Some problems of the calculation of three-dimensional boundary layer flows on general configurations

NASA Technical Reports Server (NTRS)

Cebeci, T.; Kaups, K.; Mosinskis, G. J.; Rehn, J. A.

1973-01-01

An accurate solution of the three-dimensional boundary layer equations over general configurations such as those encountered in aircraft and space shuttle design requires a very efficient, fast, and accurate numerical method with suitable turbulence models for the Reynolds stresses. The efficiency, speed, and accuracy of a three-dimensional numerical method together with the turbulence models for the Reynolds stresses are examined. The numerical method is the implicit two-point finite difference approach (Box Method) developed by Keller and applied to the boundary layer equations by Keller and Cebeci. In addition, a study of some of the problems that may arise in the solution of these equations for three-dimensional boundary layer flows over general configurations.

Lichnerowicz-type equations with sign-changing nonlinearities on complete manifolds with boundary

NASA Astrophysics Data System (ADS)

Albanese, Guglielmo; Rigoli, Marco

2017-12-01

We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary (M , ∂ M , 〈 , 〉) and nonlinear Neumann conditions. This kind of nonlinear problems arise quite naturally in the study of solutions for the Einstein-scalar field equations of General Relativity in the framework of the so called Conformal Method.

Variational formulation for Black-Scholes equations in stochastic volatility models

NASA Astrophysics Data System (ADS)

Gyulov, Tihomir B.; Valkov, Radoslav L.

2012-11-01

In this note we prove existence and uniqueness of weak solutions to a boundary value problem arising from stochastic volatility models in financial mathematics. Our settings are variational in weighted Sobolev spaces. Nevertheless, as it will become apparent our variational formulation agrees well with the stochastic part of the problem.

An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology

NASA Astrophysics Data System (ADS)

Beretta, Elena; Cavaterra, Cecilia; Cerutti, M. Cristina; Manzoni, Andrea; Ratti, Luca

2017-10-01

In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential in the myocardial tissue. The goal is the detection of an inhomogeneity \

Existence of solutions of a two-dimensional boundary value problem for a system of nonlinear equations arising in growing cell populations.

PubMed

Jeribi, Aref; Krichen, Bilel; Mefteh, Bilel

2013-01-01

In the paper [A. Ben Amar, A. Jeribi, and B. Krichen, Fixed point theorems for block operator matrix and an application to a structured problem under boundary conditions of Rotenberg's model type, to appear in Math. Slovaca. (2014)], the existence of solutions of the two-dimensional boundary value problem (1) and (2) was discussed in the product Banach space L(p)×L(p) for p∈(1, ∞). Due to the lack of compactness on L1 spaces, the analysis did not cover the case p=1. The purpose of this work is to extend the results of Ben Amar et al. to the case p=1 by establishing new variants of fixed-point theorems for a 2×2 operator matrix, involving weakly compact operators.

High order solution of Poisson problems with piecewise constant coefficients and interface jumps

NASA Astrophysics Data System (ADS)

Marques, Alexandre Noll; Nave, Jean-Christophe; Rosales, Rodolfo Ruben

2017-04-01

We present a fast and accurate algorithm to solve Poisson problems in complex geometries, using regular Cartesian grids. We consider a variety of configurations, including Poisson problems with interfaces across which the solution is discontinuous (of the type arising in multi-fluid flows). The algorithm is based on a combination of the Correction Function Method (CFM) and Boundary Integral Methods (BIM). Interface and boundary conditions can be treated in a fast and accurate manner using boundary integral equations, and the associated BIM. Unfortunately, BIM can be costly when the solution is needed everywhere in a grid, e.g. fluid flow problems. We use the CFM to circumvent this issue. The solution from the BIM is used to rewrite the problem as a series of Poisson problems in rectangular domains-which requires the BIM solution at interfaces/boundaries only. These Poisson problems involve discontinuities at interfaces, of the type that the CFM can handle. Hence we use the CFM to solve them (to high order of accuracy) with finite differences and a Fast Fourier Transform based fast Poisson solver. We present 2-D examples of the algorithm applied to Poisson problems involving complex geometries, including cases in which the solution is discontinuous. We show that the algorithm produces solutions that converge with either 3rd or 4th order of accuracy, depending on the type of boundary condition and solution discontinuity.

Analysis of Inlet-Compressor Acoustic Interactions Using Coupled CFD Codes

NASA Technical Reports Server (NTRS)

Suresh, A.; Townsend, S. E.; Cole, G. L.; Slater, J. W.; Chima, R.

1998-01-01

A problem that arises in the numerical simulation of supersonic inlets is the lack of a suitable boundary condition at the engine face. In this paper, a coupled approach, in which the inlet computation is coupled dynamically to a turbomachinery computation, is proposed as a means to overcome this problem. The specific application chosen for validation of this approach is the collapsing bump experiment performed at the University of Cincinnati. The computed results are found to be in reasonable agreement with experimental results. The coupled simulation results could also be used to aid development of a simplified boundary condition.

Multiple shooting algorithms for jump-discontinuous problems in optimal control and estimation

NASA Technical Reports Server (NTRS)

Mook, D. J.; Lew, Jiann-Shiun

1991-01-01

Multiple shooting algorithms are developed for jump-discontinuous two-point boundary value problems arising in optimal control and optimal estimation. Examples illustrating the origin of such problems are given to motivate the development of the solution algorithms. The algorithms convert the necessary conditions, consisting of differential equations and transversality conditions, into algebraic equations. The solution of the algebraic equations provides exact solutions for linear problems. The existence and uniqueness of the solution are proved.

A reciprocal theorem for a mixture theory. [development of linearized theory of interacting media

NASA Technical Reports Server (NTRS)

Martin, C. J.; Lee, Y. M.

1972-01-01

A dynamic reciprocal theorem for a linearized theory of interacting media is developed. The constituents of the mixture are a linear elastic solid and a linearly viscous fluid. In addition to Steel's field equations, boundary conditions and inequalities on the material constants that have been shown by Atkin, Chadwick and Steel to be sufficient to guarantee uniqueness of solution to initial-boundary value problems are used. The elements of the theory are given and two different boundary value problems are considered. The reciprocal theorem is derived with the aid of the Laplace transform and the divergence theorem and this section is concluded with a discussion of the special cases which arise when one of the constituents of the mixture is absent.

On the effects of nonlinear boundary conditions in diffusive logistic equations on bounded domains

NASA Astrophysics Data System (ADS)

Cantrell, Robert Stephen; Cosner, Chris

We study a diffusive logistic equation with nonlinear boundary conditions. The equation arises as a model for a population that grows logistically inside a patch and crosses the patch boundary at a rate that depends on the population density. Specifically, the rate at which the population crosses the boundary is assumed to decrease as the density of the population increases. The model is motivated by empirical work on the Glanville fritillary butterfly. We derive local and global bifurcation results which show that the model can have multiple equilibria and in some parameter ranges can support Allee effects. The analysis leads to eigenvalue problems with nonstandard boundary conditions.

Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies

NASA Technical Reports Server (NTRS)

Winget, J. M.; Hughes, T. J. R.

1985-01-01

The particular problems investigated in the present study arise from nonlinear transient heat conduction. One of two types of nonlinearities considered is related to a material temperature dependence which is frequently needed to accurately model behavior over the range of temperature of engineering interest. The second nonlinearity is introduced by radiation boundary conditions. The finite element equations arising from the solution of nonlinear transient heat conduction problems are formulated. The finite element matrix equations are temporally discretized, and a nonlinear iterative solution algorithm is proposed. Algorithms for solving the linear problem are discussed, taking into account the form of the matrix equations, Gaussian elimination, cost, and iterative techniques. Attention is also given to approximate factorization, implementational aspects, and numerical results.

Applied mathematical problems in modern electromagnetics

NASA Astrophysics Data System (ADS)

Kriegsman, Gregory

1994-05-01

We have primarily investigated two classes of electromagnetic problems. The first contains the quantitative description of microwave heating of dispersive and conductive materials. Such problems arise, for example, when biological tissue are exposed, accidentally or purposefully, to microwave radiation. Other instances occur in ceramic processing, such as sintering and microwave assisted chemical vapor infiltration and other industrial drying processes, such as the curing of paints and concrete. The second class characterizes the scattering of microwaves by complex targets which possess two or more disparate length and/or time scales. Spatially complex scatterers arise in a variety of applications, such as large gratings and slowly changing guiding structures. The former are useful in developing microstrip energy couplers while the later can be used to model anatomical subsystems (e.g., the open guiding structure composed of two legs and the adjoining lower torso). Temporally complex targets occur in applications involving dispersive media whose relaxation times differ by orders of magnitude from thermal and/or electromagnetic time scales. For both cases the mathematical description of the problems gives rise to complicated ill-conditioned boundary value problems, whose accurate solutions require a blend of both asymptotic techniques, such as multiscale methods and matched asymptotic expansions, and numerical methods incorporating radiation boundary conditions, such as finite differences and finite elements.

General Boundary Conditions for a Majorana Single-Particle in a Box in (1 + 1) Dimensions

NASA Astrophysics Data System (ADS)

De Vincenzo, Salvatore; Sánchez, Carlet

2018-05-01

We consider the problem of a Majorana single-particle in a box in (1 + 1) dimensions. We show that the most general set of boundary conditions for the equation that models this particle is composed of two families of boundary conditions, each one with a real parameter. Within this set, we only have four confining boundary conditions—but infinite not confining boundary conditions. Our results are also valid when we include a Lorentz scalar potential in this equation. No other Lorentz potential can be added. We also show that the four confining boundary conditions for the Majorana particle are precisely the four boundary conditions that mathematically can arise from the general linear boundary condition used in the MIT bag model. Certainly, the four boundary conditions for the Majorana particle are also subject to the Majorana condition.

Metaheuristic optimisation methods for approximate solving of singular boundary value problems

NASA Astrophysics Data System (ADS)

Sadollah, Ali; Yadav, Neha; Gao, Kaizhou; Su, Rong

2017-07-01

This paper presents a novel approximation technique based on metaheuristics and weighted residual function (WRF) for tackling singular boundary value problems (BVPs) arising in engineering and science. With the aid of certain fundamental concepts of mathematics, Fourier series expansion, and metaheuristic optimisation algorithms, singular BVPs can be approximated as an optimisation problem with boundary conditions as constraints. The target is to minimise the WRF (i.e. error function) constructed in approximation of BVPs. The scheme involves generational distance metric for quality evaluation of the approximate solutions against exact solutions (i.e. error evaluator metric). Four test problems including two linear and two non-linear singular BVPs are considered in this paper to check the efficiency and accuracy of the proposed algorithm. The optimisation task is performed using three different optimisers including the particle swarm optimisation, the water cycle algorithm, and the harmony search algorithm. Optimisation results obtained show that the suggested technique can be successfully applied for approximate solving of singular BVPs.

Collocation for an integral equation arising in duct acoustics

NASA Technical Reports Server (NTRS)

Moss, W. F.

1986-01-01

A mathematical model is developed to describe the effect of aircraft-engine inlet geometry on the reflected and radiated acoustic field without flow, as studied experimentally using a spinning-mode synthesizer by Silcox (1983). The acoustic pressure in the inlet interior and exterior is modeled by a pure cylindrical azimuthal mode for the Helmholtz equation with hardwall boundary and by the Helmholtz equation and the radiation condition at infinity, respectively. The analytical approach to the solution of the resulting boundary-value problem and the program implementation are explained; numerical results are presented in tables and graphs; and the uniqueness of the problem is demonstrated.

Solving Differential Equations Using Modified Picard Iteration

ERIC Educational Resources Information Center

Robin, W. A.

2010-01-01

Many classes of differential equations are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures. The classes of differential equations considered include typical initial value, boundary value and eigenvalue problems arising in physics and…

On Stable Wall Boundary Conditions for the Hermite Discretization of the Linearised Boltzmann Equation

NASA Astrophysics Data System (ADS)

Sarna, Neeraj; Torrilhon, Manuel

2018-01-01

We define certain criteria, using the characteristic decomposition of the boundary conditions and energy estimates, which a set of stable boundary conditions for a linear initial boundary value problem, involving a symmetric hyperbolic system, must satisfy. We first use these stability criteria to show the instability of the Maxwell boundary conditions proposed by Grad (Commun Pure Appl Math 2(4):331-407, 1949). We then recognise a special block structure of the moment equations which arises due to the recursion relations and the orthogonality of the Hermite polynomials; the block structure will help us in formulating stable boundary conditions for an arbitrary order Hermite discretization of the Boltzmann equation. The formulation of stable boundary conditions relies upon an Onsager matrix which will be constructed such that the newly proposed boundary conditions stay close to the Maxwell boundary conditions at least in the lower order moments.

A First Step towards Variational Methods in Engineering

ERIC Educational Resources Information Center

Periago, Francisco

2003-01-01

In this paper, a didactical proposal is presented to introduce the variational methods for solving boundary value problems to engineering students. Starting from a couple of simple models arising in linear elasticity and heat diffusion, the concept of weak solution for these models is motivated and the existence, uniqueness and continuous…

Boundary violations and departments of psychiatry.

PubMed

Garfinkel, P E; Dorian, B; Sadavoy, J; Bagby, R M

1997-09-01

To explore a number of issues related to boundary violations in psychiatry, including the relationship between the individual physician and his or her patient and broader issues related to various dilemmas arising in academic departments of psychiatry. Several potentially troublesome scenarios are presented and discussed in the contexts of 1) the doctor-patient relationship, 2) sexual boundary violations, and 3) nonsexual forms of exploitation, such as finances, confidentiality, dual relationships, and relationships with industry. A number of examples of boundary problems involving psychiatrists have been explored, and although some of these behaviours are clearly forbidden and harmful, others are less clear and require careful consideration if the profession is to arrive at a thoughtful consensus.

A parabolic variational inequality arising from the valuation of strike reset options

NASA Astrophysics Data System (ADS)

Yang, Zhou; Yi, Fahuai; Dai, Min

A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a one-dimensional parabolic variational inequality, or equivalently, a free boundary problem, where the free boundary just corresponds to the optimal reset strategy adopted by the holder of the option. This paper is concerned with the theoretical analysis of the model. The existence and uniqueness of the solution are established. Furthermore, we study properties of the free boundary. The monotonicity and C smoothness of the free boundary are proven in some situations.

Functional level-set derivative for a polymer self consistent field theory Hamiltonian

NASA Astrophysics Data System (ADS)

Ouaknin, Gaddiel; Laachi, Nabil; Bochkov, Daniil; Delaney, Kris; Fredrickson, Glenn H.; Gibou, Frederic

2017-09-01

We derive functional level-set derivatives for the Hamiltonian arising in self-consistent field theory, which are required to solve free boundary problems in the self-assembly of polymeric systems such as block copolymer melts. In particular, we consider Dirichlet, Neumann and Robin boundary conditions. We provide numerical examples that illustrate how these shape derivatives can be used to find equilibrium and metastable structures of block copolymer melts with a free surface in both two and three spatial dimensions.

Low frequency acoustic and electromagnetic scattering

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Maccamy, R. C.

1986-01-01

This paper deals with two classes of problems arising from acoustics and electromagnetics scattering in the low frequency stations. The first class of problem is solving Helmholtz equation with Dirichlet boundary conditions on an arbitrary two dimensional body while the second one is an interior-exterior interface problem with Helmholtz equation in the exterior. Low frequency analysis show that there are two intermediate problems which solve the above problems accurate to 0(k/2/ log k) where k is the frequency. These solutions greatly differ from the zero frequency approximations. For the Dirichlet problem numerical examples are shown to verify the theoretical estimates.

Mean Field Type Control with Congestion (II): An Augmented Lagrangian Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr; Laurière, Mathieu

This work deals with a numerical method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential equations arising from the model were discussed and existence and uniqueness were proved. Here, the focus is put on numerical methods: a monotone finite difference scheme is proposed and shown to have a variational interpretation. Then an Alternating Direction Method of Multipliers for solving the variational problem is addressed. It is based on an augmented Lagrangian. Two kinds of boundary conditionsmore » are considered: periodic conditions and more realistic boundary conditions associated to state constrained problems. Various test cases and numerical results are presented.« less

A classical Perron method for existence of smooth solutions to boundary value and obstacle problems for degenerate-elliptic operators via holomorphic maps

NASA Astrophysics Data System (ADS)

Feehan, Paul M. N.

2017-09-01

We prove existence of solutions to boundary value problems and obstacle problems for degenerate-elliptic, linear, second-order partial differential operators with partial Dirichlet boundary conditions using a new version of the Perron method. The elliptic operators considered have a degeneracy along a portion of the domain boundary which is similar to the degeneracy of a model linear operator identified by Daskalopoulos and Hamilton [9] in their study of the porous medium equation or the degeneracy of the Heston operator [21] in mathematical finance. Existence of a solution to the partial Dirichlet problem on a half-ball, where the operator becomes degenerate on the flat boundary and a Dirichlet condition is only imposed on the spherical boundary, provides the key additional ingredient required for our Perron method. Surprisingly, proving existence of a solution to this partial Dirichlet problem with ;mixed; boundary conditions on a half-ball is more challenging than one might expect. Due to the difficulty in developing a global Schauder estimate and due to compatibility conditions arising where the ;degenerate; and ;non-degenerate boundaries; touch, one cannot directly apply the continuity or approximate solution methods. However, in dimension two, there is a holomorphic map from the half-disk onto the infinite strip in the complex plane and one can extend this definition to higher dimensions to give a diffeomorphism from the half-ball onto the infinite ;slab;. The solution to the partial Dirichlet problem on the half-ball can thus be converted to a partial Dirichlet problem on the slab, albeit for an operator which now has exponentially growing coefficients. The required Schauder regularity theory and existence of a solution to the partial Dirichlet problem on the slab can nevertheless be obtained using previous work of the author and C. Pop [16]. Our Perron method relies on weak and strong maximum principles for degenerate-elliptic operators, concepts of continuous subsolutions and supersolutions for boundary value and obstacle problems for degenerate-elliptic operators, and maximum and comparison principle estimates previously developed by the author [13].

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

DTIC Science & Technology

2014-03-01

accuracy, with rapid convergence over each physical time step, typically less than five Newton iter - ations. 1 Contents 1 Introduction 3 2 Hyperbolic...however, we employ the Gauss - Seidel (GS) relaxation, which is also an O(N) method for the discretization arising from hyperbolic advection-diffusion system...advection-diffusion scheme. The linear dependency of the iterations on Table 1: Boundary layer problem ( Convergence criteria: Residuals < 10−8.) log10Re

An iterative Riemann solver for systems of hyperbolic conservation law s, with application to hyperelastic solid mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miller, Gregory H.

2003-08-06

In this paper we present a general iterative method for the solution of the Riemann problem for hyperbolic systems of PDEs. The method is based on the multiple shooting method for free boundary value problems. We demonstrate the method by solving one-dimensional Riemann problems for hyperelastic solid mechanics. Even for conditions representative of routine laboratory conditions and military ballistics, dramatic differences are seen between the exact and approximate Riemann solution. The greatest discrepancy arises from misallocation of energy between compressional and thermal modes by the approximate solver, resulting in nonphysical entropy and temperature estimates. Several pathological conditions arise in commonmore » practice, and modifications to the method to handle these are discussed. These include points where genuine nonlinearity is lost, degeneracies, and eigenvector deficiencies that occur upon melting.« less

The Use of Kruskal-Newton Diagrams for Differential Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

T. Fishaleck and R.B. White

2008-02-19

The method of Kruskal-Newton diagrams for the solution of differential equations with boundary layers is shown to provide rapid intuitive understanding of layer scaling and can result in the conceptual simplification of some problems. The method is illustrated using equations arising in the theory of pattern formation and in plasma physics.

Singular boundary value problem for the integrodifferential equation in an insurance model with stochastic premiums: Analysis and numerical solution

NASA Astrophysics Data System (ADS)

Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.

2012-10-01

A singular boundary value problem for a second-order linear integrodifferential equation with Volterra and non-Volterra integral operators is formulated and analyzed. The equation is defined on ℝ+, has a weak singularity at zero and a strong singularity at infinity, and depends on several positive parameters. Under natural constraints on the coefficients of the equation, existence and uniqueness theorems for this problem with given limit boundary conditions at singular points are proved, asymptotic representations of the solution are given, and an algorithm for its numerical determination is described. Numerical computations are performed and their interpretation is given. The problem arises in the study of the survival probability of an insurance company over infinite time (as a function of its initial surplus) in a dynamic insurance model that is a modification of the classical Cramer-Lundberg model with a stochastic process rate of premium under a certain investment strategy in the financial market. A comparative analysis of the results with those produced by the model with deterministic premiums is given.

Boundary Concentration for Eigenvalue Problems Related to the Onset of Superconductivity

NASA Astrophysics Data System (ADS)

del Pino, Manuel; Felmer, Patricio L.; Sternberg, Peter

We examine the asymptotic behavior of the eigenvalue μ(h) and corresponding eigenfunction associated with the variational problem in the regime h>>1. Here A is any vector field with curl equal to 1. The problem arises within the Ginzburg-Landau model for superconductivity with the function μ(h) yielding the relationship between the critical temperature vs. applied magnetic field strength in the transition from normal to superconducting state in a thin mesoscopic sample with cross-section Ω 2. We first carry out a rigorous analysis of the associated problem on a half-plane and then rigorously justify some of the formal arguments of [BS], obtaining an expansion for μ while also proving that the first eigenfunction decays to zero somewhere along the sample boundary when Ω is not a disc. For interior decay, we demonstrate that the rate is exponential.

Fluid-membrane tethers: minimal surfaces and elastic boundary layers.

PubMed

Powers, Thomas R; Huber, Greg; Goldstein, Raymond E

2002-04-01

Thin cylindrical tethers are common lipid bilayer membrane structures, arising in situations ranging from micromanipulation experiments on artificial vesicles to the dynamic structure of the Golgi apparatus. We study the shape and formation of a tether in terms of the classical soap-film problem, which is applied to the case of a membrane disk under tension subject to a point force. A tether forms from the elastic boundary layer near the point of application of the force, for sufficiently large displacement. Analytic results for various aspects of the membrane shape are given.

Wavefunction Engineering of Spintronic devices in ZnO/MgO and GaN/AlN Quantum Structures Doped with Transition Metal Ions

DTIC Science & Technology

2006-08-01

2005). 7. " Dependence of the interband transitions on the In mole-fraction and the applied electric field in InxGaj_xAs/In0. 52Al0.48As multiple... tunneling boundary conditions for open structures. The boundary conditions at interfaces require the maintenance of derivative operator ordering...computational methods for the solution of Schr6dinger’s equations for scattering/ tunneling structures as well as for the eigenvalue problems that arise for

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frayce, D.; Khayat, R.E.; Derdouri, A.

The dual reciprocity boundary element method (DRBEM) is implemented to solve three-dimensional transient heat conduction problems in the presence of arbitrary sources, typically as these problems arise in materials processing. The DRBEM has a major advantage over conventional BEM, since it avoids the computation of volume integrals. These integrals stem from transient, nonlinear, and/or source terms. Thus there is no need to discretize the inner domain, since only a number of internal points are needed for the computation. The validity of the method is assessed upon comparison with results from benchmark problems where analytical solutions exist. There is generally goodmore » agreement. Comparison against finite element results is also favorable. Calculations are carried out in order to assess the influence of the number and location of internal nodes. The influence of the ratio of the numbers of internal to boundary nodes is also examined.« less

Role of buoyancy and heat release in fire modeling, propagation, and instability

Treesearch

Shahid M. Mughal; Yousuff M. Hussaini; Scott L. Goodrick; Philip Cunningham

2007-01-01

In an investigation of the dynamics of coupled fluid-combustion-buoyancy driven problems, an idealised model formulation is used to investigate the role of buoyancy and heat release in an evolving boundary layer, with particular emphasis on examining underlying fluid dynamics to explain observed phenomena arising in forest fire propagation. The role played by the...

An iterative truncation method for unbounded electromagnetic problems using varying order finite elements

NASA Astrophysics Data System (ADS)

Paul, Prakash

2009-12-01

The finite element method (FEM) is used to solve three-dimensional electromagnetic scattering and radiation problems. Finite element (FE) solutions of this kind contain two main types of error: discretization error and boundary error. Discretization error depends on the number of free parameters used to model the problem, and on how effectively these parameters are distributed throughout the problem space. To reduce the discretization error, the polynomial order of the finite elements is increased, either uniformly over the problem domain or selectively in those areas with the poorest solution quality. Boundary error arises from the condition applied to the boundary that is used to truncate the computational domain. To reduce the boundary error, an iterative absorbing boundary condition (IABC) is implemented. The IABC starts with an inexpensive boundary condition and gradually improves the quality of the boundary condition as the iteration continues. An automatic error control (AEC) is implemented to balance the two types of error. With the AEC, the boundary condition is improved when the discretization error has fallen to a low enough level to make this worth doing. The AEC has these characteristics: (i) it uses a very inexpensive truncation method initially; (ii) it allows the truncation boundary to be very close to the scatterer/radiator; (iii) it puts more computational effort on the parts of the problem domain where it is most needed; and (iv) it can provide as accurate a solution as needed depending on the computational price one is willing to pay. To further reduce the computational cost, disjoint scatterers and radiators that are relatively far from each other are bounded separately and solved using a multi-region method (MRM), which leads to savings in computational cost. A simple analytical way to decide whether the MRM or the single region method will be computationally cheaper is also described. To validate the accuracy and savings in computation time, different shaped metallic and dielectric obstacles (spheres, ogives, cube, flat plate, multi-layer slab etc.) are used for the scattering problems. For the radiation problems, waveguide excited antennas (horn antenna, waveguide with flange, microstrip patch antenna) are used. Using the AEC the peak reduction in computation time during the iteration is typically a factor of 2, compared to the IABC using the same element orders throughout. In some cases, it can be as high as a factor of 4.

A note on the regularity of solutions of infinite dimensional Riccati equations

NASA Technical Reports Server (NTRS)

Burns, John A.; King, Belinda B.

1994-01-01

This note is concerned with the regularity of solutions of algebraic Riccati equations arising from infinite dimensional LQR and LQG control problems. We show that distributed parameter systems described by certain parabolic partial differential equations often have a special structure that smoothes solutions of the corresponding Riccati equation. This analysis is motivated by the need to find specific representations for Riccati operators that can be used in the development of computational schemes for problems where the input and output operators are not Hilbert-Schmidt. This situation occurs in many boundary control problems and in certain distributed control problems associated with optimal sensor/actuator placement.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Donnelly, William; Freidel, Laurent

We consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting for studying entanglement entropy of regions of space. We present a general formalism to associate a gauge-invariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In Yang-Mills theory the new degrees of freedom are a choice of gauge on the boundary, transformations of which are generated by the normal component of the nonabelian electric field. In general relativity the new degrees of freedommore » are the location of a codimension-2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension-2 boundary, and position-dependent linear deformations of its normal plane. We find the observables which generate these symmetries, consisting of the conformal normal metric and curvature of the normal connection. We discuss the implications for the problem of defining entanglement entropy in quantum gravity. Finally, our work suggests that the Bekenstein-Hawking entropy may arise from the different ways of gluing together two partial Cauchy surfaces at a cross-section of the horizon.« less

Numerical reconstruction of unknown Robin inclusions inside a heat conductor by a non-iterative method

NASA Astrophysics Data System (ADS)

Nakamura, Gen; Wang, Haibing

2017-05-01

Consider the problem of reconstructing unknown Robin inclusions inside a heat conductor from boundary measurements. This problem arises from active thermography and is formulated as an inverse boundary value problem for the heat equation. In our previous works, we proposed a sampling-type method for reconstructing the boundary of the Robin inclusion and gave its rigorous mathematical justification. This method is non-iterative and based on the characterization of the solution to the so-called Neumann- to-Dirichlet map gap equation. In this paper, we give a further investigation of the reconstruction method from both the theoretical and numerical points of view. First, we clarify the solvability of the Neumann-to-Dirichlet map gap equation and establish a relation of its solution to the Green function associated with an initial-boundary value problem for the heat equation inside the Robin inclusion. This naturally provides a way of computing this Green function from the Neumann-to-Dirichlet map and explains what is the input for the linear sampling method. Assuming that the Neumann-to-Dirichlet map gap equation has a unique solution, we also show the convergence of our method for noisy measurements. Second, we give the numerical implementation of the reconstruction method for two-dimensional spatial domains. The measurements for our inverse problem are simulated by solving the forward problem via the boundary integral equation method. Numerical results are presented to illustrate the efficiency and stability of the proposed method. By using a finite sequence of transient input over a time interval, we propose a new sampling method over the time interval by single measurement which is most likely to be practical.

A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ciraolo, Giulio, E-mail: g.ciraolo@math.unipa.it; Gargano, Francesco, E-mail: gargano@math.unipa.it; Sciacca, Vincenzo, E-mail: sciacca@math.unipa.it

2013-08-01

We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.

Quaternion regularization in celestial mechanics, astrodynamics, and trajectory motion control. III

NASA Astrophysics Data System (ADS)

Chelnokov, Yu. N.

2015-09-01

The present paper1 analyzes the basic problems arising in the solution of problems of the optimum control of spacecraft (SC) trajectory motion (including the Lyapunov instability of solutions of conjugate equations) using the principle of the maximum. The use of quaternion models of astrodynamics is shown to allow: (1) the elimination of singular points in the differential phase and conjugate equations and in their partial analytical solutions; (2) construction of the first integrals of the new quaternion; (3) a considerable decrease of the dimensions of systems of differential equations of boundary value optimization problems with their simultaneous simplification by using the new quaternion variables related with quaternion constants of motion by rotation transformations; (4) construction of general solutions of differential equations for phase and conjugate variables on the sections of SC passive motion in the simplest and most convenient form, which is important for the solution of optimum pulse SC transfers; (5) the extension of the possibilities of the analytical investigation of differential equations of boundary value problems with the purpose of identifying the basic laws of optimum control and motion of SC; (6) improvement of the computational stability of the solution of boundary value problems; (7) a decrease in the required volume of computation.

Two-phase Hele-Shaw flow with a moving contact line

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weinstein, S.J.; Ungar, L.H.; Dussan, E.B.

1988-01-01

An asymptotic analysis is presented for Hele-Shaw viscous fingering with a moving contact line at flow rates. As in problems where a thin film is present instead of a contact line, the narrow gap limit is nonuniform, and interfacial boundary conditions valid for the Hele-Shaw equations must be determined in order to predict the flow field and interface shape. Many well-posed boundary-value problems can be identified, each corresponding to a different flow regime characterized by the relative sizes of the capillary number (dimensionless velocity) and the dimensionless gap width. These problems incorporate terms corresponding to the gapwise component of themore » interfacial curvature (the curvature in the cross-sectional view of the Hele-Shaw cell) and spanwise curvature (seen in the top view of the cell) in different ways. Nonunique interface solutions typically arise as in the analogous thin film problems. The relationships between the curvature terms, the spectra of allowable solutions, and the implications for stability are discussed.« less

Improvements to Level Set, Immersed Boundary methods for Interface Tracking

NASA Astrophysics Data System (ADS)

Vogl, Chris; Leveque, Randy

2014-11-01

It is not uncommon to find oneself solving a moving boundary problem under flow in the context of some application. Of particular interest is when the moving boundary exerts a curvature-dependent force on the liquid. Such a force arises when observing a boundary that is resistant to bending or has surface tension. Numerically speaking, stable numerical computation of the curvature can be difficult as it is often described in terms of high-order derivatives of either marker particle positions or of a level set function. To address this issue, the level set method is modified to track not only the position of the boundary, but the curvature as well. The definition of the signed-distance function that is used to modify the level set method is also used to develop an interpolation-free, closest-point method. These improvements are used to simulate a bending-resistant, inextensible boundary under shear flow to highlight area and volume conservation, as well as stable curvature calculation. Funded by a NSF MSPRF grant.

A family of position- and orientation-independent embedded boundary methods for viscous flow and fluid-structure interaction problems

NASA Astrophysics Data System (ADS)

Huang, Daniel Z.; De Santis, Dante; Farhat, Charbel

2018-07-01

The Finite Volume method with Exact two-material Riemann Problems (FIVER) is both a computational framework for multi-material flows characterized by large density jumps, and an Embedded Boundary Method (EBM) for computational fluid dynamics and highly nonlinear Fluid-Structure Interaction (FSI) problems. This paper deals with the EBM aspect of FIVER. For FSI problems, this EBM has already demonstrated the ability to address viscous effects along wall boundaries, and large deformations and topological changes of such boundaries. However, like for most EBMs - also known as immersed boundary methods - the performance of FIVER in the vicinity of a wall boundary can be sensitive with respect to the position and orientation of this boundary relative to the embedding mesh. This is mainly due to ill-conditioning issues that arise when an embedded interface becomes too close to a node of the embedding mesh, which may lead to spurious oscillations in the computed solution gradients at the wall boundary. This paper resolves these issues by introducing an alternative definition of the active/inactive status of a mesh node that leads to the removal of all sources of potential ill-conditioning from all spatial approximations performed by FIVER in the vicinity of a fluid-structure interface. It also makes two additional contributions. The first one is a new procedure for constructing the fluid-structure half Riemann problem underlying the semi-discretization by FIVER of the convective fluxes. This procedure eliminates one extrapolation from the conventional treatment of the wall boundary conditions and replaces it by an interpolation, which improves robustness. The second contribution is a post-processing algorithm for computing quantities of interest at the wall that achieves smoothness in the computed solution and its gradients. Lessons learned from these enhancements and contributions that are triggered by the new definition of the status of a mesh node are then generalized and exploited to eliminate from the original version of the FIVER method its sensitivities with respect to both of the position and orientation of the wall boundary relative to the embedding mesh, while maintaining the original definition of the status of a mesh node. This leads to a family of second-generation FIVER methods whose performance is illustrated in this paper for several flow and FSI problems. These include a challenging flow problem over a bird wing characterized by a feather-induced surface roughness, and a complex flexible flapping wing problem for which experimental data is available.

Guidance and control strategies for aerospace vehicles

NASA Technical Reports Server (NTRS)

Naidu, Desineni S.; Hibey, Joseph L.

1988-01-01

The optimal control problem arising in coplanar, orbital transfer employing aeroassist technology is addressed. The maneuver involves the transfer from high Earth orbit to low Earth orbit. A performance index is chosen the minimize the fuel consumpltion for the transfer. Simulations are carried out for establishing a corridor of entry conditions which are suitable for flying the spacecraft through the atmosphere. A highlight of the paper is the application of an efficient multiple shooting method for taming the notorious nonlinear, two-point, boundary value problem resulting from optimization procedure.

Eigenvalue problems for Beltrami fields arising in a three-dimensional toroidal magnetohydrodynamic equilibrium problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hudson, S. R.; Hole, M. J.; Dewar, R. L.

2007-05-15

A generalized energy principle for finite-pressure, toroidal magnetohydrodynamic (MHD) equilibria in general three-dimensional configurations is proposed. The full set of ideal-MHD constraints is applied only on a discrete set of toroidal magnetic surfaces (invariant tori), which act as barriers against leakage of magnetic flux, helicity, and pressure through chaotic field-line transport. It is argued that a necessary condition for such invariant tori to exist is that they have fixed, irrational rotational transforms. In the toroidal domains bounded by these surfaces, full Taylor relaxation is assumed, thus leading to Beltrami fields {nabla}xB={lambda}B, where {lambda} is constant within each domain. Two distinctmore » eigenvalue problems for {lambda} arise in this formulation, depending on whether fluxes and helicity are fixed, or boundary rotational transforms. These are studied in cylindrical geometry and in a three-dimensional toroidal region of annular cross section. In the latter case, an application of a residue criterion is used to determine the threshold for connected chaos.« less

Analysis of a Two-Dimensional Thermal Cloaking Problem on the Basis of Optimization

NASA Astrophysics Data System (ADS)

Alekseev, G. V.

2018-04-01

For a two-dimensional model of thermal scattering, inverse problems arising in the development of tools for cloaking material bodies on the basis of a mixed thermal cloaking strategy are considered. By applying the optimization approach, these problems are reduced to optimization ones in which the role of controls is played by variable parameters of the medium occupying the cloaking shell and by the heat flux through a boundary segment of the basic domain. The solvability of the direct and optimization problems is proved, and an optimality system is derived. Based on its analysis, sufficient conditions on the input data are established that ensure the uniqueness and stability of optimal solutions.

Weak variations of Lipschitz graphs and stability of phase boundaries

NASA Astrophysics Data System (ADS)

Grabovsky, Yury; Kucher, Vladislav A.; Truskinovsky, Lev

2011-03-01

In the case of Lipschitz extremals of vectorial variational problems, an important class of strong variations originates from smooth deformations of the corresponding non-smooth graphs. These seemingly singular variations, which can be viewed as combinations of weak inner and outer variations, produce directions of differentiability of the functional and lead to singularity-centered necessary conditions on strong local minima: an equality, arising from stationarity, and an inequality, implying configurational stability of the singularity set. To illustrate the underlying coupling between inner and outer variations, we study in detail the case of smooth surfaces of gradient discontinuity representing, for instance, martensitic phase boundaries in non-linear elasticity.

HADY-I, a FORTRAN program for the compressible stability analysis of three-dimensional boundary layers. [on swept and tapered wings

NASA Technical Reports Server (NTRS)

El-Hady, N. M.

1981-01-01

A computer program HADY-I for calculating the linear incompressible or compressible stability characteristics of the laminar boundary layer on swept and tapered wings is described. The eigenvalue problem and its adjoint arising from the linearized disturbance equations with the appropriate boundary conditions are solved numerically using a combination of Newton-Raphson interative scheme and a variable step size integrator based on the Runge-Kutta-Fehlburh fifth-order formulas. The integrator is used in conjunction with a modified Gram-Schmidt orthonormalization procedure. The computer program HADY-I calculates the growth rates of crossflow or streamwise Tollmien-Schlichting instabilities. It also calculates the group velocities of these disturbances. It is restricted to parallel stability calculations, where the boundary layer (meanflow) is assumed to be parallel. The meanflow solution is an input to the program.

Model Predictive Optimal Control of a Time-Delay Distributed-Parameter Systems

NASA Technical Reports Server (NTRS)

Nguyen, Nhan

2006-01-01

This paper presents an optimal control method for a class of distributed-parameter systems governed by first order, quasilinear hyperbolic partial differential equations that arise in many physical systems. Such systems are characterized by time delays since information is transported from one state to another by wave propagation. A general closed-loop hyperbolic transport model is controlled by a boundary control embedded in a periodic boundary condition. The boundary control is subject to a nonlinear differential equation constraint that models actuator dynamics of the system. The hyperbolic equation is thus coupled with the ordinary differential equation via the boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to implement a model predictive control design for a wind tunnel to eliminate a transport delay effect that causes a poor Mach number regulation.

Local subsystems in gauge theory and gravity

DOE PAGES

Donnelly, William; Freidel, Laurent

2016-09-16

We consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting for studying entanglement entropy of regions of space. We present a general formalism to associate a gauge-invariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In Yang-Mills theory the new degrees of freedom are a choice of gauge on the boundary, transformations of which are generated by the normal component of the nonabelian electric field. In general relativity the new degrees of freedommore » are the location of a codimension-2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension-2 boundary, and position-dependent linear deformations of its normal plane. We find the observables which generate these symmetries, consisting of the conformal normal metric and curvature of the normal connection. We discuss the implications for the problem of defining entanglement entropy in quantum gravity. Finally, our work suggests that the Bekenstein-Hawking entropy may arise from the different ways of gluing together two partial Cauchy surfaces at a cross-section of the horizon.« less

Study of Varying Boundary Layer Height on Turret Flow Structures

DTIC Science & Technology

2011-06-01

fluid dynamics. The difficulties of the problem arise in modeling several complex flow features including separation, reattachment, three-dimensional...impossible. In this case, the approach is to create a model to calculate the properties of interest. The main issue with resolving turbulent flows...operation and their effect is modeled through subgrid scale models . As a result, the the most important turbulent scales are resolved and the

Discretization of three-dimensional free surface flows and moving boundary problems via elliptic grid methods based on variational principles

NASA Astrophysics Data System (ADS)

Fraggedakis, D.; Papaioannou, J.; Dimakopoulos, Y.; Tsamopoulos, J.

2017-09-01

A new boundary-fitted technique to describe free surface and moving boundary problems is presented. We have extended the 2D elliptic grid generator developed by Dimakopoulos and Tsamopoulos (2003) [19] and further advanced by Chatzidai et al. (2009) [18] to 3D geometries. The set of equations arises from the fulfillment of the variational principles established by Brackbill and Saltzman (1982) [21], and refined by Christodoulou and Scriven (1992) [22]. These account for both smoothness and orthogonality of the grid lines of tessellated physical domains. The elliptic-grid equations are accompanied by new boundary constraints and conditions which are based either on the equidistribution of the nodes on boundary surfaces or on the existing 2D quasi-elliptic grid methodologies. The capabilities of the proposed algorithm are first demonstrated in tests with analytically described complex surfaces. The sequence in which these tests are presented is chosen to help the reader build up experience on the best choice of the elliptic grid parameters. Subsequently, the mesh equations are coupled with the Navier-Stokes equations, in order to reveal the full potential of the proposed methodology in free surface flows. More specifically, the problem of gas assisted injection in ducts of circular and square cross-sections is examined, where the fluid domain experiences extreme deformations. Finally, the flow-mesh solver is used to calculate the equilibrium shapes of static menisci in capillary tubes.

Survival probability of diffusion with trapping in cellular neurobiology

NASA Astrophysics Data System (ADS)

Holcman, David; Marchewka, Avi; Schuss, Zeev

2005-09-01

The problem of diffusion with absorption and trapping sites arises in the theory of molecular signaling inside and on the membranes of biological cells. In particular, this problem arises in the case of spine-dendrite communication, where the number of calcium ions, modeled as random particles, is regulated across the spine microstructure by pumps, which play the role of killing sites, while the end of the dendritic shaft is an absorbing boundary. We develop a general mathematical framework for diffusion in the presence of absorption and killing sites and apply it to the computation of the time-dependent survival probability of ions. We also compute the ratio of the number of absorbed particles at a specific location to the number of killed particles. We show that the ratio depends on the distribution of killing sites. The biological consequence is that the position of the pumps regulates the fraction of calcium ions that reach the dendrite.

Asymptotic stability of shear-flow solutions to incompressible viscous free boundary problems with and without surface tension

NASA Astrophysics Data System (ADS)

Tice, Ian

2018-04-01

This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a rigid plane and with an upper boundary given by a free surface. The fluid is subject to a constant external force with a horizontal component, which arises in modeling the motion of such a fluid down an inclined plane, after a coordinate change. We consider the problem both with and without surface tension for horizontally periodic flows. This problem gives rise to shear-flow equilibrium solutions, and the main thrust of this paper is to study the asymptotic stability of the equilibria in certain parameter regimes. We prove that there exists a parameter regime in which sufficiently small perturbations of the equilibrium at time t=0 give rise to global-in-time solutions that return to equilibrium exponentially in the case with surface tension and almost exponentially in the case without surface tension. We also establish a vanishing surface tension limit, which connects the solutions with and without surface tension.

The production and phonetic representation of fake geminates in English

PubMed Central

Oh, Grace E.; Redford, Melissa A.

2011-01-01

The current study focused on the production of non-contrastive geminates across different boundary types in English to investigate the hypothesis that word-internal heteromorphemic geminates may differ from those that arise across a word boundary. In this study, word-internal geminates arising from affixation, and described as either assimilated or concatenated, were matched to heteromorphemic geminates arising from sequences of identical consonants that spanned a word boundary and to word-internal singletons. Word-internal geminates were found to be longer than matched singletons in absolute and relative terms. By contrast, heteromorphemic geminates that occurred at word boundaries were only longer than matched singletons in absolute terms. In addition, heteromorphemic geminates in two word phrases were typically “pulled apart” in careful speech; that is, speakers marked the boundaries between free morphemes with pitch changes and pauses. Morpheme boundaries in words with bound affixes were very rarely highlighted in this way. These results are taken to indicate that most word-internal heteromorphemic geminates are represented as a single long consonant in the speech plan rather than as a consonant sequence. Only those geminates that arise in two word phrases exhibit phonetic characteristics that are fully consistent with the representation of two identical consonants crossing a morpheme boundary. PMID:22611293

The Line-drawing Problem in Disease Definition.

PubMed

Rogers, Wendy A; Walker, Mary Jean

2017-08-01

Biological dysfunction is regarded, in many accounts, as necessary and perhaps sufficient for disease. But although disease is conceptualized as all-or-nothing, biological functions often differ by degree. A tension is created by attempting to use a continuous variable as the basis for a categorical definition, raising questions about how we are to pinpoint the boundary between health and disease. This is the line-drawing problem. In this paper, we show how the line-drawing problem arises within "dysfunction-requiring" accounts of disease, such as those of Christopher Boorse and Jerome Wakefield. We then provide several detailed examples to establish that biological dysfunction cannot provide a boundary. We examine potential ways of resolving the line-drawing problem, either by dropping one of the claims that generates it, or by appealing to additional criteria. We argue that two of these options are plausible, and that each of these can be applied with regard to different diseases. © The Author 2017. Published by Oxford University Press, on behalf of the Journal of Medicine and Philosophy Inc. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations That Arise from Nonlinear Two-Point Boundary Value Problems

NASA Technical Reports Server (NTRS)

Sidi, Avram; Pennline, James A.

1999-01-01

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations that Arise from Nonlinear Two-Point Boundary Value Problems

NASA Technical Reports Server (NTRS)

Sidi, Avram; Pennline, James A.

1999-01-01

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

When fast and slow interfaces grow together: Connection to the half-space problem of the Kardar-Parisi-Zhang class

NASA Astrophysics Data System (ADS)

Ito, Yasufumi; Takeuchi, Kazumasa A.

2018-04-01

We study height fluctuations of interfaces in the (1 +1 ) -dimensional Kardar-Parisi-Zhang (KPZ) class, growing at different speeds in the left half and the right half of space. Carrying out simulations of the discrete polynuclear growth model with two different growth rates, combined with the standard setting for the droplet, flat, and stationary geometries, we find that the fluctuation properties at and near the boundary are described by the KPZ half-space problem developed in the theoretical literature. In particular, in the droplet case, the distribution at the boundary is given by the largest-eigenvalue distribution of random matrices in the Gaussian symplectic ensemble, often called the GSE Tracy-Widom distribution. We also characterize crossover from the full-space statistics to the half-space one, which arises when the difference between the two growth speeds is small.

A computer program to trace seismic ray distribution in complex two-dimensional geological models

USGS Publications Warehouse

Yacoub, Nazieh K.; Scott, James H.

1970-01-01

A computer program has been developed to trace seismic rays and their amplitudes and energies through complex two-dimensional geological models, for which boundaries between elastic units are defined by a series of digitized X-, Y-coordinate values. Input data for the program includes problem identification, control parameters, model coordinates and elastic parameter for the elastic units. The program evaluates the partitioning of ray amplitude and energy at elastic boundaries, computes the total travel time, total travel distance and other parameters for rays arising at the earth's surface. Instructions are given for punching program control cards and data cards, and for arranging input card decks. An example of printer output for a simple problem is presented. The program is written in FORTRAN IV language. The listing of the program is shown in the Appendix, with an example output from a CDC-6600 computer.

Development of Condensing Mesh Method for Corner Domain at Numerical Simulation Magnetic System

NASA Astrophysics Data System (ADS)

Perepelkin, E.; Tarelkin, A.; Polyakova, R.; Kovalenko, A.

2018-05-01

A magnetostatic problem arises in searching for the distribution of the magnetic field generated by magnet systems of many physics research facilities, e.g., accelerators. The domain in which the boundaryvalue problem is solved often has a piecewise smooth boundary. In this case, numerical calculations of the problem require the consideration of the solution behavior in the corner domain. In this work we obtained the upper estimation of the magnetic field growth and propose a method of condensing the differential grid near the corner domain of vacuum in case of 3-dimensional space based on this estimation. An example of calculating a real model problem for SDP NICA in the domain containing a corner point is given.

Homogenization of Winkler-Steklov spectral conditions in three-dimensional linear elasticity

NASA Astrophysics Data System (ADS)

Gómez, D.; Nazarov, S. A.; Pérez, M. E.

2018-04-01

We consider a homogenization Winkler-Steklov spectral problem that consists of the elasticity equations for a three-dimensional homogeneous anisotropic elastic body which has a plane part of the surface subject to alternating boundary conditions on small regions periodically placed along the plane. These conditions are of the Dirichlet type and of the Winkler-Steklov type, the latter containing the spectral parameter. The rest of the boundary of the body is fixed, and the period and size of the regions, where the spectral parameter arises, are of order ɛ . For fixed ɛ , the problem has a discrete spectrum, and we address the asymptotic behavior of the eigenvalues {β _k^ɛ }_{k=1}^{∞} as ɛ → 0. We show that β _k^ɛ =O(ɛ ^{-1}) for each fixed k, and we observe a common limit point for all the rescaled eigenvalues ɛ β _k^ɛ while we make it evident that, although the periodicity of the structure only affects the boundary conditions, a band-gap structure of the spectrum is inherited asymptotically. Also, we provide the asymptotic behavior for certain "groups" of eigenmodes.

Convergence issues in domain decomposition parallel computation of hovering rotor

NASA Astrophysics Data System (ADS)

Xiao, Zhongyun; Liu, Gang; Mou, Bin; Jiang, Xiong

2018-05-01

Implicit LU-SGS time integration algorithm has been widely used in parallel computation in spite of its lack of information from adjacent domains. When applied to parallel computation of hovering rotor flows in a rotating frame, it brings about convergence issues. To remedy the problem, three LU factorization-based implicit schemes (consisting of LU-SGS, DP-LUR and HLU-SGS) are investigated comparatively. A test case of pure grid rotation is designed to verify these algorithms, which show that LU-SGS algorithm introduces errors on boundary cells. When partition boundaries are circumferential, errors arise in proportion to grid speed, accumulating along with the rotation, and leading to computational failure in the end. Meanwhile, DP-LUR and HLU-SGS methods show good convergence owing to boundary treatment which are desirable in domain decomposition parallel computations.

Multi-level adaptive finite element methods. 1: Variation problems

NASA Technical Reports Server (NTRS)

Brandt, A.

1979-01-01

A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.

Influence of the boundary conditions on heat and mass transfer in spacer-filled channels

NASA Astrophysics Data System (ADS)

Ciofalo, M.; La Cerva, M. F.; Di Liberto, M.; Tamburini, A.

2017-11-01

The purpose of this study is to discuss some problems which arise in heat or mass transfer in complex channels, with special reference to the spacer-filled channels adopted in membrane processes. Among the issues addressed are the consistent definition of local and mean heat or mass transfer coefficients; the influence of the wall boundary conditions; the influence of one-side versus two-side heat/mass transfer. Most of the results discussed were obtained by finite volume CFD simulations concerning heat transfer in Membrane Distillation or mass transfer in Electrodialysis and Reverse Electrodialysis, but many of the conclusions apply also to different processes involving geometrically complex channels

HEATING 7. 1 user's manual

DOE Office of Scientific and Technical Information (OSTI.GOV)

Childs, K.W.

1991-07-01

HEATING is a FORTRAN program designed to solve steady-state and/or transient heat conduction problems in one-, two-, or three- dimensional Cartesian, cylindrical, or spherical coordinates. A model may include multiple materials, and the thermal conductivity, density, and specific heat of each material may be both time- and temperature-dependent. The thermal conductivity may be anisotropic. Materials may undergo change of phase. Thermal properties of materials may be input or may be extracted from a material properties library. Heating generation rates may be dependent on time, temperature, and position, and boundary temperatures may be time- and position-dependent. The boundary conditions, which maymore » be surface-to-boundary or surface-to-surface, may be specified temperatures or any combination of prescribed heat flux, forced convection, natural convection, and radiation. The boundary condition parameters may be time- and/or temperature-dependent. General graybody radiation problems may be modeled with user-defined factors for radiant exchange. The mesh spacing may be variable along each axis. HEATING is variably dimensioned and utilizes free-form input. Three steady-state solution techniques are available: point-successive-overrelaxation iterative method with extrapolation, direct-solution (for one-dimensional or two-dimensional problems), and conjugate gradient. Transient problems may be solved using one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method (which for some circumstances allows a time step greater than the CEP stability criterion). The solution of the system of equations arising from the implicit techniques is accomplished by point-successive-overrelaxation iteration and includes procedures to estimate the optimum acceleration parameter.« less

On a numerical method for solving integro-differential equations with variable coefficients with applications in finance

NASA Astrophysics Data System (ADS)

Kudryavtsev, O.; Rodochenko, V.

2018-03-01

We propose a new general numerical method aimed to solve integro-differential equations with variable coefficients. The problem under consideration arises in finance where in the context of pricing barrier options in a wide class of stochastic volatility models with jumps. To handle the effect of the correlation between the price and the variance, we use a suitable substitution for processes. Then we construct a Markov-chain approximation for the variation process on small time intervals and apply a maturity randomization technique. The result is a system of boundary problems for integro-differential equations with constant coefficients on the line in each vertex of the chain. We solve the arising problems using a numerical Wiener-Hopf factorization method. The approximate formulae for the factors are efficiently implemented by means of the Fast Fourier Transform. Finally, we use a recurrent procedure that moves backwards in time on the variance tree. We demonstrate the convergence of the method using Monte-Carlo simulations and compare our results with the results obtained by the Wiener-Hopf method with closed-form expressions of the factors.

A fast summation method for oscillatory lattice sums

NASA Astrophysics Data System (ADS)

Denlinger, Ryan; Gimbutas, Zydrunas; Greengard, Leslie; Rokhlin, Vladimir

2017-02-01

We present a fast summation method for lattice sums of the type which arise when solving wave scattering problems with periodic boundary conditions. While there are a variety of effective algorithms in the literature for such calculations, the approach presented here is new and leads to a rigorous analysis of Wood's anomalies. These arise when illuminating a grating at specific combinations of the angle of incidence and the frequency of the wave, for which the lattice sums diverge. They were discovered by Wood in 1902 as singularities in the spectral response. The primary tools in our approach are the Euler-Maclaurin formula and a steepest descent argument. The resulting algorithm has super-algebraic convergence and requires only milliseconds of CPU time.

Optimal Artificial Boundary Condition Configurations for Sensitivity-Based Model Updating and Damage Detection

DTIC Science & Technology

2010-09-01

matrix is used in many methods, like Jacobi or Gauss Seidel , for solving linear systems. Also, no partial pivoting is necessary for a strictly column...problems that arise during the procedure, which in general, converges to the solving of a linear system. The most common issue with the solution is the... iterative procedure to find an appropriate subset of parameters that produce an optimal solution commonly known as forward selection. Then, the

Unified treatment of microscopic boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method

NASA Astrophysics Data System (ADS)

Nguyen, Van-Dung; Wu, Ling; Noels, Ludovic

2017-03-01

This work provides a unified treatment of arbitrary kinds of microscopic boundary conditions usually considered in the multi-scale computational homogenization method for nonlinear multi-physics problems. An efficient procedure is developed to enforce the multi-point linear constraints arising from the microscopic boundary condition either by the direct constraint elimination or by the Lagrange multiplier elimination methods. The macroscopic tangent operators are computed in an efficient way from a multiple right hand sides linear system whose left hand side matrix is the stiffness matrix of the microscopic linearized system at the converged solution. The number of vectors at the right hand side is equal to the number of the macroscopic kinematic variables used to formulate the microscopic boundary condition. As the resolution of the microscopic linearized system often follows a direct factorization procedure, the computation of the macroscopic tangent operators is then performed using this factorized matrix at a reduced computational time.

On Raviart-Thomas and VMS formulations for flow in heterogeneous materials.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Turner, Daniel Zack

It is well known that the continuous Galerkin method (in its standard form) is not locally conservative, yet many stabilized methods are constructed by augmenting the standard Galerkin weak form. In particular, the Variational Multiscale (VMS) method has achieved popularity for combating numerical instabilities that arise for mixed formulations that do not otherwise satisfy the LBB condition. Among alternative methods that satisfy local and global conservation, many employ Raviart-Thomas function spaces. The lowest order Raviart-Thomas finite element formulation (RT0) consists of evaluating fluxes over the midpoint of element edges and constant pressures within the element. Although the RT0 element posesmore » many advantages, it has only been shown viable for triangular or tetrahedral elements (quadrilateral variants of this method do not pass the patch test). In the context of heterogenous materials, both of these methods have been used to model the mixed form of the Darcy equation. This work aims, in a comparative fashion, to evaluate the strengths and weaknesses of either approach for modeling Darcy flow for problems with highly varying material permeabilities and predominantly open flow boundary conditions. Such problems include carbon sequestration and enhanced oil recovery simulations for which the far-field boundary is typically described with some type of pressure boundary condition. We intend to show the degree to which the VMS formulation violates local mass conservation for these types of problems and compare the performance of the VMS and RT0 methods at boundaries between disparate permeabilities.« less

An algorithmic framework for multiobjective optimization.

PubMed

Ganesan, T; Elamvazuthi, I; Shaari, Ku Zilati Ku; Vasant, P

2013-01-01

Multiobjective (MO) optimization is an emerging field which is increasingly being encountered in many fields globally. Various metaheuristic techniques such as differential evolution (DE), genetic algorithm (GA), gravitational search algorithm (GSA), and particle swarm optimization (PSO) have been used in conjunction with scalarization techniques such as weighted sum approach and the normal-boundary intersection (NBI) method to solve MO problems. Nevertheless, many challenges still arise especially when dealing with problems with multiple objectives (especially in cases more than two). In addition, problems with extensive computational overhead emerge when dealing with hybrid algorithms. This paper discusses these issues by proposing an alternative framework that utilizes algorithmic concepts related to the problem structure for generating efficient and effective algorithms. This paper proposes a framework to generate new high-performance algorithms with minimal computational overhead for MO optimization.

An Algorithmic Framework for Multiobjective Optimization

PubMed Central

Ganesan, T.; Elamvazuthi, I.; Shaari, Ku Zilati Ku; Vasant, P.

2013-01-01

Multiobjective (MO) optimization is an emerging field which is increasingly being encountered in many fields globally. Various metaheuristic techniques such as differential evolution (DE), genetic algorithm (GA), gravitational search algorithm (GSA), and particle swarm optimization (PSO) have been used in conjunction with scalarization techniques such as weighted sum approach and the normal-boundary intersection (NBI) method to solve MO problems. Nevertheless, many challenges still arise especially when dealing with problems with multiple objectives (especially in cases more than two). In addition, problems with extensive computational overhead emerge when dealing with hybrid algorithms. This paper discusses these issues by proposing an alternative framework that utilizes algorithmic concepts related to the problem structure for generating efficient and effective algorithms. This paper proposes a framework to generate new high-performance algorithms with minimal computational overhead for MO optimization. PMID:24470795

First principles cable braid electromagnetic penetration model

DOE PAGES

Warne, Larry Kevin; Langston, William L.; Basilio, Lorena I.; ...

2016-01-01

The model for penetration of a wire braid is rigorously formulated. Integral formulas are developed from energy principles for both self and transfer immittances in terms of potentials for the fields. The detailed boundary value problem for the wire braid is also set up in a very efficient manner; the braid wires act as sources for the potentials in the form of a sequence of line multi-poles with unknown coefficients that are determined by means of conditions arising from the wire surface boundary conditions. Approximations are introduced to relate the local properties of the braid wires to a simplified infinitemore » periodic planar geometry. Furthermore, this is used to treat nonuniform coaxial geometries including eccentric interior coaxial arrangements and an exterior ground plane.« less

Point-particle effective field theory I: classical renormalization and the inverse-square potential

NASA Astrophysics Data System (ADS)

Burgess, C. P.; Hayman, Peter; Williams, M.; Zalavári, László

2017-04-01

Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's singularity. These ambiguities are usually resolved by developing a self-adjoint extension of the original prob-lem; a non-unique procedure that leaves undetermined which extension should apply in specific physical systems. We take the guesswork out of this picture by using techniques of effective field theory to derive the required boundary conditions at the origin in terms of the effective point-particle action describing the physics of the source. In this picture ambiguities in boundary conditions boil down to the allowed choices for the source action, but casting them in terms of an action provides a physical criterion for their determination. The resulting extension is self-adjoint if the source action is real (and involves no new degrees of freedom), and not otherwise (as can also happen for reasonable systems). We show how this effective-field picture provides a simple framework for understanding well-known renormalization effects that arise in these systems, including how renormalization-group techniques can resum non-perturbative interactions that often arise, particularly for non-relativistic applications. In particular we argue why the low-energy effective theory tends to produce a universal RG flow of this type and describe how this can lead to the phenomenon of reaction catalysis, in which physical quantities (like scattering cross sections) can sometimes be surprisingly large compared to the underlying scales of the source in question. We comment in passing on the possible relevance of these observations to the phenomenon of the catalysis of baryon-number violation by scattering from magnetic monopoles.

Physics from geometry: Non-Kahler compactifications, black rings anddS/CFT

NASA Astrophysics Data System (ADS)

Cyrier, Michelle

The spectrum that arises in four dimensions from compactification of ten dimensional string theory onto six dimensional manifolds is determined entirely by the geometry of the compactification manifold. The massless spectrum for compactifications on Calabi-Yau threefolds, which are Kahler and have complex structure, is well understood. In chapter 2 of this thesis, We study the compactification of heterotic string theory on manifolds that are non-Kahler. Such manifolds arise as a solution for compactifications of heterotic string theory with nonzero H-flux. We begin the study of the massless spectrum arising from compactification using this construction by counting zero modes of the linearized equations of motion for the gaugino in the supergravity approximation. We rephrase the question in terms of a cohomology problem and show that for a trivial gauge bundle, this cohomology reduces to the Dolbeault cohomology of the 3-fold, which we then compute. Another check of string theory is to study the entropy of black holes made in string theory. In Chapter 3, We review the microstate counting of four dimensional black holes made from M theory. We then describe a new solution in five dimensions, the supersymmetric black ring, and describe its microscopic entropy using a similar counting. These agree with the semi-classical Bekenstein-Hawking entropy for these black holes. Finally, one powerful tool for quantum gravity is the holographic duality of string theory in an Anti de Sitter background and a theory living on its conformal boundary. Strominger conjectured a similar duality between quantum gravity in a de Sitter background and the corresponding theory on its boundary. In chapter 4 we examine issues with different representations of the conformal field theory on the boundary for a massive quantum field theory living in the bulk and try to write down a sensible CFT.

Proceedings of the Strategic Computing Natural Language Workshop Held in Marina del Rey, California on 1-2 May 1986.

DTIC Science & Technology

1986-05-01

more specific top level goals supporting this single broad objective are to produce technology that will: 1. enable the operation of military systems...the boundary between semantics and pragmatics. These are problems that arise in single sentences, even though one may have to look beyond the single ...instances of metonymy seem to require only type knowledge. (4) At the most abstract level, interpretation requires the constructive proof of a single

Sub-optimal control of unsteady boundary layer separation and optimal control of Saltzman-Lorenz model

NASA Astrophysics Data System (ADS)

Sardesai, Chetan R.

The primary objective of this research is to explore the application of optimal control theory in nonlinear, unsteady, fluid dynamical settings. Two problems are considered: (1) control of unsteady boundary-layer separation, and (2) control of the Saltzman-Lorenz model. The unsteady boundary-layer equations are nonlinear partial differential equations that govern the eruptive events that arise when an adverse pressure gradient acts on a boundary layer at high Reynolds numbers. The Saltzman-Lorenz model consists of a coupled set of three nonlinear ordinary differential equations that govern the time-dependent coefficients in truncated Fourier expansions of Rayleigh-Renard convection and exhibit deterministic chaos. Variational methods are used to derive the nonlinear optimal control formulations based on cost functionals that define the control objective through a performance measure and a penalty function that penalizes the cost of control. The resulting formulation consists of the nonlinear state equations, which must be integrated forward in time, and the nonlinear control (adjoint) equations, which are integrated backward in time. Such coupled forward-backward time integrations are computationally demanding; therefore, the full optimal control problem for the Saltzman-Lorenz model is carried out, while the more complex unsteady boundary-layer case is solved using a sub-optimal approach. The latter is a quasi-steady technique in which the unsteady boundary-layer equations are integrated forward in time, and the steady control equation is solved at each time step. Both sub-optimal control of the unsteady boundary-layer equations and optimal control of the Saltzman-Lorenz model are found to be successful in meeting the control objectives for each problem. In the case of boundary-layer separation, the control results indicate that it is necessary to eliminate the recirculation region that is a precursor to the unsteady boundary-layer eruptions. In the case of the Saltzman-Lorenz model, it is possible to control the system about either of the two unstable equilibrium points representing clockwise and counterclockwise rotation of the convection roles in a parameter regime for which the uncontrolled solution would exhibit deterministic chaos.

Repeated Red-Black ordering

NASA Astrophysics Data System (ADS)

Ciarlet, P.

1994-09-01

Hereafter, we describe and analyze, from both a theoretical and a numerical point of view, an iterative method for efficiently solving symmetric elliptic problems with possibly discontinuous coefficients. In the following, we use the Preconditioned Conjugate Gradient method to solve the symmetric positive definite linear systems which arise from the finite element discretization of the problems. We focus our interest on sparse and efficient preconditioners. In order to define the preconditioners, we perform two steps: first we reorder the unknowns and then we carry out a (modified) incomplete factorization of the original matrix. We study numerically and theoretically two preconditioners, the second preconditioner corresponding to the one investigated by Brand and Heinemann [2]. We prove convergence results about the Poisson equation with either Dirichlet or periodic boundary conditions. For a meshsizeh, Brand proved that the condition number of the preconditioned system is bounded byO(h-1/2) for Dirichlet boundary conditions. By slightly modifying the preconditioning process, we prove that the condition number is bounded byO(h-1/3).

Morphological instabilities of rapidly solidified binary alloys under weak flow

NASA Astrophysics Data System (ADS)

Kowal, Katarzyna; Davis, Stephen

2017-11-01

Additive manufacturing, or three-dimensional printing, offers promising advantages over existing manufacturing techniques. However, it is still subject to a range of undesirable effects. One of these involves the onset of flow resulting from sharp thermal gradients within the laser melt pool, affecting the morphological stability of the solidified alloys. We examine the linear stability of the interface of a rapidly solidifying binary alloy under weak boundary-layer flow by performing an asymptotic analysis for a singular perturbation problem that arises as a result of departures from the equilibrium phase diagram. Under no flow, the problem involves cellular and pulsatile instabilities, stabilised by surface tension and attachment kinetics. We find that travelling waves appear as a result of flow and we map out the effect of flow on two absolute stability boundaries as well as on the cells and solute bands that have been observed in experiments under no flow. This work is supported by the National Institute of Standards and Technology [Grant Number 70NANB14H012].

A Tensor-Train accelerated solver for integral equations in complex geometries

NASA Astrophysics Data System (ADS)

Corona, Eduardo; Rahimian, Abtin; Zorin, Denis

2017-04-01

We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical compression and inversion scheme for matrices arising from the discretization of integral equations. For a broad range of problems, computational and storage costs of the inversion scheme are extremely modest O (log ⁡ N) and once the inverse is computed, it can be applied in O (Nlog ⁡ N) . We analyze the QTT ranks for hierarchically low rank matrices and discuss its relationship to commonly used hierarchical compression techniques such as FMM and HSS. We prove that the QTT ranks are bounded for translation-invariant systems and argue that this behavior extends to non-translation invariant volume and boundary integrals. For volume integrals, the QTT decomposition provides an efficient direct solver requiring significantly less memory compared to other fast direct solvers. We present results demonstrating the remarkable performance of the QTT-based solver when applied to both translation and non-translation invariant volume integrals in 3D. For boundary integral equations, we demonstrate that using a QTT decomposition to construct preconditioners for a Krylov subspace method leads to an efficient and robust solver with a small memory footprint. We test the QTT preconditioners in the iterative solution of an exterior elliptic boundary value problem (Laplace) formulated as a boundary integral equation in complex, multiply connected geometries.

A numerical study of different projection-based model reduction techniques applied to computational homogenisation

NASA Astrophysics Data System (ADS)

Soldner, Dominic; Brands, Benjamin; Zabihyan, Reza; Steinmann, Paul; Mergheim, Julia

2017-10-01

Computing the macroscopic material response of a continuum body commonly involves the formulation of a phenomenological constitutive model. However, the response is mainly influenced by the heterogeneous microstructure. Computational homogenisation can be used to determine the constitutive behaviour on the macro-scale by solving a boundary value problem at the micro-scale for every so-called macroscopic material point within a nested solution scheme. Hence, this procedure requires the repeated solution of similar microscopic boundary value problems. To reduce the computational cost, model order reduction techniques can be applied. An important aspect thereby is the robustness of the obtained reduced model. Within this study reduced-order modelling (ROM) for the geometrically nonlinear case using hyperelastic materials is applied for the boundary value problem on the micro-scale. This involves the Proper Orthogonal Decomposition (POD) for the primary unknown and hyper-reduction methods for the arising nonlinearity. Therein three methods for hyper-reduction, differing in how the nonlinearity is approximated and the subsequent projection, are compared in terms of accuracy and robustness. Introducing interpolation or Gappy-POD based approximations may not preserve the symmetry of the system tangent, rendering the widely used Galerkin projection sub-optimal. Hence, a different projection related to a Gauss-Newton scheme (Gauss-Newton with Approximated Tensors- GNAT) is favoured to obtain an optimal projection and a robust reduced model.

The influence of initial conditions on dispersion and reactions

NASA Astrophysics Data System (ADS)

Wood, B. D.

2016-12-01

In various generalizations of the reaction-dispersion problem, researchers have developed frameworks in which the apparent dispersion coefficient can be negative. Such dispersion coefficients raise several difficult questions. Most importantly, the presence of a negative dispersion coefficient at the macroscale leads to a macroscale representation that illustrates an apparent decrease in entropy with increasing time; this, then, appears to be in violation of basic thermodynamic principles. In addition, the proposition of a negative dispersion coefficient leads to an inherently ill-posed mathematical transport equation. The ill-posedness of the problem arises because there is no unique initial condition that corresponds to a later-time concentration distribution (assuming that if discontinuous initial conditions are allowed). In this presentation, we explain how the phenomena of negative dispersion coefficients actually arise because the governing differential equation for early times should, when derived correctly, incorporate a term that depends upon the initial and boundary conditions. The process of reactions introduces a similar phenomena, where the structure of the initial and boundary condition influences the form of the macroscopic balance equations. When upscaling is done properly, new equations are developed that include source terms that are not present in the classical (late-time) reaction-dispersion equation. These source terms depend upon the structure of the initial condition of the reacting species, and they decrease exponentially in time (thus, they converge to the conventional equations at asymptotic times). With this formulation, the resulting dispersion tensor is always positive-semi-definite, and the reaction terms directly incorporate information about the state of mixedness of the system. This formulation avoids many of the problems that would be engendered by defining negative-definite dispersion tensors, and properly represents the effective rate of reaction at early times.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Warne, Larry K.; Langston, William L.; Basilio, Lorena I.

The model for penetration of a wire braid is rigorously formulated. Integral formulas are developed from energy principles and reciprocity for both self and transfer immittances in terms of potentials for the fields. The detailed boundary value problem for the wire braid is also setup in a very efficient manner; the braid wires act as sources for the potentials in the form of a sequence of line multipoles with unknown coefficients that are determined by means of conditions arising from the wire surface boundary conditions. Approximations are introduced to relate the local properties of the braid wires to a simplifiedmore » infinite periodic planar geometry. This is used in a simplified application of reciprocity to be able to treat nonuniform coaxial geometries including eccentric interior coaxial arrangements and an exterior ground plane.« less

Radiative transfer in a polluted urban planetary boundary layer

NASA Technical Reports Server (NTRS)

Viskanta, R.; Johnson, R. O.; Bergstrom, R. W.

1977-01-01

Radiative transfer in a polluted urban atmosphere is studied using a dynamic model. The diurnal nature of radiative transfer for summer conditions is simulated for an urban area 40 km in extent and the effects of various parameters arising in the problem are investigated. The results of numerical computations show that air pollution has the potential of playing a major role in the radiative regime of the urban area. Absorption of solar energy by aerosols in realistic models of urban atmosphere are of the same order of magnitude as that due to water vapor. The predicted effect of the air pollution aerosol in the city is to warm the earth-atmosphere system, and the net effect of gaseous pollutant is to warm the surface and cool the planetary boundary layer, particularly near the top.

Transport of reacting solutes subject to a moving dissolution boundary: Numerical methods and solutions

USGS Publications Warehouse

Willis, Catherine; Rubin, Jacob

1987-01-01

A moving boundary problem which arises during transport with precipitation-dissolution reactions is solved by three different numerical methods. Two of these methods (one explicit and one implicit) are based on an integral formulation of mass balance and lead to an approximation of a weak solution. These methods are compared to a front-tracking scheme. Although the two approaches are conceptually different, the numerical solutions showed good agreement. As the ratio of dispersion to convection decreases, the methods based on the integral formulation become computationally more efficient. Specific reactions were modeled to examine the dependence of the system on the physical and chemical parameters. Although the water flow rate does not explicitly appear in the equation for the velocity of the moving boundary, the speed of the boundary depends more on the flux rate than on the dispersion coefficient. The discontinuity in the gradient of the solute concentration profile at the boundary increases with convection and with the initial concentration of the mineral. Our implicit method is extended to allow participation of the solutes in complexation reactions as well as the precipitation-dissolution reaction. This extension is easily made and does not change the basic method.

Optimal boundary regularity for a singular Monge-Ampère equation

NASA Astrophysics Data System (ADS)

Jian, Huaiyu; Li, You

2018-06-01

In this paper we study the optimal global regularity for a singular Monge-Ampère type equation which arises from a few geometric problems. We find that the global regularity does not depend on the smoothness of domain, but it does depend on the convexity of the domain. We introduce (a , η) type to describe the convexity. As a result, we show that the more convex is the domain, the better is the regularity of the solution. In particular, the regularity is the best near angular points.

A Comparison of Some Difference Schemes for a Parabolic Problem of Zero-Coupon Bond Pricing

NASA Astrophysics Data System (ADS)

Chernogorova, Tatiana; Vulkov, Lubin

2009-11-01

This paper describes a comparison of some numerical methods for solving a convection-diffusion equation subjected by dynamical boundary conditions which arises in the zero-coupon bond pricing. The one-dimensional convection-diffusion equation is solved by using difference schemes with weights including standard difference schemes as the monotone Samarskii's scheme, FTCS and Crank-Nicolson methods. The schemes are free of spurious oscillations and satisfy the positivity and maximum principle as demanded for the financial and diffusive solution. Numerical results are compared with analytical solutions.

Simulating wave-turbulence on thin elastic plates with arbitrary boundary conditions

NASA Astrophysics Data System (ADS)

van Rees, Wim M.; Mahadevan, L.

2016-11-01

The statistical characteristics of interacting waves are described by the theory of wave turbulence, with the study of deep water gravity wave turbulence serving as a paradigmatic physical example. Here we consider the elastic analog of this problem in the context of flexural waves arising from vibrations of a thin elastic plate. Such flexural waves generate the unique sounds of so-called thunder machines used in orchestras - thin metal plates that make a thunder-like sound when forcefully shaken. Wave turbulence in elastic plates is typically investigated numerically using spectral simulations with periodic boundary conditions, which are not very realistic. We will present the results of numerical simulations of the dynamics of thin elastic plates in physical space, with arbitrary shapes, boundary conditions, anisotropy and inhomogeneity, and show first results on wave turbulence beyond the conventionally studied rectangular plates. Finally, motivated by a possible method to measure ice-sheet thicknesses in the open ocean, we will further discuss the behavior of a vibrating plate when floating on an inviscid fluid.

Singular perturbation analysis of AOTV-related trajectory optimization problems

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Bae, Gyoung H.

1990-01-01

The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality constraint was imposed on the full order AOTV point mass equations of motion, using a simple aerodynamic heating rate model.

Can inequality be tamed through boundary work? A qualitative study of health promotion aimed at reducing health inequalities.

PubMed

Pedersen, Pia Vivian; Hjelmar, Ulf; Høybye, Mette Terp; Rod, Morten Hulvej

2017-07-01

This paper examines the organisational dynamics that arise in health promotion aimed at reducing health inequalities. The paper draws on ethnographic fieldwork among public health officers in Danish municipalities and qualitative interviews from an evaluation of health promotion programmes targeting homeless and other marginalised citizens. Analytically, we focus on 'boundary work', i.e. the ways in which social and symbolic boundaries are established, maintained, transgressed and negotiated, both at the administrative level and among frontline professionals. The paper discusses three types of boundary work: (i) demarcating professional domains; (ii) setting the boundaries of the task itself; and (iii) managing administrative boundaries. The main argument is that the production, maintenance and transgression of these three types of boundaries constitute central and time-consuming aspects of the practices of public health professionals, and that boundary work constitutes an important element in professional practices seeking to 'tame a wicked problem', such as social inequalities in health. A cross-cutting feature of the three types of boundary work is the management of the divide between health and social issues, which the professionals seemingly seek to uphold and transgress at the same time. The paper thus contributes to ongoing discussions of intersectoral action to address health inequalities. Furthermore, it extends the scope and application of the concept of boundary work in the sociology of public health by suggesting that the focus in previous research on professional demarcation be broadened in order to capture other types of boundaries that shape, and are shaped by, professional practices. Copyright © 2017 Elsevier Ltd. All rights reserved.

A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions

NASA Astrophysics Data System (ADS)

Reimer, Ashton S.; Cheviakov, Alexei F.

2013-03-01

A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.

A framework for discrete stochastic simulation on 3D moving boundary domains

DOE PAGES

Drawert, Brian; Hellander, Stefan; Trogdon, Michael; ...

2016-11-14

We have developed a method for modeling spatial stochastic biochemical reactions in complex, three-dimensional, and time-dependent domains using the reaction-diffusion master equation formalism. In particular, we look to address the fully coupled problems that arise in systems biology where the shape and mechanical properties of a cell are determined by the state of the biochemistry and vice versa. To validate our method and characterize the error involved, we compare our results for a carefully constructed test problem to those of a microscale implementation. Finally, we demonstrate the effectiveness of our method by simulating a model of polarization and shmoo formationmore » during the mating of yeast. The method is generally applicable to problems in systems biology where biochemistry and mechanics are coupled, and spatial stochastic effects are critical.« less

Computational procedures for mixed equations with shock waves

NASA Technical Reports Server (NTRS)

Yu, N. J.; Seebass, R.

1974-01-01

This paper discusses the procedures we have developed to treat a canonical problem involving a mixed nonlinear equation with boundary data that imply a discontinuous solution. This equation arises in various physical contexts and is basic to the description of the nonlinear acoustic behavior of a shock wave near a caustic. The numerical scheme developed is of second order, treats discontinuities as such by applying the appropriate jump conditions across them, and eliminates the numerical dissipation and dispersion associated with large gradients. Our results are compared with the results of a first-order scheme and with those of a second-order scheme we have developed. The algorithm used here can easily be generalized to more complicated problems, including transonic flows with imbedded shocks.

Optimization design of hydroturbine rotors according to the efficiency-strength criteria

NASA Astrophysics Data System (ADS)

Bannikov, D. V.; Yesipov, D. V.; Cherny, S. G.; Chirkov, D. V.

2010-12-01

The hydroturbine runner designing [1] is optimized by efficient methods for calculation of head loss in entire flow-through part of the turbine and deformation state of the blade. Energy losses are found at modelling of the spatial turbulent flow and engineering semi-empirical formulae. State of deformation is determined from the solution of the linear problem of elasticity for the isolated blade at hydrodynamic pressure with the method of boundary elements. With the use of the proposed system, the problem of the turbine runner design with the capacity of 640 MW providing the preset dependence of efficiency on the turbine work mode (efficiency criterion) is solved. The arising stresses do not exceed the critical value (strength criterion).

Heating 7.2 user`s manual

DOE Office of Scientific and Technical Information (OSTI.GOV)

Childs, K.W.

1993-02-01

HEATING is a general-purpose conduction heat transfer program written in Fortran 77. HEATING can solve steady-state and/or transient heat conduction problems in one-, two-, or three-dimensional Cartesian, cylindrical, or spherical coordinates. A model may include multiple materials, and the thermal conductivity, density, and specific heat of each material may be both time- and temperature-dependent. The thermal conductivity may also be anisotropic. Materials may undergo change of phase. Thermal properties of materials may be input or may be extracted from a material properties library. Heat-generation rates may be dependent on time, temperature, and position, and boundary temperatures may be time- andmore » position-dependent. The boundary conditions, which may be surface-to-environment or surface-to-surface, may be specified temperatures or any combination of prescribed heat flux, forced convection, natural convection, and radiation. The boundary condition parameters may be time- and/or temperature-dependent. General gray-body radiation problems may be modeled with user-defined factors for radiant exchange. The mesh spacing may be variable along each axis. HEATING uses a runtime memory allocation scheme to avoid having to recompile to match memory requirements for each specific problem. HEATING utilizes free-form input. Three steady-state solution techniques are available: point-successive-overrelaxation iterative method with extrapolation, direct-solution, and conjugate gradient. Transient problems may be solved using any one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method. The solution of the system of equations arising from the implicit techniques is accomplished by point-successive-overrelaxation iteration and includes procedures to estimate the optimum acceleration parameter.« less

Heating 7. 2 user's manual

DOE Office of Scientific and Technical Information (OSTI.GOV)

Childs, K.W.

1993-02-01

HEATING is a general-purpose conduction heat transfer program written in Fortran 77. HEATING can solve steady-state and/or transient heat conduction problems in one-, two-, or three-dimensional Cartesian, cylindrical, or spherical coordinates. A model may include multiple materials, and the thermal conductivity, density, and specific heat of each material may be both time- and temperature-dependent. The thermal conductivity may also be anisotropic. Materials may undergo change of phase. Thermal properties of materials may be input or may be extracted from a material properties library. Heat-generation rates may be dependent on time, temperature, and position, and boundary temperatures may be time- andmore » position-dependent. The boundary conditions, which may be surface-to-environment or surface-to-surface, may be specified temperatures or any combination of prescribed heat flux, forced convection, natural convection, and radiation. The boundary condition parameters may be time- and/or temperature-dependent. General gray-body radiation problems may be modeled with user-defined factors for radiant exchange. The mesh spacing may be variable along each axis. HEATING uses a runtime memory allocation scheme to avoid having to recompile to match memory requirements for each specific problem. HEATING utilizes free-form input. Three steady-state solution techniques are available: point-successive-overrelaxation iterative method with extrapolation, direct-solution, and conjugate gradient. Transient problems may be solved using any one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method. The solution of the system of equations arising from the implicit techniques is accomplished by point-successive-overrelaxation iteration and includes procedures to estimate the optimum acceleration parameter.« less

How the venetian blind percept emerges from the laminar cortical dynamics of 3D vision

PubMed Central

Cao, Yongqiang; Grossberg, Stephen

2014-01-01

The 3D LAMINART model of 3D vision and figure-ground perception is used to explain and simulate a key example of the Venetian blind effect and to show how it is related to other well-known perceptual phenomena such as Panum's limiting case. The model proposes how lateral geniculate nucleus (LGN) and hierarchically organized laminar circuits in cortical areas V1, V2, and V4 interact to control processes of 3D boundary formation and surface filling-in that simulate many properties of 3D vision percepts, notably consciously seen surface percepts, which are predicted to arise when filled-in surface representations are integrated into surface-shroud resonances between visual and parietal cortex. Interactions between layers 4, 3B, and 2/3 in V1 and V2 carry out stereopsis and 3D boundary formation. Both binocular and monocular information combine to form 3D boundary and surface representations. Surface contour surface-to-boundary feedback from V2 thin stripes to V2 pale stripes combines computationally complementary boundary and surface formation properties, leading to a single consistent percept, while also eliminating redundant 3D boundaries, and triggering figure-ground perception. False binocular boundary matches are eliminated by Gestalt grouping properties during boundary formation. In particular, a disparity filter, which helps to solve the Correspondence Problem by eliminating false matches, is predicted to be realized as part of the boundary grouping process in layer 2/3 of cortical area V2. The model has been used to simulate the consciously seen 3D surface percepts in 18 psychophysical experiments. These percepts include the Venetian blind effect, Panum's limiting case, contrast variations of dichoptic masking and the correspondence problem, the effect of interocular contrast differences on stereoacuity, stereopsis with polarity-reversed stereograms, da Vinci stereopsis, and perceptual closure. These model mechanisms have also simulated properties of 3D neon color spreading, binocular rivalry, 3D Necker cube, and many examples of 3D figure-ground separation. PMID:25309467

How the venetian blind percept emerges from the laminar cortical dynamics of 3D vision.

PubMed

Cao, Yongqiang; Grossberg, Stephen

2014-01-01

The 3D LAMINART model of 3D vision and figure-ground perception is used to explain and simulate a key example of the Venetian blind effect and to show how it is related to other well-known perceptual phenomena such as Panum's limiting case. The model proposes how lateral geniculate nucleus (LGN) and hierarchically organized laminar circuits in cortical areas V1, V2, and V4 interact to control processes of 3D boundary formation and surface filling-in that simulate many properties of 3D vision percepts, notably consciously seen surface percepts, which are predicted to arise when filled-in surface representations are integrated into surface-shroud resonances between visual and parietal cortex. Interactions between layers 4, 3B, and 2/3 in V1 and V2 carry out stereopsis and 3D boundary formation. Both binocular and monocular information combine to form 3D boundary and surface representations. Surface contour surface-to-boundary feedback from V2 thin stripes to V2 pale stripes combines computationally complementary boundary and surface formation properties, leading to a single consistent percept, while also eliminating redundant 3D boundaries, and triggering figure-ground perception. False binocular boundary matches are eliminated by Gestalt grouping properties during boundary formation. In particular, a disparity filter, which helps to solve the Correspondence Problem by eliminating false matches, is predicted to be realized as part of the boundary grouping process in layer 2/3 of cortical area V2. The model has been used to simulate the consciously seen 3D surface percepts in 18 psychophysical experiments. These percepts include the Venetian blind effect, Panum's limiting case, contrast variations of dichoptic masking and the correspondence problem, the effect of interocular contrast differences on stereoacuity, stereopsis with polarity-reversed stereograms, da Vinci stereopsis, and perceptual closure. These model mechanisms have also simulated properties of 3D neon color spreading, binocular rivalry, 3D Necker cube, and many examples of 3D figure-ground separation.

Oops, You're Stepping on My Boundaries!

ERIC Educational Resources Information Center

Marshall, Anne

Boundaries are limits that define us as separate from others. Although this concept is a familiar one in personal and addictions counseling, it is seldom discussed in career development or career counseling. Yet boundary issues arise constantly in working relationships, in the job-application process, among employees, and especially with…

Extremal Optimization for estimation of the error threshold in topological subsystem codes at T = 0

NASA Astrophysics Data System (ADS)

Millán-Otoya, Jorge E.; Boettcher, Stefan

2014-03-01

Quantum decoherence is a problem that arises in implementations of quantum computing proposals. Topological subsystem codes (TSC) have been suggested as a way to overcome decoherence. These offer a higher optimal error tolerance when compared to typical error-correcting algorithms. A TSC has been translated into a planar Ising spin-glass with constrained bimodal three-spin couplings. This spin-glass has been considered at finite temperature to determine the phase boundary between the unstable phase and the stable phase, where error recovery is possible.[1] We approach the study of the error threshold problem by exploring ground states of this spin-glass with the Extremal Optimization algorithm (EO).[2] EO has proven to be a effective heuristic to explore ground state configurations of glassy spin-systems.[3

Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bokanowski, Olivier, E-mail: boka@math.jussieu.fr; Picarelli, Athena, E-mail: athena.picarelli@inria.fr; Zidani, Hasnaa, E-mail: hasnaa.zidani@ensta.fr

2015-02-15

This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system ofmore » controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.« less

Orbiter entry aerothermodynamics

NASA Technical Reports Server (NTRS)

Ried, R. C.

1985-01-01

The challenge in the definition of the entry aerothermodynamic environment arising from the challenge of a reliable and reusable Orbiter is reviewed in light of the existing technology. Select problems pertinent to the orbiter development are discussed with reference to comprehensive treatments. These problems include boundary layer transition, leeward-side heating, shock/shock interaction scaling, tile gap heating, and nonequilibrium effects such as surface catalysis. Sample measurements obtained from test flights of the Orbiter are presented with comparison to preflight expectations. Numerical and wind tunnel simulations gave efficient information for defining the entry environment and an adequate level of preflight confidence. The high quality flight data provide an opportunity to refine the operational capability of the orbiter and serve as a benchmark both for the development of aerothermodynamic technology and for use in meeting future entry heating challenges.

Optimal solar sail planetocentric trajectories

NASA Technical Reports Server (NTRS)

Sackett, L. L.

1977-01-01

The analysis of solar sail planetocentric optimal trajectory problem is described. A computer program was produced to calculate optimal trajectories for a limited performance analysis. A square sail model is included and some consideration is given to a heliogyro sail model. Orbit to a subescape point and orbit to orbit transfer are considered. Trajectories about the four inner planets can be calculated and shadowing, oblateness, and solar motion may be included. Equinoctial orbital elements are used to avoid the classical singularities, and the method of averaging is applied to increase computational speed. Solution of the two-point boundary value problem which arises from the application of optimization theory is accomplished with a Newton procedure. Time optimal trajectories are emphasized, but a penalty function has been considered to prevent trajectories which intersect a planet's surface.

A minimally-resolved immersed boundary model for reaction-diffusion problems

NASA Astrophysics Data System (ADS)

Pal Singh Bhalla, Amneet; Griffith, Boyce E.; Patankar, Neelesh A.; Donev, Aleksandar

2013-12-01

We develop an immersed boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a minimally-resolved "blob" using many fewer degrees of freedom per particle than standard discretization approaches. More complicated or more highly resolved particle shapes can be built out of a collection of reactive blobs. We demonstrate numerically that the blob model can provide an accurate representation at low to moderate packing densities of the reactive particles, at a cost not much larger than solving a Poisson equation in the same domain. Unlike multipole expansion methods, our method does not require analytically computed Green's functions, but rather, computes regularized discrete Green's functions on the fly by using a standard grid-based discretization of the Poisson equation. This allows for great flexibility in implementing different boundary conditions, coupling to fluid flow or thermal transport, and the inclusion of other effects such as temporal evolution and even nonlinearities. We develop multigrid-based preconditioners for solving the linear systems that arise when using implicit temporal discretizations or studying steady states. In the diffusion-limited case the resulting linear system is a saddle-point problem, the efficient solution of which remains a challenge for suspensions of many particles. We validate our method by comparing to published results on reaction-diffusion in ordered and disordered suspensions of reactive spheres.

Active stability augmentation of large space structures: A stochastic control problem

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1987-01-01

A problem in SCOLE is that of slewing an offset antenna on a long flexible beam-like truss attached to the space shuttle, with rather stringent pointing accuracy requirements. The relevant methodology aspects in robust feedback-control design for stability augmentation of the beam using on-board sensors is examined. It is framed as a stochastic control problem, boundary control of a distributed parameter system described by partial differential equations. While the framework is mathematical, the emphasis is still on an engineering solution. An abstract mathematical formulation is developed as a nonlinear wave equation in a Hilbert space. That the system is controllable is shown and a feedback control law that is robust in the sense that it does not require quantitative knowledge of system parameters is developed. The stochastic control problem that arises in instrumenting this law using appropriate sensors is treated. Using an engineering first approximation which is valid for small damping, formulas for optimal choice of the control gain are developed.

Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Luo, Xu-Dan; Musslimani, Ziad H.

2018-01-01

In 2013, a new nonlocal symmetry reduction of the well-known AKNS (an integrable system of partial differential equations, introduced by and named after Mark J. Ablowitz, David J. Kaup, and Alan C. Newell et al. (1974)) scattering problem was found. It was shown to give rise to a new nonlocal PT symmetric and integrable Hamiltonian nonlinear Schrödinger (NLS) equation. Subsequently, the inverse scattering transform was constructed for the case of rapidly decaying initial data and a family of spatially localized, time periodic one-soliton solutions was found. In this paper, the inverse scattering transform for the nonlocal NLS equation with nonzero boundary conditions at infinity is presented in four different cases when the data at infinity have constant amplitudes. The direct and inverse scattering problems are analyzed. Specifically, the direct problem is formulated, the analytic properties of the eigenfunctions and scattering data and their symmetries are obtained. The inverse scattering problem, which arises from a novel nonlocal system, is developed via a left-right Riemann-Hilbert problem in terms of a suitable uniformization variable and the time dependence of the scattering data is obtained. This leads to a method to linearize/solve the Cauchy problem. Pure soliton solutions are discussed, and explicit 1-soliton solution and two 2-soliton solutions are provided for three of the four different cases corresponding to two different signs of nonlinearity and two different values of the phase difference between plus and minus infinity. In another case, there are no solitons.

Scattering of elastic waves from thin shapes in three dimensions using the composite boundary integral equation formulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Y.; Rizzo, F.J.

1997-08-01

In this paper, the composite boundary integral equation (BIE) formulation is applied to scattering of elastic waves from thin shapes with small but {ital finite} thickness (open cracks or thin voids, thin inclusions, thin-layer interfaces, etc.), which are modeled with {ital two surfaces}. This composite BIE formulation, which is an extension of the Burton and Miller{close_quote}s formulation for acoustic waves, uses a linear combination of the conventional BIE and the hypersingular BIE. For thin shapes, the conventional BIE, as well as the hypersingular BIE, will degenerate (or nearly degenerate) if they are applied {ital individually} on the two surfaces. Themore » composite BIE formulation, however, will not degenerate for such problems, as demonstrated in this paper. Nearly singular and hypersingular integrals, which arise in problems involving thin shapes modeled with two surfaces, are transformed into sums of weakly singular integrals and nonsingular line integrals. Thus, no finer mesh is needed to compute these nearly singular integrals. Numerical examples of elastic waves scattered from penny-shaped cracks with varying openings are presented to demonstrate the effectiveness of the composite BIE formulation. {copyright} {ital 1997 Acoustical Society of America.}« less

Receptivity of flat-plate boundary layer in a non-uniform free stream (vorticity normal to the plate)

NASA Technical Reports Server (NTRS)

Kogan, M. N.

1994-01-01

Recent progress in both the linear and nonlinear aspects of stability theory has highlighted the importance of the receptivity problem. One of the most unclear aspects of receptivity study is the receptivity of boundary-layer flow normal to vortical disturbances. Some experimental and theoretical results permit the proposition that quasi-steady outer-flow vortical disturbances may trigger by-pass transition. In present work such interaction is investigated for vorticity normal to a leading edge. The interest in these types of vortical disturbances arise from theoretical work, where it was shown that small sinusoidal variations of upstream velocity along the spanwise direction can produce significant variations in the boundary-layer profile. In the experimental part of this work, such non-uniform flow was created and the laminar-turbulent transition in this flow was investigated. The experiment was carried out in a low-turbulence direct-flow wind tunnel T-361 at the Central Aerohydrodynamic Institute (TsAGI). The non-uniform flow was produced by laminar or turbulent wakes behind a wire placed normal to the plate upstream of the leading edge. The theoretical part of the work is devoted to studying the unstable disturbance evolution in a boundary layer with strongly non-uniform velocity profiles similar to that produced by outer-flow vorticity. Specifically, the Tollmien-Schlichting wave development in the boundary layer flow with spanwise variations of velocity is investigated.

Implications of Spatial Data Variations for Protected Areas Management: An Example from East Africa

NASA Astrophysics Data System (ADS)

Dowhaniuk, Nicholas; Hartter, Joel; Ryan, Sadie J.

2014-09-01

Geographic information systems and remote sensing technologies have become an important tool for visualizing conservation management and developing solutions to problems associated with conservation. When multiple organizations separately develop spatial data representations of protected areas, implicit error arises due to variation between data sets. We used boundary data produced by three conservation organizations (International Union for the Conservation of Nature, World Resource Institute, and Uganda Wildlife Authority), for seven Ugandan parks, to study variation in the size represented and the location of boundaries. We found variation in the extent of overlapping total area encompassed by the three data sources, ranging from miniscule (0.4 %) differences to quite large ones (9.0 %). To underscore how protected area boundary discrepancies may have implications to protected area management, we used a landcover classification, defining crop, shrub, forest, savanna, and grassland. The total area in the different landcover classes varied most in smaller protected areas (those less than 329 km2), with forest and cropland area estimates varying up to 65 %. The discrepancies introduced by boundary errors could, in this hypothetical case, generate erroneous findings and could have a significant impact on conservation, such as local-scale management for encroachment and larger-scale assessments of deforestation.

Implications of spatial data variations for protected areas management: an example from East Africa.

PubMed

Dowhaniuk, Nicholas; Hartter, Joel; Ryan, Sadie J

2014-09-01

Geographic information systems and remote sensing technologies have become an important tool for visualizing conservation management and developing solutions to problems associated with conservation. When multiple organizations separately develop spatial data representations of protected areas, implicit error arises due to variation between data sets. We used boundary data produced by three conservation organizations (International Union for the Conservation of Nature, World Resource Institute, and Uganda Wildlife Authority), for seven Ugandan parks, to study variation in the size represented and the location of boundaries. We found variation in the extent of overlapping total area encompassed by the three data sources, ranging from miniscule (0.4 %) differences to quite large ones (9.0 %). To underscore how protected area boundary discrepancies may have implications to protected area management, we used a landcover classification, defining crop, shrub, forest, savanna, and grassland. The total area in the different landcover classes varied most in smaller protected areas (those less than 329 km(2)), with forest and cropland area estimates varying up to 65 %. The discrepancies introduced by boundary errors could, in this hypothetical case, generate erroneous findings and could have a significant impact on conservation, such as local-scale management for encroachment and larger-scale assessments of deforestation.

Voltera's Solution of the Wave Equation as Applied to Three-Dimensional Supersonic Airfoil Problems

NASA Technical Reports Server (NTRS)

Heslet, Max A; Lomax, Harvard; Jones, Arthur L

1947-01-01

A surface integral is developed which yields solutions of the linearized partial differential equation for supersonic flow. These solutions satisfy boundary conditions arising in wing theory. Particular applications of this general method are made, using acceleration potentials, to flat surfaces and to uniformly loaded lifting surfaces. Rectangular and trapezoidal plan forms are considered along with triangular forms adaptable to swept-forward and swept-back wings. The case of the triangular plan form in sideslip is also included. Emphasis is placed on the systematic application of the method to the lifting surfaces considered and on the possibility of further application.

Spectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems

NASA Astrophysics Data System (ADS)

Plestenjak, Bor; Gheorghiu, Călin I.; Hochstenbach, Michiel E.

2015-10-01

In numerous science and engineering applications a partial differential equation has to be solved on some fairly regular domain that allows the use of the method of separation of variables. In several orthogonal coordinate systems separation of variables applied to the Helmholtz, Laplace, or Schrödinger equation leads to a multiparameter eigenvalue problem (MEP); important cases include Mathieu's system, Lamé's system, and a system of spheroidal wave functions. Although multiparameter approaches are exploited occasionally to solve such equations numerically, MEPs remain less well known, and the variety of available numerical methods is not wide. The classical approach of discretizing the equations using standard finite differences leads to algebraic MEPs with large matrices, which are difficult to solve efficiently. The aim of this paper is to change this perspective. We show that by combining spectral collocation methods and new efficient numerical methods for algebraic MEPs it is possible to solve such problems both very efficiently and accurately. We improve on several previous results available in the literature, and also present a MATLAB toolbox for solving a wide range of problems.

Multigrid method based on the transformation-free HOC scheme on nonuniform grids for 2D convection diffusion problems

NASA Astrophysics Data System (ADS)

Ge, Yongbin; Cao, Fujun

2011-05-01

In this paper, a multigrid method based on the high order compact (HOC) difference scheme on nonuniform grids, which has been proposed by Kalita et al. [J.C. Kalita, A.K. Dass, D.C. Dalal, A transformation-free HOC scheme for steady convection-diffusion on non-uniform grids, Int. J. Numer. Methods Fluids 44 (2004) 33-53], is proposed to solve the two-dimensional (2D) convection diffusion equation. The HOC scheme is not involved in any grid transformation to map the nonuniform grids to uniform grids, consequently, the multigrid method is brand-new for solving the discrete system arising from the difference equation on nonuniform grids. The corresponding multigrid projection and interpolation operators are constructed by the area ratio. Some boundary layer and local singularity problems are used to demonstrate the superiority of the present method. Numerical results show that the multigrid method with the HOC scheme on nonuniform grids almost gets as equally efficient convergence rate as on uniform grids and the computed solution on nonuniform grids retains fourth order accuracy while on uniform grids just gets very poor solution for very steep boundary layer or high local singularity problems. The present method is also applied to solve the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation and the numerical solutions of the lid-driven cavity flow problem are obtained and compared with solutions available in the literature.

On the solution of integral equations with a generalized cauchy kernal

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

A certain class of singular integral equations that may arise from the mixed boundary value problems in nonhonogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernal has strong singularities of the form (t-x)(-2), x(n-2) (t+x)(n), (n is = or 2, 0 x, t b). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

What is involved in medicines management across care boundaries? A qualitative study of healthcare practitioners' experiences in the case of acute kidney injury

PubMed Central

Morris, Rebecca L; Blakeman, Tom; Ashcroft, Darren M

2017-01-01

Objectives To examine the role of individual and collective cognitive work in managing medicines for acute kidney injury (AKI), this being an example of a clinical scenario that crosses the boundaries of care organisations and specialties. Design Qualitative design, informed by a realist perspective and using semistructured interviews as the data source. The data were analysed using template analysis. Setting Primary, secondary and intermediate care in England. Participants 12 General practitioners, 10 community pharmacists, 7 hospital doctors and 7 hospital pharmacists, all with experience of involvement in preventing or treating AKI. Results We identified three main themes concerning participants' experiences of managing medicines in AKI. In the first theme, challenges arising from the clinical context, AKI is identified as a technically complex condition to identify and treat, often requiring judgements to be made about renal functioning against the context of the patient's general well-being. In the second theme, challenges arising from the organisational context, the crossing of professional and organisational boundaries is seen to introduce problems for the coordination of clinical activities, for example by disrupting information flows. In the third theme, meeting the challenges, participants identify ways in which they overcome the challenges they face in order to ensure effective medicines management, for example by adapting their work practices and tools. Conclusions These themes indicate the critical role of cognitive work on the part of healthcare practitioners, as individuals and as teams, in ensuring effective medicines management during AKI. Our findings suggest that the capabilities underlying this work, for example decision-making, communication and team coordination, should be the focus of training and work design interventions to improve medicines management for AKI or for other conditions. PMID:28100559

Feature extraction and classification algorithms for high dimensional data

NASA Technical Reports Server (NTRS)

Lee, Chulhee; Landgrebe, David

1993-01-01

Feature extraction and classification algorithms for high dimensional data are investigated. Developments with regard to sensors for Earth observation are moving in the direction of providing much higher dimensional multispectral imagery than is now possible. In analyzing such high dimensional data, processing time becomes an important factor. With large increases in dimensionality and the number of classes, processing time will increase significantly. To address this problem, a multistage classification scheme is proposed which reduces the processing time substantially by eliminating unlikely classes from further consideration at each stage. Several truncation criteria are developed and the relationship between thresholds and the error caused by the truncation is investigated. Next an approach to feature extraction for classification is proposed based directly on the decision boundaries. It is shown that all the features needed for classification can be extracted from decision boundaries. A characteristic of the proposed method arises by noting that only a portion of the decision boundary is effective in discriminating between classes, and the concept of the effective decision boundary is introduced. The proposed feature extraction algorithm has several desirable properties: it predicts the minimum number of features necessary to achieve the same classification accuracy as in the original space for a given pattern recognition problem; and it finds the necessary feature vectors. The proposed algorithm does not deteriorate under the circumstances of equal means or equal covariances as some previous algorithms do. In addition, the decision boundary feature extraction algorithm can be used both for parametric and non-parametric classifiers. Finally, some problems encountered in analyzing high dimensional data are studied and possible solutions are proposed. First, the increased importance of the second order statistics in analyzing high dimensional data is recognized. By investigating the characteristics of high dimensional data, the reason why the second order statistics must be taken into account in high dimensional data is suggested. Recognizing the importance of the second order statistics, there is a need to represent the second order statistics. A method to visualize statistics using a color code is proposed. By representing statistics using color coding, one can easily extract and compare the first and the second statistics.

Wall-touching kink mode calculations with the M3D code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Breslau, J. A., E-mail: jbreslau@pppl.gov; Bhattacharjee, A.

This paper seeks to address a controversy regarding the applicability of the 3D nonlinear extended MHD code M3D [W. Park et al., Phys. Plasmas 6, 1796 (1999)] and similar codes to calculations of the electromagnetic interaction of a disrupting tokamak plasma with the surrounding vessel structures. M3D is applied to a simple test problem involving an external kink mode in an ideal cylindrical plasma, used also by the Disruption Simulation Code (DSC) as a model case for illustrating the nature of transient vessel currents during a major disruption. While comparison of the results with those of the DSC is complicatedmore » by effects arising from the higher dimensionality and complexity of M3D, we verify that M3D is capable of reproducing both the correct saturation behavior of the free boundary kink and the “Hiro” currents arising when the kink interacts with a conducting tile surface interior to the ideal wall.« less

Utility of palmatolepids and icriodontids in recognizing Upper Devonian Series, Stage, and possible substage boundaries

USGS Publications Warehouse

Ziegler, W.; Sandberg, C.A.

2000-01-01

Conodonts are accepted internationally to define Devonian Series and Stage boundaries. Hence, the evolution and taxonomy of pelagic palmatolepids, primarily Palmatolepis and its direct ancestor Mesotaxis, and shallow-water icriodontids, Icriodus, Pelekysgnathus, and "Icriodus", are the major tools for recognizing subdivisions of the Upper Devonian. Palmatolepids are the basis for the Late Devonian Standard Conodont Zonation (ZIEGLER & SANDBERG 1990), whereas icriodontids are the basis for the alternative, integrated shallow-water zonation (SANDBERG & DREESEN 1984). However, an alternative palmatolepid taxonomy for some Frasnian species has been employed recently by some conodont workers using the Montagne Noire (M.N.) zonation, shape analyses of Pa elements, and multielement reconstructions of KLAPPER (1989), KLAPPER & FOSTER (1993); and KLAPPER et al. (1996). Herein, the evolution of palmatolepids and icriodontids is summarized in terms of our zonation and some of the taxonomic differences with the alternative M.N. zonation are exemplified. One of the problems in relating the Standard and M.N. zonations arises from previous errors of interpretation and drafting of the Martenberg section in Germany. This section was designated the reference section for the Frasnian transitans through jamieae Zones by ZIEGLER & SANDBERG (1990). Herein, the early and middle Frasnian zonal boundaries at Martenberg are improved by re-study of our old and recent collections from three profiles, spaced only 4 m apart. Serious problems exist with the Global Stratotype Sections and Points (GSSP's), selected by the Subcommission on Devonian Stratigraphy, following the paleontologic definition of the bases of the Frasnian, Famennian, and Tournaisian Stages, because of the difficulty in making global correlations from these GSSP's. Our summary of these problems should be helpful if future workers decide to relocate these GSSP's.

An ill-posed parabolic evolution system for dispersive deoxygenation-reaeration in water

NASA Astrophysics Data System (ADS)

Azaïez, M.; Ben Belgacem, F.; Hecht, F.; Le Bot, C.

2014-01-01

We consider an inverse problem that arises in the management of water resources and pertains to the analysis of surface water pollution by organic matter. Most physically relevant models used by engineers derive from various additions and corrections to enhance the earlier deoxygenation-reaeration model proposed by Streeter and Phelps in 1925, the unknowns being the biochemical oxygen demand (BOD) and the dissolved oxygen (DO) concentrations. The one we deal with includes Taylor’s dispersion to account for the heterogeneity of the contamination in all space directions. The system we obtain is then composed of two reaction-dispersion equations. The particularity is that both Neumann and Dirichlet boundary conditions are available on the DO tracer while the BOD density is free of any conditions. In fact, for real-life concerns, measurements on the DO are easy to obtain and to save. On the contrary, collecting data on the BOD is a sensitive task and turns out to be a lengthy process. The global model pursues the reconstruction of the BOD density, and especially of its flux along the boundary. Not only is this problem plainly worth studying for its own interest but it could also be a mandatory step in other applications such as the identification of the location of pollution sources. The non-standard boundary conditions generate two difficulties in mathematical and computational grounds. They set up a severe coupling between both equations and they are the cause of the ill-posed data reconstruction problem. Existence and stability fail. Identifiability is therefore the only positive result one can search for; it is the central purpose of the paper. Finally, we have performed some computational experiments to assess the capability of the mixed finite element in missing data recovery.

Wall-Resolved Large-Eddy Simulation of Flow Separation Over NASA Wall-Mounted Hump

NASA Technical Reports Server (NTRS)

Uzun, Ali; Malik, Mujeeb R.

2017-01-01

This paper reports the findings from a study that applies wall-resolved large-eddy simulation to investigate flow separation over the NASA wall-mounted hump geometry. Despite its conceptually simple flow configuration, this benchmark problem has proven to be a challenging test case for various turbulence simulation methods that have attempted to predict flow separation arising from the adverse pressure gradient on the aft region of the hump. The momentum-thickness Reynolds number of the incoming boundary layer has a value that is near the upper limit achieved by recent direct numerical simulation and large-eddy simulation of incompressible turbulent boundary layers. The high Reynolds number of the problem necessitates a significant number of grid points for wall-resolved calculations. The present simulations show a significant improvement in the separation-bubble length prediction compared to Reynolds-Averaged Navier-Stokes calculations. The current simulations also provide good overall prediction of the skin-friction distribution, including the relaminarization observed over the front portion of the hump due to the strong favorable pressure gradient. We discuss a number of problems that were encountered during the course of this work and present possible solutions. A systematic study regarding the effect of domain span, subgrid-scale model, tunnel back pressure, upstream boundary layer conditions and grid refinement is performed. The predicted separation-bubble length is found to be sensitive to the span of the domain. Despite the large number of grid points used in the simulations, some differences between the predictions and experimental observations still exist (particularly for Reynolds stresses) in the case of the wide-span simulation, suggesting that additional grid resolution may be required.

A Spectral Multi-Domain Penalty Method for Elliptic Problems Arising From a Time-Splitting Algorithm For the Incompressible Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Diamantopoulos, Theodore; Rowe, Kristopher; Diamessis, Peter

2017-11-01

The Collocation Penalty Method (CPM) solves a PDE on the interior of a domain, while weakly enforcing boundary conditions at domain edges via penalty terms, and naturally lends itself to high-order and multi-domain discretization. Such spectral multi-domain penalty methods (SMPM) have been used to solve the Navier-Stokes equations. Bounds for penalty coefficients are typically derived using the energy method to guarantee stability for time-dependent problems. The choice of collocation points and penalty parameter can greatly affect the conditioning and accuracy of a solution. Effort has been made in recent years to relate various high-order methods on multiple elements or domains under the umbrella of the Correction Procedure via Reconstruction (CPR). Most applications of CPR have focused on solving the compressible Navier-Stokes equations using explicit time-stepping procedures. A particularly important aspect which is still missing in the context of the SMPM is a study of the Helmholtz equation arising in many popular time-splitting schemes for the incompressible Navier-Stokes equations. Stability and convergence results for the SMPM for the Helmholtz equation will be presented. Emphasis will be placed on the efficiency and accuracy of high-order methods.

The year 2000 threat: preparing radiology for nine realms of risk.

PubMed

Berland, L L

1999-01-01

The year 2000 computer problem arises from a long-standing and often-duplicated computer programming error. Affected programs use only two digits to represent years, which may lead to a variety of computer malfunctions and data errors related to crossing from 1999 (99) to 2000 (00), at which point computers may interpret 00 as 1900 or other incorrect dates. Radiology and medicine may be seriously affected by this problem as it relates to the function of its equipment; business functions such as scheduling, billing and purchasing; the reliability of infrastructure such as power and telecommunications; the availability of supplies; and many other issues. It is crucial that radiologists, as practitioners of one of the most computer-oriented medical specialties, help lead the effort to ensure continuity of operations as the year 2000 boundary approaches and passes. This article provides suggestions for a structured approach, as well as tools and checklists, to guide project leaders attempting to identify and remediate year 2000-associated problems within radiology facilities.

An automatic multigrid method for the solution of sparse linear systems

NASA Technical Reports Server (NTRS)

Shapira, Yair; Israeli, Moshe; Sidi, Avram

1993-01-01

An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies.

TranAir: A full-potential, solution-adaptive, rectangular grid code for predicting subsonic, transonic, and supersonic flows about arbitrary configurations. Theory document

NASA Technical Reports Server (NTRS)

Johnson, F. T.; Samant, S. S.; Bieterman, M. B.; Melvin, R. G.; Young, D. P.; Bussoletti, J. E.; Hilmes, C. L.

1992-01-01

A new computer program, called TranAir, for analyzing complex configurations in transonic flow (with subsonic or supersonic freestream) was developed. This program provides accurate and efficient simulations of nonlinear aerodynamic flows about arbitrary geometries with the ease and flexibility of a typical panel method program. The numerical method implemented in TranAir is described. The method solves the full potential equation subject to a set of general boundary conditions and can handle regions with differing total pressure and temperature. The boundary value problem is discretized using the finite element method on a locally refined rectangular grid. The grid is automatically constructed by the code and is superimposed on the boundary described by networks of panels; thus no surface fitted grid generation is required. The nonlinear discrete system arising from the finite element method is solved using a preconditioned Krylov subspace method embedded in an inexact Newton method. The solution is obtained on a sequence of successively refined grids which are either constructed adaptively based on estimated solution errors or are predetermined based on user inputs. Many results obtained by using TranAir to analyze aerodynamic configurations are presented.

An algebraic homotopy method for generating quasi-three-dimensional grids for high-speed configurations

NASA Technical Reports Server (NTRS)

Moitra, Anutosh

1989-01-01

A fast and versatile procedure for algebraically generating boundary conforming computational grids for use with finite-volume Euler flow solvers is presented. A semi-analytic homotopic procedure is used to generate the grids. Grids generated in two-dimensional planes are stacked to produce quasi-three-dimensional grid systems. The body surface and outer boundary are described in terms of surface parameters. An interpolation scheme is used to blend between the body surface and the outer boundary in order to determine the field points. The method, albeit developed for analytically generated body geometries is equally applicable to other classes of geometries. The method can be used for both internal and external flow configurations, the only constraint being that the body geometries be specified in two-dimensional cross-sections stationed along the longitudinal axis of the configuration. Techniques for controlling various grid parameters, e.g., clustering and orthogonality are described. Techniques for treating problems arising in algebraic grid generation for geometries with sharp corners are addressed. A set of representative grid systems generated by this method is included. Results of flow computations using these grids are presented for validation of the effectiveness of the method.

(2,2) and (0,4) supersymmetric boundary conditions in 3d N =4 theories and type IIB branes

NASA Astrophysics Data System (ADS)

Chung, Hee-Joong; Okazaki, Tadashi

2017-10-01

The half-BPS boundary conditions preserving N =(2 ,2 ) and N =(0 ,4 ) supersymmetry in 3d N =4 supersymmetric gauge theories are examined. The BPS equations admit decomposition of the bulk supermultiplets into specific boundary supermultiplets of preserved supersymmetry. Nahm-like equations arise in the vector multiplet BPS boundary condition preserving N =(0 ,4 ) supersymmetry, and Robin-type boundary conditions appear for the hypermultiplet coupled to the vector multiplet when N =(2 ,2 ) supersymmetry is preserved. The half-BPS boundary conditions are realized in the brane configurations of type IIB string theory.

Multidimensional equilibria and their stability in copolymer-solvent mixtures

NASA Astrophysics Data System (ADS)

Glasner, Karl; Orizaga, Saulo

2018-06-01

This paper discusses localized equilibria which arise in copolymer-solvent mixtures. A free boundary problem associated with the sharp-interface limit of a density functional model is used to identify both lamellar and concentric domain patterns composed of a finite number of layers. Stability of these morphologies is studied through explicit linearization of the free boundary evolution. For the multilayered lamellar configuration, transverse instability is observed for sufficiently small dimensionless interfacial energies. Additionally, a crossover between small and large wavelength instabilities is observed depending on whether solvent-polymer or monomer-monomer interfacial energy is dominant. Concentric domain patterns resembling multilayered micelles and vesicles exhibit bifurcations wherein they only exist for sufficiently small dimensionless interfacial energies. The bifurcation of large radii vesicle solutions is studied analytically, and a crossover from a supercritical case with only one solution branch to a subcritical case with two is observed. Linearized stability of these configurations shows that azimuthal perturbation may lead to instabilities as interfacial energy is decreased.

Self-organization of muscle cell structure and function.

PubMed

Grosberg, Anna; Kuo, Po-Ling; Guo, Chin-Lin; Geisse, Nicholas A; Bray, Mark-Anthony; Adams, William J; Sheehy, Sean P; Parker, Kevin Kit

2011-02-01

The organization of muscle is the product of functional adaptation over several length scales spanning from the sarcomere to the muscle bundle. One possible strategy for solving this multiscale coupling problem is to physically constrain the muscle cells in microenvironments that potentiate the organization of their intracellular space. We hypothesized that boundary conditions in the extracellular space potentiate the organization of cytoskeletal scaffolds for directed sarcomeregenesis. We developed a quantitative model of how the cytoskeleton of neonatal rat ventricular myocytes organizes with respect to geometric cues in the extracellular matrix. Numerical results and in vitro assays to control myocyte shape indicated that distinct cytoskeletal architectures arise from two temporally-ordered, organizational processes: the interaction between actin fibers, premyofibrils and focal adhesions, as well as cooperative alignment and parallel bundling of nascent myofibrils. Our results suggest that a hierarchy of mechanisms regulate the self-organization of the contractile cytoskeleton and that a positive feedback loop is responsible for initiating the break in symmetry, potentiated by extracellular boundary conditions, is required to polarize the contractile cytoskeleton.

Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics

NASA Astrophysics Data System (ADS)

Rangan, Aaditya V.; Cai, David; Tao, Louis

2007-02-01

Recently developed kinetic theory and related closures for neuronal network dynamics have been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The moment equations arising from the kinetic theory are a system of (1 + 1)-dimensional nonlinear partial differential equations (PDE) on a bounded domain with nonlinear boundary conditions. The PDEs themselves are self-consistently specified by parameters which are functions of the boundary values of the solution. The moment equations can be stiff in space and time. Numerical methods are presented here for efficiently and accurately solving these moment equations. The essential ingredients in our numerical methods include: (i) the system is discretized in time with an implicit Euler method within a spectral deferred correction framework, therefore, the PDEs of the kinetic theory are reduced to a sequence, in time, of boundary value problems (BVPs) with nonlinear boundary conditions; (ii) a set of auxiliary parameters is introduced to recast the original BVP with nonlinear boundary conditions as BVPs with linear boundary conditions - with additional algebraic constraints on the auxiliary parameters; (iii) a careful combination of two Newton's iterates for the nonlinear BVP with linear boundary condition, interlaced with a Newton's iterate for solving the associated algebraic constraints is constructed to achieve quadratic convergence for obtaining the solutions with self-consistent parameters. It is shown that a simple fixed-point iteration can only achieve a linear convergence for the self-consistent parameters. The practicability and efficiency of our numerical methods for solving the moment equations of the kinetic theory are illustrated with numerical examples. It is further demonstrated that the moment equations derived from the kinetic theory of neuronal network dynamics can very well capture the coarse-grained dynamical properties of integrate-and-fire neuronal networks.

On the solution of integral equations with a generalized cauchy kernel

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

In this paper a certain class of singular integral equations that may arise from the mixed boundary value problems in nonhomogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernel has strong singularities of the form (t-x) sup-2, x sup n-2 (t+x) sup n, (n or = 2, 0x,tb). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin, Shi, E-mail: sjin@wisc.edu; Institute of Natural Sciences, Department of Mathematics, MOE-LSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240; Lu, Hanqing, E-mail: hanqing@math.wisc.edu

2017-04-01

In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (inmore » the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.« less

Biological growth in bodies with incoherent interfaces

NASA Astrophysics Data System (ADS)

Swain, Digendranath; Gupta, Anurag

2018-01-01

A general theory of thermodynamically consistent biomechanical-biochemical growth in a body, considering mass addition in the bulk and at an incoherent interface, is developed. The incoherency arises due to incompatibility of growth and elastic distortion tensors at the interface. The incoherent interface therefore acts as an additional source of internal stress besides allowing for rich growth kinematics. All the biochemicals in the model are essentially represented in terms of nutrient concentration fields, in the bulk and at the interface. A nutrient balance law is postulated which, combined with mechanical balances and kinetic laws, yields an initial-boundary-value problem coupling the evolution of bulk and interfacial growth, on the one hand, and the evolution of growth and nutrient concentration on the other. The problem is solved, and discussed in detail, for two distinct examples: annual ring formation during tree growth and healing of cutaneous wounds in animals.

Numerical modeling process of embolization arteriovenous malformation

NASA Astrophysics Data System (ADS)

Cherevko, A. A.; Gologush, T. S.; Petrenko, I. A.; Ostapenko, V. V.

2017-10-01

Cerebral arteriovenous malformation is a difficult, dangerous, and most frequently encountered vascular failure of development. It consists of vessels of very small diameter, which perform a discharge of blood from the artery to the vein. In this regard it can be adequately modeled using porous medium. Endovascular embolization of arteriovenous malformation is effective treatment of such pathologies. However, the danger of intraoperative rupture during embolization still exists. The purpose is to model this process and build an optimization algorithm for arteriovenous malformation embolization. To study the different embolization variants, the initial-boundary value problems, describing the process of embolization, were solved numerically by using a new modification of CABARET scheme. The essential moments of embolization process were modeled in our numerical experiments. This approach well reproduces the essential features of discontinuous two-phase flows, arising in the embolization problems. It can be used for further study on the process of embolization.

Boundary-integral methods in elasticity and plasticity. [solutions of boundary value problems

NASA Technical Reports Server (NTRS)

Mendelson, A.

1973-01-01

Recently developed methods that use boundary-integral equations applied to elastic and elastoplastic boundary value problems are reviewed. Direct, indirect, and semidirect methods using potential functions, stress functions, and displacement functions are described. Examples of the use of these methods for torsion problems, plane problems, and three-dimensional problems are given. It is concluded that the boundary-integral methods represent a powerful tool for the solution of elastic and elastoplastic problems.

Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle

PubMed Central

Brzezicki, Samuel J.

2017-01-01

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function. PMID:28690412

Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle.

PubMed

Crowdy, Darren G; Brzezicki, Samuel J

2017-06-01

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function.

On degenerate coupled transport processes in porous media with memory phenomena

NASA Astrophysics Data System (ADS)

Beneš, Michal; Pažanin, Igor

2018-06-01

In this paper we prove the existence of weak solutions to degenerate parabolic systems arising from the fully coupled moisture movement, solute transport of dissolved species and heat transfer through porous materials. Physically relevant mixed Dirichlet-Neumann boundary conditions and initial conditions are considered. Existence of a global weak solution of the problem is proved by means of semidiscretization in time, proving necessary uniform estimates and by passing to the limit from discrete approximations. Degeneration occurs in the nonlinear transport coefficients which are not assumed to be bounded below and above by positive constants. Degeneracies in transport coefficients are overcome by proving suitable a-priori $L^{\\infty}$-estimates based on De Giorgi and Moser iteration technique.

Aerodynamic Design of Axial-flow Compressors. Volume III

NASA Technical Reports Server (NTRS)

Johnson, Irving A; Bullock, Robert O; Graham, Robert W; Costilow, Eleanor L; Huppert, Merle C; Benser, William A; Herzig, Howard Z; Hansen, Arthur G; Jackson, Robert J; Yohner, Peggy L;

Medical image segmentation using genetic algorithms.

PubMed

Maulik, Ujjwal

2009-03-01

Genetic algorithms (GAs) have been found to be effective in the domain of medical image segmentation, since the problem can often be mapped to one of search in a complex and multimodal landscape. The challenges in medical image segmentation arise due to poor image contrast and artifacts that result in missing or diffuse organ/tissue boundaries. The resulting search space is therefore often noisy with a multitude of local optima. Not only does the genetic algorithmic framework prove to be effective in coming out of local optima, it also brings considerable flexibility into the segmentation procedure. In this paper, an attempt has been made to review the major applications of GAs to the domain of medical image segmentation.

Hypo-Elastic Model for Lung Parenchyma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Freed, Alan D.; Einstein, Daniel R.

2012-03-01

A simple elastic isotropic constitutive model for the spongy tissue in lung is derived from the theory of hypoelasticity. The model is shown to exhibit a pressure dependent behavior that has been interpreted by some as indicating extensional anisotropy. In contrast, we show that this behavior arises natural from an analysis of isotropic hypoelastic invariants, and is a likely result of non-linearity, not anisotropy. The response of the model is determined analytically for several boundary value problems used for material characterization. These responses give insight into both the material behavior as well as admissible bounds on parameters. The model ismore » characterized against published experimental data for dog lung. Future work includes non-elastic model behavior.« less

A methodology for constraining power in finite element modeling of radiofrequency ablation.

PubMed

Jiang, Yansheng; Possebon, Ricardo; Mulier, Stefaan; Wang, Chong; Chen, Feng; Feng, Yuanbo; Xia, Qian; Liu, Yewei; Yin, Ting; Oyen, Raymond; Ni, Yicheng

2017-07-01

Radiofrequency ablation (RFA) is a minimally invasive thermal therapy for the treatment of cancer, hyperopia, and cardiac tachyarrhythmia. In RFA, the power delivered to the tissue is a key parameter. The objective of this study was to establish a methodology for the finite element modeling of RFA with constant power. Because of changes in the electric conductivity of tissue with temperature, a nonconventional boundary value problem arises in the mathematic modeling of RFA: neither the voltage (Dirichlet condition) nor the current (Neumann condition), but the power, that is, the product of voltage and current was prescribed on part of boundary. We solved the problem using Lagrange multiplier: the product of the voltage and current on the electrode surface is constrained to be equal to the Joule heating. We theoretically proved the equality between the product of the voltage and current on the surface of the electrode and the Joule heating in the domain. We also proved the well-posedness of the problem of solving the Laplace equation for the electric potential under a constant power constraint prescribed on the electrode surface. The Pennes bioheat transfer equation and the Laplace equation for electric potential augmented with the constraint of constant power were solved simultaneously using the Newton-Raphson algorithm. Three problems for validation were solved. Numerical results were compared either with an analytical solution deduced in this study or with results obtained by ANSYS or experiments. This work provides the finite element modeling of constant power RFA with a firm mathematical basis and opens pathway for achieving the optimal RFA power. Copyright © 2016 John Wiley & Sons, Ltd.

A multilevel preconditioner for domain decomposition boundary systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bramble, J.H.; Pasciak, J.E.; Xu, Jinchao.

1991-12-11

In this note, we consider multilevel preconditioning of the reduced boundary systems which arise in non-overlapping domain decomposition methods. It will be shown that the resulting preconditioned systems have condition numbers which be bounded in the case of multilevel spaces on the whole domain and grow at most proportional to the number of levels in the case of multilevel boundary spaces without multilevel extensions into the interior.

Deleterious localized stress fields: the effects of boundaries and stiffness tailoring in anisotropic laminated plates

PubMed Central

Weaver, P. M.

2016-01-01

The safe design of primary load-bearing structures requires accurate prediction of stresses, especially in the vicinity of geometric discontinuities where deleterious three-dimensional stress fields can be induced. Even for thin-walled structures significant through-thickness stresses arise at edges and boundaries, and this is especially precarious for laminates of advanced fibre-reinforced composites because through-thickness stresses are the predominant drivers in delamination failure. Here, we use a higher-order equivalent single-layer model derived from the Hellinger–Reissner mixed variational principle to examine boundary layer effects in laminated plates comprising constant-stiffness and variable-stiffness laminae and deforming statically in cylindrical bending. The results show that zigzag deformations, which arise due to layerwise differences in the transverse shear moduli, drive boundary layers towards clamped edges and are therefore critically important in quantifying localized stress gradients. The relative significance of the boundary layer scales with the degree of layerwise anisotropy and the thickness to characteristic length ratio. Finally, we demonstrate that the phenomenon of alternating positive and negative transverse shearing deformation through the thickness of composite laminates, previously only observed at clamped boundaries, can also occur at other locations as a result of smoothly varying the material properties over the in-plane dimensions of the laminate. PMID:27843401

The use of MACSYMA for solving elliptic boundary value problems

NASA Technical Reports Server (NTRS)

Thejll, Peter; Gilbert, Robert P.

1990-01-01

A boundary method is presented for the solution of elliptic boundary value problems. An approach based on the use of complete systems of solutions is emphasized. The discussion is limited to the Dirichlet problem, even though the present method can possibly be adapted to treat other boundary value problems.

Solving Fluid Structure Interaction Problems with an Immersed Boundary Method

NASA Technical Reports Server (NTRS)

Barad, Michael F.; Brehm, Christoph; Kiris, Cetin C.

2016-01-01

An immersed boundary method for the compressible Navier-Stokes equations can be used for moving boundary problems as well as fully coupled fluid-structure interaction is presented. The underlying Cartesian immersed boundary method of the Launch Ascent and Vehicle Aerodynamics (LAVA) framework, based on the locally stabilized immersed boundary method previously presented by the authors, is extended to account for unsteady boundary motion and coupled to linear and geometrically nonlinear structural finite element solvers. The approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems. Keywords: Immersed Boundary Method, Higher-Order Finite Difference Method, Fluid Structure Interaction.

A robust interpolation procedure for producing tidal current ellipse inputs for regional and coastal ocean numerical models

NASA Astrophysics Data System (ADS)

Byun, Do-Seong; Hart, Deirdre E.

2017-04-01

Regional and/or coastal ocean models can use tidal current harmonic forcing, together with tidal harmonic forcing along open boundaries in order to successfully simulate tides and tidal currents. These inputs can be freely generated using online open-access data, but the data produced are not always at the resolution required for regional or coastal models. Subsequent interpolation procedures can produce tidal current forcing data errors for parts of the world's coastal ocean where tidal ellipse inclinations and phases move across the invisible mathematical "boundaries" between 359° and 0° degrees (or 179° and 0°). In nature, such "boundaries" are in fact smooth transitions, but if these mathematical "boundaries" are not treated correctly during interpolation, they can produce inaccurate input data and hamper the accurate simulation of tidal currents in regional and coastal ocean models. These avoidable errors arise due to procedural shortcomings involving vector embodiment problems (i.e., how a vector is represented mathematically, for example as velocities or as coordinates). Automated solutions for producing correct tidal ellipse parameter input data are possible if a series of steps are followed correctly, including the use of Cartesian coordinates during interpolation. This note comprises the first published description of scenarios where tidal ellipse parameter interpolation errors can arise, and of a procedure to successfully avoid these errors when generating tidal inputs for regional and/or coastal ocean numerical models. We explain how a straightforward sequence of data production, format conversion, interpolation, and format reconversion steps may be used to check for the potential occurrence and avoidance of tidal ellipse interpolation and phase errors. This sequence is demonstrated via a case study of the M2 tidal constituent in the seas around Korea but is designed to be universally applicable. We also recommend employing tidal ellipse parameter calculation methods that avoid the use of Foreman's (1978) "northern semi-major axis convention" since, as revealed in our analysis, this commonly used conversion can result in inclination interpolation errors even when Cartesian coordinate-based "vector embodiment" solutions are employed.

Applications of conformal field theory to problems in 2D percolation

NASA Astrophysics Data System (ADS)

Simmons, Jacob Joseph Harris

This thesis explores critical two-dimensional percolation in bounded regions in the continuum limit. The main method which we employ is conformal field theory (CFT). Our specific results follow from the null-vector structure of the c = 0 CFT that applies to critical two-dimensional percolation. We also make use of the duality symmetry obeyed at the percolation point, and the fact that percolation may be understood as the q-state Potts model in the limit q → 1. Our first results describe the correlations between points in the bulk and boundary intervals or points, i.e. the probability that the various points or intervals are in the same percolation cluster. These quantities correspond to order-parameter profiles under the given conditions, or cluster connection probabilities. We consider two specific cases: an anchoring interval, and two anchoring points. We derive results for these and related geometries using the CFT null-vectors for the corresponding boundary condition changing (bcc) operators. In addition, we exhibit several exact relationships between these probabilities. These relations between the various bulk-boundary connection probabilities involve parameters of the CFT called operator product expansion (OPE) coefficients. We then compute several of these OPE coefficients, including those arising in our new probability relations. Beginning with the familiar CFT operator φ1,2, which corresponds to a free-fixed spin boundary change in the q-state Potts model, we then develop physical interpretations of the bcc operators. We argue that, when properly normalized, higher-order bcc operators correspond to successive fusions of multiple φ1,2, operators. Finally, by identifying the derivative of φ1,2 with the operator φ1,4, we derive several new quantities called first crossing densities. These new results are then combined and integrated to obtain the three previously known crossing quantities in a rectangle: the probability of a horizontal crossing cluster, the probability of a cluster crossing both horizontally and vertically, and the expected number of horizontal crossing clusters. These three results were known to be solutions to a certain fifth-order differential equation, but until now no physically meaningful explanation had appeared. This differential equation arises naturally in our derivation.

Different Kinds of Causality in Event Cognition

ERIC Educational Resources Information Center

Radvansky, Gabriel A.; Tamplin, Andrea K.; Armendarez, Joseph; Thompson, Alexis N.

2014-01-01

Narrative memory is better for information that is more causally connected and occurs at event boundaries, such as a causal break. However, it is unclear whether there are common or distinct influences of causality. For the event boundaries that arise as a result of causal breaks, the events that follow may subsequently become more causally…

Generalized continuum modeling of scale-dependent crystalline plasticity

NASA Astrophysics Data System (ADS)

Mayeur, Jason R.

The use of metallic material systems (e.g. pure metals, alloys, metal matrix composites) in a wide range of engineering applications from medical devices to electronic components to automobiles continues to motivate the development of improved constitutive models to meet increased performance demands while minimizing cost. Emerging technologies often incorporate materials in which the dominant microstructural features have characteristic dimensions reaching into the submicron and nanometer regime. Metals comprised of such fine microstructures often exhibit unique and size-dependent mechanical response, and classical approaches to constitutive model development at engineering (continuum) scales, being local in nature, are inadequate for describing such behavior. Therefore, traditional modeling frameworks must be augmented and/or reformulated to account for such phenomena. Crystal plasticity constitutive models have proven quite capable of capturing first-order microstructural effects such as grain orientation (elastic/plastic anisotropy), grain morphology, phase distribution, etc. on the deformation behavior of both single and polycrystals, yet suffer from the same limitations as other local continuum theories with regard to capturing scale-dependent mechanical response. This research is focused on the development, numerical implementation, and application of a generalized (nonlocal) theory of single crystal plasticity capable of describing the scale-dependent mechanical response of both single and polycrystalline metals that arises as a result of heterogeneous deformation. This research developed a dislocation-based theory of micropolar single crystal plasticity. The majority of nonlocal crystal plasticity theories are predicated on the connection between gradients of slip and geometrically necessary dislocations. Due to the diversity of existing nonlocal crystal plasticity theories, a review, summary, and comparison of representative model classes is presented in Chapter 2 from a unified dislocation-based perspective. The discussion of the continuum crystal plasticity theories is prefaced by a brief review of discrete dislocation plasticity, which facilitates the comparison of certain model aspects and also serves as a reference for latter segments of the research which make connection to this constitutive description. Chapter 2 has utility not only as a literature review, but also as a synthesis and analysis of competing and alternative nonlocal crystal plasticity modeling strategies from a common viewpoint. The micropolar theory of single crystal plasticity is presented in Chapter 3. Two different types of flow criteria are considered - the so-called single and multicriterion theories, and several variations of the dislocation-based strength models appropriate for each theory are presented and discussed. The numerical implementation of the two-dimensional version of the constitutive theory is given in Chapter 4. A user element subroutine for the implicit commercial finite element code Abaqus/Standard is developed and validated through the solution of initial-boundary value problems with closed-form solutions. Convergent behavior of the subroutine is also demonstrated for an initial-boundary value problem exhibiting strain localization. In Chapter 5, the models are employed to solve several standard initial-boundary value problems for heterogeneously deforming single crystals including simple shearing of a semi-infinite constrained thin film, pure bending of thin films, and simple shearing of a metal matrix composite with elastic inclusions. The simulation results are compared to those obtained from the solution of equivalent boundary value problems using discrete dislocation dynamics and alternative generalized crystal plasticity theories. Comparison and calibration with respect to the former provides guidance in the specification of non-traditional material parameters that arise in the model formulation and demonstrates its effectiveness at capturing the heterogeneous deformation fields and size-dependent mechanical behavior predicted by a finer scale constitutive description. Finally, in Chapter 6, the models are applied to simulate the deformation behavior of small polycrystalline ensembles. Several grain boundary constitutive descriptions are explored and the response characteristics are analyzed with respect to experimental observations as well as results obtained from discrete dislocation dynamics and alternative nonlocal crystal plasticity theories. Particular attention is focused on how the various grain boundary descriptions serve to either locally concentrate or diffuse deformation heterogeneity as a function of grain size.

Multiscale Modeling of Grain-Boundary Fracture: Cohesive Zone Models Parameterized From Atomistic Simulations

NASA Technical Reports Server (NTRS)

Glaessgen, Edward H.; Saether, Erik; Phillips, Dawn R.; Yamakov, Vesselin

2006-01-01

A multiscale modeling strategy is developed to study grain boundary fracture in polycrystalline aluminum. Atomistic simulation is used to model fundamental nanoscale deformation and fracture mechanisms and to develop a constitutive relationship for separation along a grain boundary interface. The nanoscale constitutive relationship is then parameterized within a cohesive zone model to represent variations in grain boundary properties. These variations arise from the presence of vacancies, intersticies, and other defects in addition to deviations in grain boundary angle from the baseline configuration considered in the molecular dynamics simulation. The parameterized cohesive zone models are then used to model grain boundaries within finite element analyses of aluminum polycrystals.

Triangles with Integer Dimensions

ERIC Educational Resources Information Center

Gilbertson, Nicholas J.; Rogers, Kimberly Cervello

2016-01-01

Interesting and engaging mathematics problems can come from anywhere. Sometimes great problems arise from interesting contexts. At other times, interesting problems arise from asking "what if" questions while appreciating the structure and beauty of mathematics. The intriguing problem described in this article resulted from the second…

Memoryless control of boundary concentrations of diffusing particles.

PubMed

Singer, A; Schuss, Z; Nadler, B; Eisenberg, R S

2004-12-01

Flux between regions of different concentration occurs in nearly every device involving diffusion, whether an electrochemical cell, a bipolar transistor, or a protein channel in a biological membrane. Diffusion theory has calculated that flux since the time of Fick (1855), and the flux has been known to arise from the stochastic behavior of Brownian trajectories since the time of Einstein (1905), yet the mathematical description of the behavior of trajectories corresponding to different types of boundaries is not complete. We consider the trajectories of noninteracting particles diffusing in a finite region connecting two baths of fixed concentrations. Inside the region, the trajectories of diffusing particles are governed by the Langevin equation. To maintain average concentrations at the boundaries of the region at their values in the baths, a control mechanism is needed to set the boundary dynamics of the trajectories. Different control mechanisms are used in Langevin and Brownian simulations of such systems. We analyze models of controllers and derive equations for the time evolution and spatial distribution of particles inside the domain. Our analysis shows a distinct difference between the time evolution and the steady state concentrations. While the time evolution of the density is governed by an integral operator, the spatial distribution is governed by the familiar Fokker-Planck operator. The boundary conditions for the time dependent density depend on the model of the controller; however, this dependence disappears in the steady state, if the controller is of a renewal type. Renewal-type controllers, however, produce spurious boundary layers that can be catastrophic in simulations of charged particles, because even a tiny net charge can have global effects. The design of a nonrenewal controller that maintains concentrations of noninteracting particles without creating spurious boundary layers at the interface requires the solution of the time-dependent Fokker-Planck equation with absorption of outgoing trajectories and a source of ingoing trajectories on the boundary (the so called albedo problem).

The Boundary Function Method. Fundamentals

NASA Astrophysics Data System (ADS)

Kot, V. A.

2017-03-01

The boundary function method is proposed for solving applied problems of mathematical physics in the region defined by a partial differential equation of the general form involving constant or variable coefficients with a Dirichlet, Neumann, or Robin boundary condition. In this method, the desired function is defined by a power polynomial, and a boundary function represented in the form of the desired function or its derivative at one of the boundary points is introduced. Different sequences of boundary equations have been set up with the use of differential operators. Systems of linear algebraic equations constructed on the basis of these sequences allow one to determine the coefficients of a power polynomial. Constitutive equations have been derived for initial boundary-value problems of all the main types. With these equations, an initial boundary-value problem is transformed into the Cauchy problem for the boundary function. The determination of the boundary function by its derivative with respect to the time coordinate completes the solution of the problem.

A fully implicit finite element method for bidomain models of cardiac electromechanics

PubMed Central

Dal, Hüsnü; Göktepe, Serdar; Kaliske, Michael; Kuhl, Ellen

2012-01-01

We propose a novel, monolithic, and unconditionally stable finite element algorithm for the bidomain-based approach to cardiac electromechanics. We introduce the transmembrane potential, the extracellular potential, and the displacement field as independent variables, and extend the common two-field bidomain formulation of electrophysiology to a three-field formulation of electromechanics. The intrinsic coupling arises from both excitation-induced contraction of cardiac cells and the deformation-induced generation of intra-cellular currents. The coupled reaction-diffusion equations of the electrical problem and the momentum balance of the mechanical problem are recast into their weak forms through a conventional isoparametric Galerkin approach. As a novel aspect, we propose a monolithic approach to solve the governing equations of excitation-contraction coupling in a fully coupled, implicit sense. We demonstrate the consistent linearization of the resulting set of non-linear residual equations. To assess the algorithmic performance, we illustrate characteristic features by means of representative three-dimensional initial-boundary value problems. The proposed algorithm may open new avenues to patient specific therapy design by circumventing stability and convergence issues inherent to conventional staggered solution schemes. PMID:23175588

Theory and implementation of H-matrix based iterative and direct solvers for Helmholtz and elastodynamic oscillatory kernels

NASA Astrophysics Data System (ADS)

Chaillat, Stéphanie; Desiderio, Luca; Ciarlet, Patrick

2017-12-01

In this work, we study the accuracy and efficiency of hierarchical matrix (H-matrix) based fast methods for solving dense linear systems arising from the discretization of the 3D elastodynamic Green's tensors. It is well known in the literature that standard H-matrix based methods, although very efficient tools for asymptotically smooth kernels, are not optimal for oscillatory kernels. H2-matrix and directional approaches have been proposed to overcome this problem. However the implementation of such methods is much more involved than the standard H-matrix representation. The central questions we address are twofold. (i) What is the frequency-range in which the H-matrix format is an efficient representation for 3D elastodynamic problems? (ii) What can be expected of such an approach to model problems in mechanical engineering? We show that even though the method is not optimal (in the sense that more involved representations can lead to faster algorithms) an efficient solver can be easily developed. The capabilities of the method are illustrated on numerical examples using the Boundary Element Method.

The complex variable boundary element method: Applications in determining approximative boundaries

USGS Publications Warehouse

Hromadka, T.V.

1984-01-01

The complex variable boundary element method (CVBEM) is used to determine approximation functions for boundary value problems of the Laplace equation such as occurs in potential theory. By determining an approximative boundary upon which the CVBEM approximator matches the desired constant (level curves) boundary conditions, the CVBEM is found to provide the exact solution throughout the interior of the transformed problem domain. Thus, the acceptability of the CVBEM approximation is determined by the closeness-of-fit of the approximative boundary to the study problem boundary. ?? 1984.

Analytical study and numerical solution of the inverse source problem arising in thermoacoustic tomography

NASA Astrophysics Data System (ADS)

Holman, Benjamin R.

In recent years, revolutionary "hybrid" or "multi-physics" methods of medical imaging have emerged. By combining two or three different types of waves these methods overcome limitations of classical tomography techniques and deliver otherwise unavailable, potentially life-saving diagnostic information. Thermoacoustic (and photoacoustic) tomography is the most developed multi-physics imaging modality. Thermo- and photo- acoustic tomography require reconstructing initial acoustic pressure in a body from time series of pressure measured on a surface surrounding the body. For the classical case of free space wave propagation, various reconstruction techniques are well known. However, some novel measurement schemes place the object of interest between reflecting walls that form a de facto resonant cavity. In this case, known methods cannot be used. In chapter 2 we present a fast iterative reconstruction algorithm for measurements made at the walls of a rectangular reverberant cavity with a constant speed of sound. We prove the convergence of the iterations under a certain sufficient condition, and demonstrate the effectiveness and efficiency of the algorithm in numerical simulations. In chapter 3 we consider the more general problem of an arbitrarily shaped resonant cavity with a non constant speed of sound and present the gradual time reversal method for computing solutions to the inverse source problem. It consists in solving back in time on the interval [0, T] the initial/boundary value problem for the wave equation, with the Dirichlet boundary data multiplied by a smooth cutoff function. If T is sufficiently large one obtains a good approximation to the initial pressure; in the limit of large T such an approximation converges (under certain conditions) to the exact solution.

Standing Firm on Slippery Slopes: Understanding Ethical Boundaries in Student Affairs Work

ERIC Educational Resources Information Center

Liddell, Debora; Hornak, Anne M.; Ignelzi, Michael G.

2016-01-01

Understanding ethical boundaries in student affairs work can be challenging and difficult to navigate for student affairs professionals. The purpose of this article is to examine the complexities of dual relationships and the ethical issues that may arise. As a result, the authors offer tools to (a) identify various perspectives in resolving…

Pattern formations and optimal packing.

PubMed

Mityushev, Vladimir

2016-04-01

Patterns of different symmetries may arise after solution to reaction-diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after numerical solution to the corresponding initial-boundary value problems. We demonstrate an intimate connection between pattern formations and optimal random packing on the plane. The main study is based on the following two points. First, the diffusive flux in reaction-diffusion systems is approximated by piecewise linear functions in the framework of structural approximations. This leads to a discrete network approximation of the considered continuous problem. Second, the discrete energy minimization yields optimal random packing of the domains (disks) in the representative cell. Therefore, the general problem of pattern formations based on the reaction-diffusion equations is reduced to the geometric problem of random packing. It is demonstrated that all random packings can be divided onto classes associated with classes of isomorphic graphs obtained from the Delaunay triangulation. The unique optimal solution is constructed in each class of the random packings. If the number of disks per representative cell is finite, the number of classes of isomorphic graphs, hence, the number of optimal packings is also finite. Copyright © 2016 Elsevier Inc. All rights reserved.

Monge-Ampére simulation of fourth order PDEs in two dimensions with application to elastic-electrostatic contact problems

NASA Astrophysics Data System (ADS)

DiPietro, Kelsey L.; Lindsay, Alan E.

2017-11-01

We present an efficient moving mesh method for the simulation of fourth order nonlinear partial differential equations (PDEs) in two dimensions using the Parabolic Monge-Ampére (PMA) equation. PMA methods have been successfully applied to the simulation of second order problems, but not on systems with higher order equations which arise in many topical applications. Our main application is the resolution of fine scale behavior in PDEs describing elastic-electrostatic interactions. The PDE system considered has multiple parameter dependent singular solution modalities, including finite time singularities and sharp interface dynamics. We describe how to construct a dynamic mesh algorithm for such problems which incorporates known self similar or boundary layer scalings of the underlying equation to locate and dynamically resolve fine scale solution features in these singular regimes. We find a key step in using the PMA equation for mesh generation in fourth order problems is the adoption of a high order representation of the transformation from the computational to physical mesh. We demonstrate the efficacy of the new method on a variety of examples and establish several new results and conjectures on the nature of self-similar singularity formation in higher order PDEs.

Multifactor estimation of ecological risks using numerical simulation

NASA Astrophysics Data System (ADS)

Voskoboynikova, G.; Shalamov, K.; Khairetdinov, M.; Kovalevsky, V.

2017-10-01

In this paper, the problem of interaction of acoustic waves falling at a given angle on a snow layer on the ground and seismic waves arising both in this layer and in the ground is considered. A system of differential equations with boundary conditions describing the propagation of incident and reflected acoustic waves in the air refracted and reflected from the boundary of seismic waves in elastic media (snow and ground) is constructed and solved for a three-layer air-snow layer-ground model. The coefficients of reflection and refraction are calculated in the case of an acoustic wave falling onto both the ground and snow on the ground. The ratio of the energy of the refracted waves to the energy of the falling acoustic wave is obtained. It is noted that snow has a strong influence on the energy transfer into the ground, which can decrease by more than an order of magnitude. The numerical results obtained are consistent with the results of field experiments with a vibrational source performed by the Siberian Branch of the Russian Academy of Sciences.

Thermal boundary resistances of carbon nanotubes in contact with metals and polymers.

PubMed

Li, Qingwei; Liu, Changhong; Fan, Shoushan

2009-11-01

In recent years carbon-nanotube-based thermal interface materials have shown great potential for solving the thermal management problem of integrated circuits and nanodevices. For a long time, the exceptionally high thermal boundary resistances (TBRs) between carbon nanotubes (CNTs) and their surroundings have been suspected as a major factor to restraining their performance. But so far, there are few or no reported work to determine or compare the TBRs between CNTs and various materials. In this paper, we carefully design and carry out the TBR measurements of CNTs in contact with metal and polymer materials, and we present a conclusion that the CNT/polymer generally gives a lower TBR compared to the CNT/metal, which seems a little counterintuitive. We further suggest that the larger CNT-metal TBRs arise from the smaller phonon-mode overlapping between the CNT and the metals at low frequencies, and the low phonon transmission coefficient at the metal-CNT interface in the intermediate and high frequency range. This work may inspire deeper understanding of the TBR and shed light on related theoretical and applied research.

Scalar discrete nonlinear multipoint boundary value problems

NASA Astrophysics Data System (ADS)

Rodriguez, Jesus; Taylor, Padraic

2007-06-01

In this paper we provide sufficient conditions for the existence of solutions to scalar discrete nonlinear multipoint boundary value problems. By allowing more general boundary conditions and by imposing less restrictions on the nonlinearities, we obtain results that extend previous work in the area of discrete boundary value problems [Debra L. Etheridge, Jesus Rodriguez, Periodic solutions of nonlinear discrete-time systems, Appl. Anal. 62 (1996) 119-137; Debra L. Etheridge, Jesus Rodriguez, Scalar discrete nonlinear two-point boundary value problems, J. Difference Equ. Appl. 4 (1998) 127-144].

Error analysis of finite difference schemes applied to hyperbolic initial boundary value problems

NASA Technical Reports Server (NTRS)

Skollermo, G.

1979-01-01

Finite difference methods for the numerical solution of mixed initial boundary value problems for hyperbolic equations are studied. The reported investigation has the objective to develop a technique for the total error analysis of a finite difference scheme, taking into account initial approximations, boundary conditions, and interior approximation. Attention is given to the Cauchy problem and the initial approximation, the homogeneous problem in an infinite strip with inhomogeneous boundary data, the reflection of errors in the boundaries, and two different boundary approximations for the leapfrog scheme with a fourth order accurate difference operator in space.

The Problems of Diagnosis and Remediation of Dyscalculia.

ERIC Educational Resources Information Center

Price, Nigel; Youe, Simon

2000-01-01

Focuses on the problems of diagnosis and remediation of dyscalculia. Explores whether there is justification for believing that specific difficulty with mathematics arises jointly with a specific language problem, or whether a specific difficulty with mathematics can arise independently of problems with language. Uses a case study to illuminate…

Solving the hypersingular boundary integral equation for the Burton and Miller formulation.

PubMed

Langrenne, Christophe; Garcia, Alexandre; Bonnet, Marc

2015-11-01

This paper presents an easy numerical implementation of the Burton and Miller (BM) formulation, where the hypersingular Helmholtz integral is regularized by identities from the associated Laplace equation and thus needing only the evaluation of weakly singular integrals. The Helmholtz equation and its normal derivative are combined directly with combinations at edge or corner collocation nodes not used when the surface is not smooth. The hypersingular operators arising in this process are regularized and then evaluated by an indirect procedure based on discretized versions of the Calderón identities linking the integral operators for associated Laplace problems. The method is valid for acoustic radiation and scattering problems involving arbitrarily shaped three-dimensional bodies. Unlike other approaches using direct evaluation of hypersingular integrals, collocation points still coincide with mesh nodes, as is usual when using conforming elements. Using higher-order shape functions (with the boundary element method model size kept fixed) reduces the overall numerical integration effort while increasing the solution accuracy. To reduce the condition number of the resulting BM formulation at low frequencies, a regularized version α = ik/(k(2 )+ λ) of the classical BM coupling factor α = i/k is proposed. Comparisons with the combined Helmholtz integral equation Formulation method of Schenck are made for four example configurations, two of them featuring non-smooth surfaces.

Moving walls and geometric phases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Facchi, Paolo, E-mail: paolo.facchi@ba.infn.it; INFN, Sezione di Bari, I-70126 Bari; Garnero, Giancarlo, E-mail: giancarlo.garnero@uniba.it

2016-09-15

We unveil the existence of a non-trivial Berry phase associated to the dynamics of a quantum particle in a one dimensional box with moving walls. It is shown that a suitable choice of boundary conditions has to be made in order to preserve unitarity. For these boundary conditions we compute explicitly the geometric phase two-form on the parameter space. The unboundedness of the Hamiltonian describing the system leads to a natural prescription of renormalization for divergent contributions arising from the boundary.

How visual illusions illuminate complementary brain processes: illusory depth from brightness and apparent motion of illusory contours

PubMed Central

Grossberg, Stephen

2014-01-01

Neural models of perception clarify how visual illusions arise from adaptive neural processes. Illusions also provide important insights into how adaptive neural processes work. This article focuses on two illusions that illustrate a fundamental property of global brain organization; namely, that advanced brains are organized into parallel cortical processing streams with computationally complementary properties. That is, in order to process certain combinations of properties, each cortical stream cannot process complementary properties. Interactions between these streams, across multiple processing stages, overcome their complementary deficiencies to compute effective representations of the world, and to thereby achieve the property of complementary consistency. The two illusions concern how illusory depth can vary with brightness, and how apparent motion of illusory contours can occur. Illusory depth from brightness arises from the complementary properties of boundary and surface processes, notably boundary completion and surface-filling in, within the parvocellular form processing cortical stream. This illusion depends upon how surface contour signals from the V2 thin stripes to the V2 interstripes ensure complementary consistency of a unified boundary/surface percept. Apparent motion of illusory contours arises from the complementary properties of form and motion processes across the parvocellular and magnocellular cortical processing streams. This illusion depends upon how illusory contours help to complete boundary representations for object recognition, how apparent motion signals can help to form continuous trajectories for target tracking and prediction, and how formotion interactions from V2-to-MT enable completed object representations to be continuously tracked even when they move behind intermittently occluding objects through time. PMID:25389399

Recurrence relations for orthogonal polynomials for PDEs in polar and cylindrical geometries.

PubMed

Richardson, Megan; Lambers, James V

2016-01-01

This paper introduces two families of orthogonal polynomials on the interval (-1,1), with weight function [Formula: see text]. The first family satisfies the boundary condition [Formula: see text], and the second one satisfies the boundary conditions [Formula: see text]. These boundary conditions arise naturally from PDEs defined on a disk with Dirichlet boundary conditions and the requirement of regularity in Cartesian coordinates. The families of orthogonal polynomials are obtained by orthogonalizing short linear combinations of Legendre polynomials that satisfy the same boundary conditions. Then, the three-term recurrence relations are derived. Finally, it is shown that from these recurrence relations, one can efficiently compute the corresponding recurrences for generalized Jacobi polynomials that satisfy the same boundary conditions.

Numerical Boundary Conditions for Computational Aeroacoustics Benchmark Problems

NASA Technical Reports Server (NTRS)

Tam, Chritsopher K. W.; Kurbatskii, Konstantin A.; Fang, Jun

1997-01-01

Category 1, Problems 1 and 2, Category 2, Problem 2, and Category 3, Problem 2 are solved computationally using the Dispersion-Relation-Preserving (DRP) scheme. All these problems are governed by the linearized Euler equations. The resolution requirements of the DRP scheme for maintaining low numerical dispersion and dissipation as well as accurate wave speeds in solving the linearized Euler equations are now well understood. As long as 8 or more mesh points per wavelength is employed in the numerical computation, high quality results are assured. For the first three categories of benchmark problems, therefore, the real challenge is to develop high quality numerical boundary conditions. For Category 1, Problems 1 and 2, it is the curved wall boundary conditions. For Category 2, Problem 2, it is the internal radiation boundary conditions inside the duct. For Category 3, Problem 2, they are the inflow and outflow boundary conditions upstream and downstream of the blade row. These are the foci of the present investigation. Special nonhomogeneous radiation boundary conditions that generate the incoming disturbances and at the same time allow the outgoing reflected or scattered acoustic disturbances to leave the computation domain without significant reflection are developed. Numerical results based on these boundary conditions are provided.

Existence and non-uniqueness of similarity solutions of a boundary-layer problem

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Lakin, W. D.

1986-01-01

A Blasius boundary value problem with inhomogeneous lower boundary conditions f(0) = 0 and f'(0) = - lambda with lambda strictly positive was considered. The Crocco variable formulation of this problem has a key term which changes sign in the interval of interest. It is shown that solutions of the boundary value problem do not exist for values of lambda larger than a positive critical value lambda. The existence of solutions is proven for 0 lambda lambda by considering an equivalent initial value problem. It is found however that for 0 lambda lambda, solutions of the boundary value problem are nonunique. Physically, this nonuniqueness is related to multiple values of the skin friction.

Existence and non-uniqueness of similarity solutions of a boundary layer problem

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Lakin, W. D.

1984-01-01

A Blasius boundary value problem with inhomogeneous lower boundary conditions f(0) = 0 and f'(0) = - lambda with lambda strictly positive was considered. The Crocco variable formulation of this problem has a key term which changes sign in the interval of interest. It is shown that solutions of the boundary value problem do not exist for values of lambda larger than a positive critical value lambda. The existence of solutions is proven for 0 lambda lambda by considering an equivalent initial value problem. It is found however that for 0 lambda lambda, solutions of the boundary value problem are nonunique. Physically, this nonuniqueness is related to multiple values of the skin friction.

A New Method for Coronal Magnetic Field Reconstruction

NASA Astrophysics Data System (ADS)

Yi, Sibaek; Choe, Gwang-Son; Cho, Kyung-Suk; Kim, Kap-Sung

2017-08-01

A precise way of coronal magnetic field reconstruction (extrapolation) is an indispensable tool for understanding of various solar activities. A variety of reconstruction codes have been developed so far and are available to researchers nowadays, but they more or less bear this and that shortcoming. In this paper, a new efficient method for coronal magnetic field reconstruction is presented. The method imposes only the normal components of magnetic field and current density at the bottom boundary to avoid the overspecification of the reconstruction problem, and employs vector potentials to guarantee the divergence-freeness. In our method, the normal component of current density is imposed, not by adjusting the tangential components of A, but by adjusting its normal component. This allows us to avoid a possible numerical instability that on and off arises in codes using A. In real reconstruction problems, the information for the lateral and top boundaries is absent. The arbitrariness of the boundary conditions imposed there as well as various preprocessing brings about the diversity of resulting solutions. We impose the source surface condition at the top boundary to accommodate flux imbalance, which always shows up in magnetograms. To enhance the convergence rate, we equip our code with a gradient-method type accelerator. Our code is tested on two analytical force-free solutions. When the solution is given only at the bottom boundary, our result surpasses competitors in most figures of merits devised by Schrijver et al. (2006). We have also applied our code to a real active region NOAA 11974, in which two M-class flares and a halo CME took place. The EUV observation shows a sudden appearance of an erupting loop before the first flare. Our numerical solutions show that two entwining flux tubes exist before the flare and their shackling is released after the CME with one of them opened up. We suggest that the erupting loop is created by magnetic reconnection between two entwining flux tubes and later appears in the coronagraph as the major constituent of the observed CME.

On the membrane approximation in isothermal film casting

NASA Astrophysics Data System (ADS)

Hagen, Thomas

2014-08-01

In this work, a one-dimensional model for isothermal film casting is studied. Film casting is an important engineering process to manufacture thin films and sheets from a highly viscous polymer melt. The model equations account for variations in film width and film thickness, and arise from thinness and kinematic assumptions for the free liquid film. The first aspect of our study is a rigorous discussion of the existence and uniqueness of stationary solutions. This objective is approached via the argument principle, exploiting the homotopy invariance of a family of analytic functions. As our second objective, we analyze the linearization of the governing equations about stationary solutions. It is shown that solutions for the associated boundary-initial value problem are given by a strongly continuous semigroup of bounded linear operators. To reach this result, we cast the relevant Cauchy problem in a more accessible form. These transformed equations allow us insight into the regularity of the semigroup, thus yielding the validity of the spectral mapping theorem for the semigroup and the spectrally determined growth property.

`Relativistic' corrections to the mass of a plucked guitar string

NASA Astrophysics Data System (ADS)

Kolodrubetz, Michael; Polkovnikov, Anatoli

Quantum systems respond non-adiabaticity when parameters controlling them are ramped at a finite rate. If the parameters themselves are dynamical - for instance the position of a box that defines the boundary of a quantum field - the feedback of these excitations gives rise to effective Newtonian equations of motion for the parameter. For the age old problem of photons in a box, this correction gives rise to a mass proportional to the energy of the photons. We show that a similar correction arises for a classical guitar string plucked with energy E; moving clamps at the ends of the string requires inertial mass m = 2 E /cs2 , where cs is the speed of sound. This quasi-relativistic effect should be observable in freshman physics level experiments. We then comment on how these simple methods have been readily extended to treat problems such as ramps and quenches of strongly-interacting superconductors and dynamical trapping near a quantum critical point.

The free versus fixed geodetic boundary value problem for different combinations of geodetic observables

NASA Astrophysics Data System (ADS)

Grafarend, E. W.; Heck, B.; Knickmeyer, E. H.

1985-03-01

Various formulations of the geodetic fixed and free boundary value problem are presented, depending upon the type of boundary data. For the free problem, boundary data of type astronomical latitude, astronomical longitude and a pair of the triplet potential, zero and first-order vertical gradient of gravity are presupposed. For the fixed problem, either the potential or gravity or the vertical gradient of gravity is assumed to be given on the boundary. The potential and its derivatives on the boundary surface are linearized with respect to a reference potential and a reference surface by Taylor expansion. The Eulerian and Lagrangean concepts of a perturbation theory of the nonlinear geodetic boundary value problem are reviewed. Finally the boundary value problems are solved by Hilbert space techniques leading to new generalized Stokes and Hotine functions. Reduced Stokes and Hotine functions are recommended for numerical reasons. For the case of a boundary surface representing the topography a base representation of the solution is achieved by solving an infinite dimensional system of equations. This system of equations is obtained by means of the product-sum-formula for scalar surface spherical harmonics with Wigner 3j-coefficients.

Excitation of secondary Love and Rayleigh waves in athree-dimensional sedimentary basin evaluated by the direct boundary element method with normal modes

NASA Astrophysics Data System (ADS)

Hatayama, Ken; Fujiwara, Hiroyuki

1998-05-01

This paper aims to present a new method to calculate surface waves in 3-D sedimentary basin models, based on the direct boundary element method (BEM) with vertical boundaries and normal modes, and to evaluate the excitation of secondary surface waves observed remarkably in basins. Many authors have so far developed numerical techniques to calculate the total 3-D wavefield. However, the calculation of the total wavefield does not match our purpose, because the secondary surface waves excited on the basin boundaries will be contaminated by other undesirable waves. In this paper, we prove that, in principle, it is possible to extract surface waves excited on part of the basin boundaries from the total 3-D wavefield with a formulation that uses the reflection and transmission operators defined in the space domain. In realizing this extraction in the BEM algorithm, we encounter the problem arising from the lateral and vertical truncations of boundary surfaces extending infinitely in the half-space. To compensate the truncations, we first introduce an approximate algorithm using 2.5-D and 1-D wavefields for reference media, where a 2.5-D wavefield means a 3-D wavefield with a 2-D subsurface structure, and we then demonstrate the extraction. Finally, we calculate the secondary surface waves excited on the arc shape (horizontal section) of a vertical basin boundary subject to incident SH and SV plane waves propagating perpendicularly to the chord of the arc. As a result, we find that in the SH-incident case the Love waves are predominantly excited, rather than the Rayleigh waves and that in the SV-wave incident case the Love waves as well as the Rayleigh waves are excited. This suggests that the Love waves are more detectable than the Rayleigh waves in the horizontal components of observed recordings.

Guidance and control strategies for aerospace vehicles

NASA Technical Reports Server (NTRS)

Naidu, Desineni S.; Hibey, Joseph L.

1989-01-01

The optimal control problem arising in coplanar orbital transfer employing aeroassist technology and the fuel-optimal control problem arising in orbital transfer vehicles employing aeroassist technology are addressed.

Developments in boundary element methods - 2

NASA Astrophysics Data System (ADS)

Banerjee, P. K.; Shaw, R. P.

This book is a continuation of the effort to demonstrate the power and versatility of boundary element methods which began in Volume 1 of this series. While Volume 1 was designed to introduce the reader to a selected range of problems in engineering for which the method has been shown to be efficient, the present volume has been restricted to time-dependent problems in engineering. Boundary element formulation for melting and solidification problems in considered along with transient flow through porous elastic media, applications of boundary element methods to problems of water waves, and problems of general viscous flow. Attention is given to time-dependent inelastic deformation of metals by boundary element methods, the determination of eigenvalues by boundary element methods, transient stress analysis of tunnels and caverns of arbitrary shape due to traveling waves, an analysis of hydrodynamic loads by boundary element methods, and acoustic emissions from submerged structures.

An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

NASA Astrophysics Data System (ADS)

Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

2018-06-01

This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

Advances in Numerical Boundary Conditions for Computational Aeroacoustics

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.

1997-01-01

Advances in Computational Aeroacoustics (CAA) depend critically on the availability of accurate, nondispersive, least dissipative computation algorithm as well as high quality numerical boundary treatments. This paper focuses on the recent developments of numerical boundary conditions. In a typical CAA problem, one often encounters two types of boundaries. Because a finite computation domain is used, there are external boundaries. On the external boundaries, boundary conditions simulating the solution outside the computation domain are to be imposed. Inside the computation domain, there may be internal boundaries. On these internal boundaries, boundary conditions simulating the presence of an object or surface with specific acoustic characteristics are to be applied. Numerical boundary conditions, both external or internal, developed for simple model problems are reviewed and examined. Numerical boundary conditions for real aeroacoustic problems are also discussed through specific examples. The paper concludes with a description of some much needed research in numerical boundary conditions for CAA.

Applying Graph Theory to Problems in Air Traffic Management

NASA Technical Reports Server (NTRS)

Farrahi, Amir Hossein; Goldbert, Alan; Bagasol, Leonard Neil; Jung, Jaewoo

2017-01-01

Graph theory is used to investigate three different problems arising in air traffic management. First, using a polynomial reduction from a graph partitioning problem, it is shown that both the airspace sectorization problem and its incremental counterpart, the sector combination problem are NP-hard, in general, under several simple workload models. Second, using a polynomial time reduction from maximum independent set in graphs, it is shown that for any fixed e, the problem of finding a solution to the minimum delay scheduling problem in traffic flow management that is guaranteed to be within n1-e of the optimal, where n is the number of aircraft in the problem instance, is NP-hard. Finally, a problem arising in precision arrival scheduling is formulated and solved using graph reachability. These results demonstrate that graph theory provides a powerful framework for modeling, reasoning about, and devising algorithmic solutions to diverse problems arising in air traffic management.

Applying Graph Theory to Problems in Air Traffic Management

NASA Technical Reports Server (NTRS)

Farrahi, Amir H.; Goldberg, Alan T.; Bagasol, Leonard N.; Jung, Jaewoo

2017-01-01

Graph theory is used to investigate three different problems arising in air traffic management. First, using a polynomial reduction from a graph partitioning problem, it isshown that both the airspace sectorization problem and its incremental counterpart, the sector combination problem are NP-hard, in general, under several simple workload models. Second, using a polynomial time reduction from maximum independent set in graphs, it is shown that for any fixed e, the problem of finding a solution to the minimum delay scheduling problem in traffic flow management that is guaranteed to be within n1-e of the optimal, where n is the number of aircraft in the problem instance, is NP-hard. Finally, a problem arising in precision arrival scheduling is formulated and solved using graph reachability. These results demonstrate that graph theory provides a powerful framework for modeling, reasoning about, and devising algorithmic solutions to diverse problems arising in air traffic management.

Optimal Control Problems with Switching Points. Ph.D. Thesis, 1990 Final Report

NASA Technical Reports Server (NTRS)

Seywald, Hans

1991-01-01

The main idea of this report is to give an overview of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.

On solvability of boundary value problems for hyperbolic fourth-order equations with nonlocal boundary conditions of integral type

NASA Astrophysics Data System (ADS)

Popov, Nikolay S.

2017-11-01

Solvability of some initial-boundary value problems for linear hyperbolic equations of the fourth order is studied. A condition on the lateral boundary in these problems relates the values of a solution or the conormal derivative of a solution to the values of some integral operator applied to a solution. Nonlocal boundary-value problems for one-dimensional hyperbolic second-order equations with integral conditions on the lateral boundary were considered in the articles by A.I. Kozhanov. Higher-dimensional hyperbolic equations of higher order with integral conditions on the lateral boundary were not studied earlier. The existence and uniqueness theorems of regular solutions are proven. The method of regularization and the method of continuation in a parameter are employed to establish solvability.

Homogeneous and Non-Homogeneous Boundary Value Problems for First Order Linear Hyperbolic Systems Arising in Fluid Mechanics. Part II.

DTIC Science & Technology

1982-03-01

use indifferently the notations du and dtu . We begin with the uniqueness result: Proposition 3.1. Let f e LI(I;X), U0 e X and let u e L1 (I;X) be a...multiplying both sides of the last equation (scalarly in Xt) by u one gets ( dtu (itt), u (it))t+ ((L+B)u (1)(t), u ()(t))t " (f() (t),u (t)) t. On the other...lIX), u 0 e X and u e L1 CI;y) n AC(IX) such that u -w on I x R!-, dtu (i) + (L+B)u f ()(A) () (1) 1 MA U (0) -O U ( u0 in X, f + f in L (IPX) and u

Implementation of Hybrid V-Cycle Multilevel Methods for Mixed Finite Element Systems with Penalty

NASA Technical Reports Server (NTRS)

Lai, Chen-Yao G.

1996-01-01

The goal of this paper is the implementation of hybrid V-cycle hierarchical multilevel methods for the indefinite discrete systems which arise when a mixed finite element approximation is used to solve elliptic boundary value problems. By introducing a penalty parameter, the perturbed indefinite system can be reduced to a symmetric positive definite system containing the small penalty parameter for the velocity unknown alone. We stabilize the hierarchical spatial decomposition approach proposed by Cai, Goldstein, and Pasciak for the reduced system. We demonstrate that the relative condition number of the preconditioner is bounded uniformly with respect to the penalty parameter, the number of levels and possible jumps of the coefficients as long as they occur only across the edges of the coarsest elements.

On the freestream matching condition for stagnation point turbulent flows

NASA Technical Reports Server (NTRS)

Speziale, C. G.

1989-01-01

The problem of plane stagnation point flow with freestream turbulence is examined from a basic theoretical standpoint. It is argued that the singularity which arises from the standard kappa-epsilon model is not due to a defect in the model but results from the use of an inconsistent freestream boundary condition. The inconsistency lies in the implementation of a production equals dissipation equilibrium hypothesis in conjunction with a freestream mean velocity field that corresponds to homogeneous plane strain - a turbulent flow which does not reach such a simple equilibrium. Consequently, the adjustment that has been made in the constants of the epsilon-transport equation to eliminate this singularity is not self-consistent since it is tantamount to artificially imposing an equilibrium structure on a turbulent flow which is known not to have one.

Analysis of Heat Transfer Phenomenon in Magnetohydrodynamic Casson Fluid Flow Through Cattaneo-Christov Heat Diffusion Theory

NASA Astrophysics Data System (ADS)

Ramesh, G. K.; Gireesha, B. J.; Shehzad, S. A.; Abbasi, F. M.

2017-07-01

Heat transport phenomenon of two-dimensional magnetohydrodynamic Casson fluid flow by employing Cattaneo-Christov heat diffusion theory is described in this work. The term of heat absorption/generation is incorporated in the mathematical modeling of present flow problem. The governing mathematical expressions are solved for velocity and temperature profiles using RKF 45 method along with shooting technique. The importance of arising nonlinear quantities namely velocity, temperature, skin-friction and temperature gradient are elaborated via plots. It is explored that the Casson parameter retarded the liquid velocity while it enhances the fluid temperature. Further, we noted that temperature and thickness of temperature boundary layer are weaker in case of Cattaneo-Christov heat diffusion model when matched with the profiles obtained for Fourier’s theory of heat flux.

Mixed boundary value problems in mechanics

NASA Technical Reports Server (NTRS)

Erdogan, F.

1975-01-01

Certain boundary value problems were studied over a domain D which may contain the point at infinity and may be multiply connected. Contours forming the boundary are assumed to consist of piecewise smooth arcs. Mixed boundary value problems are those with points of flux singularity on the boundary; these are points on the surface, either side of which at least one of the differential operator has different behavior. The physical system was considered to be described by two quantities, the potential and the flux type quantities. Some of the examples that were illustrated included problems in potential theory and elasticity.

A two-dimensional Riemann solver with self-similar sub-structure - Alternative formulation based on least squares projection

NASA Astrophysics Data System (ADS)

Balsara, Dinshaw S.; Vides, Jeaniffer; Gurski, Katharine; Nkonga, Boniface; Dumbser, Michael; Garain, Sudip; Audit, Edouard

2016-01-01

Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The self-similar formulation of Balsara [16] proves especially useful for this purpose. While that work is based on a Galerkin projection, in this paper we present an analogous self-similar formulation that is based on a different interpretation. In the present formulation, we interpret the shock jumps at the boundary of the strongly-interacting state quite literally. The enforcement of the shock jump conditions is done with a least squares projection (Vides, Nkonga and Audit [67]). With that interpretation, we again show that the multidimensional Riemann solver can be endowed with sub-structure. However, we find that the most efficient implementation arises when we use a flux vector splitting and a least squares projection. An alternative formulation that is based on the full characteristic matrices is also presented. The multidimensional Riemann solvers that are demonstrated here use one-dimensional HLLC Riemann solvers as building blocks. Several stringent test problems drawn from hydrodynamics and MHD are presented to show that the method works. Results from structured and unstructured meshes demonstrate the versatility of our method. The reader is also invited to watch a video introduction to multidimensional Riemann solvers on http://www.nd.edu/ dbalsara/Numerical-PDE-Course.

A simple analytical method for determining the atmospheric dispersion of upward-directed high velocity releases

NASA Astrophysics Data System (ADS)

Palazzi, E.

The evaluation of atmospheric dispersion of a cloud, arising from a sudden release of flammable or toxic materials, is an essential tool for properly designing flares, vents and other safety devices and to quantify the potential risk related to the existing ones or arising from the various kinds of accidents which can occur in chemical plants. Among the methods developed to treat the important case of upward-directed jets, Hoehne's procedure for determining the behaviour and extent of flammability zone is extensively utilized, particularly concerning petrochemical plants. In a previous study, a substantial simplification of the aforesaid procedure was achieved, by correlating the experimental data with an empirical formula, allowing to obtain a mathematical description of the boundaries of the flammable cloud. Following a theoretical approach, a most general model is developed in the present work, applicable to the various kinds of design problems and/or risk evaluation regarding upward-directed releases from high velocity sources. It is also demonstrated that the model gives conservative results, if applied outside the range of the Hoehne's experimental conditions. Moreover, with simple modifications, the same approach could be easily applied to deal with the atmospheric dispersion of anyhow directed releases.

Unraveling the origins of electromechanical response in mixed-phase Bismuth Ferrite

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vasudevan, Rama K; Okatan, M. B.; Liu, Y. Y.

The origin of giant electromechanical response in a mixed-phase rhombohedral-tetragonal BiFeO3 thin film is probed using sub-coercive scanning probe microscopy based multiple-harmonic measurements. Significant contributions to the strain arise from a second-order harmonic response localized at the phase boundaries. Strain and dissipation data, backed by thermodynamic calculations suggest that the source of the enhanced electromechanical response is the motion of phase boundaries. These findings elucidate the key role of labile phase boundaries, both natural and artificial, in achieving thin films with giant electromechanical properties.

Inequalities, Assessment and Computer Algebra

ERIC Educational Resources Information Center

Sangwin, Christopher J.

2015-01-01

The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary…

Hybrid finite-difference/lattice Boltzmann simulations of microchannel and nanochannel acoustic streaming driven by surface acoustic waves

NASA Astrophysics Data System (ADS)

Tan, Ming K.; Yeo, Leslie Y.

2018-04-01

A two-dimensional hybrid numerical method that allows full coupling of the elastic motion in a piezoelectric solid (modeled using a finite-difference time-domain technique) with the resultant compressional flow in a fluid (simulated using a lattice Boltzmann scheme) is developed to study the acoustic streaming that arises in both microchannels and nanochannels under surface acoustic wave (SAW) excitation. In addition to verifying the model through a comparison of the simulations with results from experimental and numerical studies of microchannel and nanochannel flows driven by both standing and traveling SAWs in the literature, we highlight salient features of the flow field that arise and discuss the underlying mechanisms responsible for the flow. In microchannels, boundary layer streaming is the dominant mechanism when the channel height is below the sound wavelength in the liquid, whereas Eckart streaming—arising as a consequence of the attenuation of the sound wave in the liquid—dominates in the form of periodic vortices for larger channel heights. The absence of Eckart streaming and the overlapping of boundary layers in nanochannels with heights below the boundary layer thickness, on the other hand, give rise to a time-averaged dynamic acoustic pressure that results in an inertial-dominant flow, which paradoxically possesses a parabolic-like velocity profile resembling pressure-driven laminar flow. In contrast, if the nanochannel were to be filled instead with air, the significantly lower fluid density leads to a considerable reduction in the dynamic acoustic pressure and hence inertial forcing such that boundary layer streaming once again dominates, asymptotically imposing a slip condition along the channel surface that results in a negative pluglike velocity profile.

Positivity and Almost Positivity of Biharmonic Green's Functions under Dirichlet Boundary Conditions

NASA Astrophysics Data System (ADS)

Grunau, Hans-Christoph; Robert, Frédéric

2010-03-01

In general, for higher order elliptic equations and boundary value problems like the biharmonic equation and the linear clamped plate boundary value problem, neither a maximum principle nor a comparison principle or—equivalently—a positivity preserving property is available. The problem is rather involved since the clamped boundary conditions prevent the boundary value problem from being reasonably written as a system of second order boundary value problems. It is shown that, on the other hand, for bounded smooth domains {Ω subsetmathbb{R}^n} , the negative part of the corresponding Green’s function is “small” when compared with its singular positive part, provided {n≥q 3} . Moreover, the biharmonic Green’s function in balls {Bsubsetmathbb{R}^n} under Dirichlet (that is, clamped) boundary conditions is known explicitly and is positive. It has been known for some time that positivity is preserved under small regular perturbations of the domain, if n = 2. In the present paper, such a stability result is proved for {n≥q 3}.

Numerical methods for stiff systems of two-point boundary value problems

NASA Technical Reports Server (NTRS)

Flaherty, J. E.; Omalley, R. E., Jr.

1983-01-01

Numerical procedures are developed for constructing asymptotic solutions of certain nonlinear singularly perturbed vector two-point boundary value problems having boundary layers at one or both endpoints. The asymptotic approximations are generated numerically and can either be used as is or to furnish a general purpose two-point boundary value code with an initial approximation and the nonuniform computational mesh needed for such problems. The procedures are applied to a model problem that has multiple solutions and to problems describing the deformation of thin nonlinear elastic beam that is resting on an elastic foundation.

Higher modes of the Orr-Sommerfeld problem for boundary layer flows

NASA Technical Reports Server (NTRS)

Lakin, W. D.; Grosch, C. E.

1983-01-01

The discrete spectrum of the Orr-Sommerfeld problem of hydrodynamic stability for boundary layer flows in semi-infinite regions is examined. Related questions concerning the continuous spectrum are also addressed. Emphasis is placed on the stability problem for the Blasius boundary layer profile. A general theoretical result is given which proves that the discrete spectrum of the Orr-Sommerfeld problem for boundary layer profiles (U(y), 0,0) has only a finite number of discrete modes when U(y) has derivatives of all orders. Details are given of a highly accurate numerical technique based on collocation with splines for the calculation of stability characteristics. The technique includes replacement of 'outer' boundary conditions by asymptotic forms based on the proper large parameter in the stability problem. Implementation of the asymptotic boundary conditions is such that there is no need to make apriori distinctions between subcases of the discrete spectrum or between the discrete and continuous spectrums. Typical calculations for the usual Blasius problem are presented.

Strongly nonlinear theory of rapid solidification near absolute stability

NASA Astrophysics Data System (ADS)

Kowal, Katarzyna N.; Altieri, Anthony L.; Davis, Stephen H.

2017-10-01

We investigate the nonlinear evolution of the morphological deformation of a solid-liquid interface of a binary melt under rapid solidification conditions near two absolute stability limits. The first of these involves the complete stabilization of the system to cellular instabilities as a result of large enough surface energy. We derive nonlinear evolution equations in several limits in this scenario and investigate the effect of interfacial disequilibrium on the nonlinear deformations that arise. In contrast to the morphological stability problem in equilibrium, in which only cellular instabilities appear and only one absolute stability boundary exists, in disequilibrium the system is prone to oscillatory instabilities and a second absolute stability boundary involving attachment kinetics arises. Large enough attachment kinetics stabilize the oscillatory instabilities. We derive a nonlinear evolution equation to describe the nonlinear development of the solid-liquid interface near this oscillatory absolute stability limit. We find that strong asymmetries develop with time. For uniform oscillations, the evolution equation for the interface reduces to the simple form f''+(βf')2+f =0 , where β is the disequilibrium parameter. Lastly, we investigate a distinguished limit near both absolute stability limits in which the system is prone to both cellular and oscillatory instabilities and derive a nonlinear evolution equation that captures the nonlinear deformations in this limit. Common to all these scenarios is the emergence of larger asymmetries in the resulting shapes of the solid-liquid interface with greater departures from equilibrium and larger morphological numbers. The disturbances additionally sharpen near the oscillatory absolute stability boundary, where the interface becomes deep-rooted. The oscillations are time-periodic only for small-enough initial amplitudes and their frequency depends on a single combination of physical parameters, including the morphological number, as well as the amplitude. The critical amplitude, at which solutions loose periodicity, depends on a single combination of parameters independent of the morphological number that indicate that non-periodic growth is most commonly present for moderate disequilibrium parameters. The spatial distribution of the interface develops deepening roots at late times. Similar spatial distributions are also seen in the limit in which both the cellular and oscillatory modes are close to absolute stability, and the roots deepen with larger departures from the two absolute stability boundaries.

Improved Hurricane Boundary Layer Observations with the Imaging Wind and Rain Airborne Profiler

NASA Technical Reports Server (NTRS)

Esteban-Fernandez, Daniel; Changy, P.; Carswell, J.; Contreras, R.; Chu, T.

2006-01-01

During the NOAA/NESDIS 2005 Hurricane Season (HS2005) and the 2006 Winter Experiment, the University of Massachusetts (UMass) installed two instruments on the NOAA N42RF WP-3D research aircraft: the Imaging Wind and Rain Airborne Profiler (IWRAP) and the Simultaneous Frequency Microwave Radiometer (SFMR). IWRAP is a dual-band (C- and Ku), dual-polarized pencil-beam airborne radar that profiles the volume backscatter and Doppler velocity from rain and that also measures the ocean backscatter response. It simultaneously profiles along four separate incidence angles while conically scanning at 60 RPM. SFMR is a C-band nadir viewing radiometer that measures the emission from the ocean surface and intervening atmosphere simultaneously at six frequencies. It is designed to obtain the surface wind speed and the column average rain rate. Both instruments have previously been flown during the 2002, 2003 and 2004 hurricane seasons. For the HS2005, the IWRAP system was modified to implement a raw data acquisition system. The importance of the raw data system arises when trying to profile the atmosphere all the way down to the surface with a non-nadir looking radar system. With this particular geometry, problems arise mainly from the fact that both rain and ocean provide a return echo coincident in time through the antenna s main lobe. This paper shows how this limitation has been removed and presents initial results demonstrating its new capabilities to derive the atmospheric boundary layer (ABL) wind field within the inner core of hurricanes to much lower altitudes than the ones the original system was capable of, and to analyze the spectral response of the ocean backscatter and the rain under different wind and rain conditions.

On Takens’ last problem: tangencies and time averages near heteroclinic networks

NASA Astrophysics Data System (ADS)

Labouriau, Isabel S.; Rodrigues, Alexandre A. P.

2017-05-01

We obtain a structurally stable family of smooth ordinary differential equations exhibiting heteroclinic tangencies for a dense subset of parameters. We use this to find vector fields C 2-close to an element of the family exhibiting a tangency, for which the set of solutions with historic behaviour contains an open set. This provides an affirmative answer to Takens’ last problem (Takens 2008 Nonlinearity 21 T33-6). A limited solution with historic behaviour is one for which the time averages do not converge as time goes to infinity. Takens’ problem asks for dynamical systems where historic behaviour occurs persistently for initial conditions in a set with positive Lebesgue measure. The family appears in the unfolding of a degenerate differential equation whose flow has an asymptotically stable heteroclinic cycle involving two-dimensional connections of non-trivial periodic solutions. We show that the degenerate problem also has historic behaviour, since for an open set of initial conditions starting near the cycle, the time averages approach the boundary of a polygon whose vertices depend on the centres of gravity of the periodic solutions and their Floquet multipliers. We illustrate our results with an explicit example where historic behaviour arises C 2-close of a \\mathbf{SO}(2) -equivariant vector field.

Three-dimensional thermocapillary flow regimes with evaporation

NASA Astrophysics Data System (ADS)

Bekezhanova, V. B.; Goncharova, O. N.

2017-10-01

A three-dimensional problem of evaporative convection in a system of the immiscible media with a common thermocapillary interface is studied. New exact solution, which is a generalization of the Ostroumov - Birikh solution of the Navier - Stokes equations in the Oberbeck - Boussinesq approximation, is presented in order to describe the joint flows of the liquid and gas - vapor mixture in an infinite channel with a rectangular cross-section. The motion occurs in the bulk force field under action of a constant longitudinal temperature gradient. The velocity components depend only on the transverse coordinates. The functions of pressure, temperature and concentration of vapor in the gas are characterized by the linear dependence on the longitudinal coordinate. In the framework of the problem statement, which takes into account diffusive mass flux through the interface and zero vapor flux at the upper boundary of the channel, the influence of the gravity and intensity of the thermal action on flow structure is studied. The original three-dimensional problem is reduced to a chain of two-dimensional problems which are solved numerically with help of modification of the method of alternating directions. Arising flows can be characterized as a translational-rotational motion, under that the symmetrical double, quadruple or sextuple vortex structures are formed. Quantity, shape and structure of the vortexes also depend on properties of the working media.

Forced cubic Schrödinger equation with Robin boundary data: large-time asymptotics

PubMed Central

Kaikina, Elena I.

2013-01-01

We consider the initial-boundary-value problem for the cubic nonlinear Schrödinger equation, formulated on a half-line with inhomogeneous Robin boundary data. We study traditionally important problems of the theory of nonlinear partial differential equations, such as the global-in-time existence of solutions to the initial-boundary-value problem and the asymptotic behaviour of solutions for large time. PMID:24204185

Wall touching kink mode calculations with the M3D code

NASA Astrophysics Data System (ADS)

Breslau, J. A.

2014-10-01

In recent years there have been a number of results published concerning the transient vessel currents and forces occurring during a tokamak VDE, as predicted by simulations with the nonlinear MHD code M3D. The nature of the simulations is such that these currents and forces occur at the boundary of the computational domain, making the proper choice of boundary conditions critical to the reliability of the results. The M3D boundary condition includes the prescription that the normal component of the velocity vanish at the wall. It has been argued that this prescription invalidates the calculations because it would seem to rule out the possibility of advection of plasma surface currents into the wall. This claim has been tested by applying M3D to an idealized case - a kink-unstable plasma column - in order to abstract the essential physics from the complications involved in the attempt to model real devices. While comparison of the results is complicated by effects arising from the higher dimensionality and complexity of M3D, we have verified that M3D is capable of reproducing both the correct saturation behavior of the free boundary kink and the ``Hiro'' currents arising when the kink interacts with a conducting tile surface interior to the ideal wall.

Optimal analytic method for the nonlinear Hasegawa-Mima equation

NASA Astrophysics Data System (ADS)

Baxter, Mathew; Van Gorder, Robert A.; Vajravelu, Kuppalapalle

2014-05-01

The Hasegawa-Mima equation is a nonlinear partial differential equation that describes the electric potential due to a drift wave in a plasma. In the present paper, we apply the method of homotopy analysis to a slightly more general Hasegawa-Mima equation, which accounts for hyper-viscous damping or viscous dissipation. First, we outline the method for the general initial/boundary value problem over a compact rectangular spatial domain. We use a two-stage method, where both the convergence control parameter and the auxiliary linear operator are optimally selected to minimize the residual error due to the approximation. To do the latter, we consider a family of operators parameterized by a constant which gives the decay rate of the solutions. After outlining the general method, we consider a number of concrete examples in order to demonstrate the utility of this approach. The results enable us to study properties of the initial/boundary value problem for the generalized Hasegawa-Mima equation. In several cases considered, we are able to obtain solutions with extremely small residual errors after relatively few iterations are computed (residual errors on the order of 10-15 are found in multiple cases after only three iterations). The results demonstrate that selecting a parameterized auxiliary linear operator can be extremely useful for minimizing residual errors when used concurrently with the optimal homotopy analysis method, suggesting that this approach can prove useful for a number of nonlinear partial differential equations arising in physics and nonlinear mechanics.

Plasma diffusion at the magnetopause? The case of lower hybrid drift waves

NASA Technical Reports Server (NTRS)

Treumann, R. A.; Labelle, J.; Pottelette, R.; Gary, S. P.

1990-01-01

The diffusion expected from the quasilinear theory of the lower hybrid drift instability at the Earth's magnetopause is recalculated. The resulting diffusion coefficient is in principle just marginally large enough to explain the thickness of the boundary layer under quiet conditions, based on observational upper limits for the wave intensities. Thus, one possible model for the boundary layer could involve equilibrium between the diffusion arising from lower hybrid waves and various low processes. However, some recent data and simulations seems to indicate that the magnetopause is not consistent with such a soft diffusive equilibrium model. Furthermore, investigation of the nonlinear equations for the lower hybrid waves for magnetopause parameters indicates that the quasilinear state may never arise because coalescence to large wavelengths, followed by collapse once a critical wavelengths is reached, occur on a time scale faster than the quasilinear diffusion. In this case, an inhomogeneous boundary layer is to be expected. More simulations are required over longer time periods to explore whether this nonlinear evolution really takes place at the magnetopause.

A fast direct solver for boundary value problems on locally perturbed geometries

NASA Astrophysics Data System (ADS)

Zhang, Yabin; Gillman, Adrianna

2018-03-01

Many applications including optimal design and adaptive discretization techniques involve solving several boundary value problems on geometries that are local perturbations of an original geometry. This manuscript presents a fast direct solver for boundary value problems that are recast as boundary integral equations. The idea is to write the discretized boundary integral equation on a new geometry as a low rank update to the discretized problem on the original geometry. Using the Sherman-Morrison formula, the inverse can be expressed in terms of the inverse of the original system applied to the low rank factors and the right hand side. Numerical results illustrate for problems where perturbation is localized the fast direct solver is three times faster than building a new solver from scratch.

Integral Method of Boundary Characteristics: Neumann Condition

NASA Astrophysics Data System (ADS)

Kot, V. A.

2018-05-01

A new algorithm, based on systems of identical equalities with integral and differential boundary characteristics, is proposed for solving boundary-value problems on the heat conduction in bodies canonical in shape at a Neumann boundary condition. Results of a numerical analysis of the accuracy of solving heat-conduction problems with variable boundary conditions with the use of this algorithm are presented. The solutions obtained with it can be considered as exact because their errors comprise hundredths and ten-thousandths of a persent for a wide range of change in the parameters of a problem.

Stress-intensity factor calculations using the boundary force method

NASA Technical Reports Server (NTRS)

Tan, P. W.; Raju, I. S.; Newman, J. C., Jr.

1987-01-01

The Boundary Force Method (BFM) was formulated for the three fundamental problems of elasticity: the stress boundary value problem, the displacement boundary value problem, and the mixed boundary value problem. Because the BFM is a form of an indirect boundary element method, only the boundaries of the region of interest are modeled. The elasticity solution for the stress distribution due to concentrated forces and a moment applied at an arbitrary point in a cracked infinite plate is used as the fundamental solution. Thus, unlike other boundary element methods, here the crack face need not be modeled as part of the boundary. The formulation of the BFM is described and the accuracy of the method is established by analyzing a center-cracked specimen subjected to mixed boundary conditions and a three-hole cracked configuration subjected to traction boundary conditions. The results obtained are in good agreement with accepted numerical solutions. The method is then used to generate stress-intensity solutions for two common cracked configurations: an edge crack emanating from a semi-elliptical notch, and an edge crack emanating from a V-notch. The BFM is a versatile technique that can be used to obtain very accurate stress intensity factors for complex crack configurations subjected to stress, displacement, or mixed boundary conditions. The method requires a minimal amount of modeling effort.

Hydrodynamic lubrication of rigid nonconformal contacts in combined rolling and normal motion

NASA Technical Reports Server (NTRS)

Ghosh, M. K.; Hamrock, B. J.; Brewe, D. E.

1984-01-01

A numerical solution to the problem of hydrodynamic lubrication of rigid point contacts with an isoviscous, incompressible lubricant was obtained. The hydrodynamic load-carrying capacity under unsteady (or dynamic) conditions arising from the combined effects of squeeze motion superposed upon the entraining motion was determined for both normal approach and separation. Superposed normal motion considerably increases net load-carrying capacity during normal approach and substantially reduces net load-carrying capacity during separation. Geometry was also found to have a significant influence on the dynamic load-carrying capacity. The ratio of dynamic to steady state load-carrying capacity increases with increasing geometry parameter for normal approach and decreases during separation. The cavitation (film rupture) boundary is also influenced significantly by the normal motion, moving downstream during approach and upstream during separation. For sufficiently high normal separation velocity the rupture boundary may even move upstream of the minimum-film-thickness position. Sixty-three cases were used to derive a functional relationship for the ratio of the dynamic to steady state load-carrying capacity in terms of the dimensionless normal velocity parameter (incorporating normal velocity, entraining velocity, and film thickness) and the geometry parameter.

Hydrodynamic lubrication of rigid nonconformal contacts in combined rolling and normal motion

NASA Technical Reports Server (NTRS)

Ghosh, M. K.; Hamrock, B. J.; Brewe, D.

1985-01-01

A numerical solution to the problem of hydrodynamic lubrication of rigid point contacts with an isoviscous, incompressible lubricant was obtained. The hydrodynamic load-carrying capacity under unsteady (or dynamic) conditions arising from the combined effects of squeeze motion superposed upon the entraining motion was determined for both normal approach and separation. Superposed normal motion considerably increases net load-carrying capacity during normal approach and substantially reduces net load-carrying capacity during separation. Geometry was also found to have a significant influence on the dynamic load-carrying capacity. The ratio of dynamic to steady state load-carrying capacity increases with increasing geometry parameter for normal approach and decreases during separation. The cavitation (film rupture) boundary is also influenced significantly by the normal motion, moving downstream during approach and upstream during separation. For sufficiently high normal separation velocity the rupture boundary may even move upstream of the minimum-film-thickness position. Sixty-three cases were used to derive a functional relationship for the ratio of the dynamic to steady state load-carrying capacity in terms of the dimensionless normal velocity parameter (incorporating normal velocity, entraining velocity, and film thickness) and the geometry parameter.

A study of flux transfer events at different planets

NASA Technical Reports Server (NTRS)

Russell, C. T.

1995-01-01

Flux transfer events (FTEs) are disturbances in and near the magnetopause current layer that cause a characteristic signature in the component of the magnetic field parallel to the average boundary normal. These disturbances have been observed at Mercury, Earth and Jupiter but not at Saturn, Uranus or Neptune. At Earth, FTEs last about 1 minute and repeat about every 8 but at Mercury, a much smaller magnetosphere, the events last seconds and are tens of seconds apart. These features have been interpreted in terms of magnetospheric flux ropes connected to the interplanetary magnetic field, arising as the result of reconnection. An analogous phenomenon occurs at Venus where magnetic flux ropes arise at the ionosphere, a boundary between a very strongly magnetized one. However, here the flux ropes do not appear to be due to reconnection.

Low- and high-order accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Silva, Goncalo, E-mail: goncalo.nuno.silva@gmail.com; Talon, Laurent, E-mail: talon@fast.u-psud.fr; Ginzburg, Irina, E-mail: irina.ginzburg@irstea.fr

The present contribution focuses on the accuracy of reflection-type boundary conditions in the Stokes–Brinkman–Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the two-relaxation-time (TRT) collision and the Brinkman-force based scheme (BF), called BF-TRT scheme. In parallel, we compare it with the Stokes–Brinkman–Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BF-TRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocity-proportional resistance force. This correction modifies themore » effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in lattice-aligned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the no-slip wall condition supported by traditional LBM boundary schemes, such as the bounce-back rule. For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition at an arbitrary wall/boundary-node distance and that supports a higher order accuracy in the accommodation of the TRT-Brinkman solutions. For their modeling, we consider the standard BF scheme and its improved version, called IBF; this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows. Our framework extends the one- and two-point families of linear and parabolic link-wise boundary schemes, respectively called B-LI and B-MLI, which avoid the interference of the Brinkman viscosity correction in their closure relations. The performance of LBM and FEM is thoroughly evaluated in three benchmark tests, which are run throughout three distinctive permeability regimes. The first configuration is a horizontal porous channel, studied with a symbolic approach, where we construct the exact solutions of FEM and BF/IBF with different boundary schemes. The second problem refers to an inclined porous channel flow, which brings in as new challenge the formation of spurious boundary layers in LBM; that is, numerical artefacts that arise due to a deficient accommodation of the bulk solution by the low-accurate boundary scheme. The third problem considers a porous flow past a periodic square array of solid cylinders, which intensifies the previous two tests with the simulation of a more complex flow pattern. The ensemble of numerical tests provides guidelines on the effect of grid resolution and the TRT free collision parameter over the accuracy and the quality of the velocity field, spanning from Stokes to Darcy permeability regimes. It is shown that, with the use of the high-order accurate boundary schemes, the simple, uniform-mesh-based TRT-LBM formulation can even surpass the accuracy of FEM employing hardworking body-fitted meshes.« less

Low- and high-order accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes

NASA Astrophysics Data System (ADS)

Silva, Goncalo; Talon, Laurent; Ginzburg, Irina

2017-04-01

The present contribution focuses on the accuracy of reflection-type boundary conditions in the Stokes-Brinkman-Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the two-relaxation-time (TRT) collision and the Brinkman-force based scheme (BF), called BF-TRT scheme. In parallel, we compare it with the Stokes-Brinkman-Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BF-TRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocity-proportional resistance force. This correction modifies the effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in lattice-aligned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the no-slip wall condition supported by traditional LBM boundary schemes, such as the bounce-back rule. For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition at an arbitrary wall/boundary-node distance and that supports a higher order accuracy in the accommodation of the TRT-Brinkman solutions. For their modeling, we consider the standard BF scheme and its improved version, called IBF; this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows. Our framework extends the one- and two-point families of linear and parabolic link-wise boundary schemes, respectively called B-LI and B-MLI, which avoid the interference of the Brinkman viscosity correction in their closure relations. The performance of LBM and FEM is thoroughly evaluated in three benchmark tests, which are run throughout three distinctive permeability regimes. The first configuration is a horizontal porous channel, studied with a symbolic approach, where we construct the exact solutions of FEM and BF/IBF with different boundary schemes. The second problem refers to an inclined porous channel flow, which brings in as new challenge the formation of spurious boundary layers in LBM; that is, numerical artefacts that arise due to a deficient accommodation of the bulk solution by the low-accurate boundary scheme. The third problem considers a porous flow past a periodic square array of solid cylinders, which intensifies the previous two tests with the simulation of a more complex flow pattern. The ensemble of numerical tests provides guidelines on the effect of grid resolution and the TRT free collision parameter over the accuracy and the quality of the velocity field, spanning from Stokes to Darcy permeability regimes. It is shown that, with the use of the high-order accurate boundary schemes, the simple, uniform-mesh-based TRT-LBM formulation can even surpass the accuracy of FEM employing hardworking body-fitted meshes.

New Boundary Constraints for Elliptic Systems used in Grid Generation Problems

NASA Technical Reports Server (NTRS)

Kaul, Upender K.; Clancy, Daniel (Technical Monitor)

2002-01-01

This paper discusses new boundary constraints for elliptic partial differential equations as used in grid generation problems in generalized curvilinear coordinate systems. These constraints, based on the principle of local conservation of thermal energy in the vicinity of the boundaries, are derived using the Green's Theorem. They uniquely determine the so called decay parameters in the source terms of these elliptic systems. These constraints' are designed for boundary clustered grids where large gradients in physical quantities need to be resolved adequately. It is observed that the present formulation also works satisfactorily for mild clustering. Therefore, a closure for the decay parameter specification for elliptic grid generation problems has been provided resulting in a fully automated elliptic grid generation technique. Thus, there is no need for a parametric study of these decay parameters since the new constraints fix them uniquely. It is also shown that for Neumann type boundary conditions, these boundary constraints uniquely determine the solution to the internal elliptic problem thus eliminating the non-uniqueness of the solution of an internal Neumann boundary value grid generation problem.

Completed Beltrami-Michell formulation for analyzing mixed boundary value problems in elasticity

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Kaljevic, Igor; Hopkins, Dale A.; Saigal, Sunil

1995-01-01

In elasticity, the method of forces, wherein stress parameters are considered as the primary unknowns, is known as the Beltrami-Michell formulation (BMF). The existing BMF can only solve stress boundary value problems; it cannot handle the more prevalent displacement of mixed boundary value problems of elasticity. Therefore, this formulation, which has restricted application, could not become a true alternative to the Navier's displacement method, which can solve all three types of boundary value problems. The restrictions in the BMF have been alleviated by augmenting the classical formulation with a novel set of conditions identified as the boundary compatibility conditions. This new method, which completes the classical force formulation, has been termed the completed Beltrami-Michell formulation (CBMF). The CBMF can solve general elasticity problems with stress, displacement, and mixed boundary conditions in terms of stresses as the primary unknowns. The CBMF is derived from the stationary condition of the variational functional of the integrated force method. In the CBMF, stresses for kinematically stable structures can be obtained without any reference to the displacements either in the field or on the boundary. This paper presents the CBMF and its derivation from the variational functional of the integrated force method. Several examples are presented to demonstrate the applicability of the completed formulation for analyzing mixed boundary value problems under thermomechanical loads. Selected example problems include a cylindrical shell wherein membrane and bending responses are coupled, and a composite circular plate.

Topological defects in open string field theory

NASA Astrophysics Data System (ADS)

Kojita, Toshiko; Maccaferri, Carlo; Masuda, Toru; Schnabl, Martin

2018-04-01

We show how conformal field theory topological defects can relate solutions of open string field theory for different boundary conditions. To this end we generalize the results of Graham and Watts to include the action of defects on boundary condition changing fields. Special care is devoted to the general case when nontrivial multiplicities arise upon defect action. Surprisingly the fusion algebra of defects is realized on open string fields only up to a (star algebra) isomorphism.

Transition from single to multiple double layers. [of plasma

NASA Technical Reports Server (NTRS)

Chan, C.; Hershkowitz, N.

1982-01-01

Laboratory results are presented to define parameters which allow the boundary conditions to control the characteristics of double layers of plasma. It is shown that multiple double layers arise when the ratio of Debye length to system length decreases, a result which is in line with boundary layer theory. The significance of inclusion of the system length is noted to render BGK treatments of double layers, wherein the length is neglected, invalid.

Plasma diffusion at the magnetopause - The case of lower hybrid drift waves

NASA Technical Reports Server (NTRS)

Treumann, R. A.; Labelle, J.; Pottelette, R.

1991-01-01

The diffusion expected from the quasi-linear theory of the lower hybrid drift instability at the earth's magnetopause is recalculated. The resulting diffusion coefficient is marginally large enough to explain the thickness of the boundary layer under quiet conditions, based on observational upper limits for the wave intensities. Thus, one possible model for the boundary layer could involve equilibrium between the diffusion arising from lower hybrid waves and various loss processes.

Accurate boundary conditions for exterior problems in gas dynamics

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Hariharan, S. I.

1988-01-01

The numerical solution of exterior problems is typically accomplished by introducing an artificial, far field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.

Accurate boundary conditions for exterior problems in gas dynamics

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Hariharan, S. I.

1988-01-01

The numerical solution of exterior problems is typically accomplished by introducing an artificial, far-field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far-field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.

Computation of the shock-wave boundary layer interaction with flow separation

NASA Technical Reports Server (NTRS)

Ardonceau, P.; Alziary, T.; Aymer, D.

1980-01-01

The boundary layer concept is used to describe the flow near the wall. The external flow is approximated by a pressure displacement relationship (tangent wedge in linearized supersonic flow). The boundary layer equations are solved in finite difference form and the question of the presence and unicity of the solution is considered for the direct problem (assumed pressure) or converse problem (assumed displacement thickness, friction ratio). The coupling algorithm presented implicitly processes the downstream boundary condition necessary to correctly define the interacting boundary layer problem. The algorithm uses a Newton linearization technique to provide a fast convergence.

Chern-Simons theory with Wilson lines and boundary in the BV-BFV formalism

NASA Astrophysics Data System (ADS)

Alekseev, Anton; Barmaz, Yves; Mnev, Pavel

2013-05-01

We consider the Chern-Simons theory with Wilson lines in 3D and in 1D in the BV-BFV formalism of Cattaneo-Mnev-Reshetikhin. In particular, we allow for Wilson lines to end on the boundary of the space-time manifold. In the toy model of 1D Chern-Simons theory, the quantized BFV boundary action coincides with the Kostant cubic Dirac operator which plays an important role in representation theory. In the case of 3D Chern-Simons theory, the boundary action turns out to be the odd (degree 1) version of the BF model with source terms for the B field at the points where the Wilson lines meet the boundary. The boundary space of states arising as the cohomology of the quantized BFV action coincides with the space of conformal blocks of the corresponding WZW model.

Efficient algorithms for analyzing the singularly perturbed boundary value problems of fractional order

NASA Astrophysics Data System (ADS)

Sayevand, K.; Pichaghchi, K.

2018-04-01

In this paper, we were concerned with the description of the singularly perturbed boundary value problems in the scope of fractional calculus. We should mention that, one of the main methods used to solve these problems in classical calculus is the so-called matched asymptotic expansion method. However we shall note that, this was not achievable via the existing classical definitions of fractional derivative, because they do not obey the chain rule which one of the key elements of the matched asymptotic expansion method. In order to accommodate this method to fractional derivative, we employ a relatively new derivative so-called the local fractional derivative. Using the properties of local fractional derivative, we extend the matched asymptotic expansion method to the scope of fractional calculus and introduce a reliable new algorithm to develop approximate solutions of the singularly perturbed boundary value problems of fractional order. In the new method, the original problem is partitioned into inner and outer solution equations. The reduced equation is solved with suitable boundary conditions which provide the terminal boundary conditions for the boundary layer correction. The inner solution problem is next solved as a solvable boundary value problem. The width of the boundary layer is approximated using appropriate resemblance function. Some theoretical results are established and proved. Some illustrating examples are solved and the results are compared with those of matched asymptotic expansion method and homotopy analysis method to demonstrate the accuracy and efficiency of the method. It can be observed that, the proposed method approximates the exact solution very well not only in the boundary layer, but also away from the layer.

Analytic Approximations to the Free Boundary and Multi-dimensional Problems in Financial Derivatives Pricing

NASA Astrophysics Data System (ADS)

Lau, Chun Sing

This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark prices obtained by numerical integration or Monte Carlo simulation. By exploiting an explicit relationship between the option price and the underlying probability distribution, we further derive an approximate distribution function for the general basket-spread variable. It can be used to approximate the transition probability distribution of any linear combination of correlated GBMs. Finally, an implicit perturbation is applied to reduce the pricing errors by factors of up to 100. When compared against the existing methods, the basket-spread option formula coupled with the implicit perturbation turns out to be one of the most robust and accurate approximation methods.

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis,Michael J.

2006-01-01

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

COMPLEX VARIABLE BOUNDARY ELEMENT METHOD: APPLICATIONS.

USGS Publications Warehouse

Hromadka, T.V.; Yen, C.C.; Guymon, G.L.

1985-01-01

The complex variable boundary element method (CVBEM) is used to approximate several potential problems where analytical solutions are known. A modeling result produced from the CVBEM is a measure of relative error in matching the known boundary condition values of the problem. A CVBEM error-reduction algorithm is used to reduce the relative error of the approximation by adding nodal points in boundary regions where error is large. From the test problems, overall error is reduced significantly by utilizing the adaptive integration algorithm.

Well-posedness of the free boundary problem in compressible elastodynamics

NASA Astrophysics Data System (ADS)

Trakhinin, Yuri

2018-02-01

We study the free boundary problem for the flow of a compressible isentropic inviscid elastic fluid. At the free boundary moving with the velocity of the fluid particles the columns of the deformation gradient are tangent to the boundary and the pressure vanishes outside the flow domain. We prove the local-in-time existence of a unique smooth solution of the free boundary problem provided that among three columns of the deformation gradient there are two which are non-collinear vectors at each point of the initial free boundary. If this non-collinearity condition fails, the local-in-time existence is proved under the classical Rayleigh-Taylor sign condition satisfied at the first moment. By constructing an Hadamard-type ill-posedness example for the frozen coefficients linearized problem we show that the simultaneous failure of the non-collinearity condition and the Rayleigh-Taylor sign condition leads to Rayleigh-Taylor instability.

Exact solution for a two-phase Stefan problem with variable latent heat and a convective boundary condition at the fixed face

NASA Astrophysics Data System (ADS)

Bollati, Julieta; Tarzia, Domingo A.

2018-04-01

Recently, in Tarzia (Thermal Sci 21A:1-11, 2017) for the classical two-phase Lamé-Clapeyron-Stefan problem an equivalence between the temperature and convective boundary conditions at the fixed face under a certain restriction was obtained. Motivated by this article we study the two-phase Stefan problem for a semi-infinite material with a latent heat defined as a power function of the position and a convective boundary condition at the fixed face. An exact solution is constructed using Kummer functions in case that an inequality for the convective transfer coefficient is satisfied generalizing recent works for the corresponding one-phase free boundary problem. We also consider the limit to our problem when that coefficient goes to infinity obtaining a new free boundary problem, which has been recently studied in Zhou et al. (J Eng Math 2017. https://doi.org/10.1007/s10665-017-9921-y).

EPR-dosimetry of ionizing radiation

NASA Astrophysics Data System (ADS)

Popova, Mariia; Vakhnin, Dmitrii; Tyshchenko, Igor

2017-09-01

This article discusses the problems that arise during the radiation sterilization of medical products. It is propose the solution based on alanine EPR-dosimetry. The parameters of spectrometer and methods of absorbed dose calculation are given. In addition, the problems that arise during heavy particles irradiation are investigated.

Boundary Element Method in a Self-Gravitating Elastic Half-Space and Its Application to Deformation Induced by Magma Chambers

NASA Astrophysics Data System (ADS)

Fang, M.; Hager, B. H.

2014-12-01

In geophysical applications the boundary element method (BEM) often carries the essential physics in addition to being an efficient numerical scheme. For use of the BEM in a self-gravitating uniform half-space, we made extra effort and succeeded in deriving the fundamental solution analytically in closed-form. A problem that goes deep into the heart of the classic BEM is encountered when we try to apply the new fundamental solution in BEM for deformation field induced by a magma chamber or a fluid-filled reservoir. The central issue of the BEM is the singular integral arising from determination of the boundary values. A widely employed technique is to rescale the singular boundary point into a small finite volume and then shrink it to extract the limits. This operation boils down to the calculation of the so-called C-matrix. Authors in the past take the liberty of either adding or subtracting a small volume. By subtracting a small volume, the C-matrix is (1/2)I on a smooth surface, where I is the identity matrix; by adding a small volume, we arrive at the same C-matrix in the form of I - (1/2)I. This evenness is a result of the spherical symmetry of Kelvin's fundamental solution employed. When the spherical symmetry is broken by gravity, the C-matrix is polarized. And we face the choice between right and wrong, for adding and subtracting a small volume yield different C-matrices. Close examination reveals that both derivations, addition and subtraction of a small volume, are ad hoc. To resolve the issue we revisit the Somigliana identity with a new derivation and careful step-by-step anatomy. The result proves that even though both adding and subtracting a small volume appear to twist the original boundary, only addition essentially modifies the original boundary and consequently modifies the physics of the original problem in a subtle way. The correct procedure is subtraction. We complete a new BEM theory by introducing in full analytical form what we call the singular stress tensor for the fundamental solution. We partition the stress tensor of the fundamental solution into a singular part and a regular part. In this way all singular integrals systematically shift into the easy singular stress tensor. Applications of this new BEM to deformation and gravitational perturbation induced by magma chambers of finite volume will be presented.

Boundary effects and the onset of Taylor vortices

NASA Astrophysics Data System (ADS)

Rucklidge, A. M.; Champneys, A. R.

2004-05-01

It is well established that the onset of spatially periodic vortex states in the Taylor-Couette flow between rotating cylinders occurs at the value of Reynolds number predicted by local bifurcation theory. However, the symmetry breaking induced by the top and bottom plates means that the true situation should be a disconnected pitchfork. Indeed, experiments have shown that the fold on the disconnected branch can occur at more than double the Reynolds number of onset. This leads to an apparent contradiction: why should Taylor vortices set in so sharply at the Reynolds number predicted by the symmetric theory, given such large symmetry-breaking effects caused by the boundary conditions? This paper offers a generic explanation. The details are worked out using a Swift-Hohenberg pattern formation model that shares the same qualitative features as the Taylor-Couette flow. Onset occurs via a wall mode whose exponential tail penetrates further into the bulk of the domain as the driving parameter increases. In a large domain of length L, we show that the wall mode creates significant amplitude in the centre at parameter values that are O( L-2) away from the value of onset in the problem with ideal boundary conditions. We explain this as being due to a Hamiltonian Hopf bifurcation in space, which occurs at the same parameter value as the pitchfork bifurcation of the temporal dynamics. The disconnected anomalous branch remains O(1) away from the onset parameter since it does not arise as a bifurcation from the wall mode.

Metallurgical Aspects of Layered Cracks in Hot-Rolled Plates

NASA Astrophysics Data System (ADS)

Farber, V. M.; Arabey, A. B.; Khotinov, V. A.; Morozova, A. N.; Karabanalov, M. S.

2018-03-01

The nature of separations arising in hot-rolled plates from high-toughness steels of the new generation like 05G2B and of cleavages arising in traditional building steels of type 09G2S is studied. Like and unlike features of separations and cleavages are determined. The concept of "critical stress σb^{cr} " describing the strength of the interlayer boundaries responsible for formation of layered cracks is used to analyze various factors responsible for the susceptibility of rolled plates to layered fracture.

Numerical solution of system of boundary value problems using B-spline with free parameter

NASA Astrophysics Data System (ADS)

Gupta, Yogesh

2017-01-01

This paper deals with method of B-spline solution for a system of boundary value problems. The differential equations are useful in various fields of science and engineering. Some interesting real life problems involve more than one unknown function. These result in system of simultaneous differential equations. Such systems have been applied to many problems in mathematics, physics, engineering etc. In present paper, B-spline and B-spline with free parameter methods for the solution of a linear system of second-order boundary value problems are presented. The methods utilize the values of cubic B-spline and its derivatives at nodal points together with the equations of the given system and boundary conditions, ensuing into the linear matrix equation.

State space approach to mixed boundary value problems.

NASA Technical Reports Server (NTRS)

Chen, C. F.; Chen, M. M.

1973-01-01

A state-space procedure for the formulation and solution of mixed boundary value problems is established. This procedure is a natural extension of the method used in initial value problems; however, certain special theorems and rules must be developed. The scope of the applications of the approach includes beam, arch, and axisymmetric shell problems in structural analysis, boundary layer problems in fluid mechanics, and eigenvalue problems for deformable bodies. Many classical methods in these fields developed by Holzer, Prohl, Myklestad, Thomson, Love-Meissner, and others can be either simplified or unified under new light shed by the state-variable approach. A beam problem is included as an illustration.

Computation of Transonic Nozzle Sound Transmission and Rotor Problems by the Dispersion-Relation-Preserving Scheme

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Aganin, Alexei

2000-01-01

The transonic nozzle transmission problem and the open rotor noise radiation problem are solved computationally. Both are multiple length scales problems. For efficient and accurate numerical simulation, the multiple-size-mesh multiple-time-step Dispersion-Relation-Preserving scheme is used to calculate the time periodic solution. To ensure an accurate solution, high quality numerical boundary conditions are also needed. For the nozzle problem, a set of nonhomogeneous, outflow boundary conditions are required. The nonhomogeneous boundary conditions not only generate the incoming sound waves but also, at the same time, allow the reflected acoustic waves and entropy waves, if present, to exit the computation domain without reflection. For the open rotor problem, there is an apparent singularity at the axis of rotation. An analytic extension approach is developed to provide a high quality axis boundary treatment.

Computer analysis of multicircuit shells of revolution by the field method

NASA Technical Reports Server (NTRS)

Cohen, G. A.

1975-01-01

The field method, presented previously for the solution of even-order linear boundary value problems defined on one-dimensional open branch domains, is extended to boundary value problems defined on one-dimensional domains containing circuits. This method converts the boundary value problem into two successive numerically stable initial value problems, which may be solved by standard forward integration techniques. In addition, a new method for the treatment of singular boundary conditions is presented. This method, which amounts to a partial interchange of the roles of force and displacement variables, is problem independent with respect to both accuracy and speed of execution. This method was implemented in a computer program to calculate the static response of ring stiffened orthotropic multicircuit shells of revolution to asymmetric loads. Solutions are presented for sample problems which illustrate the accuracy and efficiency of the method.

Fermionic edge states and new physics

NASA Astrophysics Data System (ADS)

Govindarajan, T. R.; Tibrewala, Rakesh

2015-08-01

We investigate the properties of the Dirac operator on manifolds with boundaries in the presence of the Atiyah-Patodi-Singer boundary condition. An exact counting of the number of edge states for boundaries with isometry of a sphere is given. We show that the problem with the above boundary condition can be mapped to one where the manifold is extended beyond the boundary and the boundary condition is replaced by a delta function potential of suitable strength. We also briefly highlight how the problem of the self-adjointness of the operators in the presence of moving boundaries can be simplified by suitable transformations which render the boundary fixed and modify the Hamiltonian and the boundary condition to reflect the effect of moving boundary.

On the use of Lagrangian variables in descriptions of unsteady boundary-layer separation

NASA Technical Reports Server (NTRS)

Cowley, Stephen J.; Vandommelen, Leon L.; Lam, Shui T.

1990-01-01

The Lagrangian description of unsteady boundary layer separation is reviewed from both analytical and numerical perspectives. It is explained in simple terms how particle distortion gives rise to unsteady separation, and why a theory centered on Lagrangian coordinates provides the clearest description of this phenomenon. Some of the more recent results for unsteady three dimensional compressible separation are included. The different forms of separation that can arise from symmetries are emphasized. A possible description of separation is also included when the detaching vorticity layer exits the classical boundary layer region, but still remains much closer to the surface than a typical body-lengthscale.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luo, Yousong, E-mail: yousong.luo@rmit.edu.au

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.

Development of stress boundary conditions in smoothed particle hydrodynamics (SPH) for the modeling of solids deformation

NASA Astrophysics Data System (ADS)

Douillet-Grellier, Thomas; Pramanik, Ranjan; Pan, Kai; Albaiz, Abdulaziz; Jones, Bruce D.; Williams, John R.

2017-10-01

This paper develops a method for imposing stress boundary conditions in smoothed particle hydrodynamics (SPH) with and without the need for dummy particles. SPH has been used for simulating phenomena in a number of fields, such as astrophysics and fluid mechanics. More recently, the method has gained traction as a technique for simulation of deformation and fracture in solids, where the meshless property of SPH can be leveraged to represent arbitrary crack paths. Despite this interest, application of boundary conditions within the SPH framework is typically limited to imposed velocity or displacement using fictitious dummy particles to compensate for the lack of particles beyond the boundary interface. While this is enough for a large variety of problems, especially in the case of fluid flow, for problems in solid mechanics there is a clear need to impose stresses upon boundaries. In addition to this, the use of dummy particles to impose a boundary condition is not always suitable or even feasibly, especially for those problems which include internal boundaries. In order to overcome these difficulties, this paper first presents an improved method for applying stress boundary conditions in SPH with dummy particles. This is then followed by a proposal of a formulation which does not require dummy particles. These techniques are then validated against analytical solutions to two common problems in rock mechanics, the Brazilian test and the penny-shaped crack problem both in 2D and 3D. This study highlights the fact that SPH offers a good level of accuracy to solve these problems and that results are reliable. This validation work serves as a foundation for addressing more complex problems involving plasticity and fracture propagation.

NASA Ames three-dimensional potential flow analyses system (POTFAN) boundary condition code (BCDN), version 1

NASA Technical Reports Server (NTRS)

Davis, J. E.; Medan, R. T.

1977-01-01

This segment of the POTFAN system is used to generate right hand sides (boundary conditions) of the system of equations associated with the flow field under consideration. These specified flow boundary conditions are encountered in the oblique derivative boundary value problem (boundary value problem of the third kind) and contain the Neumann boundary condition as a special case. Arbitrary angle of attack and/or sideslip and/or rotation rates may be specified, as well as an arbitrary, nonuniform external flow field and the influence of prescribed singularity distributions.

Guidance and flight control law development for hypersonic vehicles

NASA Technical Reports Server (NTRS)

Calise, A. J.; Markopoulos, N.

1993-01-01

During the third reporting period our efforts were focused on a reformulation of the optimal control problem involving active state-variable inequality constraints. In the reformulated problem the optimization is carried out not with respect to all controllers, but only with respect to asymptotic controllers leading to the state constraint boundary. Intimately connected with the traditional formulation is the fact that when the reduced solution for such problems lies on a state constraint boundary, the corresponding boundary layer transitions are of finite time in the stretched time scale. Thus, it has been impossible so far to apply the classical asymptotic boundary layer theory to such problems. Moreover, the traditional formulation leads to optimal controllers that are one-sided, that is, they break down when a disturbance throws the system on the prohibited side of the state constraint boundary.

Comments on numerical solution of boundary value problems of the Laplace equation and calculation of eigenvalues by the grid method

NASA Technical Reports Server (NTRS)

Lyusternik, L. A.

1980-01-01

The mathematics involved in numerically solving for the plane boundary value of the Laplace equation by the grid method is developed. The approximate solution of a boundary value problem for the domain of the Laplace equation by the grid method consists of finding u at the grid corner which satisfies the equation at the internal corners (u=Du) and certain boundary value conditions at the boundary corners.

Bifurcation and stability analysis of rotating chemical spirals in circular domains: Boundary-induced meandering and stabilization

NASA Astrophysics Data System (ADS)

Bär, Markus; Bangia, Anil K.; Kevrekidis, Ioannis G.

2003-05-01

Recent experimental and model studies have revealed that the domain size may strongly influence the dynamics of rotating spirals in two-dimensional pattern forming chemical reactions. Hartmann et al. [Phys. Rev. Lett. 76, 1384 (1996)], report a frequency increase of spirals in circular domains with diameters substantially smaller than the spiral wavelength in a large domain for the catalytic NO+CO reaction on a microstructured platinum surface. Accompanying simulations with a simple reaction-diffusion system reproduced the behavior. Here, we supplement these studies by a numerical bifurcation and stability analysis of rotating spirals in a simple activator-inhibitor model. The problem is solved in a corotating frame of reference. No-flux conditions are imposed at the boundary of the circular domain. At large domain sizes, eigenvalues and eigenvectors very close to those corresponding to infinite medium translational invariance are observed. Upon decrease of domain size, we observe a simultaneous change in the rotation frequency and a deviation of these eigenvalues from being neutrally stable (zero real part). The latter phenomenon indicates that the translation symmetry of the spiral solution is appreciably broken due to the interaction with the (now nearby) wall. Various dynamical regimes are found: first, the spiral simply tries to avoid the boundary and its tip moves towards the center of the circular domain corresponding to a negative real part of the “translational” eigenvalues. This effect is noticeable at a domain radius of R

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.

PubMed

Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y C

2015-01-01

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals.

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics

PubMed Central

Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y. C.

2015-01-01

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals. PMID:26064591

Selection of facility location under environmental damage priority and using ELECTRE method.

PubMed

Gundogdu, Ceren Erdin

2011-03-01

In the recent years, the environmental problems have reached to a vital extent, which is pushing the boundaries and far beyond daily evaluations. Industrial plants, the energy sources and uncontrolled release of pollutant gases (SO2, CO2 etc.) in the production stage have the greatest share in the occurrence of unfavorable environmental conditions. For this reason, the dimension of the problems that may arise in the production stage of industrial plants is directly related to the selection of facility location. In this study, geographical regions (a total of 7 regions) of our country have been analyzed in terms of environmental values based on their basins and the unfavorable environmental problems that are currently being experienced. Considered as such, with the directives of an expert group composed of nature scientists, the criteria and alternative areas are determined using the data gathered on ecosystem, basin characteristics, and land types. Since the primary goal is to keep the environmental damages at the minimum level, comprehensive definition of the problem is constructed by consultation of the expert group and the criteria are determined. Considering the fact that it will prevent the drawbacks generated by making decisions depending on certain stereotypes toa great extent, ELECTRE (Elimination and Choice Translating Reality English - Elimination Et Choix Traduisant la Realite) method is used to determine in which geographic region our country's industrial plants should be located.

An O(N) and parallel approach to integral problems by a kernel-independent fast multipole method: Application to polarization and magnetization of interacting particles

NASA Astrophysics Data System (ADS)

Jiang, Xikai; Li, Jiyuan; Zhao, Xujun; Qin, Jian; Karpeev, Dmitry; Hernandez-Ortiz, Juan; de Pablo, Juan J.; Heinonen, Olle

2016-08-01

Large classes of materials systems in physics and engineering are governed by magnetic and electrostatic interactions. Continuum or mesoscale descriptions of such systems can be cast in terms of integral equations, whose direct computational evaluation requires O(N2) operations, where N is the number of unknowns. Such a scaling, which arises from the many-body nature of the relevant Green's function, has precluded wide-spread adoption of integral methods for solution of large-scale scientific and engineering problems. In this work, a parallel computational approach is presented that relies on using scalable open source libraries and utilizes a kernel-independent Fast Multipole Method (FMM) to evaluate the integrals in O(N) operations, with O(N) memory cost, thereby substantially improving the scalability and efficiency of computational integral methods. We demonstrate the accuracy, efficiency, and scalability of our approach in the context of two examples. In the first, we solve a boundary value problem for a ferroelectric/ferromagnetic volume in free space. In the second, we solve an electrostatic problem involving polarizable dielectric bodies in an unbounded dielectric medium. The results from these test cases show that our proposed parallel approach, which is built on a kernel-independent FMM, can enable highly efficient and accurate simulations and allow for considerable flexibility in a broad range of applications.

Congested Aggregation via Newtonian Interaction

NASA Astrophysics Data System (ADS)

Craig, Katy; Kim, Inwon; Yao, Yao

2018-01-01

We consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal Newtonian attraction and a hard height constraint. This provides a counterpoint to existing literature on repulsive-attractive nonlocal interaction models, where the repulsive effects instead arise from an interaction kernel or the addition of diffusion. We formulate our model as the Wasserstein gradient flow of an interaction energy, with a penalization to enforce the constraint on the height of the density. From this perspective, the problem can be seen as a singular limit of the Keller-Segel equation with degenerate diffusion. Two key properties distinguish our problem from previous work on height constrained equations: nonconvexity of the interaction kernel (which places the model outside the scope of classical gradient flow theory) and nonlocal dependence of the velocity field on the density (which causes the problem to lack a comparison principle). To overcome these obstacles, we combine recent results on gradient flows of nonconvex energies with viscosity solution theory. We characterize the dynamics of patch solutions in terms of a Hele-Shaw type free boundary problem and, using this characterization, show that in two dimensions patch solutions converge to a characteristic function of a disk in the long-time limit, with an explicit rate on the decay of the energy. We believe that a key contribution of the present work is our blended approach, combining energy methods with viscosity solution theory.

An O( N) and parallel approach to integral problems by a kernel-independent fast multipole method: Application to polarization and magnetization of interacting particles

DOE PAGES

Jiang, Xikai; Li, Jiyuan; Zhao, Xujun; ...

2016-08-10

Large classes of materials systems in physics and engineering are governed by magnetic and electrostatic interactions. Continuum or mesoscale descriptions of such systems can be cast in terms of integral equations, whose direct computational evaluation requires O( N 2) operations, where N is the number of unknowns. Such a scaling, which arises from the many-body nature of the relevant Green's function, has precluded wide-spread adoption of integral methods for solution of large-scale scientific and engineering problems. In this work, a parallel computational approach is presented that relies on using scalable open source libraries and utilizes a kernel-independent Fast Multipole Methodmore » (FMM) to evaluate the integrals in O( N) operations, with O( N) memory cost, thereby substantially improving the scalability and efficiency of computational integral methods. We demonstrate the accuracy, efficiency, and scalability of our approach in the context of two examples. In the first, we solve a boundary value problem for a ferroelectric/ferromagnetic volume in free space. In the second, we solve an electrostatic problem involving polarizable dielectric bodies in an unbounded dielectric medium. Lastly, the results from these test cases show that our proposed parallel approach, which is built on a kernel-independent FMM, can enable highly efficient and accurate simulations and allow for considerable flexibility in a broad range of applications.« less

Investigation of Saltwater Intrusion and Recirculation of Seawater for Henry Constant Dispersion and Velocity-Dependent Dispersion Problems and Field-Scale Problem

NASA Astrophysics Data System (ADS)

Motz, L. H.; Kalakan, C.

2013-12-01

Three problems regarding saltwater intrusion, namely the Henry constant dispersion and velocity-dependent dispersion problems and a larger, field-scale velocity-dependent dispersion problem, have been investigated to determine quantitatively how saltwater intrusion and the recirculation of seawater at a coastal boundary are related to the freshwater inflow and the density-driven buoyancy flux. Based on dimensional analysis, saltwater intrusion and the recirculation of seawater are dependent functions of the independent ratio of freshwater advective flux relative to the density-driven vertical buoyancy flux, defined as az (or a for an isotropic aquifer), and the aspect ratio of horizontal and vertical dimensions of the cross-section. For the Henry constant dispersion problem, in which the aquifer is isotropic, saltwater intrusion and recirculation are related to an additional independent dimensionless parameter that is the ratio of the constant dispersion coefficient treated as a scalar quantity, the porosity, and the freshwater advective flux, defined as b. For the Henry velocity-dependent dispersion problem, the ratio b is zero, and saltwater intrusion and recirculation are related to an additional independent dimensionless parameter that is the ratio of the vertical and horizontal dispersivities, or rα = αz/αx. For an anisotropic aquifer, saltwater intrusion and recirculation are also dependent on the ratio of vertical and horizontal hydraulic conductivities, or rK = Kz/Kx. For the field-scale velocity-dependent dispersion problem, saltwater intrusion and recirculation are dependent on the same independent ratios as the Henry velocity-dependent dispersion problem. In the two-dimensional cross-section for all three problems, freshwater inflow occurs at an upgradient boundary, and recirculated seawater outflow occurs at a downgradient coastal boundary. The upgradient boundary is a specified-flux boundary with zero freshwater concentration, and the downgradient boundary is a specified-head boundary with a specified concentration equal to seawater. Equivalent freshwater heads are specified at the downstream boundary to account for density differences between freshwater and saltwater at the downstream boundary. The three problems were solved using the numerical groundwater flow and transport code SEAWAT for two conditions, i.e., first for the uncoupled condition in which the fluid density is constant and thus the flow and transport equations are uncoupled in a constant-density flowfield, and then for the coupled condition in which the fluid density is a function of the total dissolved solids concentration and thus the flow and transport equations are coupled in a variable-density flowfield. A wide range of results for the landward extent of saltwater intrusion and the amount of recirculation of seawater at the coastal boundary was obtained by varying the independent dimensionless ratio az (or a in problem one) in all three problems. The dimensionless dispersion ratio b was also varied in problem one, and the dispersivity ratio rα and the hydraulic conductivity ratio rK were also varied in problems two and three.

Integrable boundary value problems for elliptic type Toda lattice in a disk

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guerses, Metin; Habibullin, Ismagil; Zheltukhin, Kostyantyn

The concept of integrable boundary value problems for soliton equations on R and R{sub +} is extended to regions enclosed by smooth curves. Classes of integrable boundary conditions in a disk for the Toda lattice and its reductions are found.

Estimates of green tensors for certain boundary value problems

NASA Technical Reports Server (NTRS)

Solonnikov, V.

1988-01-01

Consider the first boundary value problem for a stationary Navier-Stokes system in a bounded three-dimensional region Omega with the boundary S: delta v = grad p+f, div v=0, v/s=0. Odqvist (1930) developed the potential theory and formulated the Green tensor for the above problem. The basic singular solution used by Odqvist to express the Green tensor is given. A theorem generalizing his results is presented along with four associated theorems. A specific problem associated with the study of the differential properties of the solution of stationary problems of magnetohydrodynamics is examined.

Role of intraspecific competition in the coexistence of mobile populations in spatially extended ecosystems.

PubMed

Yang, Rui; Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

2010-06-01

Evolutionary-game based models of nonhierarchical, cyclically competing populations have become paradigmatic for addressing the fundamental problem of species coexistence in spatially extended ecosystems. We study the role of intraspecific competition in the coexistence and find that the competition can strongly promote the coexistence for high individual mobility in the sense that stable coexistence can arise in parameter regime where extinction would occur without the competition. The critical value of the competition rate beyond which the coexistence is induced is found to be independent of the mobility. We derive a theoretical model based on nonlinear partial differential equations to predict the critical competition rate and the boundaries between the coexistence and extinction regions in a relevant parameter space. We also investigate pattern formation and well-mixed spatiotemporal population dynamics to gain further insights into our findings. (c) 2010 American Institute of Physics.

A partially reflecting random walk on spheres algorithm for electrical impedance tomography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maire, Sylvain, E-mail: maire@univ-tln.fr; Simon, Martin, E-mail: simon@math.uni-mainz.de

2015-12-15

In this work, we develop a probabilistic estimator for the voltage-to-current map arising in electrical impedance tomography. This novel so-called partially reflecting random walk on spheres estimator enables Monte Carlo methods to compute the voltage-to-current map in an embarrassingly parallel manner, which is an important issue with regard to the corresponding inverse problem. Our method uses the well-known random walk on spheres algorithm inside subdomains where the diffusion coefficient is constant and employs replacement techniques motivated by finite difference discretization to deal with both mixed boundary conditions and interface transmission conditions. We analyze the global bias and the variance ofmore » the new estimator both theoretically and experimentally. Subsequently, the variance of the new estimator is considerably reduced via a novel control variate conditional sampling technique which yields a highly efficient hybrid forward solver coupling probabilistic and deterministic algorithms.« less

Homogenization techniques for population dynamics in strongly heterogeneous landscapes.

PubMed

Yurk, Brian P; Cobbold, Christina A

2018-12-01

An important problem in spatial ecology is to understand how population-scale patterns emerge from individual-level birth, death, and movement processes. These processes, which depend on local landscape characteristics, vary spatially and may exhibit sharp transitions through behavioural responses to habitat edges, leading to discontinuous population densities. Such systems can be modelled using reaction-diffusion equations with interface conditions that capture local behaviour at patch boundaries. In this work we develop a novel homogenization technique to approximate the large-scale dynamics of the system. We illustrate our approach, which also generalizes to multiple species, with an example of logistic growth within a periodic environment. We find that population persistence and the large-scale population carrying capacity is influenced by patch residence times that depend on patch preference, as well as movement rates in adjacent patches. The forms of the homogenized coefficients yield key theoretical insights into how large-scale dynamics arise from the small-scale features.

Integrodifference equations in patchy landscapes : II: population level consequences.

PubMed

Musgrave, Jeffrey; Lutscher, Frithjof

2014-09-01

We analyze integrodifference equations (IDEs) in patchy landscapes. Movement is described by a dispersal kernel that arises from a random walk model with patch dependent diffusion, settling, and mortality rates, and it incorporates individual behavior at an interface between two patch types. Growth follows a simple Beverton-Holt growth or linear decay. We obtain explicit formulae for the critical domain-size problem, and we illustrate how different individual behavior at the boundary between two patch types affects this quantity. We also study persistence conditions on an infinite, periodic, patchy landscape. We observe that if the population can persist on the landscape, the spatial profile of the invasion evolves into a discontinuous traveling periodic wave that moves with constant speed. Assuming linear determinacy, we calculate the dispersion relation and illustrate how movement behavior affects invasion speed. Numerical simulations justify our approach by showing a close correspondence between the spread rate obtained from the dispersion relation and from numerical simulations.

Application of Contraction Mappings to the Control of Nonlinear Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Killingsworth, W. R., Jr.

1972-01-01

The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.

Bose–Einstein condensation temperature of finite systems

NASA Astrophysics Data System (ADS)

Xie, Mi

2018-05-01

In studies of the Bose–Einstein condensation of ideal gases in finite systems, the divergence problem usually arises in the equation of state. In this paper, we present a technique based on the heat kernel expansion and zeta function regularization to solve the divergence problem, and obtain the analytical expression of the Bose–Einstein condensation temperature for general finite systems. The result is represented by the heat kernel coefficients, where the asymptotic energy spectrum of the system is used. Besides the general case, for systems with exact spectra, e.g. ideal gases in an infinite slab or in a three-sphere, the sums of the spectra can be obtained exactly and the calculation of corrections to the critical temperatures is more direct. For a system confined in a bounded potential, the form of the heat kernel is different from the usual heat kernel expansion. We show that as long as the asymptotic form of the global heat kernel can be found, our method works. For Bose gases confined in three- and two-dimensional isotropic harmonic potentials, we obtain the higher-order corrections to the usual results of the critical temperatures. Our method can also be applied to the problem of generalized condensation, and we give the correction of the boundary on the second critical temperature in a highly anisotropic slab.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berenstein, David; Kavli Institute for Theoretical Physics, University of California at Santa Barbara, California 93106; Correa, Diego H.

We study an XXX open spin chain with variable number of sites, where the variability is introduced only at the boundaries. This model arises naturally in the study of giant gravitons in the anti-de Sitter-space/conformal field-theory correspondence. We show how to quantize the spin chain by mapping its states to a bosonic lattice of finite length with sources and sinks of particles at the boundaries. Using coherent states, we show how the Hamiltonian for the bosonic lattice gives the correct description of semiclassical open strings ending on giant gravitons.

Gravity-Wave Dynamics in the Atmosphere

DTIC Science & Technology

2010-02-01

boundaries of domain. The viscous boundary layers are used as an artificial radiation condition. 25 The inclusion of viscous terms in an explicit temporal... evolution equations become Volterra equations of the second kind given by Kc11aT +K c 12bT + ˆ x −∞ dx′ (K11xa ′ T +K12xb ′ T )− 1 2 α2a + bxY = 0...nonlinear wavepackets arising from shear-flow instabilities. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18

Intrinsic rotation from a residual stress at the boundary of a cylindrical laboratory plasma.

PubMed

Yan, Z; Xu, M; Diamond, P H; Holland, C; Müller, S H; Tynan, G R; Yu, J H

2010-02-12

An azimuthally symmetric radially sheared azimuthal flow is driven by a nondiffusive, or residual, turbulent stress localized to a narrow annular region at the boundary of a cylindrical magnetized helicon plasma device. A no-slip condition, imposed by ion-neutral flow damping outside the annular region, combined with a diffusive stress arising from turbulent and collisional viscous damping in the central plasma region, leads to net plasma rotation in the absence of momentum input.

Polarization of the interference field during reflection of electromagnetic waves from an intermedia boundary

NASA Astrophysics Data System (ADS)

Bulakhov, M. G.; Buyanov, Yu. I.; Yakubov, V. P.

1996-10-01

It has been shown that a full vector measurement of the total field allows one to uniquely distinguish the incident and reflected waves at each observation point without the use of a spatial difference based on an analysis of the polarization structure of the interference pattern which arises during reflection of electromagnetic waves from an intermedia boundary. We have investigated the stability of these procedures with respect to measurement noise by means of numerical modeling.

Comment on “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition” by A. Aziz, Comm. Nonlinear Sci. Numer. Simul. 2009;14:1064-8

NASA Astrophysics Data System (ADS)

Magyari, Eugen

2011-01-01

In a recent paper published in this Journal the title problem has been investigated numerically. In the present paper the exact solution for the temperature boundary layer is given in terms of the solution of the flow problem (the Blasius problem) in a compact integral form.

Performance of mixed formulations for the particle finite element method in soil mechanics problems

NASA Astrophysics Data System (ADS)

Monforte, Lluís; Carbonell, Josep Maria; Arroyo, Marcos; Gens, Antonio

2017-07-01

This paper presents a computational framework for the numerical analysis of fluid-saturated porous media at large strains. The proposal relies, on one hand, on the particle finite element method (PFEM), known for its capability to tackle large deformations and rapid changing boundaries, and, on the other hand, on constitutive descriptions well established in current geotechnical analyses (Darcy's law; Modified Cam Clay; Houlsby hyperelasticity). An important feature of this kind of problem is that incompressibility may arise either from undrained conditions or as a consequence of material behaviour; incompressibility may lead to volumetric locking of the low-order elements that are typically used in PFEM. In this work, two different three-field mixed formulations for the coupled hydromechanical problem are presented, in which either the effective pressure or the Jacobian are considered as nodal variables, in addition to the solid skeleton displacement and water pressure. Additionally, several mixed formulations are described for the simplified single-phase problem due to its formal similitude to the poromechanical case and its relevance in geotechnics, since it may approximate the saturated soil behaviour under undrained conditions. In order to use equal-order interpolants in displacements and scalar fields, stabilization techniques are used in the mass conservation equation of the biphasic medium and in the rest of scalar equations. Finally, all mixed formulations are assessed in some benchmark problems and their performances are compared. It is found that mixed formulations that have the Jacobian as a nodal variable perform better.

Adjustment of the problems of landslide GIS data

NASA Astrophysics Data System (ADS)

Uchiyama, S.; Doshida, S.; Oyagi, N.; Shimizu, F.; Inokuchi, T.

2012-12-01

Information on the distribution of landslides is a basic type of data used by countries for disaster prevention. Since 1972, 1:50,000 landslide maps have been produced at the Japanese National Research Institute for Earth Science and Disaster Prevention. From October 2000, the institute has been producing landslide GIS data and transmitting these data over the web. The area that has been published so far covers over 80% of Japan. Presently, the number of diagrams printed are 980 (March 2012). In addition, 350,000 landslide GIS data graphs have been digitized with the same diagrams as a base. Twelve years have passed since this GIS data acquisition program was launched, and in that time, several problems have been identified. These problems are listed below. 1) Scarps do not become polygonized. 2) Landslides which extend over the boundaries of the printed graphs are divided into separate elements. 3) When the time taken to read and interpret the landslide data differs, the shape of the landslides can vary between diagrams. 4) There have been cases of inaccurate positions and shapes in landslide GIS data produced since 2005. 5) Obvious mistakes are present in the attribute data. The causes of such problems are as follows: 1) Lack of technical examination at the time of the start of the production of the landslide GIS data. 2) Limitations of the landslide GIS data editing systems which were developed separately. 3) Program bugs which occur during the conversion of information input to an individual editing system into general-purpose GIS data. 4) Problems which arise during the process of the production of landslide GIS data. This project at the National Research Institute for Earth Science and Disaster Prevention is planned to be completed in 2013. By the end of the project, we hope to present a catalogue of all identified problems and formulate a plan to resolve them, and pass them on to the next generation.; Problems: For the diagram, scarps are presented by polylines and cannot be treated as polygons (topography area). Example of limitations of the individual editing system. Both the moving mass or scarp and other features are divided by the printing boundaries of the diagrams. Another example of the limitations of the editing system. When a scarp is present within the moving mass, the scarp area is hollowed out.

Efficient Parallel Formulations of Hierarchical Methods and Their Applications

NASA Astrophysics Data System (ADS)

Grama, Ananth Y.

1996-01-01

Hierarchical methods such as the Fast Multipole Method (FMM) and Barnes-Hut (BH) are used for rapid evaluation of potential (gravitational, electrostatic) fields in particle systems. They are also used for solving integral equations using boundary element methods. The linear systems arising from these methods are dense and are solved iteratively. Hierarchical methods reduce the complexity of the core matrix-vector product from O(n^2) to O(n log n) and the memory requirement from O(n^2) to O(n). We have developed highly scalable parallel formulations of a hybrid FMM/BH method that are capable of handling arbitrarily irregular distributions. We apply these formulations to astrophysical simulations of Plummer and Gaussian galaxies. We have used our parallel formulations to solve the integral form of the Laplace equation. We show that our parallel hierarchical mat-vecs yield high efficiency and overall performance even on relatively small problems. A problem containing approximately 200K nodes takes under a second to compute on 256 processors and yet yields over 85% efficiency. The efficiency and raw performance is expected to increase for bigger problems. For the 200K node problem, our code delivers about 5 GFLOPS of performance on a 256 processor T3D. This is impressive considering the fact that the problem has floating point divides and roots, and very little locality resulting in poor cache performance. A dense matrix-vector product of the same dimensions would require about 0.5 TeraBytes of memory and about 770 TeraFLOPS of computing speed. Clearly, if the loss in accuracy resulting from the use of hierarchical methods is acceptable, our code yields significant savings in time and memory. We also study the convergence of a GMRES solver built around this mat-vec. We accelerate the convergence of the solver using three preconditioning techniques: diagonal scaling, block-diagonal preconditioning, and inner-outer preconditioning. We study the performance and parallel efficiency of these preconditioned solvers. Using this solver, we solve dense linear systems with hundreds of thousands of unknowns. Solving a 105K unknown problem takes about 10 minutes on a 64 processor T3D. Until very recently, boundary element problems of this magnitude could not even be generated, let alone solved.

A boundary element alternating method for two-dimensional mixed-mode fracture problems

NASA Technical Reports Server (NTRS)

Raju, I. S.; Krishnamurthy, T.

1992-01-01

A boundary element alternating method, denoted herein as BEAM, is presented for two dimensional fracture problems. This is an iterative method which alternates between two solutions. An analytical solution for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate is used as the fundamental solution in the alternating method. A boundary element method for an uncracked finite plate is the second solution. For problems of edge cracks a technique of utilizing finite elements with BEAM is presented to overcome the inherent singularity in boundary element stress calculation near the boundaries. Several computational aspects that make the algorithm efficient are presented. Finally, the BEAM is applied to a variety of two dimensional crack problems with different configurations and loadings to assess the validity of the method. The method gives accurate stress intensity factors with minimal computing effort.

Constant-concentration boundary condition: Lessons from the HYDROCOIN variable-density groundwater benchmark problem

USGS Publications Warehouse

Konikow, Leonard F.; Sanford, W.E.; Campbell, P.J.

1997-01-01

In a solute-transport model, if a constant-concentration boundary condition is applied at a node in an active flow field, a solute flux can occur by both advective and dispersive processes. The potential for advective release is demonstrated by reexamining the Hydrologic Code Intercomparison (HYDROCOIN) project case 5 problem, which represents a salt dome overlain by a shallow groundwater system. The resulting flow field includes significant salinity and fluid density variations. Several independent teams simulated this problem using finite difference or finite element numerical models. We applied a method-of-characteristics model (MOCDENSE). The previous numerical implementations by HYDROCOIN teams of a constant-concentration boundary to represent salt release by lateral dispersion only (as stipulated in the original problem definition) was flawed because this boundary condition allows the release of salt into the flow field by both dispersion and advection. When the constant-concentration boundary is modified to allow salt release by dispersion only, significantly less salt is released into the flow field. The calculated brine distribution for case 5 depends very little on which numerical model is used, as long as the selected model is solving the proper equations. Instead, the accuracy of the solution depends strongly on the proper conceptualization of the problem, including the detailed design of the constant-concentration boundary condition. The importance and sensitivity to the manner of specification of this boundary does not appear to have been recognized previously in the analysis of this problem.

A system-approach to the elastohydrodynamic lubrication point-contact problem

NASA Technical Reports Server (NTRS)

Lim, Sang Gyu; Brewe, David E.

1991-01-01

The classical EHL (elastohydrodynamic lubrication) point contact problem is solved using a new system-approach, similar to that introduced by Houpert and Hamrock for the line-contact problem. Introducing a body-fitted coordinate system, the troublesome free-boundary is transformed to a fixed domain. The Newton-Raphson method can then be used to determine the pressure distribution and the cavitation boundary subject to the Reynolds boundary condition. This method provides an efficient and rigorous way of solving the EHL point contact problem with the aid of a supercomputer and a promising method to deal with the transient EHL point contact problem. A typical pressure distribution and film thickness profile are presented and the minimum film thicknesses are compared with the solution of Hamrock and Dowson. The details of the cavitation boundaries for various operating parameters are discussed.

An inverse problem in thermal imaging

NASA Technical Reports Server (NTRS)

Bryan, Kurt; Caudill, Lester F., Jr.

1994-01-01

This paper examines uniqueness and stability results for an inverse problem in thermal imaging. The goal is to identify an unknown boundary of an object by applying a heat flux and measuring the induced temperature on the boundary of the sample. The problem is studied both in the case in which one has data at every point on the boundary of the region and the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for various experimental configurations.

Model of convection mass transfer in titanium alloy at low energy high current electron beam action

NASA Astrophysics Data System (ADS)

Sarychev, V. D.; Granovskii, A. Yu; Nevskii, S. A.; Konovalov, S. V.; Gromov, V. E.

2017-01-01

The convection mixing model is proposed for low-energy high-current electron beam treatment of titanium alloys, pre-processed by heterogeneous plasma flows generated via explosion of carbon tape and powder TiB2. The model is based on the assumption vortices in the molten layer are formed due to the treatment by concentrated energy flows. These vortices evolve as the result of thermocapillary convection, arising because of the temperature gradient. The calculation of temperature gradient and penetration depth required solution of the heat problem with taking into account the surface evaporation. However, instead of the direct heat source the boundary conditions in phase transitions were changed in the thermal conductivity equation, assuming the evaporated material takes part in the heat exchange. The data on the penetration depth and temperature distribution are used for the thermocapillary model. The thermocapillary model embraces Navier-Stocks and convection heat transfer equations, as well as the boundary conditions with the outflow of evaporated material included. The solution of these equations by finite elements methods pointed at formation of a multi-vortices structure when electron-beam treatment and its expansion over new zones of material. As the result, strengthening particles are found at the depth exceeding manifold their penetration depth in terms of the diffusion mechanism.

IHE based interoperability - benefits and challenges.

PubMed

Wozak, Florian; Ammenwerth, Elske; Hörbst, Alexander; Sögner, Peter; Mair, Richard; Schabetsberger, Thomas

2008-01-01

Optimized workflows and communication between institutions involved in a patient's treatment process can lead to improved quality and efficiency in the healthcare sector. Electronic Health Records (EHRs) provide a patient-centered access to clinical data across institutional boundaries supporting the above mentioned aspects. Interoperability is regarded as vital success factor. However a clear definition of interoperability does not exist. The aim of this work is to define and to assess interoperability criteria as required for EHRs. The definition and assessment of interoperability criteria is supported by the analysis of existing literature and personal experience as well as by discussions with several domain experts. Criteria for interoperability addresses the following aspects: Interfaces, Semantics, Legal and organizational aspects and Security. The Integrating the Healthcare Enterprises initiative (IHE) profiles make a major contribution to these aspects, but they also arise new problems. Flexibility for adoption to different organizational/regional or other specific conditions is missing. Regional or national initiatives should get a possibility to realize their specific needs within the boundaries of IHE profiles. Security so far is an optional element which is one of IHE greatest omissions. An integrated security approach seems to be preferable. Irrespective of the so far practical significance of the IHE profiles it appears to be of great importance, that the profiles are constantly checked against practical experiences and are continuously adapted.

Cambro-ordovician sea-level fluctuations and sequence boundaries: The missing record and the evolution of new taxa

USGS Publications Warehouse

Lehnert, O.; Miller, J.F.; Leslie, Stephen A.; Repetski, J.E.; Ethington, Raymond L.

2005-01-01

The evolution of early Palaeozoic conodont faunas shows a clear connection to sea-level changes. One way that this connection manifests itself is that thick successions of carbonates are missing beneath major sequence boundaries due to karstification and erosion. From this observation arises the question of how many taxa have been lost from different conodont lineages in these incomplete successions. Although many taxa suffered extinction due to the environmental stresses associated with falling sea-levels, some must have survived in these extreme conditions. The number of taxa missing in the early Palaeozoic tropics always will be unclear, but it will be even more difficult to evaluate the missing record in detrital successions of higher latitudes. A common pattern in the evolution of Cambrian-Ordovician conodont lineages is appearances of new species at sea-level rises and disappearances at sea-level drops. This simple picture can be complicated by intervals that consistently have no representatives of a particular lineage, even after extensive sampling of the most complete sections. Presumably the lineages survived in undocumented refugia. In this paper, we give examples of evolution in Cambrian-Ordovician shallowmarine conodont faunas and highlight problems of undiscovered or truly missing segments of lineages. ?? The Palaeontological Association.

An accurate boundary element method for the exterior elastic scattering problem in two dimensions

NASA Astrophysics Data System (ADS)

Bao, Gang; Xu, Liwei; Yin, Tao

2017-11-01

This paper is concerned with a Galerkin boundary element method solving the two dimensional exterior elastic wave scattering problem. The original problem is first reduced to the so-called Burton-Miller [1] boundary integral formulation, and essential mathematical features of its variational form are discussed. In numerical implementations, a newly-derived and analytically accurate regularization formula [2] is employed for the numerical evaluation of hyper-singular boundary integral operator. A new computational approach is employed based on the series expansions of Hankel functions for the computation of weakly-singular boundary integral operators during the reduction of corresponding Galerkin equations into a discrete linear system. The effectiveness of proposed numerical methods is demonstrated using several numerical examples.

Completed Beltrami-Michell Formulation for Analyzing Radially Symmetrical Bodies

NASA Technical Reports Server (NTRS)

Kaljevic, Igor; Saigal, Sunil; Hopkins, Dale A.; Patnaik, Surya N.

1994-01-01

A force method formulation, the completed Beltrami-Michell formulation (CBMF), has been developed for analyzing boundary value problems in elastic continua. The CBMF is obtained by augmenting the classical Beltrami-Michell formulation with novel boundary compatibility conditions. It can analyze general elastic continua with stress, displacement, or mixed boundary conditions. The CBMF alleviates the limitations of the classical formulation, which can solve stress boundary value problems only. In this report, the CBMF is specialized for plates and shells. All equations of the CBMF, including the boundary compatibility conditions, are derived from the variational formulation of the integrated force method (IFM). These equations are defined only in terms of stresses. Their solution for kinematically stable elastic continua provides stress fields without any reference to displacements. In addition, a stress function formulation for plates and shells is developed by augmenting the classical Airy's formulation with boundary compatibility conditions expressed in terms of the stress function. The versatility of the CBMF and the augmented stress function formulation is demonstrated through analytical solutions of several mixed boundary value problems. The example problems include a composite circular plate and a composite circular cylindrical shell under the simultaneous actions of mechanical and thermal loads.

Application of boundary integral equations to elastoplastic problems

NASA Technical Reports Server (NTRS)

Mendelson, A.; Albers, L. U.

1975-01-01

The application of boundary integral equations to elastoplastic problems is reviewed. Details of the analysis as applied to torsion problems and to plane problems is discussed. Results are presented for the elastoplastic torsion of a square cross section bar and for the plane problem of notched beams. A comparison of different formulations as well as comparisons with experimental results are presented.

Variational data assimilation for limited-area models: solution of the open boundary control problem and its application for the Gulf of Finland

NASA Astrophysics Data System (ADS)

Sheloput, Tatiana; Agoshkov, Valery

2017-04-01

The problem of modeling water areas with `liquid' (open) lateral boundaries is discussed. There are different known methods dealing with open boundaries in limited-area models, and one of the most efficient is data assimilation. Although this method is popular, there are not so many articles concerning its implementation for recovering boundary functions. However, the problem of specifying boundary conditions at the open boundary of a limited area is still actual and important. The mathematical model of the Baltic Sea circulation, developed in INM RAS, is considered. It is based on the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations. The splitting method that is used for time approximation in the model allows to consider the data assimilation problem as a sequence of linear problems. One of such `simple' temperature (salinity) assimilation problem is investigated in the study. Using well known techniques of study and solution of inverse problems and optimal control problems [1], we propose an iterative solution algorithm and we obtain conditions for existence of the solution, for unique and dense solvability of the problem and for convergence of the iterative algorithm. The investigation shows that if observations satisfy certain conditions, the proposed algorithm converges to the solution of the boundary control problem. Particularly, it converges when observational data are given on the `liquid' boundary [2]. Theoretical results are confirmed by the results of numerical experiments. The numerical algorithm was implemented to water area of the Baltic Sea. Two numerical experiments were carried out in the Gulf of Finland: one with the application of the assimilation procedure and the other without. The analyses have shown that the surface temperature field in the first experiment is close to the observed one, while the result of the second experiment misfits. Number of iterations depends on the regularisation parameter, but generally the algorithm converges after 10 iterations. The results of the numerical experiments show that the usage of the proposed method makes sense. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments) and by the Russian Foundation for Basic Research (project 16-01-00548, the formulation of the problem and its study). [1] Agoshkov V. I. Methods of Optimal Control and Adjoint Equations in Problems of Mathematical Physics. INM RAS, Moscow, 2003 (in Russian). [2] Agoshkov V.I., Sheloput T.O. The study and numerical solution of the problem of heat and salinity transfer assuming 'liquid' boundaries // Russ. J. Numer. Anal. Math. Modelling. 2016. Vol. 31, No. 2. P. 71-80.

Mixed conduction and grain boundary effect in lithium niobate under high pressure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Qinglin; Center for High Pressure Science and Technology Advanced Research, Changchun 130012; Liu, Cailong

2015-03-30

The charge transport behavior of lithium niobate has been investigated by in situ impedance measurement up to 40.6 GPa. The Li{sup +} ionic conduction plays a dominant role in the transport process. The relaxation process is described by the Maxwell-Wagner relaxation arising at the interfaces between grains and grain boundaries. The grain boundary microstructure rearranges after the phase transition, which improves the bulk dielectric performance. The theoretical calculations show that the decrease of bulk permittivity with increasing pressure in the Pnma phase is caused by the pressure-induced enhancement of electron localization around O atoms, which limits the polarization of Nb-O electricmore » dipoles.« less

Numerical solution of the electron transport equation

NASA Astrophysics Data System (ADS)

Woods, Mark

The electron transport equation has been solved many times for a variety of reasons. The main difficulty in its numerical solution is that it is a very stiff boundary value problem. The most common numerical methods for solving boundary value problems are symmetric collocation methods and shooting methods. Both of these types of methods can only be applied to the electron transport equation if the boundary conditions are altered with unrealistic assumptions because they require too many points to be practical. Further, they result in oscillating and negative solutions, which are physically meaningless for the problem at hand. For these reasons, all numerical methods for this problem to date are a bit unusual because they were designed to try and avoid the problem of extreme stiffness. This dissertation shows that there is no need to introduce spurious boundary conditions or invent other numerical methods for the electron transport equation. Rather, there already exists methods for very stiff boundary value problems within the numerical analysis literature. We demonstrate one such method in which the fast and slow modes of the boundary value problem are essentially decoupled. This allows for an upwind finite difference method to be applied to each mode as is appropriate. This greatly reduces the number of points needed in the mesh, and we demonstrate how this eliminates the need to define new boundary conditions. This method is verified by showing that under certain restrictive assumptions, the electron transport equation has an exact solution that can be written as an integral. We show that the solution from the upwind method agrees with the quadrature evaluation of the exact solution. This serves to verify that the upwind method is properly solving the electron transport equation. Further, it is demonstrated that the output of the upwind method can be used to compute auroral light emissions.

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: Stationary modes

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1988-01-01

Spatially discrete difference approximations for hyperbolic initial-boundary-value problems (IBVPs) require numerical boundary conditions in addition to the analytical boundary conditions specified for the differential equations. Improper treatment of a numerical boundary condition can cause instability of the discrete IBVP even though the approximation is stable for the pure initial-value or Cauchy problem. In the discrete IBVP stability literature there exists a small class of discrete approximations called borderline cases. For nondissipative approximations, borderline cases are unstable according to the theory of the Gustafsson, Kreiss, and Sundstrom (GKS) but they may be Lax-Richtmyer stable or unstable in the L sub 2 norm on a finite domain. It is shown that borderline approximation can be characterized by the presence of a stationary mode for the finite-domain problem. A stationary mode has the property that it does not decay with time and a nontrivial stationary mode leads to algebraic growth of the solution norm with mesh refinement. An analytical condition is given which makes it easy to detect a stationary mode; several examples of numerical boundary conditions are investigated corresponding to borderline cases.

Nonsteady Problem for an Elastic Half-Plane with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-03-01

An approach to studying nonstationary wave processes in an elastic half-plane with mixed boundary conditions of the fourth boundary-value problem of elasticity is proposed. The Laplace and Fourier transforms are used. The sequential inversion of these transforms or the inversion of the joint transform by the Cagniard method allows obtaining the required solution (stresses, displacements) in a closed analytic form. With this approach, the problem can be solved for various types of loads

On the Measure and the Structure of the Free Boundary of the Lower Dimensional Obstacle Problem

NASA Astrophysics Data System (ADS)

Focardi, Matteo; Spadaro, Emanuele

2018-04-01

We provide a thorough description of the free boundary for the lower dimensional obstacle problem in R^{n+1} up to sets of null H^{n-1} measure. In particular, we prove (i) local finiteness of the (n-1)-dimensional Hausdorff measure of the free boundary, (ii) H^{n-1}-rectifiability of the free boundary, (iii) classification of the frequencies up to a set of Hausdorff dimension at most (n-2) and classification of the blow-ups at H^{n-1} almost every free boundary point.

A wideband fast multipole boundary element method for half-space/plane-symmetric acoustic wave problems

NASA Astrophysics Data System (ADS)

Zheng, Chang-Jun; Chen, Hai-Bo; Chen, Lei-Lei

2013-04-01

This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/plane-symmetric acoustic wave problems. The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only. Moreover, a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived, and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating, translating and saving the multipole/local expansion coefficients of the image domain. The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems. As for exterior acoustic problems, the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method. Details on the implementation of the present method are described, and numerical examples are given to demonstrate its accuracy and efficiency.

A boundary-value problem for a first-order hyperbolic system in a two-dimensional domain

NASA Astrophysics Data System (ADS)

Zhura, N. A.; Soldatov, A. P.

2017-06-01

We consider a strictly hyperbolic first-order system of three equations with constant coefficients in a bounded piecewise-smooth domain. The boundary of the domain is assumed to consist of six smooth non-characteristic arcs. A boundary-value problem in this domain is posed by alternately prescribing one or two linear combinations of the components of the solution on these arcs. We show that this problem has a unique solution under certain additional conditions on the coefficients of these combinations, the boundary of the domain and the behaviour of the solution near the characteristics passing through the corner points of the domain.

The neural mechanisms of word order processing revisited: electrophysiological evidence from Japanese.

PubMed

Wolff, Susann; Schlesewsky, Matthias; Hirotani, Masako; Bornkessel-Schlesewsky, Ina

2008-11-01

We present two ERP studies on the processing of word order variations in Japanese, a language that is suited to shedding further light on the implications of word order freedom for neurocognitive approaches to sentence comprehension. Experiment 1 used auditory presentation and revealed that initial accusative objects elicit increased processing costs in comparison to initial subjects (in the form of a transient negativity) only when followed by a prosodic boundary. A similar effect was observed using visual presentation in Experiment 2, however only for accusative but not for dative objects. These results support a relational account of word order processing, in which the costs of comprehending an object-initial word order are determined by the linearization properties of the initial object in relation to the linearization properties of possible upcoming arguments. In the absence of a prosodic boundary, the possibility for subject omission in Japanese renders it likely that the initial accusative is the only argument in the clause. Hence, no upcoming arguments are expected and no linearization problem can arise. A prosodic boundary or visual segmentation, by contrast, indicate an object-before-subject word order, thereby leading to a mismatch between argument "prominence" (e.g. in terms of thematic roles) and linear order. This mismatch is alleviated when the initial object is highly prominent itself (e.g. in the case of a dative, which can bear the higher-ranking thematic role in a two argument relation). We argue that the processing mechanism at work here can be distinguished from more general aspects of "dependency processing" in object-initial sentences.

Boundary layer flow of air over water on a flat plate

NASA Technical Reports Server (NTRS)

Nelson, John; Alving, Amy E.; Joseph, Daniel D.

1993-01-01

A non-similar boundary layer theory for air blowing over a water layer on a flat plate is formulated and studied as a two-fluid problem in which the position of the interface is unknown. The problem is considered at large Reynolds number (based on x), away from the leading edge. A simple non-similar analytic solution of the problem is derived for which the interface height is proportional to x(sub 1/4) and the water and air flow satisfy the Blasius boundary layer equations, with a linear profile in the water and a Blasius profile in the air. Numerical studies of the initial value problem suggests that this asymptotic, non-similar air-water boundary layer solution is a global attractor for all initial conditions.

Extraction of a group-pair relation: problem-solving relation from web-board documents.

PubMed

Pechsiri, Chaveevan; Piriyakul, Rapepun

2016-01-01

This paper aims to extract a group-pair relation as a Problem-Solving relation, for example a DiseaseSymptom-Treatment relation and a CarProblem-Repair relation, between two event-explanation groups, a problem-concept group as a symptom/CarProblem-concept group and a solving-concept group as a treatment-concept/repair concept group from hospital-web-board and car-repair-guru-web-board documents. The Problem-Solving relation (particularly Symptom-Treatment relation) including the graphical representation benefits non-professional persons by supporting knowledge of primarily solving problems. The research contains three problems: how to identify an EDU (an Elementary Discourse Unit, which is a simple sentence) with the event concept of either a problem or a solution; how to determine a problem-concept EDU boundary and a solving-concept EDU boundary as two event-explanation groups, and how to determine the Problem-Solving relation between these two event-explanation groups. Therefore, we apply word co-occurrence to identify a problem-concept EDU and a solving-concept EDU, and machine-learning techniques to solve a problem-concept EDU boundary and a solving-concept EDU boundary. We propose using k-mean and Naïve Bayes to determine the Problem-Solving relation between the two event-explanation groups involved with clustering features. In contrast to previous works, the proposed approach enables group-pair relation extraction with high accuracy.

Time-Domain Impedance Boundary Conditions for Computational Aeroacoustics

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Auriault, Laurent

1996-01-01

It is an accepted practice in aeroacoustics to characterize the properties of an acoustically treated surface by a quantity known as impedance. Impedance is a complex quantity. As such, it is designed primarily for frequency-domain analysis. Time-domain boundary conditions that are the equivalent of the frequency-domain impedance boundary condition are proposed. Both single frequency and model broadband time-domain impedance boundary conditions are provided. It is shown that the proposed boundary conditions, together with the linearized Euler equations, form well-posed initial boundary value problems. Unlike ill-posed problems, they are free from spurious instabilities that would render time-marching computational solutions impossible.

An arbitrary boundary with ghost particles incorporated in coupled FEM-SPH model for FSI problems

NASA Astrophysics Data System (ADS)

Long, Ting; Hu, Dean; Wan, Detao; Zhuang, Chen; Yang, Gang

2017-12-01

It is important to treat the arbitrary boundary of Fluid-Structure Interaction (FSI) problems in computational mechanics. In order to ensure complete support condition and restore the first-order consistency near the boundary of Smoothed Particle Hydrodynamics (SPH) method for coupling Finite Element Method (FEM) with SPH model, a new ghost particle method is proposed by dividing the interceptive area of kernel support domain into subareas corresponding to boundary segments of structure. The ghost particles are produced automatically for every fluid particle at each time step, and the properties of ghost particles, such as density, mass and velocity, are defined by using the subareas to satisfy the boundary condition. In the coupled FEM-SPH model, the normal and shear forces from a boundary segment of structure to a fluid particle are calculated through the corresponding ghost particles, and its opposite forces are exerted on the corresponding boundary segment, then the momentum of the present method is conservation and there is no matching requirements between the size of elements and the size of particles. The performance of the present method is discussed and validated by several FSI problems with complex geometry boundary and moving boundary.

Boundary integral equation analysis for suspension of spheres in Stokes flow

NASA Astrophysics Data System (ADS)

Corona, Eduardo; Veerapaneni, Shravan

2018-06-01

We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical expressions for evaluating the operators away from the boundary. When two particle are located close to each other, we use a truncated series expansion to compute the hydrodynamic interaction. On the other hand, we use the standard spectrally accurate quadrature scheme to evaluate smooth integrals on the far-field, and accelerate the resulting discrete sums using the fast multipole method (FMM). We employ this discretization scheme to analyze several boundary integral formulations of interest including those arising in porous media flow, active matter and magneto-hydrodynamics of rigid particles. We provide numerical results verifying the accuracy and scaling of their evaluation.

Analysis of the incomplete Galerkin method for modelling of smoothly-irregular transition between planar waveguides

NASA Astrophysics Data System (ADS)

Divakov, D.; Sevastianov, L.; Nikolaev, N.

2017-01-01

The paper deals with a numerical solution of the problem of waveguide propagation of polarized light in smoothly-irregular transition between closed regular waveguides using the incomplete Galerkin method. This method consists in replacement of variables in the problem of reduction of the Helmholtz equation to the system of differential equations by the Kantorovich method and in formulation of the boundary conditions for the resulting system. The formulation of the boundary problem for the ODE system is realized in computer algebra system Maple. The stated boundary problem is solved using Maples libraries of numerical methods.

Application of shifted Jacobi pseudospectral method for solving (in)finite-horizon min-max optimal control problems with uncertainty

NASA Astrophysics Data System (ADS)

Nikooeinejad, Z.; Delavarkhalafi, A.; Heydari, M.

2018-03-01

The difficulty of solving the min-max optimal control problems (M-MOCPs) with uncertainty using generalised Euler-Lagrange equations is caused by the combination of split boundary conditions, nonlinear differential equations and the manner in which the final time is treated. In this investigation, the shifted Jacobi pseudospectral method (SJPM) as a numerical technique for solving two-point boundary value problems (TPBVPs) in M-MOCPs for several boundary states is proposed. At first, a novel framework of approximate solutions which satisfied the split boundary conditions automatically for various boundary states is presented. Then, by applying the generalised Euler-Lagrange equations and expanding the required approximate solutions as elements of shifted Jacobi polynomials, finding a solution of TPBVPs in nonlinear M-MOCPs with uncertainty is reduced to the solution of a system of algebraic equations. Moreover, the Jacobi polynomials are particularly useful for boundary value problems in unbounded domain, which allow us to solve infinite- as well as finite and free final time problems by domain truncation method. Some numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. A comparative study between the proposed method and other existing methods shows that the SJPM is simple and accurate.

Construction Method of Analytical Solutions to the Mathematical Physics Boundary Problems for Non-Canonical Domains

NASA Astrophysics Data System (ADS)

Mobarakeh, Pouyan Shakeri; Grinchenko, Victor T.

2015-06-01

The majority of practical cases of acoustics problems requires solving the boundary problems in non-canonical domains. Therefore construction of analytical solutions of mathematical physics boundary problems for non-canonical domains is both lucrative from the academic viewpoint, and very instrumental for elaboration of efficient algorithms of quantitative estimation of the field characteristics under study. One of the main solving ideologies for such problems is based on the superposition method that allows one to analyze a wide class of specific problems with domains which can be constructed as the union of canonically-shaped subdomains. It is also assumed that an analytical solution (or quasi-solution) can be constructed for each subdomain in one form or another. However, this case implies some difficulties in the construction of calculation algorithms, insofar as the boundary conditions are incompletely defined in the intervals, where the functions appearing in the general solution are orthogonal to each other. We discuss several typical examples of problems with such difficulties, we study their nature and identify the optimal methods to overcome them.

Gas evolution from spheres

NASA Astrophysics Data System (ADS)

Longhurst, G. R.

1991-04-01

Gas evolution from spherical solids or liquids where no convective processes are active is analyzed. Three problem classes are considered: (1) constant concentration boundary, (2) Henry's law (first order) boundary, and (3) Sieverts' law (second order) boundary. General expressions are derived for dimensionless times and transport parameters appropriate to each of the classes considered. However, in the second order case, the non-linearities of the problem require the presence of explicit dimensional variables in the solution. Sample problems are solved to illustrate the method.

The Boundary Element Method Applied to the Two Dimensional Stefan Moving Boundary Problem

DTIC Science & Technology

1991-03-15

Unc), - ( UGt )t - (UG,,),,] - (UG), If we integrate this equation with respect to r from 0 to t - c and with respect to and ij on the region 11(r...and others. "Moving Boundary Problems in Phase Change Mod- els," SIGNUM Newsletter, 20: 8-12 (1985). 21. Stefan, J. "Ober einige Probleme der Theorie ...ier Wirmelcitung," S.-B. \\Vein. Akad. Mat. Natur., 98: 173-484 (1889). 22.-. "flber (lie Theorie der Eisbildung insbesondere fiber die lisbildung im

An adjoint view on flux consistency and strong wall boundary conditions to the Navier–Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stück, Arthur, E-mail: arthur.stueck@dlr.de

2015-11-15

Inconsistent discrete expressions in the boundary treatment of Navier–Stokes solvers and in the definition of force objective functionals can lead to discrete-adjoint boundary treatments that are not a valid representation of the boundary conditions to the corresponding adjoint partial differential equations. The underlying problem is studied for an elementary 1D advection–diffusion problem first using a node-centred finite-volume discretisation. The defect of the boundary operators in the inconsistently defined discrete-adjoint problem leads to oscillations and becomes evident with the additional insight of the continuous-adjoint approach. A homogenisation of the discretisations for the primal boundary treatment and the force objective functional yieldsmore » second-order functional accuracy and eliminates the defect in the discrete-adjoint boundary treatment. Subsequently, the issue is studied for aerodynamic Reynolds-averaged Navier–Stokes problems in conjunction with a standard finite-volume discretisation on median-dual grids and a strong implementation of noslip walls, found in many unstructured general-purpose flow solvers. Going out from a base-line discretisation of force objective functionals which is independent of the boundary treatment in the flow solver, two improved flux-consistent schemes are presented; based on either body wall-defined or farfield-defined control-volumes they resolve the dual inconsistency. The behaviour of the schemes is investigated on a sequence of grids in 2D and 3D.« less

A Method of Computing Electric Field Parameters on Boundaries between Two Media

ERIC Educational Resources Information Center

Rizhov, Alexander

2010-01-01

Many problems of electric field strength on a boundary between two media require college-level mathematical analysis. However, when the boundary between media is represented by a sphere or a flat plane, these types of problems can be solved algebraically, placing them within reach of high school students. This article presents a solution analysis…

[Boundaries and integrity in the "Social Contract for Spanish Science", 1907-1939].

PubMed

Gómez, Amparo

2014-01-01

This article analyzes the relationship between science and politics in Spain in the early 20th century from the perspective of the Social Contract for Science. The article shows that a genuine social contract for science was instituted in Spain during this period, although some boundary and integrity problems emerged. These problems are analyzed, showing that the boundary problems were a product of the conservative viewpoint on the relationship between science and politics, while the integrity problems involved the activation of networks of influence in the awarding of scholarships to study abroad. Finally, the analysis reveals that these problems did not invalidate the Spanish social contract for science.

Hypersonic Shock/Boundary-Layer Interaction Database

NASA Technical Reports Server (NTRS)

Settles, G. S.; Dodson, L. J.

1991-01-01

Turbulence modeling is generally recognized as the major problem obstructing further advances in computational fluid dynamics (CFD). A closed solution of the governing Navier-Stokes equations for turbulent flows of practical consequence is still far beyond grasp. At the same time, the simplified models of turbulence which are used to achieve closure of the Navier-Stokes equations are known to be rigorously incorrect. While these models serve a definite purpose, they are inadequate for the general prediction of hypersonic viscous/inviscid interactions, mixing problems, chemical nonequilibria, and a range of other phenomena which must be predicted in order to design a hypersonic vehicle computationally. Due to the complexity of turbulence, useful new turbulence models are synthesized only when great expertise is brought to bear and considerable intellectual energy is expended. Although this process is fundamentally theoretical, crucial guidance may be gained from carefully-executed basic experiments. Following the birth of a new model, its testing and validation once again demand comparisons with data of unimpeachable quality. This report concerns these issues which arise from the experimental aspects of hypersonic modeling and represents the results of the first phase of an effort to develop compressible turbulence models.

The Applied Mathematics for Power Systems (AMPS)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chertkov, Michael

2012-07-24

Increased deployment of new technologies, e.g., renewable generation and electric vehicles, is rapidly transforming electrical power networks by crossing previously distinct spatiotemporal scales and invalidating many traditional approaches for designing, analyzing, and operating power grids. This trend is expected to accelerate over the coming years, bringing the disruptive challenge of complexity, but also opportunities to deliver unprecedented efficiency and reliability. Our Applied Mathematics for Power Systems (AMPS) Center will discover, enable, and solve emerging mathematics challenges arising in power systems and, more generally, in complex engineered networks. We will develop foundational applied mathematics resulting in rigorous algorithms and simulation toolboxesmore » for modern and future engineered networks. The AMPS Center deconstruction/reconstruction approach 'deconstructs' complex networks into sub-problems within non-separable spatiotemporal scales, a missing step in 20th century modeling of engineered networks. These sub-problems are addressed within the appropriate AMPS foundational pillar - complex systems, control theory, and optimization theory - and merged or 'reconstructed' at their boundaries into more general mathematical descriptions of complex engineered networks where important new questions are formulated and attacked. These two steps, iterated multiple times, will bridge the growing chasm between the legacy power grid and its future as a complex engineered network.« less

Free-end adaptive nudged elastic band method for locating transition states in minimum energy path calculation.

PubMed

Zhang, Jiayong; Zhang, Hongwu; Ye, Hongfei; Zheng, Yonggang

2016-09-07

A free-end adaptive nudged elastic band (FEA-NEB) method is presented for finding transition states on minimum energy paths, where the energy barrier is very narrow compared to the whole paths. The previously proposed free-end nudged elastic band method may suffer from convergence problems because of the kinks arising on the elastic band if the initial elastic band is far from the minimum energy path and weak springs are adopted. We analyze the origin of the formation of kinks and present an improved free-end algorithm to avoid the convergence problem. Moreover, by coupling the improved free-end algorithm and an adaptive strategy, we develop a FEA-NEB method to accurately locate the transition state with the elastic band cut off repeatedly and the density of images near the transition state increased. Several representative numerical examples, including the dislocation nucleation in a penta-twinned nanowire, the twin boundary migration under a shear stress, and the cross-slip of screw dislocation in face-centered cubic metals, are investigated by using the FEA-NEB method. Numerical results demonstrate both the stability and efficiency of the proposed method.

Reprint of Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-04-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-03-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Principal Eigenvalue Minimization for an Elliptic Problem with Indefinite Weight and Robin Boundary Conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hintermueller, M., E-mail: hint@math.hu-berlin.de; Kao, C.-Y., E-mail: Ckao@claremontmckenna.edu; Laurain, A., E-mail: laurain@math.hu-berlin.de

2012-02-15

This paper focuses on the study of a linear eigenvalue problem with indefinite weight and Robin type boundary conditions. We investigate the minimization of the positive principal eigenvalue under the constraint that the absolute value of the weight is bounded and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining the optimal spatial arrangement of favorable and unfavorable regions for a species to survive. For rectangular domains with Neumann boundary condition, it is known that there exists a threshold value such that if the total weight is below this thresholdmore » value then the optimal favorable region is like a section of a disk at one of the four corners; otherwise, the optimal favorable region is a strip attached to the shorter side of the rectangle. Here, we investigate the same problem with mixed Robin-Neumann type boundary conditions and study how this boundary condition affects the optimal spatial arrangement.« less

Resonances and vibrations in an elevator cable system due to boundary sway

NASA Astrophysics Data System (ADS)

Gaiko, Nick V.; van Horssen, Wim T.

2018-06-01

In this paper, an analytical method is presented to study an initial-boundary value problem describing the transverse displacements of a vertically moving beam under boundary excitation. The length of the beam is linearly varying in time, i.e., the axial, vertical velocity of the beam is assumed to be constant. The bending stiffness of the beam is assumed to be small. This problem may be regarded as a model describing the lateral vibrations of an elevator cable excited at its boundaries by the wind-induced building sway. Slow variation of the cable length leads to a singular perturbation problem which is expressed in slowly changing, time-dependent coefficients in the governing differential equation. By providing an interior layer analysis, infinitely many resonance manifolds are detected. Further, the initial-boundary value problem is studied in detail using a three-timescales perturbation method. The constructed formal approximations of the solutions are in agreement with the numerical results.

A method of boundary equations for unsteady hyperbolic problems in 3D

NASA Astrophysics Data System (ADS)

Petropavlovsky, S.; Tsynkov, S.; Turkel, E.

2018-07-01

We consider interior and exterior initial boundary value problems for the three-dimensional wave (d'Alembert) equation. First, we reduce a given problem to an equivalent operator equation with respect to unknown sources defined only at the boundary of the original domain. In doing so, the Huygens' principle enables us to obtain the operator equation in a form that involves only finite and non-increasing pre-history of the solution in time. Next, we discretize the resulting boundary equation and solve it efficiently by the method of difference potentials (MDP). The overall numerical algorithm handles boundaries of general shape using regular structured grids with no deterioration of accuracy. For long simulation times it offers sub-linear complexity with respect to the grid dimension, i.e., is asymptotically cheaper than the cost of a typical explicit scheme. In addition, our algorithm allows one to share the computational cost between multiple similar problems. On multi-processor (multi-core) platforms, it benefits from what can be considered an effective parallelization in time.

On some problems in a theory of thermally and mechanically interacting continuous media. Ph.D. Thesis; [linearized theory of interacting mixture of elastic solid and viscous fluid

NASA Technical Reports Server (NTRS)

Lee, Y. M.

1971-01-01

Using a linearized theory of thermally and mechanically interacting mixture of linear elastic solid and viscous fluid, we derive a fundamental relation in an integral form called a reciprocity relation. This reciprocity relation relates the solution of one initial-boundary value problem with a given set of initial and boundary data to the solution of a second initial-boundary value problem corresponding to a different initial and boundary data for a given interacting mixture. From this general integral relation, reciprocity relations are derived for a heat-conducting linear elastic solid, and for a heat-conducting viscous fluid. An initial-boundary value problem is posed and solved for the mixture of linear elastic solid and viscous fluid. With the aid of the Laplace transform and the contour integration, a real integral representation for the displacement of the solid constituent is obtained as one of the principal results of the analysis.

Study on Combustion Characteristics and Propelling Projectile Motion Process of Bulk-Loaded Liquid Propellant

NASA Astrophysics Data System (ADS)

Xue, Xiaochun; Yu, Yonggang; Mang, Shanshan

2017-07-01

Data are presented showing that the problem of gas-liquid interaction instability is an important subject in the combustion and the propellant projectile motion process of a bulk-loaded liquid propellant gun (BLPG). The instabilities themselves arise from the sources, including fluid motion, to form a combustion gas cavity called Taylor cavity, fluid turbulence and breakup caused by liquid motion relative to the combustion chamber walls, and liquid surface breakup arising from a velocity mismatch on the gas-liquid interface. Typically, small disturbances that arise early in the BLPG combustion interior ballistic cycle can become amplified in the absence of burn rate limiting characteristics. Herein, significant attention has been given to developing and emphasizing the need for better combustion repeatability in the BLPG. Based on this goal, the concept of using different geometries of the combustion chamber is introduced and the concept of using a stepped-wall structure on the combustion chamber itself as a useful means of exerting boundary control on the combustion evolution to thus restrain the combustion instability has been verified experimentally in this work. Moreover, based on this background, the numerical simulation is devoted to a special combustion issue under transient high-pressure and high-temperature conditions, namely, studying the combustion mechanism in a stepped-wall combustion chamber with full monopropellant on one end that is stationary and the other end can move at high speed. The numerical results also show that the burning surface of the liquid propellant can be defined geometrically and combustion is well behaved as ignition and combustion progressivity are in a suitable range during each stage in this combustion chamber with a stepped-wall structure.

Conditions for the appearance of boundary-free circulation zones in supersonic axisymmetric accelerating flows

NASA Astrophysics Data System (ADS)

Savin, Andrey V.; Sokolov, Eugeny I.

2018-05-01

The mechanism of appearance of boundary-free circulation zones - circulating flows arising behind the Mach disk of an underexpanded supersonic jet is investigated. Ideas on the mechanism of formation of circulation zones and the criteria for their occurrence are formulated within the near-axis approximation. Technical possibilities of realization flows that satisfy these criteria are analyzed with the help of numerical simulation. A comparison is made with the results of a study of the formation of circulation zones in axisymmetric nozzles at the overexpansion mode.

Free-boundary toroidal Alfvén eigenmodes

NASA Astrophysics Data System (ADS)

Chen, Eugene Y.; Berk, H. L.; Breizman, B.; Zheng, L. J.

2011-05-01

A numerical study is presented for the n = 1 free-boundary toroidal Alfvén eigenmodes (TAE) in tokamaks, which shows that there is considerable sensitivity of n = 1 modes to the position of the conducting wall. An additional branch of the TAE is shown to emerge from the upper continuum as the ratio of conducting wall radius to plasma radius increases. Such phenomena arise in plasma equilibria with both circular and shaped cross sections, where the shaped profile studied here is similar to that found in Alcator C-Mod.

Computer constructed imagery of distant plasma interaction boundaries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grenstadt, E.W.; Schurr, H.D.; Tsugawa, R.K.

1982-01-01

Computer constructed sketches of plasma boundaries arising from the interaction between the solar wind and the magnetosphere can serve as both didactic and research tools. In particular, the structure of the earth's bow shock can be represented as a nonuniform surfce according to the instantaneous orientation of the IMF, and temporal changes in structural distribution can be modeled as a sequence of sketches based on observed sequences of spacecraft-based measurements. Viewed rapidly, such a sequence of sketches can be the basis for representation of plasma processes by computer animation.

Addressing the computational cost of large EIT solutions.

PubMed

Boyle, Alistair; Borsic, Andrea; Adler, Andy

2012-05-01

Electrical impedance tomography (EIT) is a soft field tomography modality based on the application of electric current to a body and measurement of voltages through electrodes at the boundary. The interior conductivity is reconstructed on a discrete representation of the domain using a finite-element method (FEM) mesh and a parametrization of that domain. The reconstruction requires a sequence of numerically intensive calculations. There is strong interest in reducing the cost of these calculations. An improvement in the compute time for current problems would encourage further exploration of computationally challenging problems such as the incorporation of time series data, wide-spread adoption of three-dimensional simulations and correlation of other modalities such as CT and ultrasound. Multicore processors offer an opportunity to reduce EIT computation times but may require some restructuring of the underlying algorithms to maximize the use of available resources. This work profiles two EIT software packages (EIDORS and NDRM) to experimentally determine where the computational costs arise in EIT as problems scale. Sparse matrix solvers, a key component for the FEM forward problem and sensitivity estimates in the inverse problem, are shown to take a considerable portion of the total compute time in these packages. A sparse matrix solver performance measurement tool, Meagre-Crowd, is developed to interface with a variety of solvers and compare their performance over a range of two- and three-dimensional problems of increasing node density. Results show that distributed sparse matrix solvers that operate on multiple cores are advantageous up to a limit that increases as the node density increases. We recommend a selection procedure to find a solver and hardware arrangement matched to the problem and provide guidance and tools to perform that selection.

Thermal issues at the SSC

NASA Technical Reports Server (NTRS)

Ranganathan, Raj P.; Dao, Bui V.

1992-01-01

A variety of heat transfer problems arise in the design of the Superconducting Super Collider (SSC). One class of problems is to minimize heat leak from the ambient to the SSC rings, since the rings contain superconducting magnets maintained at a temperature of 4 K. Another arises from the need to dump the beam of protrons (traveling around the SSC rings) on to absorbers during an abort of the collider. Yet another category of problems is the cooling of equipment to dissipate the heat generated during operation. An overview of these problems and sample heat transfer results are given in this paper.

Introducing Differential Equations Students to the Fredholm Alternative--In Staggered Doses

ERIC Educational Resources Information Center

Savoye, Philippe

2011-01-01

The development, in an introductory differential equations course, of boundary value problems in parallel with initial value problems and the Fredholm Alternative. Examples are provided of pairs of homogeneous and nonhomogeneous boundary value problems for which existence and uniqueness issues are considered jointly. How this heightens students'…

Locating CVBEM collocation points for steady state heat transfer problems

USGS Publications Warehouse

Hromadka, T.V.

1985-01-01

The Complex Variable Boundary Element Method or CVBEM provides a highly accurate means of developing numerical solutions to steady state two-dimensional heat transfer problems. The numerical approach exactly solves the Laplace equation and satisfies the boundary conditions at specified points on the boundary by means of collocation. The accuracy of the approximation depends upon the nodal point distribution specified by the numerical analyst. In order to develop subsequent, refined approximation functions, four techniques for selecting additional collocation points are presented. The techniques are compared as to the governing theory, representation of the error of approximation on the problem boundary, the computational costs, and the ease of use by the numerical analyst. ?? 1985.

Automatic Control via Thermostats of a Hyperbolic Stefan Problem with Memory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Colli, P.; Grasselli, M.; Sprekels, J.

1999-03-15

A hyperbolic Stefan problem based on the linearized Gurtin-Pipkin heat conduction law is considered. The temperature and free boundary are controlled by a thermostat acting on the boundary. This feedback control is based on temperature measurements performed by real thermal sensors located within the domain containing the two-phase system and/or at its boundary. Three different types of thermostats are analyzed: simple switch, relay switch, and a Preisach hysteresis operator. The resulting models lead to integrodifferential hyperbolic Stefan problems with nonlinear and nonlocal boundary conditions. Existence results are proved in all the cases. Uniqueness is also shown, except in the situationmore » corresponding to the ideal switch.« less

Solutions of the benchmark problems by the dispersion-relation-preserving scheme

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Shen, H.; Kurbatskii, K. A.; Auriault, L.

1995-01-01

The 7-point stencil Dispersion-Relation-Preserving scheme of Tam and Webb is used to solve all the six categories of the CAA benchmark problems. The purpose is to show that the scheme is capable of solving linear, as well as nonlinear aeroacoustics problems accurately. Nonlinearities, inevitably, lead to the generation of spurious short wave length numerical waves. Often, these spurious waves would overwhelm the entire numerical solution. In this work, the spurious waves are removed by the addition of artificial selective damping terms to the discretized equations. Category 3 problems are for testing radiation and outflow boundary conditions. In solving these problems, the radiation and outflow boundary conditions of Tam and Webb are used. These conditions are derived from the asymptotic solutions of the linearized Euler equations. Category 4 problems involved solid walls. Here, the wall boundary conditions for high-order schemes of Tam and Dong are employed. These conditions require the use of one ghost value per boundary point per physical boundary condition. In the second problem of this category, the governing equations, when written in cylindrical coordinates, are singular along the axis of the radial coordinate. The proper boundary conditions at the axis are derived by applying the limiting process of r approaches 0 to the governing equations. The Category 5 problem deals with the numerical noise issue. In the present approach, the time-independent mean flow solution is computed first. Once the residual drops to the machine noise level, the incident sound wave is turned on gradually. The solution is marched in time until a time-periodic state is reached. No exact solution is known for the Category 6 problem. Because of this, the problem is formulated in two totally different ways, first as a scattering problem then as a direct simulation problem. There is good agreement between the two numerical solutions. This offers confidence in the computed results. Both formulations are solved as initial value problems. As such, no Kutta condition is required at the trailing edge of the airfoil.

Drinking Water Corrosion Control and POU/POE: Where Are the Boundaries?

EPA Science Inventory

Protection of public health often has to go beyond regulatory limits, because the health threats do not necessarily arise under the "legal control" of the public water system. Residential and building plumbing can be a very significant contamination source under typical usage co...

Revisiting Boundary Perturbation Theory for Inhomogeneous Transport Problems

DOE PAGES

Favorite, Jeffrey A.; Gonzalez, Esteban

2017-03-10

Adjoint-based first-order perturbation theory is applied again to boundary perturbation problems. Rahnema developed a perturbation estimate that gives an accurate first-order approximation of a flux or reaction rate within a radioactive system when the boundary is perturbed. When the response of interest is the flux or leakage current on the boundary, the Roussopoulos perturbation estimate has long been used. The Rahnema and Roussopoulos estimates differ in one term. Our paper shows that the Rahnema and Roussopoulos estimates can be derived consistently, using different responses, from a single variational functional (due to Gheorghiu and Rahnema), resolving any apparent contradiction. In analyticmore » test problems, Rahnema’s estimate and the Roussopoulos estimate produce exact first derivatives of the response of interest when appropriately applied. We also present a realistic, nonanalytic test problem.« less

Brittle fracture in viscoelastic materials as a pattern-formation process

NASA Astrophysics Data System (ADS)

Fleck, M.; Pilipenko, D.; Spatschek, R.; Brener, E. A.

2011-04-01

A continuum model of crack propagation in brittle viscoelastic materials is presented and discussed. Thereby, the phenomenon of fracture is understood as an elastically induced nonequilibrium interfacial pattern formation process. In this spirit, a full description of a propagating crack provides the determination of the entire time dependent shape of the crack surface, which is assumed to be extended over a finite and self-consistently selected length scale. The mechanism of crack propagation, that is, the motion of the crack surface, is then determined through linear nonequilibrium transport equations. Here we consider two different mechanisms, a first-order phase transformation and surface diffusion. We give scaling arguments showing that steady-state solutions with a self-consistently selected propagation velocity and crack shape can exist provided that elastodynamic or viscoelastic effects are taken into account, whereas static elasticity alone is not sufficient. In this respect, inertial effects as well as viscous damping are identified to be sufficient crack tip selection mechanisms. Exploring the arising description of brittle fracture numerically, we study steady-state crack propagation in the viscoelastic and inertia limit as well as in an intermediate regime, where both effects are important. The arising free boundary problems are solved by phase field methods and a sharp interface approach using a multipole expansion technique. Different types of loading, mode I, mode III fracture, as well as mixtures of them, are discussed.

Non-local sub-characteristic zones of influence in unsteady interactive boundary-layers

NASA Technical Reports Server (NTRS)

Rothmayer, A. P.

1992-01-01

The properties of incompressible, unsteady, interactive, boundary layers are examined for a model hypersonic boundary layer and internal flow past humps or, equivalently, external flow past short-scaled humps. Using a linear high frequency analysis, it is shown that the domains of dependence within the viscous sublayer may be a strong function of position within the sublayer and may be strongly influenced by the pressure displacement interaction, or the prescribed displacement condition. Detailed calculations are presented for the hypersonic boundary layer. This effect is found to carry over directly to the fully viscous problem as well as the nonlinear problem. In the fully viscous problem, the non-local character of the domains of dependence manifests itself in the sub-characteristics. Potential implications of the domain of dependence structure on finite difference computations of unsteady boundary layers are briefly discussed.

Solving free-plasma-boundary problems with the SIESTA MHD code

NASA Astrophysics Data System (ADS)

Sanchez, R.; Peraza-Rodriguez, H.; Reynolds-Barredo, J. M.; Tribaldos, V.; Geiger, J.; Hirshman, S. P.; Cianciosa, M.

2017-10-01

SIESTA is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for 3D magnetic configurations. It is an iterative code that uses the solution obtained by the VMEC code to provide a background coordinate system and an initial guess of the solution. The final solution that SIESTA finds can exhibit magnetic islands and stochastic regions. In its original implementation, SIESTA addressed only fixed-boundary problems. This fixed boundary condition somewhat restricts its possible applications. In this contribution we describe a recent extension of SIESTA that enables it to address free-plasma-boundary situations, opening up the possibility of investigating problems with SIESTA in which the plasma boundary is perturbed either externally or internally. As an illustration, the extended version of SIESTA is applied to a configuration of the W7-X stellarator.

Applying the method of fundamental solutions to harmonic problems with singular boundary conditions

NASA Astrophysics Data System (ADS)

Valtchev, Svilen S.; Alves, Carlos J. S.

2017-07-01

The method of fundamental solutions (MFS) is known to produce highly accurate numerical results for elliptic boundary value problems (BVP) with smooth boundary conditions, posed in analytic domains. However, due to the analyticity of the shape functions in its approximation basis, the MFS is usually disregarded when the boundary functions possess singularities. In this work we present a modification of the classical MFS which can be applied for the numerical solution of the Laplace BVP with Dirichlet boundary conditions exhibiting jump discontinuities. In particular, a set of harmonic functions with discontinuous boundary traces is added to the MFS basis. The accuracy of the proposed method is compared with the results form the classical MFS.

Analytic Solution of the Problem of Additive Formation of an Inhomogeneous Elastic Spherical Body in an Arbitrary Nonstationary Central Force Field

NASA Astrophysics Data System (ADS)

Parshin, D. A.

2017-09-01

We study the processes of additive formation of spherically shaped rigid bodies due to the uniform accretion of additional matter to their surface in an arbitrary centrally symmetric force field. A special case of such a field can be the gravitational or electrostatic force field. We consider the elastic deformation of the formed body. The body is assumed to be isotropic with elasticmoduli arbitrarily varying along the radial coordinate.We assume that arbitrary initial circular stresses can arise in the additional material added to the body in the process of its formation. In the framework of linear mechanics of growing bodies, the mathematical model of the processes under study is constructed in the quasistatic approximation. The boundary value problems describing the development of stress-strain state of the object under study before the beginning of the process and during the entire process of its formation are posed. The closed analytic solutions of the posed problems are constructed by quadratures for some general types of material inhomogeneity. Important typical characteristics of the mechanical behavior of spherical bodies additively formed in the central force field are revealed. These characteristics substantially distinguish such bodies from the already completely composed bodies similar in dimensions and properties which are placed in the force field and are described by problems of mechanics of deformable solids in the classical statement disregarding the mechanical aspects of additive processes.

Application of the perturbation iteration method to boundary layer type problems.

PubMed

Pakdemirli, Mehmet

2016-01-01

The recently developed perturbation iteration method is applied to boundary layer type singular problems for the first time. As a preliminary work on the topic, the simplest algorithm of PIA(1,1) is employed in the calculations. Linear and nonlinear problems are solved to outline the basic ideas of the new solution technique. The inner and outer solutions are determined with the iteration algorithm and matched to construct a composite expansion valid within all parts of the domain. The solutions are contrasted with the available exact or numerical solutions. It is shown that the perturbation-iteration algorithm can be effectively used for solving boundary layer type problems.

Re-Innovating Recycling for Turbulent Boundary Layer Simulations

NASA Astrophysics Data System (ADS)

Ruan, Joseph; Blanquart, Guillaume

2017-11-01

Historically, turbulent boundary layers along a flat plate have been expensive to simulate numerically, in part due to the difficulty of initializing the inflow with ``realistic'' turbulence, but also due to boundary layer growth. The former has been resolved in several ways, primarily dedicating a region of at least 10 boundary layer thicknesses in width to rescale and recycle flow or by extending the region far enough downstream to allow a laminar flow to develop into turbulence. Both of these methods are relatively costly. We propose a new method to remove the need for an inflow region, thus reducing computational costs significantly. Leveraging the scale similarity of the mean flow profiles, we introduce a coordinate transformation so that the boundary layer problem can be solved as a parallel flow problem with additional source terms. The solutions in the new coordinate system are statistically homogeneous in the downstream direction and so the problem can be solved with periodic boundary conditions. The present study shows the stability of this method, its implementation and its validation for a few laminar and turbulent boundary layer cases.

Theory of viscous transonic flow over airfoils at high Reynolds number

NASA Technical Reports Server (NTRS)

Melnik, R. E.; Chow, R.; Mead, H. R.

1977-01-01

This paper considers viscous flows with unseparated turbulent boundary layers over two-dimensional airfoils at transonic speeds. Conventional theoretical methods are based on boundary layer formulations which do not account for the effect of the curved wake and static pressure variations across the boundary layer in the trailing edge region. In this investigation an extended viscous theory is developed that accounts for both effects. The theory is based on a rational analysis of the strong turbulent interaction at airfoil trailing edges. The method of matched asymptotic expansions is employed to develop formal series solutions of the full Reynolds equations in the limit of Reynolds numbers tending to infinity. Procedures are developed for combining the local trailing edge solution with numerical methods for solving the full potential flow and boundary layer equations. Theoretical results indicate that conventional boundary layer methods account for only about 50% of the viscous effect on lift, the remaining contribution arising from wake curvature and normal pressure gradient effects.

Direct numerical simulation of a compressible boundary-layer flow past an isolated three-dimensional hump in a high-speed subsonic regime

NASA Astrophysics Data System (ADS)

De Grazia, D.; Moxey, D.; Sherwin, S. J.; Kravtsova, M. A.; Ruban, A. I.

2018-02-01

In this paper we study the boundary-layer separation produced in a high-speed subsonic boundary layer by a small wall roughness. Specifically, we present a direct numerical simulation (DNS) of a two-dimensional boundary-layer flow over a flat plate encountering a three-dimensional Gaussian-shaped hump. This work was motivated by the lack of DNS data of boundary-layer flows past roughness elements in a similar regime which is typical of civil aviation. The Mach and Reynolds numbers are chosen to be relevant for aeronautical applications when considering small imperfections at the leading edge of wings. We analyze different heights of the hump: The smaller heights result in a weakly nonlinear regime, while the larger result in a fully nonlinear regime with an increasing laminar separation bubble arising downstream of the roughness element and the formation of a pair of streamwise counterrotating vortices which appear to support themselves.

The proximity of hotspots to convergent and divergent plate boundaries

NASA Technical Reports Server (NTRS)

Weinstein, Stuart A.; Olson, Peter L.

1989-01-01

An analysis of four different hotspot distributions, ranging from Morgan's (1972) original list of 19 to Vogt's (1981) list of 117 reveals that the hotspots are preferentially located near divergent plate boundaries. The probability of this proximity occurring by chance alone is quite remote, less than 0.01 for all four hotspot distributions. The same analysis also reveals that the hotspots are preferentially excluded from regions near convergent plate boundaries. The probability of this exclusion occurring by chance alone is 0.1 or less for three out of the four distributions examined. We interpret this behavior as being a consequence of the effects of large scale convective circulation on ascending mantle plumes. Mantle thermal plumes, the most probable source of hotspots, arise from instabilities in a basal thermal boundary layer. Plumes are suppressed from regions beneath convergent boundaries by descending flow and are entrained into the upwelling flow beneath spreading centers. Plate-scale convective circulation driven by subduction may also advect mantle thermal plumes toward spreading centers.

Origin of the relatively low transport mobility of graphene grown through chemical vapor deposition

PubMed Central

Song, H. S.; Li, S. L.; Miyazaki, H.; Sato, S.; Hayashi, K.; Yamada, A.; Yokoyama, N.; Tsukagoshi, K.

2012-01-01

The reasons for the relatively low transport mobility of graphene grown through chemical vapor deposition (CVD-G), which include point defect, surface contamination, and line defect, were analyzed in the current study. A series of control experiments demonstrated that the determinant factor for the low transport mobility of CVD-G did not arise from point defects or surface contaminations, but stemmed from line defects induced by grain boundaries. Electron microscopies characterized the presence of grain boundaries and indicated the polycrystalline nature of the CVD-G. Field-effect transistors based on CVD-G without the grain boundary obtained a transport mobility comparative to that of Kish graphene, which directly indicated the detrimental effect of grain boundaries. The effect of grain boundary on transport mobility was qualitatively explained using a potential barrier model. Furthermore, the conduction mechanism of CVD-G was also investigated using the temperature dependence measurements. This study can help understand the intrinsic transport features of CVD-G. PMID:22468224

A note on the solutions of some nonlinear equations arising in third-grade fluid flows: an exact approach.

PubMed

Aziz, Taha; Mahomed, F M

2014-01-01

In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed.

A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach

PubMed Central

Mahomed, F. M.

2014-01-01

In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed. PMID:25143962

Boundary elements; Proceedings of the Fifth International Conference, Hiroshima, Japan, November 8-11, 1983

NASA Astrophysics Data System (ADS)

Brebbia, C. A.; Futagami, T.; Tanaka, M.

The boundary-element method (BEM) in computational fluid and solid mechanics is examined in reviews and reports of theoretical studies and practical applications. Topics presented include the fundamental mathematical principles of BEMs, potential problems, EM-field problems, heat transfer, potential-wave problems, fluid flow, elasticity problems, fracture mechanics, plates and shells, inelastic problems, geomechanics, dynamics, industrial applications of BEMs, optimization methods based on the BEM, numerical techniques, and coupling.

Continuum calculations of continental deformation in transcurrent environments

NASA Technical Reports Server (NTRS)

Sonder, L. J.; England, P. C.; Houseman, G. A.

1986-01-01

A thin viscous sheet approximation is used to investigate continental deformation near a strike-slip boundary. The vertically averaged velocity field is calculated for a medium characterized by a power law rheology with stress exponent n. Driving stresses include those applied along boundaries of the sheet and those arising from buoyancy forces related to lateral differences in crustal thickness. Exact and approximate analytic solutions for a region with a sinusoidal strike-slip boundary condition are compared with solutions for more geologically relevant boundary conditions obtained using a finite element technique. The across-strike length scale of the deformation is approximately 1/4pi x sq rt n times the dominant wavelength of the imposed strike-slip boundary condition for both the analytic and the numerical solutions; this result is consistent with length scales observed in continental regions of large-scale transcurrent faulting. An approximate, linear relationship between displacement and rotation is found that depends only on the deformation length scale and the rheology. Calculated displacements, finite rotations, and distribution of crustal thicknesses are consistent with those observed in the region of the Pacific-North America plate boundary in California.

On solving wave equations on fixed bounded intervals involving Robin boundary conditions with time-dependent coefficients

NASA Astrophysics Data System (ADS)

van Horssen, Wim T.; Wang, Yandong; Cao, Guohua

2018-06-01

In this paper, it is shown how characteristic coordinates, or equivalently how the well-known formula of d'Alembert, can be used to solve initial-boundary value problems for wave equations on fixed, bounded intervals involving Robin type of boundary conditions with time-dependent coefficients. A Robin boundary condition is a condition that specifies a linear combination of the dependent variable and its first order space-derivative on a boundary of the interval. Analytical methods, such as the method of separation of variables (SOV) or the Laplace transform method, are not applicable to those types of problems. The obtained analytical results by applying the proposed method, are in complete agreement with those obtained by using the numerical, finite difference method. For problems with time-independent coefficients in the Robin boundary condition(s), the results of the proposed method also completely agree with those as for instance obtained by the method of separation of variables, or by the finite difference method.

KANTBP 2.0: New version of a program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach

NASA Astrophysics Data System (ADS)

Chuluunbaatar, O.; Gusev, A. A.; Vinitsky, S. I.; Abrashkevich, A. G.

2008-11-01

A FORTRAN 77 program for calculating energy values, reaction matrix and corresponding radial wave functions in a coupled-channel approximation of the hyperspherical adiabatic approach is presented. In this approach, a multi-dimensional Schrödinger equation is reduced to a system of the coupled second-order ordinary differential equations on a finite interval with homogeneous boundary conditions: (i) the Dirichlet, Neumann and third type at the left and right boundary points for continuous spectrum problem, (ii) the Dirichlet and Neumann type conditions at left boundary point and Dirichlet, Neumann and third type at the right boundary point for the discrete spectrum problem. The resulting system of radial equations containing the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite element method. As a test desk, the program is applied to the calculation of the reaction matrix and radial wave functions for 3D-model of a hydrogen-like atom in a homogeneous magnetic field. This version extends the previous version 1.0 of the KANTBP program [O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Commun. 177 (2007) 649-675]. Program summaryProgram title: KANTBP Catalogue identifier: ADZH_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZH_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 20 403 No. of bytes in distributed program, including test data, etc.: 147 563 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IV Operating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XP RAM: This depends on the number of differential equations; the number and order of finite elements; the number of hyperradial points; and the number of eigensolutions required. The test run requires 2 MB Classification: 2.1, 2.4 External routines: GAULEG and GAUSSJ [2] Nature of problem: In the hyperspherical adiabatic approach [3-5], a multidimensional Schrödinger equation for a two-electron system [6] or a hydrogen atom in magnetic field [7-9] is reduced by separating radial coordinate ρ from the angular variables to a system of the second-order ordinary differential equations containing the potential matrix elements and first-derivative coupling terms. The purpose of this paper is to present the finite element method procedure based on the use of high-order accuracy approximations for calculating approximate eigensolutions of the continuum spectrum for such systems of coupled differential equations on finite intervals of the radial variable ρ∈[ρ,ρ]. This approach can be used in the calculations of effects of electron screening on low-energy fusion cross sections [10-12]. Solution method: The boundary problems for the coupled second-order differential equations are solved by the finite element method using high-order accuracy approximations [13]. The generalized algebraic eigenvalue problem AF=EBF with respect to pair unknowns ( E,F) arising after the replacement of the differential problem by the finite-element approximation is solved by the subspace iteration method using the SSPACE program [14]. The generalized algebraic eigenvalue problem (A-EB)F=λDF with respect to pair unknowns ( λ,F) arising after the corresponding replacement of the scattering boundary problem in open channels at fixed energy value, E, is solved by the LDL factorization of symmetric matrix and back-substitution methods using the DECOMP and REDBAK programs, respectively [14]. As a test desk, the program is applied to the calculation of the reaction matrix and corresponding radial wave functions for 3D-model of a hydrogen-like atom in a homogeneous magnetic field described in [9] on finite intervals of the radial variable ρ∈[ρ,ρ]. For this benchmark model the required analytical expressions for asymptotics of the potential matrix elements and first-derivative coupling terms, and also asymptotics of radial solutions of the boundary problems for coupled differential equations have been produced with help of a MAPLE computer algebra system. Restrictions: The computer memory requirements depend on: the number of differential equations; the number and order of finite elements; the total number of hyperradial points; and the number of eigensolutions required. Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see Section 3 and [1] for details). The user must also supply subroutine POTCAL for evaluating potential matrix elements. The user should also supply subroutines ASYMEV (when solving the eigenvalue problem) or ASYMS0 and ASYMSC (when solving the scattering problem) which evaluate asymptotics of the radial wave functions at left and right boundary points in case of a boundary condition of the third type for the above problems. Running time: The running time depends critically upon: the number of differential equations; the number and order of finite elements; the total number of hyperradial points on interval [ ρ,ρ]; and the number of eigensolutions required. The test run which accompanies this paper took 2 s without calculation of matrix potentials on the Intel Pentium IV 2.4 GHz. References: [1] O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Commun. 177 (2007) 649-675; http://cpc.cs.qub.ac.uk/summaries/ADZHv10.html. [2] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986. [3] J. Macek, J. Phys. B 1 (1968) 831-843. [4] U. Fano, Rep. Progr. Phys. 46 (1983) 97-165. [5] C.D. Lin, Adv. Atom. Mol. Phys. 22 (1986) 77-142. [6] A.G. Abrashkevich, D.G. Abrashkevich, M. Shapiro, Comput. Phys. Commun. 90 (1995) 311-339. [7] M.G. Dimova, M.S. Kaschiev, S.I. Vinitsky, J. Phys. B 38 (2005) 2337-2352. [8] O. Chuluunbaatar, A.A. Gusev, V.L. Derbov, M.S. Kaschiev, L.A. Melnikov, V.V. Serov, S.I. Vinitsky, J. Phys. A 40 (2007) 11485-11524. [9] O. Chuluunbaatar, A.A. Gusev, V.P. Gerdt, V.A. Rostovtsev, S.I. Vinitsky, A.G. Abrashkevich, M.S. Kaschiev, V.V. Serov, Comput. Phys. Commun. 178 (2007) 301 330; http://cpc.cs.qub.ac.uk/summaries/AEAAv10.html. [10] H.J. Assenbaum, K. Langanke, C. Rolfs, Z. Phys. A 327 (1987) 461-468. [11] V. Melezhik, Nucl. Phys. A 550 (1992) 223-234. [12] L. Bracci, G. Fiorentini, V.S. Melezhik, G. Mezzorani, P. Pasini, Phys. Lett. A 153 (1991) 456-460. [13] A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Commun. 85 (1995) 40-64. [14] K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982.

The behavior of plasma with an arbitrary degree of degeneracy of electron gas in the conductive layer

NASA Astrophysics Data System (ADS)

Latyshev, A. V.; Gordeeva, N. M.

2017-09-01

We obtain an analytic solution of the boundary problem for the behavior (fluctuations) of an electron plasma with an arbitrary degree of degeneracy of the electron gas in the conductive layer in an external electric field. We use the kinetic Vlasov-Boltzmann equation with the Bhatnagar-Gross-Krook collision integral and the Maxwell equation for the electric field. We use the mirror boundary conditions for the reflections of electrons from the layer boundary. The boundary problem reduces to a one-dimensional problem with a single velocity. For this, we use the method of consecutive approximations, linearization of the equations with respect to the absolute distribution of the Fermi-Dirac electrons, and the conservation law for the number of particles. Separation of variables then helps reduce the problem equations to a characteristic system of equations. In the space of generalized functions, we find the eigensolutions of the initial system, which correspond to the continuous spectrum (Van Kampen mode). Solving the dispersion equation, we then find the eigensolutions corresponding to the adjoint and discrete spectra (Drude and Debye modes). We then construct the general solution of the boundary problem by decomposing it into the eigensolutions. The coefficients of the decomposition are given by the boundary conditions. This allows obtaining the decompositions of the distribution function and the electric field in explicit form.

Weak stability of the plasma-vacuum interface problem

NASA Astrophysics Data System (ADS)

Catania, Davide; D'Abbicco, Marcello; Secchi, Paolo

2016-09-01

We consider the free boundary problem for the two-dimensional plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region, the flow is governed by the usual compressible MHD equations, while in the vacuum region we consider the Maxwell system for the electric and the magnetic fields. At the free interface, driven by the plasma velocity, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary. We study the linear stability of rectilinear plasma-vacuum interfaces by computing the Kreiss-Lopatinskiĭ determinant of an associated linearized boundary value problem. Apart from possible resonances, we obtain that the piecewise constant plasma-vacuum interfaces are always weakly linearly stable, independently of the size of tangential velocity, magnetic and electric fields on both sides of the characteristic discontinuity. We also prove that solutions to the linearized problem obey an energy estimate with a loss of regularity with respect to the source terms, both in the interior domain and on the boundary, due to the failure of the uniform Kreiss-Lopatinskiĭ condition, as the Kreiss-Lopatinskiĭ determinant associated with this linearized boundary value problem has roots on the boundary of the frequency space. In the proof of the a priori estimates, a crucial part is played by the construction of symmetrizers for a reduced differential system, which has poles at which the Kreiss-Lopatinskiĭ condition may fail simultaneously.

Initial-boundary value problems associated with the Ablowitz-Ladik system

NASA Astrophysics Data System (ADS)

Xia, Baoqiang; Fokas, A. S.

2018-02-01

We employ the Ablowitz-Ladik system as an illustrative example in order to demonstrate how to analyze initial-boundary value problems for integrable nonlinear differential-difference equations via the unified transform (Fokas method). In particular, we express the solutions of the integrable discrete nonlinear Schrödinger and integrable discrete modified Korteweg-de Vries equations in terms of the solutions of appropriate matrix Riemann-Hilbert problems. We also discuss in detail, for both the above discrete integrable equations, the associated global relations and the process of eliminating of the unknown boundary values.

On Compressible Vortex Sheets

NASA Astrophysics Data System (ADS)

Secchi, Paolo

2005-05-01

We introduce the main known results of the theory of incompressible and compressible vortex sheets. Moreover, we present recent results obtained by the author with J. F. Coulombel about supersonic compressible vortex sheets in two space dimensions. The problem is a nonlinear free boundary hyperbolic problem with two difficulties: the free boundary is characteristic and the Lopatinski condition holds only in a weak sense, yielding losses of derivatives. Under a supersonic condition that precludes violent instabilities, we prove an energy estimate for the boundary value problem obtained by linearization around an unsteady piecewise solution.

Global and blowup solutions of a mixed problem with nonlinear boundary conditions for a one-dimensional semilinear wave equation

NASA Astrophysics Data System (ADS)

Kharibegashvili, S. S.; Jokhadze, O. M.

2014-04-01

A mixed problem for a one-dimensional semilinear wave equation with nonlinear boundary conditions is considered. Conditions of this type occur, for example, in the description of the longitudinal oscillations of a spring fastened elastically at one end, but not in accordance with Hooke's linear law. Uniqueness and existence questions are investigated for global and blowup solutions to this problem, in particular how they depend on the nature of the nonlinearities involved in the equation and the boundary conditions. Bibliography: 14 titles.

Boundary Approximation Methods for Sloving Elliptic Problems on Unbounded Domains

NASA Astrophysics Data System (ADS)

Li, Zi-Cai; Mathon, Rudolf

1990-08-01

Boundary approximation methods with partial solutions are presented for solving a complicated problem on an unbounded domain, with both a crack singularity and a corner singularity. Also an analysis of partial solutions near the singular points is provided. These methods are easy to apply, have good stability properties, and lead to highly accurate solutions. Hence, boundary approximation methods with partial solutions are recommended for the treatment of elliptic problems on unbounded domains provided that piecewise solution expansions, in particular, asymptotic solutions near the singularities and infinity, can be found.

Abyssal Upwelling and Downwelling and the role of boundary layers

NASA Astrophysics Data System (ADS)

McDougall, T. J.; Ferrari, R. M.

2016-02-01

The bottom-intensified mixing activity arising from the interaction of internal tides with bottom topography implies that the dianeutral advection in the ocean interior is downwards, rather than upwards as is required by continuity. The upwelling of Bottom Water through density surfaces in the deep ocean is however possible because of the sloping nature of the sea floor. A budget study of the abyss (deeper than 2000m) will be described that shows that while the upwelling of Bottom Water might be 25 Sv, this is achieved by very strong upwelling in the bottom turbulent boundary layer (of thickness 50m) of 100 Sv and strong downwelling in the ocean interior of 75 Sv. This downwelling occurs within 10 degrees of longitude of the continental boundaries. This near-boundary confined strong upwelling and downwelling clearly has implications for the Stommel-Arons circulation.

Chaotic Oscillations of Second Order Linear Hyperbolic Equations with Nonlinear Boundary Conditions: A Factorizable but Noncommutative Case

NASA Astrophysics Data System (ADS)

Li, Liangliang; Huang, Yu; Chen, Goong; Huang, Tingwen

If a second order linear hyperbolic partial differential equation in one-space dimension can be factorized as a product of two first order operators and if the two first order operators commute, with one boundary condition being the van der Pol type and the other being linear, one can establish the occurrence of chaos when the parameters enter a certain regime [Chen et al., 2014]. However, if the commutativity of the two first order operators fails to hold, then the treatment in [Chen et al., 2014] no longer works and significant new challenges arise in determining nonlinear boundary conditions that engenders chaos. In this paper, we show that by incorporating a linear memory effect, a nonlinear van der Pol boundary condition can cause chaotic oscillations when the parameter enters a certain regime. Numerical simulations illustrating chaotic oscillations are also presented.

Dynamical injections as the source of near geostationary quiet time particle spatial boundaries

NASA Technical Reports Server (NTRS)

Mauk, B. H.; Meng, C. I.

1983-01-01

The question whether the noon-dusk feature is a manifestation of the spatial structures that should arise from quasi-stationary convection is examined. The key consideration here is whether the energy dispersion of the feature can be explained. It is shown that the observed energy dispersion cannot be attributed to the standard stationary convection configurations, either perturbed or unperturbed. It is also demonstrated, using a detailed computer simulation, that the nighttime, double-spiral-shaped injection boundary (used previously to reproduce the fast changing nighttime features) is successful at reproducing the noon-dusk feature by allowing the particles to evolve for periods of 12 to 36 hours after the injection. It is stressed that the portion of the injection boundary responsible for the feature looks very different from the standard convection boundaries configuration. Conclusions are offered concerning the importance of quasi-stationary convection as the mechanism by which the near geostationary regions are populated.

Researching across Boundaries and Borders: The Challenges for Research

ERIC Educational Resources Information Center

Bowl, Marion; Cooke, Sandra; Hockings, Christine

2008-01-01

This article explores some of the challenges of conducting action research in higher education. It arises from an ongoing research project funded by the Economic and Social Research Council's Teaching and Learning Research Programme (ESRC/TLRP), "Learning and Teaching for Social Diversity and Difference", which examines the dynamics of…

Towards Understanding the Mechanism of Receptivity and Bypass Dynamics in Laminar Boundary Layers

NASA Technical Reports Server (NTRS)

Lasseigne, D. G.; Criminale, W. O.; Joslin, R. D.; Jackson, T. L.

1999-01-01

Three problems concerning laminar-turbulent transition are addressed by solving a series of initial value problems. The first problem is the calculation of resonance within the continuous spectrum of the Blasius boundary layer. The second is calculation of the growth of Tollmien-Schlichting waves that are a direct result of disturbances that only lie outside of the boundary layer. And, the third problem is the calculation of non-parallel effects. Together, these problems represent a unified approach to the study of freestream disturbance effects that could lead to transition. Solutions to the temporal, initial-value problem with an inhomogeneous forcing term imposed upon the flow is sought. By solving a series of problems, it is shown that: A transient disturbance lying completely outside of the boundary layer can lead to the growth of an unstable Tollmien-Schlichting wave. A resonance with the continuous spectrum leads to strong amplification that may provide a mechanism for bypass transition once nonlinear effects are considered. A disturbance with a very weak unstable Tollmien-Schlichting wave can lead to a much stronger Tollmien-Schlichting wave downstream, if the original disturbance has a significant portion of its energy in the continuum modes.

Automatic Generation of Boundary Conditions Using Demons Nonrigid Image Registration for Use in 3-D Modality-Independent Elastography

PubMed Central

Ou, Jao J.; Ong, Rowena E.; Miga, Michael I.

2013-01-01

Modality-independent elastography (MIE) is a method of elastography that reconstructs the elastic properties of tissue using images acquired under different loading conditions and a biomechanical model. Boundary conditions are a critical input to the algorithm and are often determined by time-consuming point correspondence methods requiring manual user input. This study presents a novel method of automatically generating boundary conditions by nonrigidly registering two image sets with a demons diffusion-based registration algorithm. The use of this method was successfully performed in silico using magnetic resonance and X-ray-computed tomography image data with known boundary conditions. These preliminary results produced boundary conditions with an accuracy of up to 80% compared to the known conditions. Demons-based boundary conditions were utilized within a 3-D MIE reconstruction to determine an elasticity contrast ratio between tumor and normal tissue. Two phantom experiments were then conducted to further test the accuracy of the demons boundary conditions and the MIE reconstruction arising from the use of these conditions. Preliminary results show a reasonable characterization of the material properties on this first attempt and a significant improvement in the automation level and viability of the method. PMID:21690002

Automatic generation of boundary conditions using demons nonrigid image registration for use in 3-D modality-independent elastography.

PubMed

Pheiffer, Thomas S; Ou, Jao J; Ong, Rowena E; Miga, Michael I

2011-09-01

Modality-independent elastography (MIE) is a method of elastography that reconstructs the elastic properties of tissue using images acquired under different loading conditions and a biomechanical model. Boundary conditions are a critical input to the algorithm and are often determined by time-consuming point correspondence methods requiring manual user input. This study presents a novel method of automatically generating boundary conditions by nonrigidly registering two image sets with a demons diffusion-based registration algorithm. The use of this method was successfully performed in silico using magnetic resonance and X-ray-computed tomography image data with known boundary conditions. These preliminary results produced boundary conditions with an accuracy of up to 80% compared to the known conditions. Demons-based boundary conditions were utilized within a 3-D MIE reconstruction to determine an elasticity contrast ratio between tumor and normal tissue. Two phantom experiments were then conducted to further test the accuracy of the demons boundary conditions and the MIE reconstruction arising from the use of these conditions. Preliminary results show a reasonable characterization of the material properties on this first attempt and a significant improvement in the automation level and viability of the method.

An Evaluation of a Phase-Lag Boundary Condition for Francis Hydroturbine Simulations Using a Pressure-Based Solver

NASA Astrophysics Data System (ADS)

Wouden, Alex; Cimbala, John; Lewis, Bryan

2014-11-01

While the periodic boundary condition is useful for handling rotational symmetry in many axisymmetric geometries, its application fails for analysis of rotor-stator interaction (RSI) in multi-stage turbomachinery flow. The inadequacy arises from the underlying geometry where the blade counts per row differ, since the blade counts are crafted to deter the destructive harmonic forces of synchronous blade passing. Therefore, to achieve the computational advantage of modeling a single blade passage per row while preserving the integrity of the RSI, a phase-lag boundary condition is adapted to OpenFOAM® software's incompressible pressure-based solver. The phase-lag construct is accomplished through restating the implicit periodic boundary condition as a constant boundary condition that is updated at each time step with phase-shifted data from the coupled cells adjacent to the boundary. Its effectiveness is demonstrated using a typical Francis hydroturbine modeled as single- and double-passages with phase-lag boundary conditions. The evaluation of the phase-lag condition is based on the correspondence of the overall computational performance and the calculated flow parameters of the phase-lag simulations with those of a baseline full-wheel simulation. Funded in part by DOE Award Number: DE-EE0002667.

Heading off boundary problems: clinical supervision as risk management.

PubMed

Walker, R; Clark, J J

1999-11-01

The effective management of risk in clinical practice includes steps to limit harm to clients resulting from ethical violations or professional misconduct. Boundary problems constitute some of the most damaging ethical violations. The authors propose an active use of clinical supervision to anticipate and head off possible ethical violations by intervening when signs of boundary problems appear. The authors encourage a facilitative, Socratic method, rather than directive approaches, to help supervisees maximize their learning about ethical complexities. Building on the idea of a slippery slope, in which seemingly insignificant acts can lead to unethical patterns of behavior, the authors discuss ten cues to potential boundary problems, including strong feelings about a client; extended sessions with clients; gift giving between clinician and client; loans, barter, and sale of goods; clinician self-disclosures; and touching and sex. The authors outline supervisory interventions to be made when the cues are detected.

A Conserving Discretization for the Free Boundary in a Two-Dimensional Stefan Problem

NASA Astrophysics Data System (ADS)

Segal, Guus; Vuik, Kees; Vermolen, Fred

1998-03-01

The dissolution of a disk-likeAl2Cuparticle is considered. A characteristic property is that initially the particle has a nonsmooth boundary. The mathematical model of this dissolution process contains a description of the particle interface, of which the position varies in time. Such a model is called a Stefan problem. It is impossible to obtain an analytical solution for a general two-dimensional Stefan problem, so we use the finite element method to solve this problem numerically. First, we apply a classical moving mesh method. Computations show that after some time steps the predicted particle interface becomes very unrealistic. Therefore, we derive a new method for the displacement of the free boundary based on the balance of atoms. This method leads to good results, also, for nonsmooth boundaries. Some numerical experiments are given for the dissolution of anAl2Cuparticle in anAl-Cualloy.

Boundary value problem for the solution of magnetic cutoff rigidities and some special applications

NASA Technical Reports Server (NTRS)

Edmonds, Larry

1987-01-01

Since a planet's magnetic field can sometimes provide a spacecraft with some protection against cosmic ray and solar flare particles, it is important to be able to quantify this protection. This is done by calculating cutoff rigidities. An alternate to the conventional method (particle trajectory tracing) is introduced, which is to treat the problem as a boundary value problem. In this approach trajectory tracing is only needed to supply boundary conditions. In some special cases, trajectory tracing is not needed at all because the problem can be solved analytically. A differential equation governing cutoff rigidities is derived for static magnetic fields. The presense of solid objects, which can block a trajectory and other force fields are not included. A few qualititative comments, on existence and uniqueness of solutions, are made which may be useful when deciding how the boundary conditions should be set up. Also included are topics on axially symmetric fields.

Elasto visco-plastic flow with special attention to boundary conditions

NASA Technical Reports Server (NTRS)

Shimazaki, Y.; Thompson, E. G.

1981-01-01

A simple but nontrivial steady-state creeping elasto visco-plastic (Maxwell fluid) radial flow problem is analyzed, with special attention given to the effects of the boundary conditions. Solutions are obtained through integration of a governing equation on stress using the Runge-Kutta method for initial value problems and finite differences for boundary value problems. A more general approach through the finite element method, an approach that solves for the velocity field rather than the stress field and that is applicable to a wide range of problems, is presented and tested using the radial flow example. It is found that steady-state flows of elasto visco-plastic materials are strongly influenced by the state of stress of material as it enters the region of interest. The importance of this boundary or initial condition in analyses involving materials coming into control volumes from unusual stress environments is emphasized.

Techniques for determining physical zones of influence

DOEpatents

Hamann, Hendrik F; Lopez-Marrero, Vanessa

2013-11-26

Techniques for analyzing flow of a quantity in a given domain are provided. In one aspect, a method for modeling regions in a domain affected by a flow of a quantity is provided which includes the following steps. A physical representation of the domain is provided. A grid that contains a plurality of grid-points in the domain is created. Sources are identified in the domain. Given a vector field that defines a direction of flow of the quantity within the domain, a boundary value problem is defined for each of one or more of the sources identified in the domain. Each of the boundary value problems is solved numerically to obtain a solution for the boundary value problems at each of the grid-points. The boundary problem solutions are post-processed to model the regions affected by the flow of the quantity on the physical representation of the domain.

Extension of the SIESTA MHD equilibrium code to free-plasma-boundary problems

DOE PAGES

Peraza-Rodriguez, Hugo; Reynolds-Barredo, J. M.; Sanchez, Raul; ...

2017-08-28

Here, SIESTA is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for three-dimensional magnetic configurations. Since SIESTA does not assume closed magnetic surfaces, the solution can exhibit magnetic islands and stochastic regions. In its original implementation SIESTA addressed only fixed-boundary problems. That is, the shape of the plasma edge, assumed to be a magnetic surface, was kept fixed as the solution iteratively converges to equilibrium. This condition somewhat restricts the possible applications of SIESTA. In this paper we discuss an extension that will enable SIESTA to address free-plasma-boundary problems, opening upmore » the possibility of investigating problems in which the plasma boundary is perturbed either externally or internally. As an illustration, SIESTA is applied to a configuration of the W7-X stellarator.« less

Extension of the SIESTA MHD equilibrium code to free-plasma-boundary problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peraza-Rodriguez, Hugo; Reynolds-Barredo, J. M.; Sanchez, Raul

Here, SIESTA is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for three-dimensional magnetic configurations. Since SIESTA does not assume closed magnetic surfaces, the solution can exhibit magnetic islands and stochastic regions. In its original implementation SIESTA addressed only fixed-boundary problems. That is, the shape of the plasma edge, assumed to be a magnetic surface, was kept fixed as the solution iteratively converges to equilibrium. This condition somewhat restricts the possible applications of SIESTA. In this paper we discuss an extension that will enable SIESTA to address free-plasma-boundary problems, opening upmore » the possibility of investigating problems in which the plasma boundary is perturbed either externally or internally. As an illustration, SIESTA is applied to a configuration of the W7-X stellarator.« less

A Chebyshev Collocation Method for Moving Boundaries, Heat Transfer, and Convection During Directional Solidification

NASA Technical Reports Server (NTRS)

Zhang, Yiqiang; Alexander, J. I. D.; Ouazzani, J.

1994-01-01

Free and moving boundary problems require the simultaneous solution of unknown field variables and the boundaries of the domains on which these variables are defined. There are many technologically important processes that lead to moving boundary problems associated with fluid surfaces and solid-fluid boundaries. These include crystal growth, metal alloy and glass solidification, melting and name propagation. The directional solidification of semi-conductor crystals by the Bridgman-Stockbarger method is a typical example of such a complex process. A numerical model of this growth method must solve the appropriate heat, mass and momentum transfer equations and determine the location of the melt-solid interface. In this work, a Chebyshev pseudospectra collocation method is adapted to the problem of directional solidification. Implementation involves a solution algorithm that combines domain decomposition, finite-difference preconditioned conjugate minimum residual method and a Picard type iterative scheme.

Bifurcation approach to a logistic elliptic equation with a homogeneous incoming flux boundary condition

NASA Astrophysics Data System (ADS)

Umezu, Kenichiro

In this paper, we consider a semilinear elliptic boundary value problem in a smooth bounded domain, having the so-called logistic nonlinearity that originates from population dynamics, with a nonlinear boundary condition. Although the logistic nonlinearity has an absorption effect in the problem, the nonlinear boundary condition is induced by the homogeneous incoming flux on the boundary. The objective of our study is to analyze the existence of a bifurcation component of positive solutions from trivial solutions and its asymptotic behavior and stability. We perform this analysis using the method developed by Lyapunov and Schmidt, based on a scaling argument.

Some boundary-value problems for anisotropic quarter plane

NASA Astrophysics Data System (ADS)

Arkhypenko, K. M.; Kryvyi, O. F.

2018-04-01

To solve the mixed boundary-value problems of the anisotropic elasticity for the anisotropic quarter plane, a method based on the use of the space of generalized functions {\\Im }{\\prime }({\\text{R}}+2) with slow growth properties was developed. The two-dimensional integral Fourier transform was used to construct the system of fundamental solutions for the anisotropic quarter plane in this space and a system of eight boundary integral relations was obtained, which allows one to reduce the mixed boundary-value problems for the anisotropic quarter plane directly to systems of singular integral equations with fixed singularities. The exact solutions of these systems were found by using the integral Mellin transform. The asymptotic behavior of solutions was investigated at the vertex of the quarter plane.

Multispectral processing based on groups of resolution elements

NASA Technical Reports Server (NTRS)

Richardson, W.; Gleason, J. M.

1975-01-01

Several nine-point rules are defined and compared with previously studied rules. One of the rules performed well in boundary areas, but with reduced efficiency in field interiors; another combined best performance on field interiors with good sensitivity to boundary detail. The basic threshold gradient and some modifications were investigated as a means of boundary point detection. The hypothesis testing methods of closed-boundary formation were also tested and evaluated. An analysis of the boundary detection problem was initiated, employing statistical signal detection and parameter estimation techniques to analyze various formulations of the problem. These formulations permit the atmospheric and sensor system effects on the data to be thoroughly analyzed. Various boundary features and necessary assumptions can also be investigated in this manner.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jo, J.C.; Shin, W.K.; Choi, C.Y.

Transient heat transfer problems with phase changes (Stefan problems) occur in many engineering situations, including potential core melting and solidification during pressurized-water-reactor severe accidents, ablation of thermal shields, melting and solidification of alloys, and many others. This article addresses the numerical analysis of nonlinear transient heat transfer with melting or solidification. An effective and simple procedure is presented for the simulation of the motion of the boundary and the transient temperature field during the phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual-reciprocity boundary-element method. The dual-reciprocity boundary-element approach providedmore » in this article is much simpler than the usual boundary-element method in applying a reciprocity principle and an available technique for dealing with the domain integral of the boundary element formulation simultaneously. In this article, attention is focused on two-dimensional melting (ablation)/solidification problems for simplicity. The accuracy and effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of some examples of one-phase ablation/solidification problems with their known semianalytical or numerical solutions where available.« less

Recursive recovery of Markov transition probabilities from boundary value data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patch, Sarah Kathyrn

1994-04-01

In an effort to mathematically describe the anisotropic diffusion of infrared radiation in biological tissue Gruenbaum posed an anisotropic diffusion boundary value problem in 1989. In order to accommodate anisotropy, he discretized the temporal as well as the spatial domain. The probabilistic interpretation of the diffusion equation is retained; radiation is assumed to travel according to a random walk (of sorts). In this random walk the probabilities with which photons change direction depend upon their previous as well as present location. The forward problem gives boundary value data as a function of the Markov transition probabilities. The inverse problem requiresmore » finding the transition probabilities from boundary value data. Problems in the plane are studied carefully in this thesis. Consistency conditions amongst the data are derived. These conditions have two effects: they prohibit inversion of the forward map but permit smoothing of noisy data. Next, a recursive algorithm which yields a family of solutions to the inverse problem is detailed. This algorithm takes advantage of all independent data and generates a system of highly nonlinear algebraic equations. Pluecker-Grassmann relations are instrumental in simplifying the equations. The algorithm is used to solve the 4 x 4 problem. Finally, the smallest nontrivial problem in three dimensions, the 2 x 2 x 2 problem, is solved.« less

Analytical methods for solving boundary value heat conduction problems with heterogeneous boundary conditions on lines. I - Review

NASA Astrophysics Data System (ADS)

Kartashov, E. M.

1986-10-01

Analytical methods for solving boundary value problems for the heat conduction equation with heterogeneous boundary conditions on lines, on a plane, and in space are briefly reviewed. In particular, the method of dual integral equations and summator series is examined with reference to stationary processes. A table of principal solutions to dual integral equations and pair summator series is proposed which presents the known results in a systematic manner. Newly obtained results are presented in addition to the known ones.

Boundary-element modelling of dynamics in external poroviscoelastic problems

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Litvinchuk, S. Yu; Ipatov, A. A.; Petrov, A. N.

2018-04-01

A problem of a spherical cavity in porous media is considered. Porous media are assumed to be isotropic poroelastic or isotropic poroviscoelastic. The poroviscoelastic formulation is treated as a combination of Biot’s theory of poroelasticity and elastic-viscoelastic correspondence principle. Such viscoelastic models as Kelvin–Voigt, Standard linear solid, and a model with weakly singular kernel are considered. Boundary field study is employed with the help of the boundary element method. The direct approach is applied. The numerical scheme is based on the collocation method, regularized boundary integral equation, and Radau stepped scheme.

Research related to improved computer aided design software package. [comparative efficiency of finite, boundary, and hybrid element methods in elastostatics

NASA Technical Reports Server (NTRS)

Walston, W. H., Jr.

1986-01-01

The comparative computational efficiencies of the finite element (FEM), boundary element (BEM), and hybrid boundary element-finite element (HVFEM) analysis techniques are evaluated for representative bounded domain interior and unbounded domain exterior problems in elastostatics. Computational efficiency is carefully defined in this study as the computer time required to attain a specified level of solution accuracy. The study found the FEM superior to the BEM for the interior problem, while the reverse was true for the exterior problem. The hybrid analysis technique was found to be comparable or superior to both the FEM and BEM for both the interior and exterior problems.

Use of Green's functions in the numerical solution of two-point boundary value problems

NASA Technical Reports Server (NTRS)

Gallaher, L. J.; Perlin, I. E.

1974-01-01

This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and systems of such equations. The second part describes procedures for numerical construction of Green's functions and considers briefly the conditions for their existence. Finally, there is a description of some numerical experiments using nonlinear problems for which the known existence, uniqueness or convergence theorems do not apply. Examples here include some problems in finding rendezvous orbits of the restricted three body system.

Mixed boundary-value problem for an orthotropic rectangular strip with variable coefficients of elasticity

NASA Astrophysics Data System (ADS)

Sargsyan, M. Z.; Poghosyan, H. M.

2018-04-01

A dynamical problem for a rectangular strip with variable coefficients of elasticity is solved by an asymptotic method. It is assumed that the strip is orthotropic, the elasticity coefficients are exponential functions of y, and mixed boundary conditions are posed. The solution of the inner problem is obtained using Bessel functions.

A Boundary Value Problem for Introductory Physics?

ERIC Educational Resources Information Center

Grundberg, Johan

2008-01-01

The Laplace equation has applications in several fields of physics, and problems involving this equation serve as paradigms for boundary value problems. In the case of the Laplace equation in a disc there is a well-known explicit formula for the solution: Poisson's integral. We show how one can derive this formula, and in addition two equivalent…

Optimal control of singularly perturbed nonlinear systems with state-variable inequality constraints

NASA Technical Reports Server (NTRS)

Calise, A. J.; Corban, J. E.

1990-01-01

The established necessary conditions for optimality in nonlinear control problems that involve state-variable inequality constraints are applied to a class of singularly perturbed systems. The distinguishing feature of this class of two-time-scale systems is a transformation of the state-variable inequality constraint, present in the full order problem, to a constraint involving states and controls in the reduced problem. It is shown that, when a state constraint is active in the reduced problem, the boundary layer problem can be of finite time in the stretched time variable. Thus, the usual requirement for asymptotic stability of the boundary layer system is not applicable, and cannot be used to construct approximate boundary layer solutions. Several alternative solution methods are explored and illustrated with simple examples.

Magnetization due to localized states on graphene grain boundary

PubMed Central

Dutta, Sudipta; Wakabayashi, Katsunori

2015-01-01

Magnetism in graphene has been found to originate from various defects, e.g., vacancy, edge formation, add-atoms etc. Here, we discuss about an alternate route of achieving magnetism in graphene via grain boundary. During chemical vapor deposition of graphene, several graphene nucleation centers grow independently and face themselves with unusual bonding environment, giving rise to the formation of grain boundaries. We investigate the origin of magnetism in such grain boundaries within first-principles calculations, by letting two nucleation centers interact with each other at their interface. We observe formation of unprecedented point defect, consisting of fused three-membered and larger carbon rings, which induces net magnetization to graphene quantum dots. In case of periodic lattices, the appearance of array of point defects leads to the formation of magnetic grain boundaries. The net magnetization on these defects arises due to the deviation from bipartite characteristics of pristine graphene. We observe magnetic grain boundary induced dispersion less flat bands near Fermi energy, showing higher localization of electrons. These flat bands can be accessed via small doping, leading to enhanced magnetism. Moreover, the grain boundaries can induce asymmetric spin conduction behavior along the cross boundary direction. These properties can be exploited for sensor and spin-filtering applications. PMID:26145161

Geophysiology, Extended Organisms, and the Problem of Emergent Homeostasis

NASA Astrophysics Data System (ADS)

Turner, S.

2001-12-01

Physiology may be broadly defined as the managed flow of matter, energy and information. Central to this concept is the attendant phenomenon of homeostasis, doing physiological work to balance the thermodynamically driven flows of matter, energy or information that naturally attend to living things. Organisms in general exhibit what might be termed a "strong" homeostasis, in which well-regulated and complex physiological machines drive the physiological fluxes of matter, energy and information within the organism and at the organism's outermost integumentary boundary. Organisms also structure their environments to manage flows of matter, energy and information between themselves and their environment. In so doing, living things constitute a sort of extended organism, in which an organism's physiology reaches beyond the outermost boundary of the skin. Geophysiology's radical promise is that physiology can arise at levels of organization higher than the organism, ranging from social insect colonies through ecosystems, perhaps even to the biosphere itself. However, a simple demonstration that organisms affect the flows of matter, energy and information in their environments is not sufficient to qualify as physiology. That amounts to a demonstration that organisms do physiological work on their environments, which is neither a radical nor a new idea. To be truly physiological, geophysiology must exhibit physiology's most essential attribute, namely homeostasis. Finding homeostasis and explaining how it works in the extended organism is geophysiology's radical challenge.

The penalty immersed boundary method and its application to aerodynamics

NASA Astrophysics Data System (ADS)

Kim, Yongsam

The Immersed Boundary (IB) method has been widely applied to problems involving a moving elastic boundary that is immersed in fluid and interacting with it. But most applications of the IB method have involved a massless elastic boundary. Extending the method to cover the case of a massive boundary has required spreading the boundary mass out onto the fluid grid and then solving the Navier-Stokes equations with a variable mass density. The variable mass density makes Fourier transform methods inapplicable, and requires a multigrid solver. Here we propose a new and simple way to give mass to the elastic boundary. The key idea of the method is to introduce two representations of each boundary: one is a massive boundary which does not interact with the fluid, and the other is messless and plays the same role as the boundary of the IB method with the massless assumption. Although they are almost the same, we allow these two representations of the boundary to be different as long as the gap between them is small. This can be ensured by connecting them with a stiff spring with a zero rest length which generates force acting on both boundaries and pulling them together. We call this the 'Penalty IB method'. It does not spread mass to the fluid grid, retains the use of Fourier transform methodology, and is easy to implement in the context of an existing IB method code for the massless case. This thesis introduces the Penalty IB method and applies it to several problems in which the mass of the boundary is important. These problems are filaments in a flowing soap film, flows past a cylinder, windsocks, flags, and parachutes.

Use of Microgravity to Control the Microstructure of Eutectics

NASA Technical Reports Server (NTRS)

Wilcox, William R.; Regel, Liya L.; Smith, Reginald W.

1999-01-01

The long term goal of this project is to be able to control the microstructure of directionally solidified eutectic alloys, through an improved understanding of the influence of convection. Prior experimental results on the influence of microgravity on the microstructure of fibrous eutectics have been contradictory. Theoretical work at Clarkson University showed that buoyancy-driven convection in the vertical Bridgman configuration is not vigorous enough to alter the concentration field in the melt sufficiently to cause a measurable change in microstructure when the eutectic grows at minimum supercooling. Currently, there are four other hypotheses that might explain the observed changes in microstructure of fibrous eutectics caused by convection: (1) Disturbance of the concentration boundary layer arising from an off-eutectic melt composition and growth at the extremum; (2) Disturbance of the concentration boundary layer of a habit-modifying impurity; (3) Disturbance of the concentration boundary layer arising from an off-eutectic interfacial composition due to non-extremum growth; and (4) A fluctuating freezing rate combined with differences in the kinetics of fiber termination and fiber formation. We favor the last of these hypotheses. Thus, the primary objective of the present grant is to determine experimentally and theoretically the influence of a periodically varying freezing rate on eutectic solidification. A secondary objective is to determine the influence of convection on the microstructure of at least one other eutectic alloy that might be suitable for flight experiments.

A modified two-layer iteration via a boundary point approach to generalized multivalued pseudomonotone mixed variational inequalities.

PubMed

Saddeek, Ali Mohamed

2017-01-01

Most mathematical models arising in stationary filtration processes as well as in the theory of soft shells can be described by single-valued or generalized multivalued pseudomonotone mixed variational inequalities with proper convex nondifferentiable functionals. Therefore, for finding the minimum norm solution of such inequalities, the current paper attempts to introduce a modified two-layer iteration via a boundary point approach and to prove its strong convergence. The results here improve and extend the corresponding recent results announced by Badriev, Zadvornov and Saddeek (Differ. Equ. 37:934-942, 2001).

Second-Order Two-Sided Estimates in Nonlinear Elliptic Problems

NASA Astrophysics Data System (ADS)

Cianchi, Andrea; Maz'ya, Vladimir G.

2018-05-01

Best possible second-order regularity is established for solutions to p-Laplacian type equations with {p \\in (1, ∞)} and a square-integrable right-hand side. Our results provide a nonlinear counterpart of the classical L 2-coercivity theory for linear problems, which is missing in the existing literature. Both local and global estimates are obtained. The latter apply to solutions to either Dirichlet or Neumann boundary value problems. Minimal regularity on the boundary of the domain is required, although our conclusions are new even for smooth domains. If the domain is convex, no regularity of its boundary is needed at all.

Program for the solution of multipoint boundary value problems of quasilinear differential equations

NASA Technical Reports Server (NTRS)

1973-01-01

Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.

Meshless method for solving fixed boundary problem of plasma equilibrium

NASA Astrophysics Data System (ADS)

Imazawa, Ryota; Kawano, Yasunori; Itami, Kiyoshi

2015-07-01

This study solves the Grad-Shafranov equation with a fixed plasma boundary by utilizing a meshless method for the first time. Previous studies have utilized a finite element method (FEM) to solve an equilibrium inside the fixed separatrix. In order to avoid difficulties of FEM (such as mesh problem, difficulty of coding, expensive calculation cost), this study focuses on the meshless methods, especially RBF-MFS and KANSA's method to solve the fixed boundary problem. The results showed that CPU time of the meshless methods was ten to one hundred times shorter than that of FEM to obtain the same accuracy.

The first boundary-value problem for a fractional diffusion-wave equation in a non-cylindrical domain

NASA Astrophysics Data System (ADS)

Pskhu, A. V.

2017-12-01

We solve the first boundary-value problem in a non-cylindrical domain for a diffusion-wave equation with the Dzhrbashyan- Nersesyan operator of fractional differentiation with respect to the time variable. We prove an existence and uniqueness theorem for this problem, and construct a representation of the solution. We show that a sufficient condition for unique solubility is the condition of Hölder smoothness for the lateral boundary of the domain. The corresponding results for equations with Riemann- Liouville and Caputo derivatives are particular cases of results obtained here.

Attention problems and pathological gaming: resolving the 'chicken and egg' in a prospective analysis.

PubMed

Ferguson, Christopher J; Ceranoglu, T Atilla

2014-03-01

Pathological gaming (PG) behaviors are behaviors which interfere with other life responsibilities. Continued debate exists regarding whether symptoms of PG behaviors are a unique phenomenon or arise from other mental health problems, including attention problems. Development of attention problems and occurrence of pathological gaming in 144 adolescents were followed during a 1-year prospective analysis. Teens and their parents reported on pathological gaming behaviors, attention problems, and current grade point average, as well as several social variables. Results were analyzed using regression and path analysis. Attention problems tended to precede pathological gaming behaviors, but the inverse was not true. Attention problems but not pathological gaming predicted lower GPA 1 year later. Current results suggest that pathological gaming arises from attention problems, but not the inverse. These results suggest that pathological gaming behaviors are symptomatic of underlying attention related mental health issues, rather than a unique phenomenon.

Plate tectonics and offshore boundary delimitation: Tunisia-Libya case at the International Court of Justice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stanley, D.J.

1983-03-01

Advances in the technology for exploiting resources of the oceans, particularly recovery of hydrocarbons and minerals in deep water, is benefiting a growing number of nations. At the same time, however, economic and political pressures have induced concern and there is now a much increased emphasis on jurisdiction to divide the offshore areas between the 132 coastal nations. Negotiations affect research operations at sea and, in consequence, marine scientists have been made aware of offshore problems as highlighted by the Law of the Sea Treaty (UNCLOS III) and complications arising from the legal versus scientific definitions of continental shelves andmore » margins. The first major offshore boundary case of international scope where plate tectonics has constituted a significant argument is the one recently brought before the International Court of Justice by Libya and Tunisia concerning the delimitation of their continental shelves. Of the two parties, Libya placed the greatest emphasis on this concept as a means to determine natural prolongation of its land territory into and under the sea. Tunisia contested Libya's use of the whole of the African continental landmass as a reference unit; in Tunisia's view, considerations of geography, geomorphology, and bathymetry are at least as relevant as are those of geology. In its landmark judgment (February 1982) - which almost certainly will have far-reaching consequences in future such boundary delimitation cases - the court pronounced that It is the outcome, not the evolution in the long-distant past, which is of importance, and that it is the present-day configuration of the coasts and sea bed which are the main factors to be considered, not geology.« less

Use of Ground Penetrating Radar to Study Gradient Media

NASA Astrophysics Data System (ADS)

Titov, A.

2016-12-01

Nowadays Ground Penetrating Radar (GPR) is often used to solve different problems of applied geophysics including the hydrological ones. This work was motivated by detection of weak reflections in the body of water observed during the surveys on the freshwater lakes using GPR. The same reflections were first analyzed by John Bradford in 2007. These reflections can arise from the thermal gradient layer or thermocline due to different dielectric permittivity of cold and warm water. We employed physical and mathematical modeling to identify the properties of such thermoclines. We have constructed a special GPR stand to study the gradient media in our laboratory. The stand consists of a water-filled plastic tank and plastic tubes, which gather the cold water under the warm water. Our stand allows for changing parameters of the gradient layer, such as limits of dielectric permittivity and the thickness of the gradient layer. GPR antenna was placed slightly under the water surface to remove the parasitic reflections. To visualize the thermal distribution, an infrared camera and thermal sensors were used. Analysis of the GPR traces after physical modeling, performed in the MATLAB environment, allows us to locate the weak reflection from the gradient layer. We observed that (i) the change of the gradient boundary values alters the amplitude of the signal, (ii) the arrival time of the impulse reflected from the gradient layer corresponds to the arrival time of the impulse reflected from the top boundary of this layer, and (iii) the shape of the signal reflected from the gradient layer coincides with the shape of the signal reflected from the non-gradient boundary between two bodies. The quantitative properties of thermocline can be determined using amplitude analysis of GPR signals. Finally, the developed methods were successfully applied to real field data.

Surface and allied studies in silicon solar cells

NASA Technical Reports Server (NTRS)

Lindholm, F. A.

1983-01-01

Two main results are presented. The first deals with a simple method that determines the minority-carrier lifetime and the effective surface recombination velocity of the quasi-neutral base of silicon solar cells. The method requires the observation of only a single transient, and is amenable to automation for in-process monitoring in manufacturing. This method, which is called short-circuit current decay, avoids distortion in the observed transient and consequent inacccuracies that arise from the presence of mobile holes and electrons stored in the p/n junction spacecharge region at the initial instant of the transient. The second main result consists in a formulation of the relevant boundary-value problems that resembles that used in linear two-port network theory. This formulation enables comparisons to be made among various contending methods for measuring material parameters of p/n junction devices, and enables the option of putting the description in the time domain of the transient studies in the form of an infinite series, although closed-form solutions are also possible.

Fluid-dynamically coupled solid propellant combustion instability - cold flow simulation

NASA Astrophysics Data System (ADS)

Ben-Reuven, M.

1983-10-01

The near-wall processes in an injected, axisymmetric, viscous flow is examined. Solid propellant rocket instability, in which cold flow simulation is evaluated as a tool to elucidate possible instability driving mechanisms is studied. One such prominent mechanism seems to be visco-acoustic coupling. The formulation is presented in terms of a singular boundary layer problem, with detail (up to second order) given only to the near wall region. The injection Reynolds number is assumed large, and its inverse square root serves as an appropriate small perturbation quantity. The injected Mach number is also small, and taken of the same order as the aforesaid small quantity. The radial-dependence of the inner solutions up to second order is solved, in polynominal form. This leaves the (x,t) dependence to much simpler partial differential equations. Particular results demonstrate the existence of a first order pressure perturbation, which arises due to the dissipative near wall processes. This pressure and the associated viscous friction coefficient are shown to agree very well with experimental injected flow data.

Analytical estimates of the PP-algorithm at low number of Doppler periods per pulse length

NASA Technical Reports Server (NTRS)

Angelova, M. D.; Stoykova, E. V.; Stoyanov, D. V.

1992-01-01

When discussing the Doppler velocity estimators, it is of significant interest to analyze their behavior at a low number of Doppler periods n(sub D) = 2v(sub r)t(sub s)/lambda is approximately equal to 1 within the resolution cell t(sub s) (v(sub 4) is the radial velocity, lambda is the wavelength). Obviously, at n(sub D) is approximately less than 1 the velocity error is essentially increased. The problem of low n(sub D) arises in the planetary boundary layer (PBL), where higher resolutions are usually required but the signal-to-noise ratio (SNR) is relatively high. In this work analytical expression for the relative root mean square (RMS) error of the PP Doppler estimator at low number of periods for a narrowband Doppler signal and arbitrary model of the noise correlation function is obtained. The results are correct at relatively high SNR. The analysis is supported by computer simulations at various SNR's.

Friction pull plug welding: chamfered heat sink pull plug design

NASA Technical Reports Server (NTRS)

Coletta, Edmond R. (Inventor); Cantrell, Mark A. (Inventor)

2002-01-01

Friction Pull Plug Welding (FPPW) is a solid state repair process for defects up to one inch in length, only requiring single sided tooling (OSL) for usage on flight hardware. Experimental data has shown that the mass of plug heat sink remaining above the top of the plate surface after a weld is completed (the plug heat sink) affects the bonding at the plug top. A minimized heat sink ensures complete bonding of the plug to the plate at the plug top. However, with a minimal heat sink three major problems can arise, the entire plug could be pulled through the plate hole, the central portion of the plug could be separated along grain boundaries, or the plug top hat can be separated from the body. The Chamfered Heat Sink Pull Plug Design allows for complete bonding along the ISL interface through an outside diameter minimal mass heat sink, while maintaining enough central mass in the plug to prevent plug pull through, central separation, and plug top hat separation.

Double stratified radiative Jeffery magneto nanofluid flow along an inclined stretched cylinder with chemical reaction and slip condition

NASA Astrophysics Data System (ADS)

Ramzan, M.; Gul, Hina; Dong Chung, Jae

2017-11-01

A mathematical model is designed to deliberate the flow of an MHD Jeffery nanofluid past a vertically inclined stretched cylinder near a stagnation point. The flow analysis is performed in attendance of thermal radiation, mixed convection and chemical reaction. Influence of thermal and solutal stratification with slip boundary condition is also considered. Apposite transformations are engaged to convert the nonlinear partial differential equations to differential equations with high nonlinearity. Convergent series solutions of the problem are established via the renowned Homotopy Analysis Method (HAM). Graphical illustrations are plotted to depict the effects of prominent arising parameters against all involved distributions. Numerically erected tables of important physical parameters like Skin friction, Nusselt and Sherwood numbers are also give. Comparative studies (with a previously examined work) are also included to endorse our results. It is noticed that the thermal stratification parameter has diminishing effect on temperature distribution. Moreover, the velocity field is a snowballing and declining function of curvature and slip parameters respectively.

Asymptotic solution of the problem for a thin axisymmetric cavern

NASA Technical Reports Server (NTRS)

Serebriakov, V. V.

1973-01-01

The boundary value problem which describes the axisymmetric separation of the flow around a body by a stationary infinite stream is considered. It is understood that the cavitation number varies over the length of the cavern. Using the asymptotic expansions for the potential of a thin body, the orders of magnitude of terms in the equations of the problem are estimated. Neglecting small quantities, a simplified boundary value problem is obtained.

The boundary element method applied to 3D magneto-electro-elastic dynamic problems

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Markov, I. P.; Kuznetsov, Iu A.

2017-11-01

Due to the coupling properties, the magneto-electro-elastic materials possess a wide number of applications. They exhibit general anisotropic behaviour. Three-dimensional transient analyses of magneto-electro-elastic solids can hardly be found in the literature. 3D direct boundary element formulation based on the weakly-singular boundary integral equations in Laplace domain is presented in this work for solving dynamic linear magneto-electro-elastic problems. Integral expressions of the three-dimensional fundamental solutions are employed. Spatial discretization is based on a collocation method with mixed boundary elements. Convolution quadrature method is used as a numerical inverse Laplace transform scheme to obtain time domain solutions. Numerical examples are provided to illustrate the capability of the proposed approach to treat highly dynamic problems.

On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Hariharan, S. I.; Maccamy, R. C.

1993-01-01

We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.

The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul; Don, Wai-Sun

1993-01-01

The conventional method of imposing time dependent boundary conditions for Runge-Kutta (RK) time advancement reduces the formal accuracy of the space-time method to first order locally, and second order globally, independently of the spatial operator. This counter intuitive result is analyzed in this paper. Two methods of eliminating this problem are proposed for the linear constant coefficient case: (1) impose the exact boundary condition only at the end of the complete RK cycle, (2) impose consistent intermediate boundary conditions derived from the physical boundary condition and its derivatives. The first method, while retaining the RK accuracy in all cases, results in a scheme with much reduced CFL condition, rendering the RK scheme less attractive. The second method retains the same allowable time step as the periodic problem. However it is a general remedy only for the linear case. For non-linear hyperbolic equations the second method is effective only for for RK schemes of third order accuracy or less. Numerical studies are presented to verify the efficacy of each approach.

Teaching an Old Dog an Old Trick: FREE-FIX and Free-Boundary Axisymmetric MHD Equilibrium

NASA Astrophysics Data System (ADS)

Guazzotto, Luca

2015-11-01

A common task in plasma physics research is the calculation of an axisymmetric equilibrium for tokamak modeling. The main unknown of the problem is the magnetic poloidal flux ψ. The easiest approach is to assign the shape of the plasma and only solve the equilibrium problem in the plasma / closed-field-lines region (the ``fixed-boundary approach''). Often, one may also need the vacuum fields, i.e. the equilibrium in the open-field-lines region, requiring either coil currents or ψ on some closed curve outside the plasma to be assigned (the ``free-boundary approach''). Going from one approach to the other is a textbook problem, involving the calculation of Green's functions and surface integrals in the plasma. However, no tools are readily available to perform this task. Here we present a code (FREE-FIX) to compute a boundary condition for a free-boundary equilibrium given only the corresponding fixed-boundary equilibrium. An improvement to the standard solution method, allowing for much faster calculations, is presented. Applications are discussed. PPPL fund 245139 and DOE grant G00009102.

A landscape analysis plan

Treesearch

Nancy E. Fleenor

2002-01-01

A Landscape Analysis Plan (LAP) sets out broad guidelines for project development within boundaries of the Kings River Sustainable Forest Ecosystems Project. The plan must be a dynamic, living document, subject to change as new information arises over the course of this very long-term project (several decades). Two watersheds, each of 32,000 acres, were dedicated to...

An Interdisciplinary Approach to Art Appreciation

ERIC Educational Resources Information Center

Law, Sophia S. M.

2010-01-01

Background: Under the challenge of many post-modern theories and critics on art and art history, the boundaries and definition of art has becoming more diverse. Conventional art appreciation no longer covers all the debates and issues arising from the complex meaning of art in the modern world. Art education today must widen students' vision of…

The numerical-analytical implementation of the cross-sections method to the open waveguide transition of the "horn" type

NASA Astrophysics Data System (ADS)

Divakov, Dmitriy; Malykh, Mikhail; Sevastianov, Leonid; Sevastianov, Anton; Tiutiunnik, Anastasiia

2017-04-01

In the paper we construct a method for approximate solution of the waveguide problem for guided modes of an open irregular waveguide transition. The method is based on straightening of the curved waveguide boundaries by introducing new variables and applying the Kantorovich method to the problem formulated in the new variables to get a system of ordinary second-order differential equations. In the method, the boundary conditions are formulated by analogy with the partial radiation conditions in the similar problem for closed waveguide transitions. The method is implemented in the symbolic-numeric form using the Maple computer algebra system. The coefficient matrices of the system of differential equations and boundary conditions are calculated symbolically, and then the obtained boundary-value problem is solved numerically using the finite difference method. The chosen coordinate functions of Kantorovich expansions provide good conditionality of the coefficient matrices. The numerical experiment simulating the propagation of guided modes in the open waveguide transition confirms the validity of the method proposed to solve the problem.

Quenching rate for a nonlocal problem arising in the micro-electro mechanical system

NASA Astrophysics Data System (ADS)

Guo, Jong-Shenq; Hu, Bei

2018-03-01

In this paper, we study the quenching rate of the solution for a nonlocal parabolic problem which arises in the study of the micro-electro mechanical system. This question is equivalent to the stabilization of the solution to the transformed problem in self-similar variables. First, some a priori estimates are provided. In order to construct a Lyapunov function, due to the lack of time monotonicity property, we then derive some very useful and challenging estimates by a delicate analysis. Finally, with this Lyapunov function, we prove that the quenching rate is self-similar which is the same as the problem without the nonlocal term, except the constant limit depends on the solution itself.

Initial-Boundary Value Problem for Two-Component Gerdjikov-Ivanov Equation with 3 × 3 Lax Pair on Half-Line

NASA Astrophysics Data System (ADS)

Zhu, Qiao-Zhen; Fan, En-Gui; Xu, Jian

2017-10-01

The Fokas unified method is used to analyze the initial-boundary value problem of two-component Gerdjikov-Ivanonv equation on the half-line. It is shown that the solution of the initial-boundary problem can be expressed in terms of the solution of a 3 × 3 Riemann-Hilbert problem. The Dirichlet to Neumann map is obtained through the global relation. Supported by grants from the National Science Foundation of China under Grant No. 11671095, National Science Foundation of China under Grant No. 11501365, Shanghai Sailing Program supported by Science and Technology Commission of Shanghai Municipality under Grant No 15YF1408100, and the Hujiang Foundation of China (B14005)

Application of the boundary integral method to immiscible displacement problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masukawa, J.; Horne, R.N.

1988-08-01

This paper presents an application of the boundary integral method (BIM) to fluid displacement problems to demonstrate its usefulness in reservoir simulation. A method for solving two-dimensional (2D), piston-like displacement for incompressible fluids with good accuracy has been developed. Several typical example problems with repeated five-spot patterns were solved for various mobility ratios. The solutions were compared with the analytical solutions to demonstrate accuracy. Singularity programming was found to be a major advantage in handling flow in the vicinity of wells. The BIM was found to be an excellent way to solve immiscible displacement problems. Unlike analytic methods, it canmore » accommodate complex boundary shapes and does not suffer from numerical dispersion at the front.« less

A locally refined rectangular grid finite element method - Application to computational fluid dynamics and computational physics

NASA Technical Reports Server (NTRS)

Young, David P.; Melvin, Robin G.; Bieterman, Michael B.; Johnson, Forrester T.; Samant, Satish S.

1991-01-01

The present FEM technique addresses both linear and nonlinear boundary value problems encountered in computational physics by handling general three-dimensional regions, boundary conditions, and material properties. The box finite elements used are defined by a Cartesian grid independent of the boundary definition, and local refinements proceed by dividing a given box element into eight subelements. Discretization employs trilinear approximations on the box elements; special element stiffness matrices are included for boxes cut by any boundary surface. Illustrative results are presented for representative aerodynamics problems involving up to 400,000 elements.

Regularization and computational methods for precise solution of perturbed orbit transfer problems

NASA Astrophysics Data System (ADS)

Woollands, Robyn Michele

The author has developed a suite of algorithms for solving the perturbed Lambert's problem in celestial mechanics. These algorithms have been implemented as a parallel computation tool that has broad applicability. This tool is composed of four component algorithms and each provides unique benefits for solving a particular type of orbit transfer problem. The first one utilizes a Keplerian solver (a-iteration) for solving the unperturbed Lambert's problem. This algorithm not only provides a "warm start" for solving the perturbed problem but is also used to identify which of several perturbed solvers is best suited for the job. The second algorithm solves the perturbed Lambert's problem using a variant of the modified Chebyshev-Picard iteration initial value solver that solves two-point boundary value problems. This method converges over about one third of an orbit and does not require a Newton-type shooting method and thus no state transition matrix needs to be computed. The third algorithm makes use of regularization of the differential equations through the Kustaanheimo-Stiefel transformation and extends the domain of convergence over which the modified Chebyshev-Picard iteration two-point boundary value solver will converge, from about one third of an orbit to almost a full orbit. This algorithm also does not require a Newton-type shooting method. The fourth algorithm uses the method of particular solutions and the modified Chebyshev-Picard iteration initial value solver to solve the perturbed two-impulse Lambert problem over multiple revolutions. The method of particular solutions is a shooting method but differs from the Newton-type shooting methods in that it does not require integration of the state transition matrix. The mathematical developments that underlie these four algorithms are derived in the chapters of this dissertation. For each of the algorithms, some orbit transfer test cases are included to provide insight on accuracy and efficiency of these individual algorithms. Following this discussion, the combined parallel algorithm, known as the unified Lambert tool, is presented and an explanation is given as to how it automatically selects which of the three perturbed solvers to compute the perturbed solution for a particular orbit transfer. The unified Lambert tool may be used to determine a single orbit transfer or for generating of an extremal field map. A case study is presented for a mission that is required to rendezvous with two pieces of orbit debris (spent rocket boosters). The unified Lambert tool software developed in this dissertation is already being utilized by several industrial partners and we are confident that it will play a significant role in practical applications, including solution of Lambert problems that arise in the current applications focused on enhanced space situational awareness.

An overview of unconstrained free boundary problems

PubMed Central

Figalli, Alessio; Shahgholian, Henrik

2015-01-01

In this paper, we present a survey concerning unconstrained free boundary problems of type where B1 is the unit ball, Ω is an unknown open set, F1 and F2 are elliptic operators (admitting regular solutions), and is a functions space to be specified in each case. Our main objective is to discuss a unifying approach to the optimal regularity of solutions to the above matching problems, and list several open problems in this direction. PMID:26261367

High Order Finite Difference Methods, Multidimensional Linear Problems and Curvilinear Coordinates

NASA Technical Reports Server (NTRS)

Nordstrom, Jan; Carpenter, Mark H.

1999-01-01

Boundary and interface conditions are derived for high order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.

Solving transient acoustic boundary value problems with equivalent sources using a lumped parameter approach.

PubMed

Fahnline, John B

2016-12-01

An equivalent source method is developed for solving transient acoustic boundary value problems. The method assumes the boundary surface is discretized in terms of triangular or quadrilateral elements and that the solution is represented using the acoustic fields of discrete sources placed at the element centers. Also, the boundary condition is assumed to be specified for the normal component of the surface velocity as a function of time, and the source amplitudes are determined to match the known elemental volume velocity vector at a series of discrete time steps. Equations are given for marching-on-in-time schemes to solve for the source amplitudes at each time step for simple, dipole, and tripole source formulations. Several example problems are solved to illustrate the results and to validate the formulations, including problems with closed boundary surfaces where long-time numerical instabilities typically occur. A simple relationship between the simple and dipole source amplitudes in the tripole source formulation is derived so that the source radiates primarily in the direction of the outward surface normal. The tripole source formulation is shown to eliminate interior acoustic resonances and long-time numerical instabilities.

The Lp Robin problem for Laplace equations in Lipschitz and (semi-)convex domains

NASA Astrophysics Data System (ADS)

Yang, Sibei; Yang, Dachun; Yuan, Wen

2018-01-01

Let n ≥ 3 and Ω be a bounded Lipschitz domain in Rn. Assume that p ∈ (2 , ∞) and the function b ∈L∞ (∂ Ω) is non-negative, where ∂Ω denotes the boundary of Ω. Denote by ν the outward unit normal to ∂Ω. In this article, the authors give two necessary and sufficient conditions for the unique solvability of the Robin problem for the Laplace equation Δu = 0 in Ω with boundary data ∂ u / ∂ ν + bu = f ∈Lp (∂ Ω), respectively, in terms of a weak reverse Hölder inequality with exponent p or the unique solvability of the Robin problem with boundary data in some weighted L2 (∂ Ω) space. As applications, the authors obtain the unique solvability of the Robin problem for the Laplace equation in the bounded (semi-)convex domain Ω with boundary data in (weighted) Lp (∂ Ω) for any given p ∈ (1 , ∞).

The effect of antiphase boundaries on the elastic properties of Ni-Mn-Ga austenite and premartensite

NASA Astrophysics Data System (ADS)

Seiner, Hanuš; Sedlák, Petr; Bodnárová, Lucie; Drahokoupil, Jan; Kopecký, Vít; Kopeček, Jaromír; Landa, Michal; Heczko, Oleg

2013-10-01

The evolution of elastic properties with temperature and magnetic field was studied in two differently heat-treated single crystals of the Ni-Mn-Ga magnetic shape memory alloy using resonant ultrasound spectroscopy. Quenching and slow furnace cooling were used to obtain different densities of antiphase boundaries. We found that the crystals exhibited pronounced differences in the c‧ elastic coefficient and related shear damping in high-temperature ferromagnetic phases (austenite and premartensite). The difference can be ascribed to the formation of fine magnetic domain patterns and pinning of the magnetic domain walls on antiphase boundaries in the material with a high density of antiphase boundaries due to quenching. The fine domain pattern arising from mutual interactions between antiphase boundaries and ferromagnetic domain walls effectively reduces the magnetocrystalline anisotropy and amplifies the contribution of magnetostriction to the elastic response of the material. As a result, the anomalous elastic softening prior to martensite transformation is significantly enhanced in the quenched sample. Thus, for any comparison of experimental data and theoretical calculations the microstructural changes induced by specific heat treatment must be taken into account.

The effect of antiphase boundaries on the elastic properties of Ni-Mn-Ga austenite and premartensite.

PubMed

Seiner, Hanuš; Sedlák, Petr; Bodnárová, Lucie; Drahokoupil, Jan; Kopecký, Vít; Kopeček, Jaromír; Landa, Michal; Heczko, Oleg

2013-10-23

The evolution of elastic properties with temperature and magnetic field was studied in two differently heat-treated single crystals of the Ni-Mn-Ga magnetic shape memory alloy using resonant ultrasound spectroscopy. Quenching and slow furnace cooling were used to obtain different densities of antiphase boundaries. We found that the crystals exhibited pronounced differences in the c' elastic coefficient and related shear damping in high-temperature ferromagnetic phases (austenite and premartensite). The difference can be ascribed to the formation of fine magnetic domain patterns and pinning of the magnetic domain walls on antiphase boundaries in the material with a high density of antiphase boundaries due to quenching. The fine domain pattern arising from mutual interactions between antiphase boundaries and ferromagnetic domain walls effectively reduces the magnetocrystalline anisotropy and amplifies the contribution of magnetostriction to the elastic response of the material. As a result, the anomalous elastic softening prior to martensite transformation is significantly enhanced in the quenched sample. Thus, for any comparison of experimental data and theoretical calculations the microstructural changes induced by specific heat treatment must be taken into account.

Boundary shape identification problems in two-dimensional domains related to thermal testing of materials

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kojima, Fumio

1988-01-01

The identification of the geometrical structure of the system boundary for a two-dimensional diffusion system is reported. The domain identification problem treated here is converted into an optimization problem based on a fit-to-data criterion and theoretical convergence results for approximate identification techniques are discussed. Results of numerical experiments to demonstrate the efficacy of the theoretical ideas are reported.

Golden Ratio in a Coupled-Oscillator Problem

ERIC Educational Resources Information Center

Moorman, Crystal M.; Goff, John Eric

2007-01-01

The golden ratio appears in a classical mechanics coupled-oscillator problem that many undergraduates may not solve. Once the symmetry is broken in a more standard problem, the golden ratio appears. Several student exercises arise from the problem considered in this paper.

Numerical Solution of Time-Dependent Problems with a Fractional-Power Elliptic Operator

NASA Astrophysics Data System (ADS)

Vabishchevich, P. N.

2018-03-01

A time-dependent problem in a bounded domain for a fractional diffusion equation is considered. The first-order evolution equation involves a fractional-power second-order elliptic operator with Robin boundary conditions. A finite-element spatial approximation with an additive approximation of the operator of the problem is used. The time approximation is based on a vector scheme. The transition to a new time level is ensured by solving a sequence of standard elliptic boundary value problems. Numerical results obtained for a two-dimensional model problem are presented.

Calculation of Rayleigh type sums for zeros of the equation arising in spectral problem

NASA Astrophysics Data System (ADS)

Kostin, A. B.; Sherstyukov, V. B.

2017-12-01

For zeros of the equation (arising in the oblique derivative problem) μ J n ‧ ( μ ) cos α + i n J n ( μ ) sin α = 0 , μ ∈ ℂ , with parameters n ∈ ℤ, α ∈ [-π/2, π/2] and the Bessel function Jn (μ) special summation relationships are proved. The obtained results are consistent with the theory of well-known Rayleigh sums calculating by zeros of the Bessel function.

A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

PubMed

Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

2016-01-01

This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.

Numerical computations on one-dimensional inverse scattering problems

NASA Technical Reports Server (NTRS)

Dunn, M. H.; Hariharan, S. I.

1983-01-01

An approximate method to determine the index of refraction of a dielectric obstacle is presented. For simplicity one dimensional models of electromagnetic scattering are treated. The governing equations yield a second order boundary value problem, in which the index of refraction appears as a functional parameter. The availability of reflection coefficients yield two additional boundary conditions. The index of refraction by a k-th order spline which can be written as a linear combination of B-splines is approximated. For N distinct reflection coefficients, the resulting N boundary value problems yield a system of N nonlinear equations in N unknowns which are the coefficients of the B-splines.

BOUNDARY VALUE PROBLEM INVOLVING THE p-LAPLACIAN ON THE SIERPIŃSKI GASKET

NASA Astrophysics Data System (ADS)

Priyadarshi, Amit; Sahu, Abhilash

In this paper, we study the following boundary value problem involving the weak p-Laplacian. -Δpu=λa(x)|u|q-1u + b(x)|u|l-1uin 𝒮∖𝒮 0; u=0on 𝒮0, where 𝒮 is the Sierpiński gasket in ℝ2, 𝒮0 is its boundary, λ > 0, p > 1, 0 < q < p - 1 < l and a,b : 𝒮→ ℝ are bounded nonnegative functions. We will show the existence of at least two nontrivial weak solutions to the above problem for a certain range of λ using the analysis of fibering maps on suitable subsets.

Computational approach to Thornley's problem by bivariate operational calculus

NASA Astrophysics Data System (ADS)

Bazhlekova, E.; Dimovski, I.

2012-10-01

Thornley's problem is an initial-boundary value problem with a nonlocal boundary condition for linear onedimensional reaction-diffusion equation, used as a mathematical model of spiral phyllotaxis in botany. Applying a bivariate operational calculus we find explicit representation of the solution, containing two convolution products of special solutions and the arbitrary initial and boundary functions. We use a non-classical convolution with respect to the space variable, extending in this way the classical Duhamel principle. The special solutions involved are represented in the form of fast convergent series. Numerical examples are considered to show the application of the present technique and to analyze the character of the solution.

Numerical Error Estimation with UQ

NASA Astrophysics Data System (ADS)

Ackmann, Jan; Korn, Peter; Marotzke, Jochem

2014-05-01

Ocean models are still in need of means to quantify model errors, which are inevitably made when running numerical experiments. The total model error can formally be decomposed into two parts, the formulation error and the discretization error. The formulation error arises from the continuous formulation of the model not fully describing the studied physical process. The discretization error arises from having to solve a discretized model instead of the continuously formulated model. Our work on error estimation is concerned with the discretization error. Given a solution of a discretized model, our general problem statement is to find a way to quantify the uncertainties due to discretization in physical quantities of interest (diagnostics), which are frequently used in Geophysical Fluid Dynamics. The approach we use to tackle this problem is called the "Goal Error Ensemble method". The basic idea of the Goal Error Ensemble method is that errors in diagnostics can be translated into a weighted sum of local model errors, which makes it conceptually based on the Dual Weighted Residual method from Computational Fluid Dynamics. In contrast to the Dual Weighted Residual method these local model errors are not considered deterministically but interpreted as local model uncertainty and described stochastically by a random process. The parameters for the random process are tuned with high-resolution near-initial model information. However, the original Goal Error Ensemble method, introduced in [1], was successfully evaluated only in the case of inviscid flows without lateral boundaries in a shallow-water framework and is hence only of limited use in a numerical ocean model. Our work consists in extending the method to bounded, viscous flows in a shallow-water framework. As our numerical model, we use the ICON-Shallow-Water model. In viscous flows our high-resolution information is dependent on the viscosity parameter, making our uncertainty measures viscosity-dependent. We will show that we can choose a sensible parameter by using the Reynolds-number as a criteria. Another topic, we will discuss is the choice of the underlying distribution of the random process. This is especially of importance in the scope of lateral boundaries. We will present resulting error estimates for different height- and velocity-based diagnostics applied to the Munk gyre experiment. References [1] F. RAUSER: Error Estimation in Geophysical Fluid Dynamics through Learning; PhD Thesis, IMPRS-ESM, Hamburg, 2010 [2] F. RAUSER, J. MAROTZKE, P. KORN: Ensemble-type numerical uncertainty quantification from single model integrations; SIAM/ASA Journal on Uncertainty Quantification, submitted

Hypersonic three-dimensional nonequilibrium boundary-layer equations in generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Lee, Jong-Hun

1993-01-01

The basic governing equations for the second-order three-dimensional hypersonic thermal and chemical nonequilibrium boundary layer are derived by means of an order-of-magnitude analysis. A two-temperature concept is implemented into the system of boundary-layer equations by simplifying the rather complicated general three-temperature thermal gas model. The equations are written in a surface-oriented non-orthogonal curvilinear coordinate system, where two curvilinear coordinates are non-orthogonial and a third coordinate is normal to the surface. The equations are described with minimum use of tensor expressions arising from the coordinate transformation, to avoid unnecessary confusion for readers. The set of equations obtained will be suitable for the development of a three-dimensional nonequilibrium boundary-layer code. Such a code could be used to determine economically the aerodynamic/aerothermodynamic loads to the surfaces of hypersonic vehicles with general configurations. In addition, the basic equations for three-dimensional stagnation flow, of which solution is required as an initial value for space-marching integration of the boundary-layer equations, are given along with the boundary conditions, the boundary-layer parameters, and the inner-outer layer matching procedure. Expressions for the chemical reaction rates and the thermodynamic and transport properties in the thermal nonequilibrium environment are explicitly given.

Addressing the need for staff support among nurses caring for the AIDS population.

PubMed

Pasacreta, J V; Jacobsen, P B

1989-01-01

More and more nurses are caring for individuals with AIDS-spectrum disorders. When nurses become involved in hospital-based AIDS treatment, major psychosocial issues can arise. In settings where nursing personnel have limited or no experience working with patients with AIDS, fear of contagion is a major issue. This fear has both rational and irrational components. In general, providing up-to-date information in a small group setting can effectively reduce irrational fears. Rational fears, which are not as easily dealt with, should be a stimulus for behavior change (e.g., adoption of precautionary guidelines for reducing the possibility of accidental infection). Different issues arise among nurses specializing in AIDS care and include burnout, a sense of professional isolation, and the need to establish personal boundaries in dealing with patients. Guidelines are offered for establishing a group approach to address these concerns and to handle the sensitive issues that may arise.

Nonstationary Deformation of an Elastic Layer with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-11-01

The analytic solution to the plane problem for an elastic layer under a nonstationary surface load is found for mixed boundary conditions: normal stress and tangential displacement are specified on one side of the layer (fourth boundary-value problem of elasticity) and tangential stress and normal displacement are specified on the other side of the layer (second boundary-value problem of elasticity). The Laplace and Fourier integral transforms are applied. The inverse Laplace and Fourier transforms are found exactly using tabulated formulas and convolution theorems for various nonstationary loads. Explicit analytical expressions for stresses and displacements are derived. Loads applied to a constant surface area and to a surface area varying in a prescribed manner are considered. Computations demonstrate the dependence of the normal stress on time and spatial coordinates. Features of wave processes are analyzed

Evolving a Puncture Black Hole with Fixed Mesh Refinement

NASA Technical Reports Server (NTRS)

Imbiriba, Breno; Baker, John; Choi, Dae-II; Centrella, Joan; Fiske. David R.; Brown, J. David; vanMeter, James R.; Olson, Kevin

2004-01-01

We present a detailed study of the effects of mesh refinement boundaries on the convergence and stability of simulations of black hole spacetimes. We find no technical problems. In our applications of this technique to the evolution of puncture initial data, we demonstrate that it is possible to simulaneously maintain second order convergence near the puncture and extend the outer boundary beyond 100M, thereby approaching the asymptotically flat region in which boundary condition problems are less difficult.

Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Goldberg, M.; Tadmor, E.

1985-01-01

New convenient stability criteria are provided in this paper for a large class of finite difference approximations to initial-boundary value problems associated with the hyperbolic system u sub t = au sub x + Bu + f in the quarter plane x or = 0, t or = 0. Using the new criteria, stability is easily established for numerous combinations of well known basic schemes and boundary conditins, thus generalizing many special cases studied in recent literature.

The application of MINIQUASI to thermal program boundary and initial value problems

NASA Technical Reports Server (NTRS)

1974-01-01

The feasibility of applying the solution techniques of Miniquasi to the set of equations which govern a thermoregulatory model is investigated. For solving nonlinear equations and/or boundary conditions, a Taylor Series expansion is required for linearization of both equations and boundary conditions. The solutions are iterative and in each iteration, a problem like the linear case is solved. It is shown that Miniquasi cannot be applied to the thermoregulatory model as originally planned.

Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Goldberg, M.; Tadmor, E.

1983-01-01

New convenient stability criteria are provided in this paper for a large class of finite difference approximations to initial-boundary value problems associated with the hyperbolic system u sub t = au sub x + Bu + f in the quarter plane x or = 0, t or = 0. Using the new criteria, stability is easily established for numerous combinations of well known basic schemes and boundary conditions, thus generalizing many special cases studied in recent literature.

A collocation-shooting method for solving fractional boundary value problems

NASA Astrophysics Data System (ADS)

Al-Mdallal, Qasem M.; Syam, Muhammed I.; Anwar, M. N.

2010-12-01

In this paper, we discuss the numerical solution of special class of fractional boundary value problems of order 2. The method of solution is based on a conjugating collocation and spline analysis combined with shooting method. A theoretical analysis about the existence and uniqueness of exact solution for the present class is proven. Two examples involving Bagley-Torvik equation subject to boundary conditions are also presented; numerical results illustrate the accuracy of the present scheme.

Boundary-layer stability and airfoil design

NASA Technical Reports Server (NTRS)

Viken, Jeffrey K.

1986-01-01

Several different natural laminar flow (NLF) airfoils have been analyzed for stability of the laminar boundary layer using linear stability codes. The NLF airfoils analyzed come from three different design conditions: incompressible; compressible with no sweep; and compressible with sweep. Some of the design problems are discussed, concentrating on those problems associated with keeping the boundary layer laminar. Also, there is a discussion on how a linear stability analysis was effectively used to improve the design for some of the airfoils.

[Kinetic theory and boundary conditions for highly inelastic spheres]. Quarterly progress report, April 1, 1993--June 30, 1993

DOE Office of Scientific and Technical Information (OSTI.GOV)

Richman, M.

1993-12-31

In this quarter, a kinetic theory was employed to set up the boundary value problem for steady, fully developed, gravity-driven flows of identical, smooth, highly inelastic spheres down bumpy inclines. The solid fraction, mean velocity, and components of the full second moment of fluctuation velocity were treated as mean fields. In addition to the balance equations for mass and momentum, the balance of the full second moment of fluctuation velocity was treated as an equation that must be satisfied by the mean fields. However, in order to simplify the resulting boundary value problem, fluxes of second moments in its isotropicmore » piece only were retained. The constitutive relations for the stresses and collisional source of second moment depend explicitly on the second moment of fluctuation velocity, and the constitutive relation for the energy flux depends on gradients of granular temperature, solid fraction, and components of the second moment. The boundary conditions require that the flows are free of stress and energy flux at their tops, and that momentum and energy are balanced at the bumpy base. The details of the boundary value problem are provided. In the next quarter, a solution procedure will be developed, and it will be employed to obtain sample numerical solutions to the boundary value problem described here.« less

Joule heating effects on electromagnetohydrodynamic flow through a peristaltically induced micro-channel with different zeta potential and wall slip

NASA Astrophysics Data System (ADS)

Ranjit, N. K.; Shit, G. C.

2017-09-01

This paper aims to develop a mathematical model for magnetohydrodynamic flow of biofluids through a hydrophobic micro-channel with periodically contracting and expanding walls under the influence of an axially applied electric field. The velocity slip effects have been taken into account at the channel walls by employing different slip lengths due to hydrophobic gating. Different temperature jump factors have also been used to investigate the thermomechanical interactions at the fluid-solid interface. The electromagnetohydrodynamic flow in a microchannel is simplified under the framework of Debye-Hückel linearization approximation. We have derived the closed-form solutions for the linearized dimensionless boundary value problem under the assumptions of long wave length and low Reynolds number. The axial velocity, temperature, pressure distribution, stream function, wall shear stress and the Nusselt number have been appraised for diverse values of the parameters approaching into the problem. Our main focus is to determine the effects of different zeta potential on the axial velocity and temperature distribution under electromagnetic environment. This study puts forward an important observation that the different zeta potential plays an important role in controlling fluid velocity. The study further reveals that the temperature increases significantly with the Joule heating parameter and the Brinkman number (arises due to the dissipation of energy).

Steady states and linear stability analysis of precipitation pattern formation at geothermal hot springs.

PubMed

Chan, Pak Yuen; Goldenfeld, Nigel

2007-10-01

A dynamical theory of geophysical precipitation pattern formation is presented and applied to irreversible calcium carbonate (travertine) deposition. Specific systems studied here are the terraces and domes observed at geothermal hot springs, such as those at Yellowstone National Park, and speleothems, particularly stalactites and stalagmites. The theory couples the precipitation front dynamics with shallow water flow, including corrections for turbulent drag and curvature effects. In the absence of capillarity and with a laminar flow profile, the theory predicts a one-parameter family of steady state solutions to the moving boundary problem describing the precipitation front. These shapes match the measured shapes near the vent at the top of observed travertine domes well. Closer to the base of the dome, the solutions deviate from observations and circular symmetry is broken by a fluting pattern, which we show is associated with capillary forces causing thin film break-up. We relate our model to that recently proposed for stalactite growth, and calculate the linear stability spectrum of both travertine domes and stalactites. Lastly, we apply the theory to the problem of precipitation pattern formation arising from turbulent flow down an inclined plane and identify a linear instability that underlies scale-invariant travertine terrace formation at geothermal hot springs.

Steady states and linear stability analysis of precipitation pattern formation at geothermal hot springs

NASA Astrophysics Data System (ADS)

Chan, Pak Yuen; Goldenfeld, Nigel

2007-10-01

A dynamical theory of geophysical precipitation pattern formation is presented and applied to irreversible calcium carbonate (travertine) deposition. Specific systems studied here are the terraces and domes observed at geothermal hot springs, such as those at Yellowstone National Park, and speleothems, particularly stalactites and stalagmites. The theory couples the precipitation front dynamics with shallow water flow, including corrections for turbulent drag and curvature effects. In the absence of capillarity and with a laminar flow profile, the theory predicts a one-parameter family of steady state solutions to the moving boundary problem describing the precipitation front. These shapes match the measured shapes near the vent at the top of observed travertine domes well. Closer to the base of the dome, the solutions deviate from observations and circular symmetry is broken by a fluting pattern, which we show is associated with capillary forces causing thin film break-up. We relate our model to that recently proposed for stalactite growth, and calculate the linear stability spectrum of both travertine domes and stalactites. Lastly, we apply the theory to the problem of precipitation pattern formation arising from turbulent flow down an inclined plane and identify a linear instability that underlies scale-invariant travertine terrace formation at geothermal hot springs.

Time-dependent boundary conditions for hyperbolic systems. II

NASA Technical Reports Server (NTRS)

Thompson, Kevin W.

1990-01-01

A general boundary condition formalism is developed for all types of boundary conditions to which hyperbolic systems are subject; the formalism makes possible a 'cookbook' approach to boundary conditions, by means of which novel boundary 'recipes' may be derived and previously devised ones may be consulted as required. Numerous useful conditions are derived for such CFD problems as subsonic and supersonic inflows and outflows, nonreflecting boundaries, force-free boundaries, constant pressure boundaries, and constant mass flux. Attention is given to the computation and integration of time derivatives.

Time-dependent boundary conditions for hyperbolic systems. II

NASA Astrophysics Data System (ADS)

Thompson, Kevin W.

1990-08-01

A general boundary condition formalism is developed for all types of boundary conditions to which hyperbolic systems are subject; the formalism makes possible a 'cookbook' approach to boundary conditions, by means of which novel boundary 'recipes' may be derived and previously devised ones may be consulted as required. Numerous useful conditions are derived for such CFD problems as subsonic and supersonic inflows and outflows, nonreflecting boundaries, force-free boundaries, constant pressure boundaries, and constant mass flux. Attention is given to the computation and integration of time derivatives.

A new approach to implement absorbing boundary condition in biomolecular electrostatics.

PubMed

Goni, Md Osman

2013-01-01

This paper discusses a novel approach to employ the absorbing boundary condition in conjunction with the finite-element method (FEM) in biomolecular electrostatics. The introduction of Bayliss-Turkel absorbing boundary operators in electromagnetic scattering problem has been incorporated by few researchers. However, in the area of biomolecular electrostatics, this boundary condition has not been investigated yet. The objective of this paper is twofold. First, to solve nonlinear Poisson-Boltzmann equation using Newton's method and second, to find an efficient and acceptable solution with minimum number of unknowns. In this work, a Galerkin finite-element formulation is used along with a Bayliss-Turkel absorbing boundary operator that explicitly accounts for the open field problem by mapping the Sommerfeld radiation condition from the far field to near field. While the Bayliss-Turkel condition works well when the artificial boundary is far from the scatterer, an acceptable tolerance of error can be achieved with the second order operator. Numerical results on test case with simple sphere show that the treatment is able to reach the same level of accuracy achieved by the analytical method while using a lower grid density. Bayliss-Turkel absorbing boundary condition (BTABC) combined with the FEM converges to the exact solution of scattering problems to within discretization error.

Integral methods of solving boundary-value problems of nonstationary heat conduction and their comparative analysis

NASA Astrophysics Data System (ADS)

Kot, V. A.

2017-11-01

The modern state of approximate integral methods used in applications, where the processes of heat conduction and heat and mass transfer are of first importance, is considered. Integral methods have found a wide utility in different fields of knowledge: problems of heat conduction with different heat-exchange conditions, simulation of thermal protection, Stefantype problems, microwave heating of a substance, problems on a boundary layer, simulation of a fluid flow in a channel, thermal explosion, laser and plasma treatment of materials, simulation of the formation and melting of ice, inverse heat problems, temperature and thermal definition of nanoparticles and nanoliquids, and others. Moreover, polynomial solutions are of interest because the determination of a temperature (concentration) field is an intermediate stage in the mathematical description of any other process. The following main methods were investigated on the basis of the error norms: the Tsoi and Postol’nik methods, the method of integral relations, the Gudman integral method of heat balance, the improved Volkov integral method, the matched integral method, the modified Hristov method, the Mayer integral method, the Kudinov method of additional boundary conditions, the Fedorov boundary method, the method of weighted temperature function, the integral method of boundary characteristics. It was established that the two last-mentioned methods are characterized by high convergence and frequently give solutions whose accuracy is not worse that the accuracy of numerical solutions.

Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives

NASA Astrophysics Data System (ADS)

Antunes, Pedro R. S.; Ferreira, Rui A. C.

2017-07-01

In this work we study boundary value problems associated to a nonlinear fractional ordinary differential equation involving left and right Caputo derivatives. We discuss the regularity of the solutions of such problems and, in particular, give precise necessary conditions so that the solutions are C1([0, 1]). Taking into account our analytical results, we address the numerical solution of those problems by the augmented -RBF method. Several examples illustrate the good performance of the numerical method.

Common Methodological Problems in Research on the Addictions.

ERIC Educational Resources Information Center

Nathan, Peter E.; Lansky, David

1978-01-01

Identifies common problems in research on the addictions and offers suggestions for remediating these methodological problems. The addictions considered include alcoholism and drug dependencies. Problems considered are those arising from inadequate, incomplete, or biased reviews of relevant literatures and methodological shortcomings of subject…

SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-08-01

This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. Themore » notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kılıç, Emre, E-mail: emre.kilic@tum.de; Eibert, Thomas F.

An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems.more » Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.« less

Viscous pressure correction in the irrotational flow outside Prandtl's boundary layer

NASA Astrophysics Data System (ADS)

Joseph, Daniel; Wang, Jing

2004-11-01

We argue that boundary layers on solid with irrotational motion outside are like a gas bubble because the shear stress vanishes at the edge of the boundary layer but the irrotational shear stress does not. This discrepancy induces a pressure correction and an additional drag which can be advertised as due to the viscous dissipation of the irrotational flow. Typically, this extra correction to the drag would be relatively small. A much more interesting implication of the extra pressure theory arises from the consideration of the effects of viscosity on the normal stress on a solid boundary which are entirely neglected in Prandtl's theory. It is very well known and easily demonstrated that as a consequence of the continuity equation the viscous normal stress must vanish on a rigid solid. It follows that all the greatly important effects of viscosity on the normal stress are buried in the pressure and the leading order effects of viscosity on the normal stress can be obtained from the viscous correction of viscous potential flow.

Flow-around modes for a rhomboid wing with a stall vortex in the shock layer

NASA Astrophysics Data System (ADS)

Zubin, M. A.; Maximov, F. A.; Ostapenko, N. A.

2017-12-01

The results of theoretical and experimental investigation of an asymmetrical hypersonic flow around a V-shaped wing with the opening angle larger than π on the modes with attached shockwaves on forward edges, when the stall flow is implemented on the leeward wing cantilever behind the kink point of the cross contour. In this case, a vortex of nonviscous nature is formed in which the velocities on the sphere exceeding the speed of sound and resulting in the occurrence of pressure shocks with an intensity sufficient for the separation of the turbulent boundary layer take place in the reverse flow according to the calculations within the framework of the ideal gas. It is experimentally established that a separation boundary layer can exist in the reverse flow, and its structure is subject to the laws inherent to the reverse flow in the separation region of the turbulent boundary layer arising in the supersonic conic flow under the action of a shockwave incident to the boundary layer.

Shuttle orbiter boundary layer transition at flight and wind tunnel conditions

NASA Technical Reports Server (NTRS)

Goodrich, W. D.; Derry, S. M.; Bertin, J. J.

1983-01-01

Hypersonic boundary layer transition data obtained on the windward centerline of the Shuttle orbiter during entry for the first five flights are presented and analyzed. Because the orbiter surface is composed of a large number of thermal protection tiles, the transition data include the effects of distributed roughness arising from tile misalignment and gaps. These data are used as a benchmark for assessing and improving the accuracy of boundary layer transition predictions based on correlations of wind tunnel data taken on both aerodynamically rough and smooth orbiter surfaces. By comparing these two data bases, the relative importance of tunnel free stream noise and surface roughness on orbiter boundary layer transition correlation parameters can be assessed. This assessment indicates that accurate predications of transition times can be made for the orbiter at hypersonic flight conditions by using roughness dominated wind tunnel data. Specifically, times of transition onset and completion is accurately predicted using a correlation based on critical and effective values of a roughness Reynolds number previously derived from wind tunnel data.

An H(mo) Interpolation Result

DTIC Science & Technology

1989-11-14

9] V. A. Kondrat’ev. Boundary problems for parabolic equations in closed domains. Trans. Mosc . Math. Soc., 15:450-504, 1966. [10] V. A. Kondrat’ev...Boundary problems for elliptic equations in domains with conical or angular points. Trans. Mosc . Math. Soc., 16:227-313, 1967. [11] Y. Maday. Analysis

Clarification of the Blurred Boundaries between Grounded Theory and Ethnography: Differences and Similarities

ERIC Educational Resources Information Center

Aldiabat, Khaldoun; Le Navenec, Carol-Lynne

2011-01-01

There is confusion among graduate students about how to select the qualitative methodology that best fits their research question. Often this confusion arises in regard to making a choice between a grounded theory methodology and an ethnographic methodology. This difficulty may stem from the fact that these students do not have a clear…

Mobilities, Moorings and Boundary Marking in Developing Semantic Technologies in Educational Practices

ERIC Educational Resources Information Center

Edwards, Richard; Tracy, Fran; Jordan, Katy

2011-01-01

While much attention has been given to the changing spaces of education introduced by new technologies, the impact of spatial theory on the discussion of such education is less well developed. Drawing upon empirical evidence from the Ensemble research project, this article examines spatially some of the possibilities and constraints that arise in…

Extreme values and the level-crossing problem: An application to the Feller process

NASA Astrophysics Data System (ADS)

Masoliver, Jaume

2014-04-01

We review the question of the extreme values attained by a random process. We relate it to level crossings to one boundary (first-passage problems) as well as to two boundaries (escape problems). The extremes studied are the maximum, the minimum, the maximum absolute value, and the range or span. We specialize in diffusion processes and present detailed results for the Wiener and Feller processes.

Reversal in the Size Dependence of Grain Rotation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Xiaoling; Tamura, Nobumichi; Mi, Zhongying

The conventional belief, based on the Read-Shockley model for the grain rotation mechanism, has been that smaller grains rotate more under stress due to the motion of grain boundary dislocations. However, in our high-pressure synchrotron Laue x-ray microdiffraction experiments, 70 nm nickel particles are found to rotate more than any other grain size. We infer that the reversal in the size dependence of the grain rotation arises from the crossover between the grain boundary dislocation-mediated and grain interior dislocation-mediated deformation mechanisms. The dislocation activities in the grain interiors are evidenced by the deformation texture of nickel nanocrystals. This new findingmore » reshapes our view on the mechanism of grain rotation and helps us to better understand the plastic deformation of nanomaterials, particularly of the competing effects of grain boundary and grain interior dislocations.« less

Classical topological paramagnetism

NASA Astrophysics Data System (ADS)

Bondesan, R.; Ringel, Z.

2017-05-01

Topological phases of matter are one of the hallmarks of quantum condensed matter physics. One of their striking features is a bulk-boundary correspondence wherein the topological nature of the bulk manifests itself on boundaries via exotic massless phases. In classical wave phenomena, analogous effects may arise; however, these cannot be viewed as equilibrium phases of matter. Here, we identify a set of rules under which robust equilibrium classical topological phenomena exist. We write simple and analytically tractable classical lattice models of spins and rotors in two and three dimensions which, at suitable parameter ranges, are paramagnetic in the bulk but nonetheless exhibit some unusual long-range or critical order on their boundaries. We point out the role of simplicial cohomology as a means of classifying, writing, and analyzing such models. This opens an experimental route for studying strongly interacting topological phases of spins.

Reversal in the Size Dependence of Grain Rotation

DOE PAGES

Zhou, Xiaoling; Tamura, Nobumichi; Mi, Zhongying; ...

2017-03-01

The conventional belief, based on the Read-Shockley model for the grain rotation mechanism, has been that smaller grains rotate more under stress due to the motion of grain boundary dislocations. However, in our high-pressure synchrotron Laue x-ray microdiffraction experiments, 70 nm nickel particles are found to rotate more than any other grain size. We infer that the reversal in the size dependence of the grain rotation arises from the crossover between the grain boundary dislocation-mediated and grain interior dislocation-mediated deformation mechanisms. The dislocation activities in the grain interiors are evidenced by the deformation texture of nickel nanocrystals. This new findingmore » reshapes our view on the mechanism of grain rotation and helps us to better understand the plastic deformation of nanomaterials, particularly of the competing effects of grain boundary and grain interior dislocations.« less

Stability of warped AdS3 vacua of topologically massive gravity

NASA Astrophysics Data System (ADS)

Anninos, Dionysios; Esole, Mboyo; Guica, Monica

2009-10-01

AdS3 vacua of topologically massive gravity (TMG) have been shown to be perturbatively unstable for all values of the coupling constant except the chiral point μl = 1. We study the possibility that the warped vacua of TMG, which exist for all values of μ, are stable under linearized perturbations. In this paper, we show that spacelike warped AdS3 vacua with Compère-Detournay boundary conditions are indeed stable in the range μl>3. This is precisely the range in which black hole solutions arise as discrete identifications of the warped AdS3 vacuum. The situation somewhat resembles chiral gravity: although negative energy modes do exist, they are all excluded by the boundary conditions, and the perturbative spectrum solely consists of boundary (pure large gauge) gravitons.

A finite element algorithm for high-lying eigenvalues with Neumann and Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Báez, G.; Méndez-Sánchez, R. A.; Leyvraz, F.; Seligman, T. H.

2014-01-01

We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions, or combinations of either for different parts of the boundary. We use an inverse power plus Gauss-Seidel algorithm to solve the generalized eigenvalue problem. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We checked the algorithm by comparing the cumulative level density of the spectrum obtained numerically with the theoretical prediction given by the Weyl formula. We found a systematic deviation due to the discretization, not to the algorithm itself.

An Immersed Boundary Method for Solving the Compressible Navier-Stokes Equations with Fluid Structure Interaction

NASA Technical Reports Server (NTRS)

Brehm, Christoph; Barad, Michael F.; Kiris, Cetin C.

2016-01-01

An immersed boundary method for the compressible Navier-Stokes equation and the additional infrastructure that is needed to solve moving boundary problems and fully coupled fluid-structure interaction is described. All the methods described in this paper were implemented in NASA's LAVA solver framework. The underlying immersed boundary method is based on the locally stabilized immersed boundary method that was previously introduced by the authors. In the present paper this method is extended to account for all aspects that are involved for fluid structure interaction simulations, such as fast geometry queries and stencil computations, the treatment of freshly cleared cells, and the coupling of the computational fluid dynamics solver with a linear structural finite element method. The current approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems in 2D and 3D. As part of the validation procedure, results from the second AIAA aeroelastic prediction workshop are also presented. The current paper is regarded as a proof of concept study, while more advanced methods for fluid structure interaction are currently being investigated, such as geometric and material nonlinearities, and advanced coupling approaches.

Boundary particle method for Laplace transformed time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Yang, Hai-Tian

2013-02-01

This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Laplace-transformed problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique (RC-MRM) is used to convert the inhomogeneous problem into the higher-order homogeneous problem. Finally, the Stehfest numerical inverse Laplace transform (NILT) is implemented to retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. In comparison with finite difference discretization, the LTBPM introduces Laplace transform and Stehfest NILT algorithm to deal with time fractional derivative term, which evades costly convolution integral calculation in time fractional derivation approximation and avoids the effect of time step on numerical accuracy and stability. Consequently, it can effectively simulate long time-history fractional diffusion systems. Error analysis and numerical experiments demonstrate that the present LTBPM is highly accurate and computationally efficient for 2D and 3D time fractional diffusion equations.

Disturbance functions of the Goertler instability on an airfoil

NASA Technical Reports Server (NTRS)

Dagenhart, J. R.; Mangalam, S. M.

1986-01-01

Goertler vortices arise in boundary layers along concave surfaces due to centrifugal effects. This paper presents some results of an experiment conducted to study the development of these vortices on an airfoil with a pressure gradient in the concave region where an attached laminar boundary layer was insured with suction through a perforated panel. A sublimating chemical technique was used to visualize Goertler vortices and the velocity field was measured by laser velocimetry. Experimental disturbance functions are compared with those predicted by the linear stability theory. The trend of vortex amplification in the concave zone and damping in the following convex region is shown to essentially follow the theoretical predictions.

Convection in a colloidal suspension in a closed horizontal cell

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smorodin, B. L., E-mail: bsmorodin@yandex.ru; Cherepanov, I. N.

2015-02-15

The experimentally detected [1] oscillatory regimes of convection in a colloidal suspension of nanoparticles with a large anomalous thermal diffusivity in a closed horizontal cell heated from below have been simulated numerically. The concentration inhomogeneity near the vertical cavity boundaries arising from the interaction of thermal-diffusion separation and convective mixing has been proven to serve as a source of oscillatory regimes (traveling waves). The dependence of the Rayleigh number at the boundary of existence of the traveling-wave regime on the aspect ratio of the closed cavity has been established. The spatial characteristics of the emerging traveling waves have been determined.

Backflow and dissipation during the quantum decay of a metastable Fermi liquid

NASA Astrophysics Data System (ADS)

Iida, Kei

1999-02-01

The particle current in a metastable Fermi liquid against a first-order phase transition is calculated at zero temperature. During fluctuations of a droplet of the stable phase, in accordance with the conservation law, not only does an unperturbed current arise from the continuity at the boundary, but a backflow is induced by the density response. Quasiparticles carrying these currents are scattered by the boundary, yielding a dissipative backflow around the droplet. An energy of the hydrodynamic mass flow of the liquid and a friction force exerted on the droplet by the quasiparticles have been obtained in terms of a potential of their interaction with the droplet.

Topographic Change of the Dichotomy Boundary Suggested by Crustal Inversion

NASA Technical Reports Server (NTRS)

Neumann, G. A.

2004-01-01

Linear negative gravity anomalies in Acidalia Planitia along the eastern edge of Tempe Terra and along the northern edge of Arabia Terra have been noted in Mars Global Surveyor gravity fields. Once proposed to represent buried fluvial channels, it is now believed that these gravity troughs mainly arise from partial compensation of the hemispheric dichotomy topographic scarp. A recent inversion for crustal structure finds that mantle compensation of the scarp is offset from the present-day topographic expression of the dichotomy boundary. The offset suggests that erosion or other forms of mass wasting occurred after lithosphere thickened and no longer accomodated topographic change through viscous relaxation.

On the boundary treatment in spectral methods for hyperbolic systems

NASA Technical Reports Server (NTRS)

Canuto, C.; Quarteroni, A.

1986-01-01

Spectral methods were successfully applied to the simulation of slow transients in gas transportation networks. Implicit time advancing techniques are naturally suggested by the nature of the problem. The correct treatment of the boundary conditions are clarified in order to avoid any stability restriction originated by the boundaries. The Beam and Warming and the Lerat schemes are unconditionally linearly stable when used with a Chebyshev pseudospectral method. Engineering accuracy for a gas transportation problem is achieved at Courant numbers up to 100.

On the boundary treatment in spectral methods for hyperbolic systems

NASA Technical Reports Server (NTRS)

Canuto, Claudio; Quarteroni, Alfio

1987-01-01

Spectral methods were successfully applied to the simulation of slow transients in gas transportation networks. Implicit time advancing techniques are naturally suggested by the nature of the problem. The correct treatment of the boundary conditions is clarified in order to avoid any stability restriction originated by the boundaries. The Beam and Warming and the Lerat schemes are unconditionally linearly stable when used with a Chebyshev pseudospectral method. Engineering accuracy for a gas transportation problem is achieved at Courant numbers up to 100.

Low thrust propulsion system effects on communication satellites.

NASA Technical Reports Server (NTRS)

Hall, D. F.; Lyon, W. C.

1972-01-01

Choice of type and placement of thrusters on spacecraft (s/c) should include consideration of their effects on other subsystems. Models are presented of the exhaust plumes of mercury, cesium, colloid, hydrazine, ammonia, and Teflon rockets. Effects arising from plume impingement on s/c surfaces, radio frequency interference, optical interference, and earth environmental contamination are discussed. Some constraints arise in the placement of mercury, cesium, and Teflon thrusters. Few problems exist with other thruster types, nor is earth contamination a problem.

The use of Lanczos's method to solve the large generalized symmetric definite eigenvalue problem

NASA Technical Reports Server (NTRS)

Jones, Mark T.; Patrick, Merrell L.

1989-01-01

The generalized eigenvalue problem, Kx = Lambda Mx, is of significant practical importance, especially in structural enginering where it arises as the vibration and buckling problem. A new algorithm, LANZ, based on Lanczos's method is developed. LANZ uses a technique called dynamic shifting to improve the efficiency and reliability of the Lanczos algorithm. A new algorithm for solving the tridiagonal matrices that arise when using Lanczos's method is described. A modification of Parlett and Scott's selective orthogonalization algorithm is proposed. Results from an implementation of LANZ on a Convex C-220 show it to be superior to a subspace iteration code.

New Finite Difference Methods Based on IIM for Inextensible Interfaces in Incompressible Flows

PubMed Central

Li, Zhilin; Lai, Ming-Chih

2012-01-01

In this paper, new finite difference methods based on the augmented immersed interface method (IIM) are proposed for simulating an inextensible moving interface in an incompressible two-dimensional flow. The mathematical models arise from studying the deformation of red blood cells in mathematical biology. The governing equations are incompressible Stokes or Navier-Stokes equations with an unknown surface tension, which should be determined in such a way that the surface divergence of the velocity is zero along the interface. Thus, the area enclosed by the interface and the total length of the interface should be conserved during the evolution process. Because of the nonlinear and coupling nature of the problem, direct discretization by applying the immersed boundary or immersed interface method yields complex nonlinear systems to be solved. In our new methods, we treat the unknown surface tension as an augmented variable so that the augmented IIM can be applied. Since finding the unknown surface tension is essentially an inverse problem that is sensitive to perturbations, our regularization strategy is to introduce a controlled tangential force along the interface, which leads to a least squares problem. For Stokes equations, the forward solver at one time level involves solving three Poisson equations with an interface. For Navier-Stokes equations, we propose a modified projection method that can enforce the pressure jump condition corresponding directly to the unknown surface tension. Several numerical experiments show good agreement with other results in the literature and reveal some interesting phenomena. PMID:23795308

Subplane-based Control Rod Decusping Techniques for the 2D/1D Method in MPACT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Graham, Aaron M; Collins, Benjamin S; Downar, Thomas

2017-01-01

The MPACT transport code is being jointly developed by Oak Ridge National Laboratory and the University of Michigan to serve as the primary neutron transport code for the Virtual Environment for Reactor Applications Core Simulator. MPACT uses the 2D/1D method to solve the transport equation by decomposing the reactor model into a stack of 2D planes. A fine mesh flux distribution is calculated in each 2D plane using the Method of Characteristics (MOC), then the planes are coupled axially through a 1D NEM-Pmore » $$_3$$ calculation. This iterative calculation is then accelerated using the Coarse Mesh Finite Difference method. One problem that arises frequently when using the 2D/1D method is that of control rod cusping. This occurs when the tip of a control rod falls between the boundaries of an MOC plane, requiring that the rodded and unrodded regions be axially homogenized for the 2D MOC calculations. Performing a volume homogenization does not properly preserve the reaction rates, causing an error known as cusping. The most straightforward way of resolving this problem is by refining the axial mesh, but this can significantly increase the computational expense of the calculation. The other way of resolving the partially inserted rod is through the use of a decusping method. This paper presents new decusping methods implemented in MPACT that can dynamically correct the rod cusping behavior for a variety of problems.« less

Professional boundaries in the era of the Internet.

PubMed

Gabbard, Glen O; Kassaw, Kristin A; Perez-Garcia, Gonzalo

2011-01-01

The era of the Internet presents new dilemmas in educating psychiatrists about professional boundaries. The objective of this overview is to clarify those dilemmas and offer recommendations for dealing with them. The characteristics of social networking sites, blogs, and search engines are reviewed with a specific focus on their potential to present problems of professional boundaries for psychiatrists. The professional boundary questions that have arisen in the expanded world of online communication can be subdivided into three areas: ethical concerns, professionalism issues, and clinical dilemmas. Only the first category involves true boundary problems as normally defined. The expansion of the Internet has redefined traditional areas of privacy and anonymity in the clinical setting. Guidelines are proposed to manage the alteration of professional boundaries, as well as issues of professionalism and clinical work, that have arisen from the complexities of cyberspace. The author discusses implications for residency training.

Holographic entanglement entropies for Schwarzschild and Reisner-Nordström black holes in asymptotically Minkowski spacetimes

NASA Astrophysics Data System (ADS)

Sun, Yuan; Zhao, Liu

2017-04-01

Holographic entanglement entropies (HEE) associated with four-dimensional Schwarzschild and Reisner-Nordström (RN) black holes in asymptotically Minkowski spacetimes are investigated. Unlike the cases of asymptotically AdS spacetimes for which the boundaries are always taken at (timelike) conformal infinities, we take the boundaries at either large but finite radial coordinates (far boundary) or very close to the black hole event horizons (near horizon boundary). The reason for such choices is that such boundaries are similar to the conformal infinity of AdS spacetime in that they are all timelike, so that there may be some hope to define dual systems with ordinary time evolution on such boundaries. Our results indicate that, in the case of far boundaries, the leading-order contribution to HEEs comes from the background Minkowski spacetime; however, the next-to-leading-order contribution which arises from the presence of the black holes is always proportional to the black hole mass, which constitutes a version of the first law of HEE for asymptotically flat spacetimes, and the higher-order contributions are always negligibly small. In the case of near horizon boundaries, the leading-order contribution to HEE is always proportional to the area of the black hole event horizon, and the case of extremal RN black holes is distinguished from the cases of nonextremal black holes in that the minimal surface defining HEE is completely immersed inside the boundary up to the second order in the perturbative expansion.

Theoretical investigations of plasma processes in the ion bombardment thruster

NASA Technical Reports Server (NTRS)

Wilhelm, H. E.

1975-01-01

A physical model for a thruster discharge was developed, consisting of a spatially diverging plasma sustained electrically between a small ring cathode and a larger ring anode in a cylindrical chamber with an axial magnetic field. The associated boundary-value problem for the coupled partial differential equations with mixed boundary conditions, which describe the electric potential and the plasma velocity fields, was solved in closed form. By means of quantum-mechanical perturbation theory, a formula for the number S(E) of atoms sputtered on the average by an ion of energy E was derived from first principles. The boundary-value problem describing the diffusion of the sputtered atoms through the surrounding rarefied electron-ion plasma to the system surfaces of ion propulsion systems was formulated and treated analytically. It is shown that outer boundary-value problems of this type lead to a complex integral equation, which requires numerical resolution.

Evaluation of Far-Field Boundary Conditions for the Gust Response Problem

NASA Technical Reports Server (NTRS)

Scott, James R.; Kreider, Kevin L.; Heminger, John A.

2002-01-01

This paper presents a detailed situ dy of four far-field boundary conditions used in solving the single airfoil gust response problem. The boundary conditions, examined are the partial Sommerfeld radiation condition with only radial derivatives, the full Sommerfeld radiation condition with both radial and tangential derivatives, the Bayliss-Turkel condition of order one, and the Hagstrom-Hariharan condition of order one. The main objectives of the study were to determine which far-field boundary condition was most accurate, which condition was least sensitive to changes in grid. and which condition was best overall in terms of both accuracy and efficiency. Through a systematic study of the flat plate gust response problem, it was determined that the Hagstrom-Hariharan condition was most accurate, the Bayliss-Turkel condition was least sensitive to changes in grid, and Bayliss-Turkel was best in terms of both accuracy and efficiency.

Diffuse-interface polycrystal plasticity: expressing grain boundaries as geometrically necessary dislocations

NASA Astrophysics Data System (ADS)

Admal, Nikhil Chandra; Po, Giacomo; Marian, Jaime

2017-12-01

The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the system is modeled as a collection of boundary-value problems with matching boundary conditions. In this paper, we develop a diffuse-interface crystal plasticity model for polycrystalline materials that results in a single boundary-value problem with a single crystal as the reference configuration. Using a multiplicative decomposition of the deformation gradient into lattice and plastic parts, i.e. F( X,t)= F L( X,t) F P( X,t), an initial stress-free polycrystal is constructed by imposing F L to be a piecewise constant rotation field R 0( X), and F P= R 0( X)T, thereby having F( X,0)= I, and zero elastic strain. This model serves as a precursor to higher order crystal plasticity models with grain boundary energy and evolution.

Beyond the functional matrix hypothesis: a network null model of human skull growth for the formation of bone articulations

PubMed Central

Esteve-Altava, Borja; Rasskin-Gutman, Diego

2014-01-01

Craniofacial sutures and synchondroses form the boundaries among bones in the human skull, providing functional, developmental and evolutionary information. Bone articulations in the skull arise due to interactions between genetic regulatory mechanisms and epigenetic factors such as functional matrices (soft tissues and cranial cavities), which mediate bone growth. These matrices are largely acknowledged for their influence on shaping the bones of the skull; however, it is not fully understood to what extent functional matrices mediate the formation of bone articulations. Aiming to identify whether or not functional matrices are key developmental factors guiding the formation of bone articulations, we have built a network null model of the skull that simulates unconstrained bone growth. This null model predicts bone articulations that arise due to a process of bone growth that is uniform in rate, direction and timing. By comparing predicted articulations with the actual bone articulations of the human skull, we have identified which boundaries specifically need the presence of functional matrices for their formation. We show that functional matrices are necessary to connect facial bones, whereas an unconstrained bone growth is sufficient to connect non-facial bones. This finding challenges the role of the brain in the formation of boundaries between bones in the braincase without neglecting its effect on skull shape. Ultimately, our null model suggests where to look for modified developmental mechanisms promoting changes in bone growth patterns that could affect the development and evolution of the head skeleton. PMID:24975579

KANTBP: A program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach

NASA Astrophysics Data System (ADS)

Chuluunbaatar, O.; Gusev, A. A.; Abrashkevich, A. G.; Amaya-Tapia, A.; Kaschiev, M. S.; Larsen, S. Y.; Vinitsky, S. I.

2007-10-01

A FORTRAN 77 program is presented which calculates energy values, reaction matrix and corresponding radial wave functions in a coupled-channel approximation of the hyperspherical adiabatic approach. In this approach, a multi-dimensional Schrödinger equation is reduced to a system of the coupled second-order ordinary differential equations on the finite interval with homogeneous boundary conditions of the third type. The resulting system of radial equations which contains the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite-element method. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials. Program summaryProgram title: KANTBP Catalogue identifier: ADZH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4224 No. of bytes in distributed program, including test data, etc.: 31 232 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IV Operating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XP RAM: depends on (a) the number of differential equations; (b) the number and order of finite-elements; (c) the number of hyperradial points; and (d) the number of eigensolutions required. Test run requires 30 MB Classification: 2.1, 2.4 External routines: GAULEG and GAUSSJ [W.H. Press, B.F. Flanery, S.A. Teukolsky, W.T. Vetterley, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986] Nature of problem: In the hyperspherical adiabatic approach [J. Macek, J. Phys. B 1 (1968) 831-843; U. Fano, Rep. Progr. Phys. 46 (1983) 97-165; C.D. Lin, Adv. Atom. Mol. Phys. 22 (1986) 77-142], a multi-dimensional Schrödinger equation for a two-electron system [A.G. Abrashkevich, D.G. Abrashkevich, M. Shapiro, Comput. Phys. Comm. 90 (1995) 311-339] or a hydrogen atom in magnetic field [M.G. Dimova, M.S. Kaschiev, S.I. Vinitsky, J. Phys. B 38 (2005) 2337-2352] is reduced by separating the radial coordinate ρ from the angular variables to a system of second-order ordinary differential equations which contain potential matrix elements and first-derivative coupling terms. The purpose of this paper is to present the finite-element method procedure based on the use of high-order accuracy approximations for calculating approximate eigensolutions for such systems of coupled differential equations. Solution method: The boundary problems for coupled differential equations are solved by the finite-element method using high-order accuracy approximations [A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Comm. 85 (1995) 40-64]. The generalized algebraic eigenvalue problem AF=EBF with respect to pair unknowns ( E,F) arising after the replacement of the differential problem by the finite-element approximation is solved by the subspace iteration method using the SSPACE program [K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982]. The generalized algebraic eigenvalue problem (A-EB)F=λDF with respect to pair unknowns (λ,F) arising after the corresponding replacement of the scattering boundary problem in open channels at fixed energy value, E, is solved by the LDL factorization of symmetric matrix and back-substitution methods using the DECOMP and REDBAK programs, respectively [K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982]. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials described in [Yu. A. Kuperin, P.B. Kurasov, Yu.B. Melnikov, S.P. Merkuriev, Ann. Phys. 205 (1991) 330-361; O. Chuluunbaatar, A.A. Gusev, S.Y. Larsen, S.I. Vinitsky, J. Phys. A 35 (2002) L513-L525; N.P. Mehta, J.R. Shepard, Phys. Rev. A 72 (2005) 032728-1-11; O. Chuluunbaatar, A.A. Gusev, M.S. Kaschiev, V.A. Kaschieva, A. Amaya-Tapia, S.Y. Larsen, S.I. Vinitsky, J. Phys. B 39 (2006) 243-269]. For this benchmark model the needed analytical expressions for the potential matrix elements and first-derivative coupling terms, their asymptotics and asymptotics of radial solutions of the boundary problems for coupled differential equations have been produced with help of a MAPLE computer algebra system. Restrictions: The computer memory requirements depend on: (a) the number of differential equations; (b) the number and order of finite-elements; (c) the total number of hyperradial points; and (d) the number of eigensolutions required. Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see Long Write-Up and listing for details). The user must also supply subroutine POTCAL for evaluating potential matrix elements. The user should supply subroutines ASYMEV (when solving the eigenvalue problem) or ASYMSC (when solving the scattering problem) that evaluate the asymptotics of the radial wave functions at the right boundary point in case of a boundary condition of the third type, respectively. Running time: The running time depends critically upon: (a) the number of differential equations; (b) the number and order of finite-elements; (c) the total number of hyperradial points on interval [0,ρ]; and (d) the number of eigensolutions required. The test run which accompanies this paper took 28.48 s without calculation of matrix potentials on the Intel Pentium IV 2.4 GHz.

Reactive transport in a partially molten system with binary solid solution

NASA Astrophysics Data System (ADS)

Jordan, J.; Hesse, M. A.

2017-12-01

Melt extraction from the Earth's mantle through high-porosity channels is required to explain the composition of the oceanic crust. Feedbacks from reactive melt transport are thought to localize melt into a network of high-porosity channels. Recent studies invoke lithological heterogeneities in the Earth's mantle to seed the localization of partial melts. Therefore, it is necessary to understand the reaction fronts that form as melt flows across the lithological interface of a heterogeneity and the background mantle. Simplified melting models of such systems aide in the interpretation and formulation of larger scale mantle models. Motivated by the aforementioned facts, we present a chromatographic analysis of reactive melt transport across lithological boundaries, using theory for hyperbolic conservation laws. This is an extension of well-known linear trace element chromatography to the coupling of major elements and energy transport. Our analysis allows the prediction of the feedbacks that arise in reactive melt transport due to melting, freezing, dissolution and precipitation for frontal reactions. This study considers the simplified case of a rigid, partially molten porous medium with binary solid solution. As melt traverses a lithological contact-modeled as a Riemann problem-a rich set of features arise, including a reacted zone between an advancing reaction front and partial chemical preservation of the initial contact. Reactive instabilities observed in this study originate at the lithological interface rather than along a chemical gradient as in most studies of mantle dynamics. We present a regime diagram that predicts where reaction fronts become unstable, thereby allowing melt localization into high-porosity channels through reactive instabilities. After constructing the regime diagram, we test the one-dimensional hyperbolic theory against two-dimensional numerical experiments. The one-dimensional hyperbolic theory is sufficient for predicting the qualitative behavior of reactive melt transport simulations conducted in two-dimensions. The theoretical framework presented can be extended to more complex and realistic phase behavior, and is therefore a useful tool for understanding nonlinear feedbacks in reactive melt transport problems relevant to mantle dynamics.

Two Legendre-Dual-Petrov-Galerkin Algorithms for Solving the Integrated Forms of High Odd-Order Boundary Value Problems

PubMed Central

Abd-Elhameed, Waleed M.; Doha, Eid H.; Bassuony, Mahmoud A.

2014-01-01

Two numerical algorithms based on dual-Petrov-Galerkin method are developed for solving the integrated forms of high odd-order boundary value problems (BVPs) governed by homogeneous and nonhomogeneous boundary conditions. Two different choices of trial functions and test functions which satisfy the underlying boundary conditions of the differential equations and the dual boundary conditions are used for this purpose. These choices lead to linear systems with specially structured matrices that can be efficiently inverted, hence greatly reducing the cost. The various matrix systems resulting from these discretizations are carefully investigated, especially their complexities and their condition numbers. Numerical results are given to illustrate the efficiency of the proposed algorithms, and some comparisons with some other methods are made. PMID:24616620

Analysis of random structure-acoustic interaction problems using coupled boundary element and finite element methods

NASA Technical Reports Server (NTRS)

Mei, Chuh; Pates, Carl S., III

1994-01-01

A coupled boundary element (BEM)-finite element (FEM) approach is presented to accurately model structure-acoustic interaction systems. The boundary element method is first applied to interior, two and three-dimensional acoustic domains with complex geometry configurations. Boundary element results are very accurate when compared with limited exact solutions. Structure-interaction problems are then analyzed with the coupled FEM-BEM method, where the finite element method models the structure and the boundary element method models the interior acoustic domain. The coupled analysis is compared with exact and experimental results for a simplistic model. Composite panels are analyzed and compared with isotropic results. The coupled method is then extended for random excitation. Random excitation results are compared with uncoupled results for isotropic and composite panels.

Eigenmode computation of cavities with perturbed geometry using matrix perturbation methods applied on generalized eigenvalue problems

NASA Astrophysics Data System (ADS)

Gorgizadeh, Shahnam; Flisgen, Thomas; van Rienen, Ursula

2018-07-01

Generalized eigenvalue problems are standard problems in computational sciences. They may arise in electromagnetic fields from the discretization of the Helmholtz equation by for example the finite element method (FEM). Geometrical perturbations of the structure under concern lead to a new generalized eigenvalue problems with different system matrices. Geometrical perturbations may arise by manufacturing tolerances, harsh operating conditions or during shape optimization. Directly solving the eigenvalue problem for each perturbation is computationally costly. The perturbed eigenpairs can be approximated using eigenpair derivatives. Two common approaches for the calculation of eigenpair derivatives, namely modal superposition method and direct algebraic methods, are discussed in this paper. Based on the direct algebraic methods an iterative algorithm is developed for efficiently calculating the eigenvalues and eigenvectors of the perturbed geometry from the eigenvalues and eigenvectors of the unperturbed geometry.

On steady motion of viscoelastic fluid of Oldroyd type

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baranovskii, E. S., E-mail: esbaranovskii@gmail.com

2014-06-01

We consider a mathematical model describing the steady motion of a viscoelastic medium of Oldroyd type under the Navier slip condition at the boundary. In the rheological relation, we use the objective regularized Jaumann derivative. We prove the solubility of the corresponding boundary-value problem in the weak setting. We obtain an estimate for the norm of a solution in terms of the data of the problem. We show that the solution set is sequentially weakly closed. Furthermore, we give an analytic solution of the boundary-value problem describing the flow of a viscoelastic fluid in a flat channel under a slipmore » condition at the walls. Bibliography: 13 titles. (paper)« less

A Novel Numerical Method for Fuzzy Boundary Value Problems

NASA Astrophysics Data System (ADS)

Can, E.; Bayrak, M. A.; Hicdurmaz

2016-05-01

In the present paper, a new numerical method is proposed for solving fuzzy differential equations which are utilized for the modeling problems in science and engineering. Fuzzy approach is selected due to its important applications on processing uncertainty or subjective information for mathematical models of physical problems. A second-order fuzzy linear boundary value problem is considered in particular due to its important applications in physics. Moreover, numerical experiments are presented to show the effectiveness of the proposed numerical method on specific physical problems such as heat conduction in an infinite plate and a fin.

Solving the Problem of Linear Viscoelasticity for Piecewise-Homogeneous Anisotropic Plates

NASA Astrophysics Data System (ADS)

Kaloerov, S. A.; Koshkin, A. A.

2017-11-01

An approximate method for solving the problem of linear viscoelasticity for thin anisotropic plates subject to transverse bending is proposed. The method of small parameter is used to reduce the problem to a sequence of boundary problems of applied theory of bending of plates solved using complex potentials. The general form of complex potentials in approximations and the boundary conditions for determining them are obtained. Problems for a plate with elliptic elastic inclusions are solved as an example. The numerical results for a plate with one, two elliptical (circular), and linear inclusions are analyzed.

Asymptotic traveling wave solution for a credit rating migration problem

NASA Astrophysics Data System (ADS)

Liang, Jin; Wu, Yuan; Hu, Bei

2016-07-01

In this paper, an asymptotic traveling wave solution of a free boundary model for pricing a corporate bond with credit rating migration risk is studied. This is the first study to associate the asymptotic traveling wave solution to the credit rating migration problem. The pricing problem with credit rating migration risk is modeled by a free boundary problem. The existence, uniqueness and regularity of the solution are obtained. Under some condition, we proved that the solution of our credit rating problem is convergent to a traveling wave solution, which has an explicit form. Furthermore, numerical examples are presented.

A walkthrough solution to the boundary overlap problem

Treesearch

Mark J. Ducey; Jeffrey H. Gove; Harry T. Valentine

2004-01-01

Existing methods for eliminating bias due to boundary overlap suffer some disadvantages in practical use, including the need to work outside the tract, restrictions on the kinds of boundaries to which they are applicable, and the possibility of significantly increased variance as a price for unbiasedness. We propose a new walkthrough method for reducing boundary...

The Riemann-Hilbert problem for nonsymmetric systems

NASA Astrophysics Data System (ADS)

Greenberg, W.; Zweifel, P. F.; Paveri-Fontana, S.

1991-12-01

A comparison of the Riemann-Hilbert problem and the Wiener-Hopf factorization problem arising in the solution of half-space singular integral equations is presented. Emphasis is on the factorization of functions lacking the reflection symmetry usual in transport theory.

Some observations on boundary conditions for numerical conservation laws

NASA Technical Reports Server (NTRS)

Kamowitz, David

1988-01-01

Four choices of outflow boundary conditions are considered for numerical conservation laws. All four methods are stable for linear problems, for which examples are presented where either a boundary layer forms or the numerical scheme, together with the boundary condition, is unstable due to the formation of a reflected shock. A simple heuristic argument is presented for determining the suitability of the boundary condition.