of Cd based on storm surge observations and simulation in the South China Sea (SCS) through a number of tropical cyclone cases. Simulation of storm surges for independent Tropical cyclones (TCs) cases indicates that the new parabolic model of Cd outperforms traditional linear models. PMID:26499262

A parabolic model of drag coefficient for storm surge simulation in the South China Sea

Science.gov (United States)

Peng, Shiqiu; Li, Yineng

2015-10-01

Drag coefficient (Cd) is an essential metric in the calculation of momentum exchange over the air-sea interface and thus has large impacts on the simulation or forecast of the upper ocean state associated with sea surface winds such as storm surges. Generally, Cd is a function of wind speed. However, the exact relationship between Cd and wind speed is still in dispute, and the widely-used formula that is a linear function of wind speed in an ocean model could lead to large bias at high wind speed. Here we establish a parabolic model of Cd based on storm surge observations and simulation in the South China Sea (SCS) through a number of tropical cyclone cases. Simulation of storm surges for independent Tropical cyclones (TCs) cases indicates that the new parabolic model of Cd outperforms traditional linear models.

Simulation of the parabolic trough solar energy generation system with Organic Rankine Cycle

International Nuclear Information System (INIS)

He, Ya-Ling; Mei, Dan-Hua; Tao, Wen-Quan; Yang, Wei-Wei; Liu, Huai-Liang

2012-01-01

Highlights: ► A parabolic trough solar power generation system with ORC is numerically simulated. ► The effects of key parameters on collector field and system performance are studied. ► Collector heat loss increases with small absorber and glass tube interlayer pressure. ► Heat collecting efficiency increases with initial increase of absorber HTO flow rate. ► Recommended thermal storage system volumes are different in year four typical days. -- Abstract: A model for a typical parabolic trough solar thermal power generation system with Organic Rankine Cycle (PT-SEGS–ORC) was built within the transient energy simulation package TRNSYS, which is formed by integrating several submodels for the trough collector system, the single-tank thermal storage system, the auxiliary power system and the heat-electricity conversion system. With this model, the effects of several key parameters, including the interlayer pressure between the absorber tube and the glass tube (p inter ), the flow rate of high temperature oil in the absorber tube (v), solar radiation intensity (I dn ) and incidence angle (θ), on the performance of the parabolic trough collector field based on the meteorological data of Xi’an city were examined. The study shows that the heat loss of the solar collector (q loss ) increases sharply with the increase in p inter at beginning and then reaches to an approximately constant value. The variation of heat collecting efficiency (η hc ) with v is quite similar to the variation of q loss with p inter . However, I dn and θ exhibit opposite effect on η hc . In addition, it is found that the optimal volume of the thermal storage system is sensitively dependent on the solar radiation intensity. The optimal volumes are 100, 150, 50, and 0 m 3 for spring equinox, summer solstice, autumnal equinox and winter solstice, respectively.

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (3).

Science.gov (United States)

Murase, Kenya

2016-01-01

In this issue, simultaneous differential equations were introduced. These differential equations are often used in the field of medical physics. The methods for solving them were also introduced, which include Laplace transform and matrix methods. Some examples were also introduced, in which Laplace transform and matrix methods were applied to solving simultaneous differential equations derived from a three-compartment kinetic model for analyzing the glucose metabolism in tissues and Bloch equations for describing the behavior of the macroscopic magnetization in magnetic resonance imaging.In the next (final) issue, partial differential equations and various methods for solving them will be introduced together with some examples in medical physics.

Stability estimates for solution of IBVP to fractional parabolic differential and difference equations

Science.gov (United States)

Ashyralyev, Allaberen; Cakir, Zafer

2016-08-01

In this work, we investigate initial-boundary value problems for fractional parabolic equations with the Neumann boundary condition. Stability estimates for the solution of this problem are established. Difference schemes for approximate solution of initial-boundary value problem are constructed. Furthermore, we give theorem on coercive stability estimates for the solution of the difference schemes.

Problem-Solving Skills Appraisal Mediates Hardiness and Suicidal Ideation among Malaysian Undergraduate Students

Science.gov (United States)

Abdollahi, Abbas; Talib, Mansor Abu; Yaacob, Siti Nor; Ismail, Zanariah

2015-01-01

Objectives Recent evidence suggests that suicidal ideation is increased among university students, it is essential to increase our knowledge concerning the etiology of suicidal ideation among university students. This study was conducted to examine the relationships between problem-solving skills appraisal, hardiness, and suicidal ideation among university students. In addition, this study was conducted to examine problem-solving skills appraisal (including the three components of problem-solving confidence, approach-avoidance style, and personal control of emotion) as a potential mediator between hardiness and suicidal ideation. Methods The participants consisted of 500 undergraduate students from Malaysian public universities. Results Structural Equation Modelling (SEM) estimated that undergraduate students with lower hardiness, poor problem-solving confidence, external personal control of emotion, and avoiding style was associated with higher suicidal ideation. Problem-solving skills appraisal (including the three components of problem-solving confidence, approach-avoidance style, and personal control of emotion) partially mediated the relationship between hardiness and suicidal ideation. Conclusion These findings underline the importance of studying mediating processes that explain how hardiness affects suicidal ideation. PMID:25830229

Problem-solving skills appraisal mediates hardiness and suicidal ideation among malaysian undergraduate students.

Science.gov (United States)

Abdollahi, Abbas; Talib, Mansor Abu; Yaacob, Siti Nor; Ismail, Zanariah

2015-01-01

Recent evidence suggests that suicidal ideation is increased among university students, it is essential to increase our knowledge concerning the etiology of suicidal ideation among university students. This study was conducted to examine the relationships between problem-solving skills appraisal, hardiness, and suicidal ideation among university students. In addition, this study was conducted to examine problem-solving skills appraisal (including the three components of problem-solving confidence, approach-avoidance style, and personal control of emotion) as a potential mediator between hardiness and suicidal ideation. The participants consisted of 500 undergraduate students from Malaysian public universities. Structural Equation Modelling (SEM) estimated that undergraduate students with lower hardiness, poor problem-solving confidence, external personal control of emotion, and avoiding style was associated with higher suicidal ideation. Problem-solving skills appraisal (including the three components of problem-solving confidence, approach-avoidance style, and personal control of emotion) partially mediated the relationship between hardiness and suicidal ideation. These findings underline the importance of studying mediating processes that explain how hardiness affects suicidal ideation.

An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems

KAUST Repository

Memon, Sajid; Nataraj, Neela; Pani, Amiya Kumar

2012-01-01

In this article, a posteriori error estimates are derived for mixed finite element Galerkin approximations to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstructions, a posteriori error estimates in L∞(L2)- and L2(L2)-norms for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on a backward Euler method, a completely discrete scheme is analyzed and a posteriori error bounds are derived, which improves upon earlier results on a posteriori estimates of mixed finite element approximations to parabolic problems. Results of numerical experiments verifying the efficiency of the estimators have also been provided. © 2012 Society for Industrial and Applied Mathematics.

Hypogravity Research and Educational Parabolic Flight Activities Conducted in Barcelona: a new Hub of Innovation in Europe

Science.gov (United States)

Perez-Poch, Antoni; González, Daniel Ventura; López, David

2016-12-01

We report on different research and educational activities related to parabolic flights conducted in Barcelona since 2008. We use a CAP10B single-engine aerobatic aircraft flying out of Sabadell Airport and operating in visual flight conditions providing up to 8 seconds of hypogravity for each parabola. Aside from biomedical experiments being conducted, different student teams have flown in parabolic flights in the framework of the international contest `Barcelona Zero-G Challenge', and have published their results in relevant symposiums and scientific journals. The platform can certainly be a good testbed for a proof-of-concept before accessing other microgravity platforms, and has proved to be excellent for motivational student campaigns.

Optimal partial-arcs in VMAT treatment planning

International Nuclear Information System (INIS)

Wala, Jeremiah; Salari, Ehsan; Chen Wei; Craft, David

2012-01-01

We present a method for improving the delivery efficiency of VMAT by extending the recently published VMAT treatment planning algorithm vmerge to automatically generate optimal partial-arc plans. A high-quality initial plan is created by solving a convex multicriteria optimization problem using 180 equi-spaced beams. This initial plan is used to form a set of dose constraints, and a set of partial-arc plans is created by searching the space of all possible partial-arc plans that satisfy these constraints. For each partial-arc, an iterative fluence map merging and sequencing algorithm (vmerge) is used to improve the delivery efficiency. Merging continues as long as the dose quality is maintained above a user-defined threshold. The final plan is selected as the partial-arc with the lowest treatment time. The complete algorithm is called pmerge. Partial-arc plans are created using pmerge for a lung, liver and prostate case, with final treatment times of 127, 245 and 147 s. Treatment times using full arcs with vmerge are 211, 357 and 178 s. The mean doses to the critical structures for the vmerge and pmerge plans are kept within 5% of those in the initial plan, and the target volume covered by the prescription isodose is maintained above 98% for the pmerge and vmerge plans. Additionally, we find that the angular distribution of fluence in the initial plans is predictive of the start and end angles of the optimal partial-arc. We conclude that VMAT delivery efficiency can be improved by employing partial-arcs without compromising dose quality, and that partial-arcs are most applicable to cases with non-centralized targets. (paper)

Optical nonlinearities associated to applied electric fields in parabolic two-dimensional quantum rings

International Nuclear Information System (INIS)

Duque, C.M.; Morales, A.L.; Mora-Ramos, M.E.; Duque, C.A.

2013-01-01

The linear and nonlinear optical absorption as well as the linear and nonlinear corrections to the refractive index are calculated in a disc shaped quantum dot under the effect of an external magnetic field and parabolic and inverse square confining potentials. The exact solutions for the two-dimensional motion of the conduction band electrons are used as the basis for a perturbation-theory treatment of the effect of a static applied electric field. In general terms, the variation of one of the different potential energy parameters – for a fixed configuration of the remaining ones – leads to either blueshifts or redshifts of the resonant peaks as well as to distinct rates of change for their amplitudes. -- Highlights: • Optical absorption and corrections to the refractive in quantum dots. • Electric and magnetic field and parabolic and inverse square potentials. • Perturbation-theory treatment of the effect of the electric field. • Induced blueshifts or redshifts of the resonant peaks are studied. • Evolution of rates of change for amplitudes of resonant peaks

Optical nonlinearities associated to applied electric fields in parabolic two-dimensional quantum rings

Energy Technology Data Exchange (ETDEWEB)

Duque, C.M., E-mail: cduque@fisica.udea.edu.co [Instituto de Física, Universidad de Antioquia, AA 1226, Medellín (Colombia); Morales, A.L. [Instituto de Física, Universidad de Antioquia, AA 1226, Medellín (Colombia); Mora-Ramos, M.E. [Instituto de Física, Universidad de Antioquia, AA 1226, Medellín (Colombia); Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, CP 62209, Cuernavaca, Morelos (Mexico); Duque, C.A. [Instituto de Física, Universidad de Antioquia, AA 1226, Medellín (Colombia)

2013-11-15

The linear and nonlinear optical absorption as well as the linear and nonlinear corrections to the refractive index are calculated in a disc shaped quantum dot under the effect of an external magnetic field and parabolic and inverse square confining potentials. The exact solutions for the two-dimensional motion of the conduction band electrons are used as the basis for a perturbation-theory treatment of the effect of a static applied electric field. In general terms, the variation of one of the different potential energy parameters – for a fixed configuration of the remaining ones – leads to either blueshifts or redshifts of the resonant peaks as well as to distinct rates of change for their amplitudes. -- Highlights: • Optical absorption and corrections to the refractive in quantum dots. • Electric and magnetic field and parabolic and inverse square potentials. • Perturbation-theory treatment of the effect of the electric field. • Induced blueshifts or redshifts of the resonant peaks are studied. • Evolution of rates of change for amplitudes of resonant peaks.

Control scheme for direct steam generation in parabolic troughs under recirculation operation mode

Energy Technology Data Exchange (ETDEWEB)

Valenzuela, L.; Zarza, E. [CIEMAT, Plataforma Solar de Almeria, Ctra. Senes s/n, P.O. Box 22, E-04200 Tabernas, Almeria (Spain); Berenguel, M. [Universidad de Almeria, Dpto. Lenguajes y Computacion, Ctra. Sacramento s/n, E-04120 Almeria (Spain); Camacho, E.F. [Universidad de Sevilla, Dpto. de Ingenieria de Sistemas y Automatica, Camino de los Descubrimientos s/n, E-41092 Sevilla (Spain)

2006-01-15

Electricity production using solar thermal energy is one of the main research areas at present in the field of renewable energies, these systems being characterised by the need of reliable control systems aimed at maintaining desired operating conditions in the face of changes in solar radiation, which is the main source of energy. A new prototype of solar system with parabolic trough collectors was implemented at the Plataforma Solar de Almeria (PSA, South-East Spain) to investigate the direct steam generation process under real solar conditions in the parabolic solar collector field of a thermal power plant prototype. This paper presents details and some results of the application of a control scheme designed and tested for the recirculation operation mode, for which the main objective is to obtain steam at constant temperature and pressure at the outlet of the solar field, so that changes produced in the inlet water conditions and/or solar radiation will only affect the amount of steam produced by the solar field. The steam quality and consequently the nominal efficiency of the plant are thus maintained. (author)

Convergence criteria for systems of nonlinear elliptic partial differential equations

International Nuclear Information System (INIS)

Sharma, R.K.

1986-01-01

This thesis deals with convergence criteria for a special system of nonlinear elliptic partial differential equations. A fixed-point algorithm is used, which iteratively solves one linearized elliptic partial differential equation at a time. Conditions are established that help foresee the convergence of the algorithm. Under reasonable hypotheses it is proved that the algorithm converges for such nonlinear elliptic systems. Extensive experimental results are reported and they show the algorithm converges in a wide variety of cases and the convergence is well correlated with the theoretical conditions introduced in this thesis

Clawpack: Building an open source ecosystem for solving hyperbolic PDEs

Science.gov (United States)

Iverson, Richard M.; Mandli, K.T.; Ahmadia, Aron J.; Berger, M.J.; Calhoun, Donna; George, David L.; Hadjimichael, Y.; Ketcheson, David I.; Lemoine, Grady L.; LeVeque, Randall J.

2016-01-01

Clawpack is a software package designed to solve nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. The package includes a number of variants aimed at different applications and user communities. Clawpack has been actively developed as an open source project for over 20 years. The latest major release, Clawpack 5, introduces a number of new features and changes to the code base and a new development model based on GitHub and Git submodules. This article provides a summary of the most significant changes, the rationale behind some of these changes, and a description of our current development model. Clawpack: building an open source ecosystem for solving hyperbolic PDEs.

Solving nonlinear, High-order partial differential equations using a high-performance isogeometric analysis framework

KAUST Repository

Cortes, Adriano Mauricio; Vignal, Philippe; Sarmiento, Adel; Garcí a, Daniel O.; Collier, Nathan; Dalcin, Lisandro; Calo, Victor M.

2014-01-01

In this paper we present PetIGA, a high-performance implementation of Isogeometric Analysis built on top of PETSc. We show its use in solving nonlinear and time-dependent problems, such as phase-field models, by taking advantage of the high-continuity of the basis functions granted by the isogeometric framework. In this work, we focus on the Cahn-Hilliard equation and the phase-field crystal equation.

Multisubband electron mobility in a parabolic quantum well structure under the influence of an applied electric field

International Nuclear Information System (INIS)

Sahoo, N.; Sahu, T.

2014-01-01

We study the multisubband electron mobility in a barrier delta doped Al x Ga 1−x As parabolic quantum well structure under the influence of an applied electric field perpendicular to the interface plane. We consider the alloy fraction x = 0.3 for barriers and vary x from 0.0 to 0.1 for the parabolic well. Electrons diffuse into the well and confine within the triangular like potentials near the interfaces due to Coulomb interaction with ionized donors. The parabolic structure potential, being opposite in nature, partly compensates the Coulomb potential. The external electric field further amends the potential structure leading to an asymmetric potential profile. Accordingly the energy levels, wave functions and occupation of subbands change. We calculate low temperature electron mobility as a function of the electric field and show that when two subbands are occupied, the mobility is mostly dominated by ionised impurity scattering mediated by intersubband effects. As the field increases transition from double subband to single subband occupancy occurs. A sudden enhancement in mobility is obtained due to curtailment of intersubband effects. Thereafter the mobility is governed by both impurity and alloy disorder scatterings. Our analysis of mobility as a function of the electric field for different structural parameters shows interesting results. (semiconductor physics)

Efficient Method for Calculating the Composite Stiffness of Parabolic Leaf Springs with Variable Stiffness for Vehicle Rear Suspension

Directory of Open Access Journals (Sweden)

Wen-ku Shi

2016-01-01

Full Text Available The composite stiffness of parabolic leaf springs with variable stiffness is difficult to calculate using traditional integral equations. Numerical integration or FEA may be used but will require computer-aided software and long calculation times. An efficient method for calculating the composite stiffness of parabolic leaf springs with variable stiffness is developed and evaluated to reduce the complexity of calculation and shorten the calculation time. A simplified model for double-leaf springs with variable stiffness is built, and a composite stiffness calculation method for the model is derived using displacement superposition and material deformation continuity. The proposed method can be applied on triple-leaf and multileaf springs. The accuracy of the calculation method is verified by the rig test and FEA analysis. Finally, several parameters that should be considered during the design process of springs are discussed. The rig test and FEA analytical results indicate that the calculated results are acceptable. The proposed method can provide guidance for the design and production of parabolic leaf springs with variable stiffness. The composite stiffness of the leaf spring can be calculated quickly and accurately when the basic parameters of the leaf spring are known.

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

Energy Technology Data Exchange (ETDEWEB)

Addona, Davide, E-mail: d.addona@campus.unimib.it [Università degli Studi di Milano Bicocca, (MILANO BICOCCA) Dipartimento di Matematica (Italy)

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.

Student Solutions Manual to Boundary Value Problems and Partial Differential Equations

CERN Document Server

Powers, David L

2005-01-01

This student solutions manual accompanies the text, Boundary Value Problems and Partial Differential Equations, 5e. The SSM is available in print via PDF or electronically, and provides the student with the detailed solutions of the odd-numbered problems contained throughout the book.Provides students with exercises that skillfully illustrate the techniques used in the text to solve science and engineering problemsNearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercisesMany exercises based on current engineering applications

On a second order of accuracy stable difference scheme for the solution of a source identification problem for hyperbolic-parabolic equations

Science.gov (United States)

Ashyralyyeva, Maral; Ashyraliyev, Maksat

2016-08-01

In the present paper, a second order of accuracy difference scheme for the approximate solution of a source identification problem for hyperbolic-parabolic equations is constructed. Theorem on stability estimates for the solution of this difference scheme and their first and second order difference derivatives is presented. In applications, this abstract result permits us to obtain the stability estimates for the solutions of difference schemes for approximate solutions of two source identification problems for hyperbolic-parabolic equations.

Solving a novel confinement problem by spartaeine salticids that are predisposed to solve problems in the context of predation.

Science.gov (United States)

Cross, Fiona R; Jackson, Robert R

2015-03-01

Intricate predatory strategies are widespread in the salticid subfamily Spartaeinae. The hypothesis we consider here is that the spartaeine species that are proficient at solving prey-capture problems are also proficient at solving novel problems. We used nine species from this subfamily in our experiments. Eight of these species (two Brettus, one Cocalus, three Cyrba, two Portia) are known for specialized invasion of other spiders' webs and for actively choosing other spiders as preferred prey ('araneophagy'). Except for Cocalus, these species also use trial and error to derive web-based signals with which they gain dynamic fine control of the resident spider's behaviour ('aggressive mimicry').The ninth species, Paracyrba wanlessi, is not araneophagic and instead specializes at preying on mosquitoes. We presented these nine species with a novel confinement problem that could be solved by trial and error. The test spider began each trial on an island in a tray of water, with an atoll surrounding the island. From the island, the spider could choose between two potential escape tactics (leap or swim), but we decided at random before the trial which tactic would fail and which tactic would achieve partial success. Our findings show that the seven aggressive-mimic species are proficient at solving the confinement problem by repeating 'correct' choices and by switching to the alternative tactic after making an 'incorrect' choice. However, as predicted, there was no evidence of C. gibbosus or P. wanlessi, the two non-aggressive-mimic species, solving the confinement problem. We discuss these findings in the context of an often-made distinction between domain-specific and domain-general cognition.

Solution of partial differential equations by agent-based simulation

International Nuclear Information System (INIS)

Szilagyi, Miklos N

2014-01-01

The purpose of this short note is to demonstrate that partial differential equations can be quickly solved by agent-based simulation with high accuracy. There is no need for the solution of large systems of algebraic equations. This method is especially useful for quick determination of potential distributions and demonstration purposes in teaching electromagnetism. (letters and comments)

A regional and nonstationary model for partial duration series of extreme rainfall

DEFF Research Database (Denmark)

Gregersen, Ida Bülow; Madsen, Henrik; Rosbjerg, Dan

2017-01-01

as the explanatory variables in the regional and temporal domain, respectively. Further analysis of partial duration series with nonstationary and regional thresholds shows that the mean exceedances also exhibit a significant variation in space and time for some rainfall durations, while the shape parameter is found...... of extreme rainfall. The framework is built on a partial duration series approach with a nonstationary, regional threshold value. The model is based on generalized linear regression solved by generalized estimation equations. It allows a spatial correlation between the stations in the network and accounts...... furthermore for variable observation periods at each station and in each year. Marginal regional and temporal regression models solved by generalized least squares are used to validate and discuss the results of the full spatiotemporal model. The model is applied on data from a large Danish rain gauge network...

Telescopic projective methods for parabolic differential equations

CERN Document Server

Gear, C W

2003-01-01

Projective methods were introduced in an earlier paper [C.W. Gear, I.G. Kevrekidis, Projective Methods for Stiff Differential Equations: problems with gaps in their eigenvalue spectrum, NEC Research Institute Report 2001-029, available from http://www.neci.nj.nec.com/homepages/cwg/projective.pdf Abbreviated version to appear in SISC] as having potential for the efficient integration of problems with a large gap between two clusters in their eigenvalue spectrum, one cluster containing eigenvalues corresponding to components that have already been damped in the numerical solution and one corresponding to components that are still active. In this paper we introduce iterated projective methods that allow for explicit integration of stiff problems that have a large spread of eigenvalues with no gaps in their spectrum as arise in the semi-discretization of PDEs with parabolic components.

Telescopic projective methods for parabolic differential equations

International Nuclear Information System (INIS)

Gear, C.W.; Kevrekidis, Ioannis G.

2003-01-01

Projective methods were introduced in an earlier paper [C.W. Gear, I.G. Kevrekidis, Projective Methods for Stiff Differential Equations: problems with gaps in their eigenvalue spectrum, NEC Research Institute Report 2001-029, available from http://www.neci.nj.nec.com/homepages/cwg/projective.pdf Abbreviated version to appear in SISC] as having potential for the efficient integration of problems with a large gap between two clusters in their eigenvalue spectrum, one cluster containing eigenvalues corresponding to components that have already been damped in the numerical solution and one corresponding to components that are still active. In this paper we introduce iterated projective methods that allow for explicit integration of stiff problems that have a large spread of eigenvalues with no gaps in their spectrum as arise in the semi-discretization of PDEs with parabolic components

Exploiting partial knowledge for efficient model analysis

OpenAIRE

Macedo, Nuno; Cunha, Alcino; Pessoa, Eduardo José Dias

2017-01-01

The advancement of constraint solvers and model checkers has enabled the effective analysis of high-level formal specification languages. However, these typically handle a specification in an opaque manner, amalgamating all its constraints in a single monolithic verification task, which often proves to be a performance bottleneck. This paper addresses this issue by proposing a solving strategy that exploits user-provided partial knowledge, namely by assigning symbolic bounds to the problem’s ...

A Hierarchical Bayesian Setting for an Inverse Problem in Linear Parabolic PDEs with Noisy Boundary Conditions

KAUST Repository

Ruggeri, Fabrizio

2016-05-12

In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given prescribed initial condition. We show how to derive the joint likelihood function for the forward problem, given some measurements of the solution field subject to Gaussian noise. Given Gaussian priors for the time-dependent Dirichlet boundary values, we analytically marginalize the joint likelihood using the linearity of the equation. Our hierarchical Bayesian approach is fully implemented in an example that involves the heat equation. In this example, the thermal diffusivity is the unknown parameter. We assume that the thermal diffusivity parameter can be modeled a priori through a lognormal random variable or by means of a space-dependent stationary lognormal random field. Synthetic data are used to test the inference. We exploit the behavior of the non-normalized log posterior distribution of the thermal diffusivity. Then, we use the Laplace method to obtain an approximated Gaussian posterior and therefore avoid costly Markov Chain Monte Carlo computations. Expected information gains and predictive posterior densities for observable quantities are numerically estimated using Laplace approximation for different experimental setups.