Nonlinear second-order multivalued boundary value problems

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

Department of Mathematics, National Technical University, Zografou Campus,. Athens 15780 ... incorporates gradient systems, evolutionary variational inequalities and the classical boundary value ... We are led to an eventual application.

Positive solutions of nonlinear fractional boundary value problems with Dirichlet boundary conditions

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Qingkai Kong

2012-02-01

Full Text Available In this paper, we study the existence and multiplicity of positive solutions of a class of nonlinear fractional boundary value problems with  Dirichlet boundary conditions. By applying the fixed point theory on cones we establish a series of criteria for the existence of one, two, any arbitrary finite number, and an infinite number of positive solutions. A criterion for the nonexistence of positive solutions is also derived. Several examples are given for demonstration.

Boundary value problems and dichotomic stability

NARCIS (Netherlands)

England, R.; Mattheij, R.M.M.

1988-01-01

Since the conditioning of a boundary value problem (BVP) is closely related to the existence of a dichotomic fundamental solution (i.e., where one set of modes is increasing and a complementary set is decreasing), it is important to have discretization methods that conserve this dichotomy property.

Analytic Solution to Shell Boundary – Value Problems

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Yu. I. Vinogradov

2015-01-01

Full Text Available Object of research is to find analytical solution to the shell boundary – value problems, i.e. to consider the solution for a class of problems concerning the mechanics of hoop closed shells strain.The objective of work is to create an analytical method to define a stress – strain state of shells under non-axisymmetric loading. Thus, a main goal is to derive the formulas – solutions of the linear ordinary differential equations with variable continuous coefficients.The partial derivative differential equations of mechanics of shells strain by Fourier's method of variables division are reduced to the system of the differential equations with ordinary derivatives. The paper presents the obtained formulas to define solutions of the uniform differential equations and received on their basis formulas to define a particular solution depending on a type of the right parts of the differential equations.The analytical algorithm of the solution of a boundary task uses an approach to transfer the boundary conditions to the randomly chosen point of an interval of changing independent variable through the solution of the canonical matrix ordinary differential equation with the subsequent solution of system of algebraic equations for compatibility of boundary conditions at this point. Efficiency of algorithm is based on the fact that the solution of the ordinary differential equations is defined as the values of Cauchy – Krylova functions, which meet initial arbitrary conditions.The results of researches presented in work are useful to experts in the field of calculus mathematics, dealing with solution of systems of linear ordinary differential equations and creation of effective analytical computing methods to solve shell boundary – value problems.

Nonlinear Elliptic Boundary Value Problems at Resonance with Nonlinear Wentzell Boundary Conditions

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Ciprian G. Gal

2017-01-01

Full Text Available Given a bounded domain Ω⊂RN with a Lipschitz boundary ∂Ω and p,q∈(1,+∞, we consider the quasilinear elliptic equation -Δpu+α1u=f in Ω complemented with the generalized Wentzell-Robin type boundary conditions of the form bx∇up-2∂nu-ρbxΔq,Γu+α2u=g on ∂Ω. In the first part of the article, we give necessary and sufficient conditions in terms of the given functions f, g and the nonlinearities α1, α2, for the solvability of the above nonlinear elliptic boundary value problems with the nonlinear boundary conditions. In other words, we establish a sort of “nonlinear Fredholm alternative” for our problem which extends the corresponding Landesman and Lazer result for elliptic problems with linear homogeneous boundary conditions. In the second part, we give some additional results on existence and uniqueness and we study the regularity of the weak solutions for these classes of nonlinear problems. More precisely, we show some global a priori estimates for these weak solutions in an L∞-setting.

State space approach to mixed boundary value problems.

Science.gov (United States)

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.

Existence of solutions to boundary value problem of fractional differential equations with impulsive

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Weihua JIANG

2016-12-01

Full Text Available In order to solve the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line, the existence of solutions to the boundary problem is specifically studied. By defining suitable Banach spaces, norms and operators, using the properties of fractional calculus and applying the contraction mapping principle and Krasnoselskii's fixed point theorem, the existence of solutions for the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line is proved, and examples are given to illustrate the existence of solutions to this kind of equation boundary value problems.

Group invariance in engineering boundary value problems

CERN Document Server

Seshadri, R

1985-01-01

REFEREN CES . 156 9 Transforma.tion of a Boundary Value Problem to an Initial Value Problem . 157 9.0 Introduction . 157 9.1 Blasius Equation in Boundary Layer Flow . 157 9.2 Longitudinal Impact of Nonlinear Viscoplastic Rods . 163 9.3 Summary . 168 REFERENCES . . . . . . . . . . . . . . . . . . 168 . 10 From Nonlinear to Linear Differential Equa.tions Using Transformation Groups. . . . . . . . . . . . . . 169 . 10.1 From Nonlinear to Linear Differential Equations . 170 10.2 Application to Ordinary Differential Equations -Bernoulli's Equation . . . . . . . . . . . 173 10.3 Application to Partial Differential Equations -A Nonlinear Chemical Exchange Process . 178 10.4 Limitations of the Inspectional Group Method . 187 10.5 Summary . 188 REFERENCES . . . . 188 11 Miscellaneous Topics . 190 11.1 Reduction of Differential Equations to Algebraic Equations 190 11.2 Reduction of Order of an Ordinary Differential Equation . 191 11.3 Transformat.ion From Ordinary to Partial Differential Equations-Search for First Inte...

Superplasticity and grain boundary character distribution in overaged Al-Li-Cu-Mg-Zr alloy

International Nuclear Information System (INIS)

Avramovic-Cingara, G.; Aust, K.T.; Perovic, D.D.; McQueen, H.J.

1995-01-01

Samples of 8091 alloy were subjected to a thermomechanical processing (TMP) treatment that included the following stages: overaging before deformation, multistage deformation at 300 deg C and strain rate change tests for superplasticity. Torsional deformation was utilized both to develop the refined microstructure and to test for superplasticity. The strain rate sensitivity, m, of the material ranged between 0.30 and 0.45 at 450 deg C for strain rates between 8 x 10 -2 and 10 -3 s -1 . The grain boundary character distribution (GBCD) of thermomechanically processed Al-Li-Cu-Mg-Zr (8091) alloy, which develops good superplastic response, has been determined by an electron backscattering diffraction technique (EBSD). All grain boundaries have been classified into one of three categories in terms of Σ values : low angle, coincidence site lattice and random high angle boundaries. Quantitative studies of grain boundary character were done after various processing stages to obtain evidence about structure evolution and indicate an increase in Σ boundary frequency following TMP. Selected area electron diffraction examination (SAD) gave evidence about the refined structure, in which the grain boundary misorientation increased EBSD how the grain boundary character was changed to high Σ values. TEM analyses indicate that the T 2 phase is responsible for substructure stabilization. There is no evidence of cavity formation during superplastic deformation by torsion, which suggests that cavity nucleation is strongly influenced by the nature of stress. (author). 32 refs., 3 tabs., 9 figs

Distributions of electric and elastic fields at domain boundaries

International Nuclear Information System (INIS)

Novak, Josef; Fousek, Jan; Maryska, Jiri; Marvan, Milan

2005-01-01

In this paper we describe the application of the finite element method (FEM) in modelling spatial distributions of electric and elastic fields in a ferroelectric crystals with two domains separated by a 90 deg. domain wall. The domain boundary is idealized as a two-dimensional defect in an electro-elastic continuum. It represents the source of inhomogenity and internal distortion in both elastic and electric fields. The main results are distributions of electric field, strain and mechanical force along the domain boundary

Positive solutions for a nonlocal boundary-value problem with vector-valued response

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Andrzej Nowakowski

2002-05-01

Full Text Available Using variational methods, we study the existence of positive solutions for a nonlocal boundary-value problem with vector-valued response. We develop duality and variational principles for this problem and present a numerical version which enables the approximation of solutions and gives a measure of a duality gap between primal and dual functional for approximate solutions for this problem.

Boundary feedback stabilization of distributed parameter systems

DEFF Research Database (Denmark)

Pedersen, Michael

1988-01-01

The author introduces the method of pseudo-differential stabilization. He notes that the theory of pseudo-differential boundary operators is a fruitful approach to problems arising in control and stabilization theory of distributed-parameter systems. The basic pseudo-differential calculus can...

Homology in Electromagnetic Boundary Value Problems

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Pellikka Matti

2010-01-01

Full Text Available We discuss how homology computation can be exploited in computational electromagnetism. We represent various cellular mesh reduction techniques, which enable the computation of generators of homology spaces in an acceptable time. Furthermore, we show how the generators can be used for setting up and analysis of an electromagnetic boundary value problem. The aim is to provide a rationale for homology computation in electromagnetic modeling software.

Modified Differential Transform Method for Two Singular Boundary Values Problems

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Yinwei Lin

2014-01-01

Full Text Available This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.

Existence results for anisotropic discrete boundary value problems

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Avci Avci

2016-06-01

Full Text Available In this article, we prove the existence of nontrivial weak solutions for a class of discrete boundary value problems. The main tools used here are the variational principle and critical point theory.

Vragov’s boundary value problem for an implicit equation of mixed type

Science.gov (United States)

Egorov, I. E.

2017-10-01

We study a Vragov boundary value problem for a third-order implicit equation of mixed type with an arbitrary manifold of type switch. These Sobolev-type equations arise in many important applied problems. Given certain constraints on the coefficients and the right-hand side of the equation, we demonstrate, using nonstationary Galerkin method and regularization method, the unique regular solvability of the boundary value problem. We also obtain an error estimate for approximate solutions of the boundary value problem in terms of the regularization parameter and the eigenvalues of the Dirichlet spectral problem for the Laplace operator.

Application of Monte Carlo method to solving boundary value problem of differential equations

International Nuclear Information System (INIS)

Zuo Yinghong; Wang Jianguo

2012-01-01

This paper introduces the foundation of the Monte Carlo method and the way how to generate the random numbers. Based on the basic thought of the Monte Carlo method and finite differential method, the stochastic model for solving the boundary value problem of differential equations is built. To investigate the application of the Monte Carlo method to solving the boundary value problem of differential equations, the model is used to solve Laplace's equations with the first boundary condition and the unsteady heat transfer equation with initial values and boundary conditions. The results show that the boundary value problem of differential equations can be effectively solved with the Monte Carlo method, and the differential equations with initial condition can also be calculated by using a stochastic probability model which is based on the time-domain finite differential equations. Both the simulation results and theoretical analyses show that the errors of numerical results are lowered as the number of simulation particles is increased. (authors)

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

Science.gov (United States)

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.

Fourth-order discrete anisotropic boundary-value problems

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Maciej Leszczynski

2015-09-01

Full Text Available In this article we consider the fourth-order discrete anisotropic boundary value problem with both advance and retardation. We apply the direct method of the calculus of variations and the mountain pass technique to prove the existence of at least one and at least two solutions. Non-existence of non-trivial solutions is also undertaken.

A Boundary Value Problem for Introductory Physics?

Science.gov (United States)

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…

Effect of Grain Boundary Character Distribution on the Impact Toughness of 410NiMo Weld Metal

DEFF Research Database (Denmark)

Divya, M.; Das, Chitta Ranjan; Chowdhury, Sandip Ghosh

2016-01-01

Grain boundary character distributions in 410NiMo weld metal were studied in the as-welded, first-stage, and second-stage postweld heat treatment (PWHT) conditions, and these were correlated with the Charpy-V impact toughness values of the material. The high impact toughness values in the weld...... metal in the as-welded and first-stage PWHT conditions compared to that in the second-stage condition are attributed to the higher fraction of low-energy I pound boundaries. A higher volume fraction of retained austenite and coarser martensite after second-stage PWHT accompanied by the formation...... in the impact toughness. In addition to this, grain refinement during 4-hour PWHT in the second stage also increased the toughness of the weld metal....

Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals

KAUST Repository

Dujardin, G. M.

2009-01-01

This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate

A combined analytic-numeric approach for some boundary-value problems

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Mustafa Turkyilmazoglu

2016-02-01

Full Text Available A combined analytic-numeric approach is undertaken in the present work for the solution of boundary-value problems in the finite or semi-infinite domains. Equations to be treated arise specifically from the boundary layer analysis of some two and three-dimensional flows in fluid mechanics. The purpose is to find quick but accurate enough solutions. Taylor expansions at either boundary conditions are computed which are next matched to the other asymptotic or exact boundary conditions. The technique is applied to the well-known Blasius as well as Karman flows. Solutions obtained in terms of series compare favorably with the existing ones in the literature.

Bifurcation of solutions to Hamiltonian boundary value problems

Science.gov (United States)

McLachlan, R. I.; Offen, C.

2018-06-01

A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of equilibria, bifurcations of boundary value problems are global in nature and may not be related to any obvious change in dynamical behaviour. Catastrophe theory is a well-developed framework which studies the bifurcations of critical points of functions. In this paper we study the bifurcations of solutions of boundary-value problems for symplectic maps, using the language of (finite-dimensional) singularity theory. We associate certain such problems with a geometric picture involving the intersection of Lagrangian submanifolds, and hence with the critical points of a suitable generating function. Within this framework, we then study the effect of three special cases: (i) some common boundary conditions, such as Dirichlet boundary conditions for second-order systems, restrict the possible types of bifurcations (for example, in generic planar systems only the A-series beginning with folds and cusps can occur); (ii) integrable systems, such as planar Hamiltonian systems, can exhibit a novel periodic pitchfork bifurcation; and (iii) systems with Hamiltonian symmetries or reversing symmetries can exhibit restricted bifurcations associated with the symmetry. This approach offers an alternative to the analysis of critical points in function spaces, typically used in the study of bifurcation of variational problems, and opens the way to the detection of more exotic bifurcations than the simple folds and cusps that are often found in examples.

Analytic approximations to nonlinear boundary value problems modeling beam-type nano-electromechanical systems

Energy Technology Data Exchange (ETDEWEB)

Zou, Li [Dalian Univ. of Technology, Dalian City (China). State Key Lab. of Structural Analysis for Industrial Equipment; Liang, Songxin; Li, Yawei [Dalian Univ. of Technology, Dalian City (China). School of Mathematical Sciences; Jeffrey, David J. [Univ. of Western Ontario, London (Canada). Dept. of Applied Mathematics

2017-06-01

Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.

Separable boundary-value problems in physics

CERN Document Server

Willatzen, Morten

2011-01-01

Innovative developments in science and technology require a thorough knowledge of applied mathematics, particularly in the field of differential equations and special functions. These are relevant in modeling and computing applications of electromagnetic theory and quantum theory, e.g. in photonics and nanotechnology. The problem of solving partial differential equations remains an important topic that is taught at both the undergraduate and graduate level. Separable Boundary-Value Problems in Physics is an accessible and comprehensive treatment of partial differential equations i

Sample path analysis and distributions of boundary crossing times

CERN Document Server

Zacks, Shelemyahu

2017-01-01

This monograph is focused on the derivations of exact distributions of first boundary crossing times of Poisson processes, compound Poisson processes, and more general renewal processes.  The content is limited to the distributions of first boundary crossing times and their applications to various stochastic models. This book provides the theory and techniques for exact computations of distributions and moments of level crossing times. In addition, these techniques could replace simulations in many cases, thus providing more insight about the phenomenona studied. This book takes a general approach for studying telegraph processes and is based on nearly thirty published papers by the author and collaborators over the past twenty five years.  No prior knowledge of advanced probability is required, making the book widely available to students and researchers in applied probability, operations research, applied physics, and applied mathematics. .

Positive Solutions of Two-Point Boundary Value Problems for Monge-Ampère Equations

Directory of Open Access Journals (Sweden)

Baoqiang Yan

2015-01-01

Full Text Available This paper considers the following boundary value problem: ((-u'(tn'=ntn-1f(u(t,  01 is odd. We establish the method of lower and upper solutions for some boundary value problems which generalizes the above equations and using this method we present a necessary and sufficient condition for the existence of positive solutions to the above boundary value problem and some sufficient conditions for the existence of positive solutions.

Electromagnetic wave theory for boundary-value problems an advanced course on analytical methods

CERN Document Server

Eom, Hyo J

2004-01-01

Electromagnetic wave theory is based on Maxwell's equations, and electromagnetic boundary-value problems must be solved to understand electromagnetic scattering, propagation, and radiation. Electromagnetic theory finds practical applications in wireless telecommunications and microwave engineering. This book is written as a text for a two-semester graduate course on electromagnetic wave theory. As such, Electromagnetic Wave Theory for Boundary-Value Problems is intended to help students enhance analytic skills by solving pertinent boundary-value problems. In particular, the techniques of Fourier transform, mode matching, and residue calculus are utilized to solve some canonical scattering and radiation problems.

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

Science.gov (United States)

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.

Quasisolutions of Inverse Boundary-Value Problem of Aerodynamics for Dense Airfoil Grids

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A.M. Elizarov

2016-12-01

Full Text Available In the process of turbomachinery development, it is of great importance to accurately design impellers and select their blade shape. One of the promising approaches to solving this problem is based on the theory of inverse boundary-value problems in aerodynamics. It helps to develop methods for profiling airfoil grids with predetermined properties in the same way as it is done for isolated airfoils. In this paper, methods have been worked out to find quasisolutions of the inverse boundary-value problem in aerodynamics for a plane airfoil grid. Two methods of quasisolution have been described. The first “`formal” method is similar, in its essence, to the method used for construction of quasisolution for an isolated airfoil. It has been shown that such quasisolutions provide satisfactory results for grids having a sufficiently large relative airfoil pitch. If pitch values are low, this method is unacceptable, because “modified” velocity distribution in some areas is significantly different from the original one in this case. For this reason, areas with significant changes in the angle of the tangent line appear in the airfoil contour and the flow region becomes multivalent. To satisfy the conditions of solvability in the case of grids having a small airfoil pitch, a new quasisolution construction method taking into account the specifics of the problem has been suggested. The desired effect has been achieved due to changes in the weighting function of the minimized functional. The comparison of the results of construction of the new quasisolution with the results obtained by the “formal” method has demonstrated that the constructed airfoils are very similar when the pitch is large. In the case of dense grids, it is clear that preference should be given to the second method, as it brings less distortion to the initial velocity distribution and, thus, allows to physically find an actual airfoil contour.

The boundary value problems of magnetotail equilibrium

International Nuclear Information System (INIS)

Birn, J.

1991-01-01

The equilibrium problem for the Earth's magnetotail is discussed under the assumption that the boundary of the tail can be prescribed or derived from the force balance with the solar wind. A general solution of this problem is presented for the two-dimensional case, where the dependence on the γ coordinate and the presence of Β gamma are neglected. These solutions are further generalized to include the γ dependence (but no Β gamma ) and an open magnetopause. In this formulation, a solution can be obtained by integration when the magnetopause boundary α(x,y), the total pressure function p(x), and the magnetic flux distribution A b (x,y) at the magnetopause are prescribed. Certain restrictions, however, may limit the free choice of these functions to yield physically reasonable, real solutions. When the interaction with the solar wind is included, the boundary location can no longer be chosen freely but follows from the force balance of the magnetotail with the solar wind. For a simplified description of this force balance a differential equation for the boundary location is derived, which generalizes an earlier result by Coroniti and Kennel (1972). It is shown that solutions of this differential equation are bounded by a maximum tail width if the plasma sheet thickness is limited. Several explicit solutions are presented, illustrating cases with and without tail flaring in the z direction, and including the restrictions of the force balance with the solar wind and of the conservation laws of adiabatic convection in a steady configuration

m-POINT BOUNDARY VALUE PROBLEM FOR SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATION AT RESONANCE

Institute of Scientific and Technical Information of China (English)

无

2012-01-01

In his paper,we obtain a general theorem concerning the existence of solutions to an m-point boundary value problem for the second-order differential equation with impulses.Moreover,the result can also be applied to study the usual m-point boundary value problem at resonance without impulses.

Numerical solution of fuzzy boundary value problems using Galerkin ...

Indian Academy of Sciences (India)

1 College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China. 2 Department of ... exact solution of fuzzy first-order boundary value problems. (BVPs). ...... edge partial financial support by the Ministerio de Economıa.

Grain-size distributions and grain boundaries of chalcopyrite-type thin films

International Nuclear Information System (INIS)

Abou-Ras, D.; Schorr, S.; Schock, H.W.

2007-01-01

CuInSe 2 , CuGaSe 2 , Cu(In,Ga)Se 2 and CuInS 2 thin-film solar absorbers in completed solar cells were studied in cross section by means of electronbackscatter diffraction. From the data acquired, grain-size distributions were extracted, and also the most frequent grain boundaries were determined. The grain-size distributions of all chalcopyrite-type thin films studied can be described well by lognormal distribution functions. The most frequent grainboundary types in these thin films are 60 - left angle 221 right angle tet and 71 - left angle 110 right angle tet (near) Σ3 twin boundaries. These results can be related directly to the importance of {112} tet planes during the topotactical growth of chalcopyrite-type thin films. Based on energetic considerations, it is assumed that the most frequent twin boundaries exhibit a 180 - left angle 221 right angle tet constellation. (orig.)

Spectral distribution of scalar particles created by a moving boundary with Robin boundary condition

International Nuclear Information System (INIS)

Mintz, B.; Farina, C; Maia Neto, P.A.; Rodrigues, R.B.

2006-01-01

We consider a massless scalar field in 1+1 dimensions satisfying a Robin boundary condition (BC) at a non-relativistic boundary. By deriving a Bogoliubov transformation between the input and output bosonic field operators, we calculate the spectral distribution of created particles. The particular cases of Dirichlet and Neumann BC may be obtained from our result as limiting cases, yielding equal spectra (this result is valid only in this space-time dimensionality). The creation effect for the field under Dirichlet BC turns out to be an upper bound for the spectra derived for Robin BC. Also, we show that the particle creation phenomenon with Robin conditions can be considerably reduced (with respect to the Dirichlet or Neumann cases) by selecting a particular mechanical oscillation frequency of the moving boundary. (author)

Application of He's variational iteration method to the fifth-order boundary value problems

International Nuclear Information System (INIS)

Shen, S

2008-01-01

Variational iteration method is introduced to solve the fifth-order boundary value problems. This method provides an efficient approach to solve this type of problems without discretization and the computation of the Adomian polynomials. Numerical results demonstrate that this method is a promising and powerful tool for solving the fifth-order boundary value problems

Recursive recovery of Markov transition probabilities from boundary value data

Energy Technology Data Exchange (ETDEWEB)

Patch, Sarah Kathyrn [Univ. of California, Berkeley, CA (United States)

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 requires 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.

Computation of Charged-Particle Transfer Maps for General Fields and Geometries Using Electromagnetic Boundary-Value Data

OpenAIRE

Dragt, A. J.; Roberts, P.; Stasevich, T. J.; Dragt, A. Bodoh-Creed A. J.; Roberts, P.; Stasevich, T. J.; Bodoh-Creed, A.; Walstrom, P. L.

2010-01-01

Three-dimensional field distributions from realistic beamline elements can be obtained only by measurement or by numerical solution of a boundary-value problem. In numerical charged-particle map generation, fields along a reference trajectory are differentiated multiple times. Any attempt to differentiate directly such field data multiple times is soon dominated by "noise" due to finite meshing and/or measurement errors. This problem can be overcome by the use of field data on a surface outsi...

Fiber optic distributed temperature sensing for the determination of the nocturnal atmospheric boundary layer height

Directory of Open Access Journals (Sweden)

C. A. Keller

2011-02-01

Full Text Available A new method for measuring air temperature profiles in the atmospheric boundary layer at high spatial and temporal resolution is presented. The measurements are based on Raman scattering distributed temperature sensing (DTS with a fiber optic cable attached to a tethered balloon. These data were used to estimate the height of the stable nocturnal boundary layer. The experiment was successfully deployed during a two-day campaign in September 2009, providing evidence that DTS is well suited for this atmospheric application. Observed stable temperature profiles exhibit an exponential shape confirming similarity concepts of the temperature inversion close to the surface. The atmospheric mixing height (MH was estimated to vary between 5 m and 50 m as a result of the nocturnal boundary layer evolution. This value is in good agreement with the MH derived from concurrent Radon-222 (²²²Rn measurements and in previous studies.

Boundary value problems of holomorphic vector functions in 1D QCs

International Nuclear Information System (INIS)

Gao Yang; Zhao Yingtao; Zhao Baosheng

2007-01-01

By means of the generalized Stroh formalism, two-dimensional (2D) problems of one-dimensional (1D) quasicrystals (QCs) elasticity are turned into the boundary value problems of holomorphic vector functions in a given region. If the conformal mapping from an ellipse to a circle is known, a general method for solving the boundary value problems of holomorphic vector functions can be presented. To illustrate its utility, by using the necessary and sufficient condition of boundary value problems of holomorphic vector functions, we consider two basic 2D problems in 1D QCs, that is, an elliptic hole and a rigid line inclusion subjected to uniform loading at infinity. For the crack problem, the intensity factors of phonon and phason fields are determined, and the physical sense of the results relative to phason and the difference between mechanical behaviors of the crack problem in crystals and QCs are figured out. Moreover, the same procedure can be used to deal with the elastic problems for 2D and three-dimensional (3D) QCs

SILICON CARBIDE GRAIN BOUNDARY DISTRIBUTIONS, IRRADIATION CONDITIONS, AND SILVER RETENTION IN IRRADIATED AGR-1 TRISO FUEL PARTICLES

Energy Technology Data Exchange (ETDEWEB)

Lillo, T. M.; Rooyen, I. J.; Aguiar, J. A.

2016-11-01

Precession electron diffraction in the transmission electron microscope was used to map grain orientation and ultimately determine grain boundary misorientation angle distributions, relative fractions of grain boundary types (random high angle, low angle or coincident site lattice (CSL)-related boundaries) and the distributions of CSL-related grain boundaries in the SiC layer of irradiated TRISO-coated fuel particles. Two particles from the AGR-1 experiment exhibiting high Ag-110m retention (>80%) were compared to a particle exhibiting low Ag-110m retention (<19%). Irradiated particles with high Ag-110m retention exhibited a lower fraction of random, high angle grain boundaries compared to the low Ag-110m retention particle. An inverse relationship between the random, high angle grain boundary fraction and Ag-110m retention is found and is consistent with grain boundary percolation theory. Also, comparison of the grain boundary distributions with previously reported unirradiated grain boundary distributions, based on SEM-based EBSD for similarly fabricated particles, showed only small differences, i.e. a greater low angle grain boundary fraction in unirradiated SiC. It was, thus, concluded that SiC layers with grain boundary distributions susceptible to Ag-110m release were present prior to irradiation. Finally, irradiation parameters were found to have little effect on the association of fission product precipitates with specific grain boundary types.

b-value distribution in and around Mt. Tarumae, Japan

Science.gov (United States)

Chiba, K.

2017-12-01

Mt. Tarumae is an active volcano located in southeastern Shikotsu caldera, Hokkaido, Japan. Recently, crustal expansion occurred in 1999-2000 and 2013 near the summit of Mt. Tarumae, with a M5.6 earthquake recorded west of the summit on 8 July 2014. In this study, I determined hypocenter distributions and then performed b-value analysis for the period between 1 August 2014 and 12 August 2016 to improve our understanding of the magma system geometry beneath the summit of Mt. Tarumae. Hypocenters are mainly distributed in two regions: 3 - 5 km west of Mt. Tarumae, and beneath the volcano. I then determined b-value distributions. Regions with relatively high b-values ( 1.3) are located at depths of -0.5 to 2.0 km beneath the summit and at depths greater than 6.0 km in the northwestern part at about 1.5 - 3.0 km from the summit, while a region with relatively low b-values ( 0.6) is located at depths of 2.0 - 6.0 km beneath the summit. Compared the b-value distributions with other geophysical observations, it was found that the high b-value region from -0.5 to 2.0 km depth corresponds to regions of lower resistivity, positive self-potential anomaly, and an inflation source observed in 1999-2000. It is thus inferred that this region is generated by crustal heterogeneity, a decrease in effective normal stress, and change of a frictional property due to the development of faults and fissures, and the circulation of hydrothermal fluids. On the other hand, the inflation source observed in 2013 was located near the boundary between the low b-value region beneath the summit and the deeper high b-value region in the northwestern part at about 1.5 - 3.0 km from the summit. Studies of other volcanoes suggest that such a high-b-value region likely corresponds to a magma chamber. From the deeper high b-value region estimated in this study, I am able to point out that the magma chamber is located to depths greater than 6.0 km in the northwestern part at about 1.5 - 3.0 km from the

Boundary-value problems for first and second order functional differential inclusions

Directory of Open Access Journals (Sweden)

Shihuang Hong

2003-03-01

Full Text Available This paper presents sufficient conditions for the existence of solutions to boundary-value problems of first and second order multi-valued differential equations in Banach spaces. Our results obtained using fixed point theorems, and lead to new existence principles.

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

Science.gov (United States)

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.

Order Reduction in High-Order Runge-Kutta Methods for Initial Boundary Value Problems

OpenAIRE

Rosales, Rodolfo Ruben; Seibold, Benjamin; Shirokoff, David; Zhou, Dong

2017-01-01

This paper studies the order reduction phenomenon for initial-boundary-value problems that occurs with many Runge-Kutta time-stepping schemes. First, a geometric explanation of the mechanics of the phenomenon is provided: the approximation error develops boundary layers, induced by a mismatch between the approximation error in the interior and at the boundaries. Second, an analysis of the modes of the numerical scheme is conducted, which explains under which circumstances boundary layers pers...

On nonseparated three-point boundary value problems for linear functional differential equations

Czech Academy of Sciences Publication Activity Database

Rontó, András; Rontó, M.

2011-01-01

Roč. 2011, - (2011), s. 326052 ISSN 1085-3375 Institutional research plan: CEZ:AV0Z10190503 Keywords : functional-differential equation * three-point boundary value problem * nonseparated boundary condition Subject RIV: BA - General Mathematics Impact factor: 1.318, year: 2011 http://www.hindawi.com/journals/ aaa /2011/326052/

Asymptotic boundary value problems for evolution inclusions

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Fürst Tomáš

2006-01-01

Full Text Available When solving boundary value problems on infinite intervals, it is possible to use continuation principles. Some of these principles take advantage of equipping the considered function spaces with topologies of uniform convergence on compact subintervals. This makes the representing solution operators compact (or condensing, but, on the other hand, spaces equipped with such topologies become more complicated. This paper shows interesting applications that use the strength of continuation principles and also presents a possible extension of such continuation principles to partial differential inclusions.

Asymptotic boundary value problems for evolution inclusions

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Tomáš Fürst

2006-02-01

Full Text Available When solving boundary value problems on infinite intervals, it is possible to use continuation principles. Some of these principles take advantage of equipping the considered function spaces with topologies of uniform convergence on compact subintervals. This makes the representing solution operators compact (or condensing, but, on the other hand, spaces equipped with such topologies become more complicated. This paper shows interesting applications that use the strength of continuation principles and also presents a possible extension of such continuation principles to partial differential inclusions.

Algebraic structures in generalized Clifford analysis and applications to boundary value problems

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José Játem

2015-12-01

Full Text Available The present article has a threefold purpose: First it is a survey of the algebraic structures of generalized Clifford-type algebras and shows the main results of the corresponding Clifford-type analysis and its application to boundary value problems known so far. Second it is aimed to implement algorithms to provide the fast and accurate computation of boundary value problems for inhomogeneous equations in the framework of the generalized Clifford analysis. Finally it is also aimed to encourage the development of a generalized discrete Clifford analysis.

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

Science.gov (United States)

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.

Laplace boundary-value problem in paraboloidal coordinates

International Nuclear Information System (INIS)

Duggen, L; Willatzen, M; Voon, L C Lew Yan

2012-01-01

This paper illustrates both a problem in mathematical physics, whereby the method of separation of variables, while applicable, leads to three ordinary differential equations that remain fully coupled via two separation constants and a five-term recurrence relation for series solutions, and an exactly solvable problem in electrostatics, as a boundary-value problem on a paraboloidal surface. In spite of the complex nature of the former, it is shown that the latter solution can be quite simple. Results are provided for the equipotential surfaces and electric field lines are given near a paraboloidal conductor. (paper)

Parallel algorithms for boundary value problems

Science.gov (United States)

Lin, Avi

1991-01-01

A general approach to solve boundary value problems numerically in a parallel environment is discussed. The basic algorithm consists of two steps: the local step where all the P available processors work in parallel, and the global step where one processor solves a tridiagonal linear system of the order P. The main advantages of this approach are twofold. First, this suggested approach is very flexible, especially in the local step and thus the algorithm can be used with any number of processors and with any of the SIMD or MIMD machines. Secondly, the communication complexity is very small and thus can be used as easily with shared memory machines. Several examples for using this strategy are discussed.

Initial-Boundary Value Problem Solution of the Nonlinear Shallow-water Wave Equations

Science.gov (United States)

Kanoglu, U.; Aydin, B.

2014-12-01

The hodograph transformation solutions of the one-dimensional nonlinear shallow-water wave (NSW) equations are usually obtained through integral transform techniques such as Fourier-Bessel transforms. However, the original formulation of Carrier and Greenspan (1958 J Fluid Mech) and its variant Carrier et al. (2003 J Fluid Mech) involve evaluation integrals. Since elliptic integrals are highly singular as discussed in Carrier et al. (2003), this solution methodology requires either approximation of the associated integrands by smooth functions or selection of regular initial/boundary data. It should be noted that Kanoglu (2004 J Fluid Mech) partly resolves this issue by simplifying the resulting integrals in closed form. Here, the hodograph transform approach is coupled with the classical eigenfunction expansion method rather than integral transform techniques and a new analytical model for nonlinear long wave propagation over a plane beach is derived. This approach is based on the solution methodology used in Aydın & Kanoglu (2007 CMES-Comp Model Eng) for wind set-down relaxation problem. In contrast to classical initial- or boundary-value problem solutions, here, the NSW equations are formulated to yield an initial-boundary value problem (IBVP) solution. In general, initial wave profile with nonzero initial velocity distribution is assumed and the flow variables are given in the form of Fourier-Bessel series. The results reveal that the developed method allows accurate estimation of the spatial and temporal variation of the flow quantities, i.e., free-surface height and depth-averaged velocity, with much less computational effort compared to the integral transform techniques such as Carrier et al. (2003), Kanoglu (2004), Tinti & Tonini (2005 J Fluid Mech), and Kanoglu & Synolakis (2006 Phys Rev Lett). Acknowledgments: This work is funded by project ASTARTE- Assessment, STrategy And Risk Reduction for Tsunamis in Europe. Grant 603839, 7th FP (ENV.2013.6.4-3 ENV

A boundary-value problem in weighted Hölder spaces for elliptic equations which degenerate at the boundary of the domain

Energy Technology Data Exchange (ETDEWEB)

Bazalii, B V; Degtyarev, S P [Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)

2013-07-31

An elliptic boundary-value problem for second-order equations with nonnegative characteristic form is investigated in the situation when there is a weak degeneracy on the boundary of the domain. A priori estimates are obtained for solutions and the problem is proved to be solvable in some weighted Hölder spaces. Bibliography: 18 titles.

The extended-domain-eigenfunction method for solving elliptic boundary value problems with annular domains

Energy Technology Data Exchange (ETDEWEB)

Aarao, J; Bradshaw-Hajek, B H; Miklavcic, S J; Ward, D A, E-mail: Stan.Miklavcic@unisa.edu.a [School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095 (Australia)

2010-05-07

Standard analytical solutions to elliptic boundary value problems on asymmetric domains are rarely, if ever, obtainable. In this paper, we propose a solution technique wherein we embed the original domain into one with simple boundaries where the classical eigenfunction solution approach can be used. The solution in the larger domain, when restricted to the original domain, is then the solution of the original boundary value problem. We call this the extended-domain-eigenfunction method. To illustrate the method's strength and scope, we apply it to Laplace's equation on an annular-like domain.

Boundary value problem for Caputo-Hadamard fractional differential equations

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Yacine Arioua

2017-09-01

Full Text Available The aim of this work is to study the existence and uniqueness solutions for boundary value problem of nonlinear fractional differential equations with Caputo-Hadamard derivative in bounded domain. We used the standard and Krasnoselskii's fixed point theorems. Some new results of existence and uniqueness solutions for Caputo-Hadamard fractional equations are obtained.

Variational methods for boundary value problems for systems of elliptic equations

CERN Document Server

Lavrent'ev, M A

2012-01-01

Famous monograph by a distinguished mathematician presents an innovative approach to classical boundary value problems. The treatment employs the basic scheme first suggested by Hilbert and developed by Tonnelli. 1963 edition.

Continuum and Discrete Initial-Boundary Value Problems and Einstein's Field Equations

Directory of Open Access Journals (Sweden)

Olivier Sarbach

2012-08-01

Full Text Available Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black-hole problem within Einstein's theory of gravitation, in which one computes the gravitational radiation emitted from the inspiral of the two black holes, merger and ringdown. Powerful mathematical tools can be used to establish qualitative statements about the solutions, such as their existence, uniqueness, continuous dependence on the initial data, or their asymptotic behavior over large time scales. However, one is often interested in computing the solution itself, and unless the partial differential equation is very simple, or the initial data possesses a high degree of symmetry, this computation requires approximation by numerical discretization. When solving such discrete problems on a machine, one is faced with a finite limit to computational resources, which leads to the replacement of the infinite continuum domain with a finite computer grid. This, in turn, leads to a discrete initial-boundary value problem. The hope is to recover, with high accuracy, the exact solution in the limit where the grid spacing converges to zero with the boundary being pushed to infinity. The goal of this article is to review some of the theory necessary to understand the continuum and discrete initial boundary-value problems arising from hyperbolic partial differential equations and to discuss its applications to numerical relativity; in particular, we present well-posed initial and initial-boundary value formulations of Einstein's equations, and we discuss multi-domain high-order finite difference and spectral methods to solve them.

Continuum and Discrete Initial-Boundary Value Problems and Einstein's Field Equations.

Science.gov (United States)

Sarbach, Olivier; Tiglio, Manuel

2012-01-01

Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black-hole problem within Einstein's theory of gravitation, in which one computes the gravitational radiation emitted from the inspiral of the two black holes, merger and ringdown. Powerful mathematical tools can be used to establish qualitative statements about the solutions, such as their existence, uniqueness, continuous dependence on the initial data, or their asymptotic behavior over large time scales. However, one is often interested in computing the solution itself, and unless the partial differential equation is very simple, or the initial data possesses a high degree of symmetry, this computation requires approximation by numerical discretization. When solving such discrete problems on a machine, one is faced with a finite limit to computational resources, which leads to the replacement of the infinite continuum domain with a finite computer grid. This, in turn, leads to a discrete initial-boundary value problem. The hope is to recover, with high accuracy, the exact solution in the limit where the grid spacing converges to zero with the boundary being pushed to infinity. The goal of this article is to review some of the theory necessary to understand the continuum and discrete initial boundary-value problems arising from hyperbolic partial differential equations and to discuss its applications to numerical relativity; in particular, we present well-posed initial and initial-boundary value formulations of Einstein's equations, and we discuss multi-domain high-order finite difference and spectral methods to solve them.

Effect of texture on grain boundary misorientation distributions in polycrystalline high temperature superconductors

International Nuclear Information System (INIS)

Goyal, A.; Specht, E.D.; Kroeger, D.M.; Mason, T.A.

1996-01-01

Computer simulations were performed to determine the most probable grain boundary misorientation distribution (GBMD) in model polycrystalline superconductors. GBMDs in polycrystalline superconductors can be expected to dictate the macroscopic transport critical current density, J c . Calculations were performed by simulating model polycrystals and then determining the GBMD. Such distributions were calculated for random materials having cubic, tetragonal, and orthorhombic crystal symmetry. In addition, since most high temperature superconductors are tetragonal or pseudotetragonal, the effect of macroscopic uniaxial and biaxial grain orientation texture on the GBMD was determined for tetragonal materials. It is found that macroscopic texture drastically alters the grain boundary misorientation distribution. The fraction of low angle boundaries increases significantly with uniaxial and biaxial texture. The results of this study are important in correlating the macroscopic transport J c with the measured grain orientation texture as determined by x-ray diffraction copyright 1996 American Institute of Physics

Properties of the distributional finite Fourier transform

OpenAIRE

Carmichael, Richard D.

2016-01-01

The analytic functions in tubes which obtain the distributional finite Fourier transform as boundary value are shown to have a strong boundedness property and to be recoverable as a Fourier-Laplace transform, a distributional finite Fourier transform, and as a Cauchy integral of a distribution associated with the boundary value.

Record Values of a Pareto Distribution.

Science.gov (United States)

Ahsanullah, M.

The record values of the Pareto distribution, labelled Pareto (II) (alpha, beta, nu), are reviewed. The best linear unbiased estimates of the parameters in terms of the record values are provided. The prediction of the sth record value based on the first m (s>m) record values are obtained. A classical Pareto distribution provides reasonably…

three solutions for a semilinear elliptic boundary value problem

Indian Academy of Sciences (India)

69

Keywords: The Laplacian operator, elliptic problem, Nehari man- ifold, three critical points, weak solution. 1. Introduction. Let Ω be a smooth bounded domain in RN , N ≥ 3 . In this work, we show the existence of at least three solutions for the semilinear elliptic boundary- value problem: (Pλ).. −∆u = f(x)|u(x)|p−2u(x) + ...

An inverse boundary value problem for the Schroedinger operator with vector potentials in two dimensions

International Nuclear Information System (INIS)

Ziqi Sun

1993-01-01

During the past few years a considerable interest has been focused on the inverse boundary value problem for the Schroedinger operator with a scalar (electric) potential. The popularity gained by this subject seems to be due to its connection with the inverse scattering problem at fixed energy, the inverse conductivity problem and other important inverse problems. This paper deals with an inverse boundary value problem for the Schroedinger operator with vector (electric and magnetic) potentials. As in the case of the scalar potential, results of this study would have immediate consequences in the inverse scattering problem for magnetic field at fixed energy. On the other hand, inverse boundary value problems for elliptic operators are of independent interest. The study is partly devoted to the understanding of the inverse boundary value problem for a class of general elliptic operator of second order. Note that a self-adjoint elliptic operator of second order with Δ as its principal symbol can always be written as a Schroedinger operator with vector potentials

The homogeneous boundary value problem of the thick spherical shell

International Nuclear Information System (INIS)

Linder, F.

1975-01-01

With the aim to solve boundary value problems in the same manner as it is attained at thin shell theory (Superposition of Membrane solution to solution of boundary values), one has to search solutions of the equations of equilibrium of the three dimensional thick shell which produce tensions at the cut edge and are zero on the whole shell surface inside and outside. This problem was solved with the premissions of the linear theory of Elasticity. The gained solution is exact and contains the symmetric and non-symmetric behaviour and is described in relatively short analytical expressions for the deformations and tensions, after the problem of the coupled system had been solved. The static condition of the two surfaces (zero tension) leads to a homogeneous system of complex equations with the index of the Legendre spherical function as Eigenvalue. One symmetrical case is calculated numerically and is compared with the method of finite elements. This comparison results in good accordance. (Auth.)

Asymptotics for inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation

Energy Technology Data Exchange (ETDEWEB)

Kaikina, Elena I., E-mail: ekaikina@matmor.unam.mx [Centro de Ciencias Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán (Mexico)

2013-11-15

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

Asymptotics for inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation

International Nuclear Information System (INIS)

Kaikina, Elena I.

2013-01-01

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

Detection of bump-on-tail reduced electron velocity distributions at the electron foreshock boundary

International Nuclear Information System (INIS)

Fitzenreiter, R.J.; Klimas, A.J.; Scudder, J.D.

1984-02-01

Reduced velocity distributions are derived from three-dimensional measurements of the velocity distribution of electrons in the 7 to 500 eV range in the electron foreshock. Bump-on-tail reduced distributions are presented for the first time at the foreshock boundary consistent with Filbert and Kellogg's proposed time-of-flight mechanism for generating the electron beams. In a significant number of boundary crossings, bump-on-tail reduced distributions were found in consecutive 3 sec measurements made 9 sec apart. It is concluded that, although the beams are linearly unstable to plasma waves according to the Penrose criterion, they persist on a time scale of 3 to 15 sec

The numerical solution of boundary value problems over an infinite domain

International Nuclear Information System (INIS)

Shepherd, M.; Skinner, R.

1976-01-01

A method is presented for the numerical solution of boundary value problems over infinite domains. An example that illustrates also the strength and accuracy of a numerical procedure for calculating Green's functions is described in detail

Existence of 2m-1 Positive Solutions for Sturm-Liouville Boundary Value Problems with Linear Functional Boundary Conditions on the Half-Line

Directory of Open Access Journals (Sweden)

Yanmei Sun

2012-01-01

Full Text Available By using the Leggett-Williams fixed theorem, we establish the existence of multiple positive solutions for second-order nonhomogeneous Sturm-Liouville boundary value problems with linear functional boundary conditions. One explicit example with singularity is presented to demonstrate the application of our main results.

Multiple positive solutions for second order impulsive boundary value problems in Banach spaces

Directory of Open Access Journals (Sweden)

Zhi-Wei Lv

2010-06-01

Full Text Available By means of the fixed point index theory of strict set contraction operators, we establish new existence theorems on multiple positive solutions to a boundary value problem for second-order impulsive integro-differential equations with integral boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result.

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

International Nuclear Information System (INIS)

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

1998-01-01

We prove the approximate controllability of several nonlinear parabolic boundary-value problems by means of two different methods: the first one can be called a Cancellation method and the second one uses the Kakutani fixed-point theorem

A free-boundary value problem related to auto ignition of ...

African Journals Online (AJOL)

We examine a free boundary value problem related to auto ignition of combustible fluid in insulation materials. The criteria for the existence of similarity solution of the model equations are established. The conditions for the existence of unique solution are also stated. The numerical results which show the influence of ...

Numerical solutions of a three-point boundary value problem with an ...

African Journals Online (AJOL)

Numerical solutions of a three-point boundary value problem with an integral condition for a third-order partial differential equation by using Laplace transform method Solutions numeriques d'un probleme pour une classe d'equations differentielles d'ordr.

Selection of flow-distributed oscillation and Turing patterns by boundary forcing in a linearly growing, oscillating medium.

Science.gov (United States)

Míguez, David G; McGraw, Patrick; Muñuzuri, Alberto P; Menzinger, Michael

2009-08-01

We studied the response of a linearly growing domain of the oscillatory chemical chlorine dioxide-iodide-malonic acid (CDIMA) medium to periodic forcing at its growth boundary. The medium is Hopf-, as well as Turing-unstable and the system is convectively unstable. The results confirm numerical predictions that two distinct modes of pattern can be excited by controlling the driving frequency at the boundary, a flow-distributed-oscillation (FDO) mode of traveling waves at low values of the forcing frequency f , and a mode of stationary Turing patterns at high values of f . The wavelengths and phase velocities of the experimental patterns were compared quantitatively with results from dynamical simulations and with predictions from linear dispersion relations. The results for the FDO waves agreed well with these predictions, and obeyed the kinematic relations expected for phase waves with frequencies selected by the boundary driving frequency. Turing patterns were also generated within the predicted range of forcing frequencies, but these developed into two-dimensional structures which are not fully accounted for by the one-dimensional numerical and analytical models. The Turing patterns excited by boundary forcing persist when the forcing is removed, demonstrating the bistability of the unforced, constant size medium. Dynamical simulations at perturbation frequencies other than those of the experiments showed that in certain ranges of forcing frequency, FDO waves become unstable, breaking up into harmonic waves of different frequency and wavelength and phase velocity.

Boundary layer and fundamental problems of hydrodynamics (compatibility of a logarithmic velocity profile in a turbulent boundary layer with the experience values)

Science.gov (United States)

Zaryankin, A. E.

2017-11-01

The compatibility of the semiempirical turbulence theory of L. Prandtl with the actual flow pattern in a turbulent boundary layer is considered in this article, and the final calculation results of the boundary layer is analyzed based on the mentioned theory. It shows that accepted additional conditions and relationships, which integrate the differential equation of L. Prandtl, associating the turbulent stresses in the boundary layer with the transverse velocity gradient, are fulfilled only in the near-wall region where the mentioned equation loses meaning and are inconsistent with the physical meaning on the main part of integration. It is noted that an introduced concept about the presence of a laminar sublayer between the wall and the turbulent boundary layer is the way of making of a physical meaning to the logarithmic velocity profile, and can be defined as adjustment of the actual flow to the formula that is inconsistent with the actual boundary conditions. It shows that coincidence of the experimental data with the actual logarithmic profile is obtained as a result of the use of not particular physical value, as an argument, but function of this value.

The polynomial property of self-adjoint elliptic boundary-value problems and an algebraic description of their attributes

International Nuclear Information System (INIS)

Nazarov, S A

1999-01-01

We describe a wide class of boundary-value problems for which the application of elliptic theory can be reduced to elementary algebraic operations and which is characterized by the following polynomial property: the sesquilinear form corresponding to the problem degenerates only on some finite-dimensional linear space P of vector polynomials. Under this condition the boundary-value problem is elliptic, and its kernel and cokernel can be expressed in terms of P. For domains with piecewise-smooth boundary or infinite ends (conic, cylindrical, or periodic), we also present fragments of asymptotic formulae for the solutions, give specific versions of general conditional theorems on the Fredholm property (in particular, by modifying the ordinary weighted norms), and compute the index of the operator corresponding to the boundary-value problem. The polynomial property is also helpful for asymptotic analysis of boundary-value problems in thin domains and junctions of such domains. Namely, simple manipulations with P permit one to find the size of the system obtained by dimension reduction as well as the orders of the differential operators occurring in that system and provide complete information on the boundary layer structure. The results are illustrated by examples from elasticity and hydromechanics

Probability distribution of magnetization in the one-dimensional Ising model: effects of boundary conditions

Energy Technology Data Exchange (ETDEWEB)

Antal, T [Physics Department, Simon Fraser University, Burnaby, BC V5A 1S6 (Canada); Droz, M [Departement de Physique Theorique, Universite de Geneve, CH 1211 Geneva 4 (Switzerland); Racz, Z [Institute for Theoretical Physics, Eoetvoes University, 1117 Budapest, Pazmany setany 1/a (Hungary)

2004-02-06

Finite-size scaling functions are investigated both for the mean-square magnetization fluctuations and for the probability distribution of the magnetization in the one-dimensional Ising model. The scaling functions are evaluated in the limit of the temperature going to zero (T {yields} 0), the size of the system going to infinity (N {yields} {infinity}) while N[1 - tanh(J/k{sub B}T)] is kept finite (J being the nearest neighbour coupling). Exact calculations using various boundary conditions (periodic, antiperiodic, free, block) demonstrate explicitly how the scaling functions depend on the boundary conditions. We also show that the block (small part of a large system) magnetization distribution results are identical to those obtained for free boundary conditions.

Discrete quintic spline for boundary value problem in plate deflation theory

Science.gov (United States)

Wong, Patricia J. Y.

2017-07-01

We propose a numerical scheme for a fourth-order boundary value problem arising from plate deflation theory. The scheme involves a discrete quintic spline, and it is of order 4 if a parameter takes a specific value, else it is of order 2. We also present a well known numerical example to illustrate the efficiency of our method as well as to compare with other numerical methods proposed in the literature.

Caring across Boundaries versus Keeping Boundaries Intact: Links between Moral Values and Interpersonal Orientations

Science.gov (United States)

Niemi, Laura; Young, Liane

2013-01-01

Prior work has established robust diversity in the extent to which different moral values are endorsed. Some people focus on values related to caring and fairness, whereas others assign additional moral weight to ingroup loyalty, respect for authority and established hierarchies, and purity concerns. Five studies explore associations between endorsement of distinct moral values and a suite of interpersonal orientations: Machiavellianism, prosocial resource distribution, Social Dominance Orientation, and reported likelihood of helping and not helping kin and close friends versus acquaintances and neighbors. We found that Machiavellianism (Studies 1, 3, 4, 5) (e.g., amorality, controlling and status-seeking behaviors) and Social Dominance Orientation (Study 4) were negatively associated with caring values, and positively associated with valuation of authority. Those higher in caring values were more likely to choose prosocial resource distributions (Studies 2, 3, 4) and to report reduced likelihood of failing to help kin/close friends or acquaintances (Study 4). Finally, greater likelihood of helping acquaintances was positively associated with all moral values tested except authority values (Study 4). The current work offers a novel approach to characterizing moral values and reveals a striking divergence between two kinds of moral values in particular: caring values and authority values. Caring values were positively linked with prosociality and negatively associated with Machiavellianism, whereas authority values were positively associated with Machiavellianism and Social Dominance Orientation. PMID:24349095

Boundary value problems on the half line in the theory of colloids

Directory of Open Access Journals (Sweden)

Ravi P. Agarwal

2002-01-01

Full Text Available We present existence results for some boundary value problems defined on infinite intervals. In particular our discussion includes a problem which arises in the theory of colloids.

The value of electricity distribution networks

International Nuclear Information System (INIS)

De Paoli, L.

2000-01-01

This article presents the results of a study aimed at evaluating parts of the distribution network of ENEL, in charge of distributing and supplying electricity to its captive market, that could be sold as a separate entity. To determine the asset value of these hypothetical companies, the discounted cash flow method has been used applied to the 147 ENEL's distributing zones. The econometric analysis shows that the relevant variables are the quantity sold to non residential and non big industrial consumers and the length of medium voltage lines. According to the available data and to the methodology chosen, the per client value of the distribution zones of ENEL varies substantially. The maximum value is bout three times the mean value and the minimum value is largely negative. The article maintains that changes in regulation could greatly modify the asset value of distribution networks. The main regulatory risks are linked to the degree of market opening, the introduction of compensation mechanisms between different distributors and the allowed maximum revenue fixed by energy Authority for a given period of time. This point is developed in the appendix where it is shown that the price cap method is decided on the basis of a rate of return which is valid at the moment of the cap fixing but that could be no longer valid if the rate of inflation varies [it

A New Numerical Algorithm for Two-Point Boundary Value Problems

OpenAIRE

Guo, Lihua; Wu, Boying; Zhang, Dazhi

2014-01-01

We present a new numerical algorithm for two-point boundary value problems. We first present the exact solution in the form of series and then prove that the n-term numerical solution converges uniformly to the exact solution. Furthermore, we establish the numerical stability and error analysis. The numerical results show the effectiveness of the proposed algorithm.

The tradable value of distributed generation

Energy Technology Data Exchange (ETDEWEB)

NONE

2005-07-01

A general guide for all generators connected to the electric power distribution network is presented. It provides an indication of the tradable value of distributed generation in prevailing market conditions. The document covers (i) the elements of value for which distributed generators may be awarded; (ii) how generators can realize these values and (iii) references to other relevant sources of information. The value an individual generator can realize depends on size, technology, operating profile, location and connection voltage. Definitions of small, medium and large generators are given. The values received by a generator will depend at least on prevailing prices, time of day and time of year. Added value may come from Renewable Obligation Certificates and Climate Change Levy Exemption Certificates. Worked examples are given for a domestic PV system, an industrial CHP scheme and a wind farm. The study was carried out by Ilex Energy Consulting and supported by the DTI.

Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals

KAUST Repository

Dujardin, G. M.

2009-08-12

This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate whether the solution becomes time-periodic after sufficiently long time. Using Fokas\\' transformation method, we show that, for the linear Schrödinger equation, the linear heat equation and the linearized KdV equation on the half-line, the solutions indeed become periodic for large time. However, for the same linear Schrödinger equation on a finite interval, we show that the solution, in general, is not asymptotically periodic; actually, the asymptotic behaviour of the solution depends on the commensurability of the time period T of the boundary data with the square of the length of the interval over. © 2009 The Royal Society.

A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ Lie-Group Shooting Method

Directory of Open Access Journals (Sweden)

Chein-Shan Liu

2013-01-01

Full Text Available The boundary layer problem for power-law fluid can be recast to a third-order p-Laplacian boundary value problem (BVP. In this paper, we transform the third-order p-Laplacian into a new system which exhibits a Lie-symmetry SL(3,ℝ. Then, the closure property of the Lie-group is used to derive a linear transformation between the boundary values at two ends of a spatial interval. Hence, we can iteratively solve the missing left boundary conditions, which are determined by matching the right boundary conditions through a finer tuning of r∈[0,1]. The present SL(3,ℝ Lie-group shooting method is easily implemented and is efficient to tackle the multiple solutions of the third-order p-Laplacian. When the missing left boundary values can be determined accurately, we can apply the fourth-order Runge-Kutta (RK4 method to obtain a quite accurate numerical solution of the p-Laplacian.

Multi-point boundary value problems for linear functional-differential equations

Czech Academy of Sciences Publication Activity Database

Domoshnitsky, A.; Hakl, Robert; Půža, Bedřich

2017-01-01

Roč. 24, č. 2 (2017), s. 193-206 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : boundary value problems * linear functional-differential equations * functional-differential inequalities Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0076/gmj-2016-0076. xml

Multi-point boundary value problems for linear functional-differential equations

Czech Academy of Sciences Publication Activity Database

Domoshnitsky, A.; Hakl, Robert; Půža, Bedřich

2017-01-01

Roč. 24, č. 2 (2017), s. 193-206 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : boundary value problems * linear functional- differential equations * functional- differential inequalities Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0076/gmj-2016-0076.xml

Infinitely many solutions for a fourth-order boundary-value problem

Directory of Open Access Journals (Sweden)

Seyyed Mohsen Khalkhali

2012-09-01

Full Text Available In this article we consider the existence of infinitely many solutions to the fourth-order boundary-value problem $$displaylines{ u^{iv}+alpha u''+eta(x u=lambda f(x,u+h(u,quad xin]0,1[cr u(0=u(1=0,cr u''(0=u''(1=0,. }$$ Our approach is based on variational methods and critical point theory.

Initial boundary-value problem for the spherically symmetric Einstein equations with fluids with tangential pressure.

Science.gov (United States)

Brito, Irene; Mena, Filipe C

2017-08-01

We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial space-like hypersurface with a time-like boundary, there exists a unique, local in time solution to the Einstein equations in a neighbourhood of the boundary. As an application, we consider a particular elastic fluid interior matched to a vacuum exterior.

Existence of Three Positive Solutions to Some p-Laplacian Boundary Value Problems

Directory of Open Access Journals (Sweden)

Moulay Rchid Sidi Ammi

2013-01-01

Full Text Available We obtain, by using the Leggett-Williams fixed point theorem, sufficient conditions that ensure the existence of at least three positive solutions to some p-Laplacian boundary value problems on time scales.

Solution matching for a three-point boundary-value problem on atime scale

Directory of Open Access Journals (Sweden)

Martin Eggensperger

2004-07-01

Full Text Available Let $mathbb{T}$ be a time scale such that $t_1, t_2, t_3 in mathbb{T}$. We show the existence of a unique solution for the three-point boundary value problem $$displaylines{ y^{DeltaDeltaDelta}(t = f(t, y(t, y^Delta(t, y^{DeltaDelta}(t, quad t in [t_1, t_3] cap mathbb{T},cr y(t_1 = y_1, quad y(t_2 = y_2, quad y(t_3 = y_3,. }$$ We do this by matching a solution to the first equation satisfying a two-point boundary conditions on $[t_1, t_2] cap mathbb{T}$ with a solution satisfying a two-point boundary conditions on $[t_2, t_3] cap mathbb{T}$.

Chebyshev Finite Difference Method for Fractional Boundary Value Problems

Directory of Open Access Journals (Sweden)

Boundary

2015-09-01

Full Text Available This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations. AMS Subject Classification: 34A08 Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points, fractional differential equation, finite difference 1. Introduction The idea of a derivative which interpolates between the familiar integer order derivatives was introduced many years ago and has gained increasing importance only in recent years due to the development of mathematical models of a certain situations in engineering, materials science, control theory, polymer modelling etc. For example see [20, 22, 25, 26]. Most fractional order differential equations describing real life situations, in general do not have exact analytical solutions. Several numerical and approximate analytical methods for ordinary differential equation Received: December 2014; Accepted: March 2015 57 Journal of Mathematical Extension Vol. 9, No. 3, (2015, 57-71 ISSN: 1735-8299 URL: http://www.ijmex.com Chebyshev Finite Difference Method for Fractional Boundary Value Problems H. Azizi Taft Branch, Islamic Azad University Abstract. This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivative

Distributed Tuning of Boundary Resources

DEFF Research Database (Denmark)

Eaton, Ben; Elaluf-Calderwood, Silvia; Sørensen, Carsten

2015-01-01

in the context of a paradoxical tension between the logic of generative and democratic innovations and the logic of infrastructural control. Boundary resources play a critical role in managing the tension as a firm that owns the infrastructure can secure its control over the service system while independent...... firms can participate in the service system. In this study, we explore the evolution of boundary resources. Drawing on Pickering’s (1993) and Barrett et al.’s (2012) conceptualizations of tuning, the paper seeks to forward our understanding of how heterogeneous actors engage in the tuning of boundary...

A priori bounds for solutions of two-point boundary value problems using differential inequalities

International Nuclear Information System (INIS)

Vidossich, G.

1979-01-01

Two point boundary value problems for systems of differential equations are studied with a new approach based on differential inequalities of first order. This leads to the following results: (i) one-sided conditions are enough, in the sense that the inner product is substituted to the norm; (ii) the upper bound exists for practically any kind of equations and boundary value problem if the interval is sufficiently small since it depends on the Peano existence theorem; (iii) the bound seems convenient when the equation has some singularity in t as well as when sigular problems are considered. (author)

Existence and uniqueness of entropy solution to initial boundary value problem for the inviscid Burgers equation

CERN Document Server

Zhu, C

2003-01-01

This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation. To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math. 3 201-30), give the formula of the corresponding viscosity solutions by Hopf-Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation.

Existence and uniqueness of entropy solution to initial boundary value problem for the inviscid Burgers equation

International Nuclear Information System (INIS)

Zhu, Changjiang; Duan, Renjun

2003-01-01

This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation. To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math. 3 201-30), give the formula of the corresponding viscosity solutions by Hopf-Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation

Partial differential equations and boundary-value problems with applications

CERN Document Server

Pinsky, Mark A

2011-01-01

Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems-rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate th

Weak value distributions for spin 1/2

Science.gov (United States)

Berry, M. V.; Dennis, M. R.; McRoberts, B.; Shukla, P.

2011-05-01

The simplest weak measurement is of a component of spin 1/2. For this observable, the probability distributions of the real and imaginary parts of the weak value, and their joint probability distribution, are calculated exactly for pre- and postselected states uniformly distributed over the surface of the Poincaré-Bloch sphere. The superweak probability, that the real part of the weak value lies outside the spectral range, is 1/3. This case, with just two eigenvalues, complements our previous calculation (Berry and Shukla 2010 J. Phys. A: Math. Theor. 43 354024) of the universal form of the weak value probability distribution for an operator with many eigenvalues.

Weak value distributions for spin 1/2

International Nuclear Information System (INIS)

Berry, M V; Dennis, M R; McRoberts, B; Shukla, P

2011-01-01

The simplest weak measurement is of a component of spin 1/2. For this observable, the probability distributions of the real and imaginary parts of the weak value, and their joint probability distribution, are calculated exactly for pre- and postselected states uniformly distributed over the surface of the Poincare-Bloch sphere. The superweak probability, that the real part of the weak value lies outside the spectral range, is 1/3. This case, with just two eigenvalues, complements our previous calculation (Berry and Shukla 2010 J. Phys. A: Math. Theor. 43 354024) of the universal form of the weak value probability distribution for an operator with many eigenvalues.

Triple solutions for multi-point boundary-value problem with p-Laplace operator

Directory of Open Access Journals (Sweden)

Yansheng Liu

2009-11-01

Full Text Available Using a fixed point theorem due to Avery and Peterson, this article shows the existence of solutions for multi-point boundary-value problem with p-Laplace operator and parameters. Also, we present an example to illustrate the results obtained.

Distribution of values of holomorphic mappings

CERN Document Server

Shabat, B V

1985-01-01

A vast literature has grown up around the value distribution theory of meromorphic functions, synthesized by Rolf Nevanlinna in the 1920s and singled out by Hermann Weyl as one of the greatest mathematical achievements of this century. The multidimensional aspect, involving the distribution of inverse images of analytic sets under holomorphic mappings of complex manifolds, has not been fully treated in the literature. This volume thus provides a valuable introduction to multivariate value distribution theory and a survey of some of its results, rich in relations to both algebraic and differential geometry and surely one of the most important branches of the modern geometric theory of functions of a complex variable. Since the book begins with preparatory material from the contemporary geometric theory of functions, only a familiarity with the elements of multidimensional complex analysis is necessary background to understand the topic. After proving the two main theorems of value distribution theory, the auth...

On the asymptotic of solutions of elliptic boundary value problems in domains with edges

International Nuclear Information System (INIS)

Nkemzi, B.

2005-10-01

Solutions of elliptic boundary value problems in three-dimensional domains with edges may exhibit singularities. The usual procedure to study these singularities is by the application of the classical Mellin transformation or continuous Fourier transformation. In this paper, we show how the asymptotic behavior of solutions of elliptic boundary value problems in general three-dimensional domains with straight edges can be investigated by means of discrete Fourier transformation. We apply this approach to time-harmonic Maxwell's equations and prove that the singular solutions can fully be described in terms of Fourier series. The representation here can easily be used to approximate three-dimensional stress intensity factors associated with edge singularities. (author)

A device adaptive inflow boundary condition for Wigner equations of quantum transport

International Nuclear Information System (INIS)

Jiang, Haiyan; Lu, Tiao; Cai, Wei

2014-01-01

In this paper, an improved inflow boundary condition is proposed for Wigner equations in simulating a resonant tunneling diode (RTD), which takes into consideration the band structure of the device. The original Frensley inflow boundary condition prescribes the Wigner distribution function at the device boundary to be the semi-classical Fermi–Dirac distribution for free electrons in the device contacts without considering the effect of the quantum interaction inside the quantum device. The proposed device adaptive inflow boundary condition includes this effect by assigning the Wigner distribution to the value obtained from the Wigner transform of wave functions inside the device at zero external bias voltage, thus including the dominant effect on the electron distribution in the contacts due to the device internal band energy profile. Numerical results on computing the electron density inside the RTD under various incident waves and non-zero bias conditions show much improvement by the new boundary condition over the traditional Frensley inflow boundary condition

Receptivity of Hypersonic Boundary Layers to Distributed Roughness and Acoustic Disturbances

Science.gov (United States)

Balakumar, P.

2013-01-01

Boundary-layer receptivity and stability of Mach 6 flows over smooth and rough seven-degree half-angle sharp-tipped cones are numerically investigated. The receptivity of the boundary layer to slow acoustic disturbances, fast acoustic disturbances, and vortical disturbances is considered. The effects of three-dimensional isolated roughness on the receptivity and stability are also simulated. The results for the smooth cone show that the instability waves are generated in the leading edge region and that the boundary layer is much more receptive to slow acoustic waves than to the fast acoustic waves. Vortical disturbances also generate unstable second modes, however the receptivity coefficients are smaller than that of the slow acoustic wave. Distributed roughness elements located near the nose region decreased the receptivity of the second mode generated by the slow acoustic wave by a small amount. Roughness elements distributed across the continuous spectrum increased the receptivity of the second mode generated by the slow and fast acoustic waves and the vorticity wave. The largest increase occurred for the vorticity wave. Roughness elements distributed across the synchronization point did not change the receptivity of the second modes generated by the acoustic waves. The receptivity of the second mode generated by the vorticity wave increased in this case, but the increase is lower than that occurred with the roughness elements located across the continuous spectrum. The simulations with an isolated roughness element showed that the second mode waves generated by the acoustic disturbances are not influenced by the small roughness element. Due to the interaction, a three-dimensional wave is generated. However, the amplitude is orders of magnitude smaller than the two-dimensional wave.

Elliptic boundary value problems with fractional regularity data the first order approach

CERN Document Server

Amenta, Alex

2018-01-01

In this monograph the authors study the well-posedness of boundary value problems of Dirichlet and Neumann type for elliptic systems on the upper half-space with coefficients independent of the transversal variable and with boundary data in fractional Hardy-Sobolev and Besov spaces. The authors use the so-called "first order approach" which uses minimal assumptions on the coefficients and thus allows for complex coefficients and for systems of equations. This self-contained exposition of the first order approach offers new results with detailed proofs in a clear and accessible way and will become a valuable reference for graduate students and researchers working in partial differential equations and harmonic analysis.

About potential of double layer and boundary value problems for Laplace equation

International Nuclear Information System (INIS)

Aleshin, M.V.

1991-01-01

An integral operator raisen by a kernel of the double layer's potential is investigated. The kernel is defined on S (S - two-digit variety of C 2 class presented by a boundary of the finite domain in R 3 ). The operator is considered on C(S). Following results are received: the operator's spectrum belongs to [-1,1]; it's eigenvalues and eigenfunctions may be found by Kellog's method; knowledge of the operator's spectrum is enough to construct it's resolvent. These properties permit to point out the determined interation processes, solving boundary value problems for Laplace equation. One of such processes - solving of Roben problem - is generalized on electrostatic problems. 6 refs

Critical current of the nonuniform Josephson transition at intergranular boundary with random dislocation distribution

International Nuclear Information System (INIS)

Mejlikhov, E.Z.; Farzetdinova, R.M.

1997-01-01

Critical current of inhomogeneous intergranular Josephson transition is calculated in the assumption concerning superconductivity suppression by local strains of boundary dislocations with random distribution

Simultaneous reconstruction of outer boundary shape and conductivity distribution in electrical impedance tomography

KAUST Repository

Hyvö nen, Nuutti

2016-01-01

The simultaneous retrieval of the exterior boundary shape and the interior admittivity distribution of an examined body in electrical impedance tomography is considered. The reconstruction method is built for the complete electrode model

Estimation of value at risk and conditional value at risk using normal mixture distributions model

Science.gov (United States)

Kamaruzzaman, Zetty Ain; Isa, Zaidi

2013-04-01

Normal mixture distributions model has been successfully applied in financial time series analysis. In this paper, we estimate the return distribution, value at risk (VaR) and conditional value at risk (CVaR) for monthly and weekly rates of returns for FTSE Bursa Malaysia Kuala Lumpur Composite Index (FBMKLCI) from July 1990 until July 2010 using the two component univariate normal mixture distributions model. First, we present the application of normal mixture distributions model in empirical finance where we fit our real data. Second, we present the application of normal mixture distributions model in risk analysis where we apply the normal mixture distributions model to evaluate the value at risk (VaR) and conditional value at risk (CVaR) with model validation for both risk measures. The empirical results provide evidence that using the two components normal mixture distributions model can fit the data well and can perform better in estimating value at risk (VaR) and conditional value at risk (CVaR) where it can capture the stylized facts of non-normality and leptokurtosis in returns distribution.

A radial distribution function-based open boundary force model for multi-centered molecules

KAUST Repository

Neumann, Philipp; Eckhardt, Wolfgang; Bungartz, Hans-Joachim

2014-01-01

We derive an expression for radial distribution function (RDF)-based open boundary forcing for molecules with multiple interaction sites. Due to the high-dimensionality of the molecule configuration space and missing rotational invariance, a

Three symmetric positive solutions of fourth-order singular nonlocal boundary value problems

Directory of Open Access Journals (Sweden)

Fuyi Xu

2011-12-01

Full Text Available In this paper, we study the existence of three positive solutions of fourth-order singular nonlocal boundary value problems. We show that there exist triple symmetric positive solutions by using Leggett-Williams fixed-point theorem. The conclusions in this paper essentially extend and improve some known results.

On the grain boundary character distribution of Incoloy 800H during dynamic recrystallization

Energy Technology Data Exchange (ETDEWEB)

Cao, Yu, E-mail: vieri32825@126.com [College of Materials Science and Engineering, Chongqing University, Chongqing 400045 (China); Di, Hongshuang [State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110819 (China); Huang, Guangjie [College of Materials Science and Engineering, Chongqing University, Chongqing 400045 (China)

2017-04-01

In this paper, we investigated the influence of hot deformation parameters on the distribution and proliferation of twin boundaries during dynamic recrystallization (DRX). The results showed that microstructure evolution is characterized by a process of “dynamic recovery (DRV)→necklace/multiple necklace→fully DRX” with increasing temperature and decreasing strain rate. The predominant proliferation mechanism of Σ3{sup n} (1 ≤ n ≤ 3) boundaries is transformed from Σ3 regeneration to new twinning during the growth of DRX grains.

On the grain boundary character distribution of Incoloy 800H during dynamic recrystallization

International Nuclear Information System (INIS)

Cao, Yu; Di, Hongshuang; Huang, Guangjie

2017-01-01

In this paper, we investigated the influence of hot deformation parameters on the distribution and proliferation of twin boundaries during dynamic recrystallization (DRX). The results showed that microstructure evolution is characterized by a process of “dynamic recovery (DRV)→necklace/multiple necklace→fully DRX” with increasing temperature and decreasing strain rate. The predominant proliferation mechanism of Σ3 n (1 ≤ n ≤ 3) boundaries is transformed from Σ3 regeneration to new twinning during the growth of DRX grains.

Solving inverse two-point boundary value problems using collage coding

Science.gov (United States)

Kunze, H.; Murdock, S.

2006-08-01

The method of collage coding, with its roots in fractal imaging, is the central tool in a recently established rigorous framework for solving inverse initial value problems for ordinary differential equations (Kunze and Vrscay 1999 Inverse Problems 15 745-70). We extend these ideas to solve the following inverse problem: given a function u(x) on [A, B] (which may be the interpolation of data points), determine a two-point boundary value problem on [A, B] which admits u(x) as a solution as closely as desired. The solution of such inverse problems may be useful in parameter estimation or determination of potential functional forms of the underlying differential equation. We discuss ways to improve results, including the development of a partitioning scheme. Several examples are considered.

The vanishing discount problem and viscosity Mather measures. Part 2: boundary value problems

OpenAIRE

Ishii, Hitoshi; Mitake, Hiroyoshi; Tran, Hung V.

2016-01-01

In arXiv:1603.01051 (Part 1 of this series), we have introduced a variational approach to studying the vanishing discount problem for fully nonlinear, degenerate elliptic, partial differential equations in a torus. We develop this approach further here to handle boundary value problems. In particular, we establish new representation formulas for solutions of discount problems, critical values, and use them to prove convergence results for the vanishing discount problems.

Analytic solutions to a family of boundary-value problems for Ginsburg-Landau type equations

Science.gov (United States)

Vassilev, V. M.; Dantchev, D. M.; Djondjorov, P. A.

2017-10-01

We consider a two-parameter family of nonlinear ordinary differential equations describing the behavior of a critical thermodynamic system, e.g., a binary liquid mixture, of film geometry within the framework of the Ginzburg-Landau theory by means of the order-parameter. We focus on the case in which the confining surfaces are strongly adsorbing but prefer different components of the mixture, i.e., the order-parameter tends to infinity at one of the boundaries and to minus infinity at the other one. We assume that the boundaries of the system are positioned at a finite distance from each other and give analytic solutions to the corresponding boundary-value problems in terms of Weierstrass and Jacobi elliptic functions.

Positive solutions of boundary value problem for singular positone and semi-positone third-order difference equations

Directory of Open Access Journals (Sweden)

Gai Gongqi

2011-01-01

Full Text Available Abstract This article studies the boundary value problems for the third-order nonlinear singular difference equations Δ 3 u ( i - 2 + λ a ( i f ( i , u ( i = 0 , i ∈ [ 2 , T + 2 ] , satisfying five kinds of different boundary value conditions. This article shows the existence of positive solutions for positone and semi-positone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone. MSC [2008]: 34B15; 39A10.

Asymptotic behaviour of solutions of the first boundary-value problem for strongly hyperbolic systems near a conical point at the boundary of the domain

International Nuclear Information System (INIS)

Hung, Nguyen M

1999-01-01

An existence and uniqueness theorem for generalized solutions of the first initial-boundary-value problem for strongly hyperbolic systems in bounded domains is established. The question of estimates in Sobolev spaces of the derivatives with respect to time of the generalized solution is discussed. It is shown that the smoothness of generalized solutions with respect to time is independent of the structure of the boundary of the domain but depends on the coefficients of the right-hand side. Results on the smoothness of the generalized solution and its asymptotic behaviour in a neighbourhood of a conical boundary point are also obtained

Characterizations of the power distribution by record values

Indian Academy of Sciences (India)

lutely continuous distribution function F(x) with probability density function f (x) and. F(0) = 0. Assume that Xn .... du = 0, 0 ≤ w < 1. (3.6). Integration (3.6) with respect to w from 0 to w1, we get the following equation ... By the theory of functional equations [1], the only continuous solution of (3.8) with boundary conditions F(0) ...

Development of gravity theory application in the internalregional inter-zone commodity movement distribution with the origin zone movement generation boundary

Science.gov (United States)

Akbardin, J.; Parikesit, D.; Riyanto, B.; TMulyono, A.

2018-05-01

Zones that produce land fishery commodity and its yields have characteristics that is limited in distribution capability because infrastructure conditions availability. High demand for fishery commodities caused to a growing distribution at inefficient distribution distance. The development of the gravity theory with the limitation of movement generation from the production zone can increase the interaction inter-zones by distribution distances effectively and efficiently with shorter movement distribution distances. Regression analysis method with multiple variable of transportation infrastructure condition based on service level and quantitative capacity is determined to estimate the 'mass' of movement generation that is formed. The resulting movement distribution (Tid) model has the equation Tid = 27.04 -0.49 tid. Based on barrier function of power model with calibration value β = 0.0496. In the way of development of the movement generation 'mass' boundary at production zone will shorten the distribution distance effectively with shorter distribution distances. Shorter distribution distances will increase the accessibility inter-zones to interact according to the magnitude of the movement generation 'mass'.

On Solutions of the Integrable Boundary Value Problem for KdV Equation on the Semi-Axis

International Nuclear Information System (INIS)

Ignatyev, M. Yu.

2013-01-01

This paper is concerned with the Korteweg–de Vries (KdV) equation on the semi-axis. The boundary value problem with inhomogeneous integrable boundary conditions is studied. We establish some characteristic properties of solutions of the problem. Also we construct a wide class of solutions of the problem using the inverse spectral method.

An analytical approximation scheme to two-point boundary value problems of ordinary differential equations

International Nuclear Information System (INIS)

Boisseau, Bruno; Forgacs, Peter; Giacomini, Hector

2007-01-01

A new (algebraic) approximation scheme to find global solutions of two-point boundary value problems of ordinary differential equations (ODEs) is presented. The method is applicable for both linear and nonlinear (coupled) ODEs whose solutions are analytic near one of the boundary points. It is based on replacing the original ODEs by a sequence of auxiliary first-order polynomial ODEs with constant coefficients. The coefficients in the auxiliary ODEs are uniquely determined from the local behaviour of the solution in the neighbourhood of one of the boundary points. The problem of obtaining the parameters of the global (connecting) solutions, analytic at one of the boundary points, reduces to find the appropriate zeros of algebraic equations. The power of the method is illustrated by computing the approximate values of the 'connecting parameters' for a number of nonlinear ODEs arising in various problems in field theory. We treat in particular the static and rotationally symmetric global vortex, the skyrmion, the Abrikosov-Nielsen-Olesen vortex, as well as the 't Hooft-Polyakov magnetic monopole. The total energy of the skyrmion and of the monopole is also computed by the new method. We also consider some ODEs coming from the exact renormalization group. The ground-state energy level of the anharmonic oscillator is also computed for arbitrary coupling strengths with good precision. (fast track communication)

Collisional plasma transport: two-dimensional scalar formulation of the initial boundary value problem and quasi one-dimensional models

International Nuclear Information System (INIS)

Mugge, J.W.

1979-10-01

The collisional plasma transport problem is formulated as an initial boundary value problem for general characteristic boundary conditions. Starting from the full set of hydrodynamic and electrodynamic equations an expansion in the electron-ion mass ratio together with a multiple timescale method yields simplified equations on each timescale. On timescales where many collisions have taken place for the simplified equations the initial boundary value problem is formulated. Through the introduction of potentials a two-dimensional scalar formulation in terms of quasi-linear integro-differential equations of second order for a domain consisting of plasma and vacuum sub-domains is obtained. (Auth.)

Initial-boundary-value problem of the self-gravitating scalar field in the Bondi-Sachs gauge

International Nuclear Information System (INIS)

Frittelli, Simonetta; Gomez, Roberto

2007-01-01

It is shown that, in the Bondi-Sachs gauge that fixes the speed of incoming light rays to the value 1, the Einstein equations coupled to a scalar field in spherical symmetry are cast into a symmetric-hyperbolic system of equations for the scalar field, lapse and shift as fundamental variables. In this system of equations, the lapse and shift are incoming characteristic fields, and the scalar field has three components: incoming, outgoing and static. A constraint-preserving boundary condition is prescribed by imposing the projection of the Einstein equation normal to the boundary at the outer value of the radial coordinate. The boundary condition specifies one of the two incoming metric fields. The remaining incoming metric field and the incoming scalar field component need to be specified arbitrarily. Numerical simulations of the scattering of the scalar field by a black hole in the nonlinear regime are presented that illustrate interesting facts about black-hole physics and the behavior of the characteristic variables of the problem

Numerical solution of large nonlinear boundary value problems by quadratic minimization techniques

International Nuclear Information System (INIS)

Glowinski, R.; Le Tallec, P.

1984-01-01

The objective of this paper is to describe the numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques. In all the different situations where these techniques were applied, the methodology remains the same and is organized as follows: 1) derive a variational formulation of the original boundary value problem, and approximate it by Galerkin methods; 2) transform this variational formulation into a quadratic minimization problem (least squares methods) or into a sequence of quadratic minimization problems (augmented lagrangian decomposition); 3) solve each quadratic minimization problem by a conjugate gradient method with preconditioning, the preconditioning matrix being sparse, positive definite, and fixed once for all in the iterative process. This paper will illustrate the methodology above on two different examples: the description of least squares solution methods and their application to the solution of the unsteady Navier-Stokes equations for incompressible viscous fluids; the description of augmented lagrangian decomposition techniques and their application to the solution of equilibrium problems in finite elasticity

Symmetry analysis and exact solutions of one class of (1+3)-dimensional boundary-value problems of the Stefan type

OpenAIRE

Kovalenko, S. S.

2014-01-01

We present the group classification of one class of (1+3)-dimensional nonlinear boundary-value problems of the Stefan type that simulate the processes of melting and evaporation of metals. The results obtained are used for the construction of the exact solution of one boundary-value problem from the class under study.

Existence and uniqueness for a two-point interface boundary value problem

Directory of Open Access Journals (Sweden)

Rakhim Aitbayev

2013-10-01

Full Text Available We obtain sufficient conditions, easily verifiable, for the existence and uniqueness of piecewise smooth solutions of a linear two-point boundary-value problem with general interface conditions. The coefficients of the differential equation may have jump discontinuities at the interface point. As an example, the conditions obtained are applied to a problem with typical interface such as perfect contact, non-perfect contact, and flux jump conditions.

Non-equilibrium grain boundary segregation of boron in austenitic stainless steel - IV. Precipitation behaviour and distribution of elements at grain boundaries

International Nuclear Information System (INIS)

Karlsson, L.; Norden, H.

1988-01-01

The distribution of elements and the precipitation behaviour at grain boundaries have been studied in boron containing AISI 316L and ''Mo-free AISI 316L'' type austenitic stainless steels. A combination of microanalytical techniques was used to study the boundary regions after cooling at 0.29-530 0 C/s from 800, 1075 or 1250 0 C. Tetragonal M/sub 2/B, M/sub 5/B/sub 3/ and M/sub 3/B/sub 2/, all rich in Fe, Cr and Mo, precipitated in the ''high B'' (40 ppm) AISI 316L steel whereas orthorhombic M/sub 2/B, rich in Cr and Fe was found in the ''Mo-free steel'' with 23 ppm B. In the ''high B steel'' a thin (<2nm), continuous layer, containing B, Cr, Mo and Fe and having a stoichiometry of typically M/sub 9/B, formed at boundaries after cooling at intermediate cooling rates. For both types of steels a boundary zone was found, after all heat treatments, with a composition differing significantly from the bulk composition. The differences were most marked after cooling at intermediate cooling rates. In both types of steel boundary depletion of Cr and enrichment of B and C occurred. It was found that non-equilibrium grain boundary segregation of boron can affect the precipitation behaviour by making the boundary composition enter a new phase field ''Non-equilibrium phases'' might also form. The synergistic effect of B and Mo on the boundary composition and precipitation behaviour, and the observed indications of C non-equilibrium segregation are discussed

Simultaneous reconstruction of outer boundary shape and conductivity distribution in electrical impedance tomography

KAUST Repository

Hyvönen, Nuutti

2016-01-05

The simultaneous retrieval of the exterior boundary shape and the interior admittivity distribution of an examined body in electrical impedance tomography is considered. The reconstruction method is built for the complete electrode model and it is based on the Frechet derivative of the corresponding current-to-voltage map with respect to the body shape. The reconstruction problem is cast into the Bayesian framework, and maximum a posteriori estimates for the admittivity and the boundary geometry are computed. The feasibility of the approach is evaluated by experimental data from water tank measurements.

Investigation of solutions of state-dependent multi-impulsive boundary value problems

Czech Academy of Sciences Publication Activity Database

Rontó, András; Rachůnková, I.; Rontó, M.; Rachůnek, L.

2017-01-01

Roč. 24, č. 2 (2017), s. 287-312 ISSN 1072-947X R&D Projects: GA ČR(CZ) GA14-06958S Institutional support: RVO:67985840 Keywords : state-dependent multi-impulsive systems * non-linear boundary value problem * parametrization technique Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0084/gmj-2016-0084. xml

Investigation of solutions of state-dependent multi-impulsive boundary value problems

Czech Academy of Sciences Publication Activity Database

Rontó, András; Rachůnková, I.; Rontó, M.; Rachůnek, L.

2017-01-01

Roč. 24, č. 2 (2017), s. 287-312 ISSN 1072-947X R&D Projects: GA ČR(CZ) GA14-06958S Institutional support: RVO:67985840 Keywords : state-dependent multi-impulsive systems * non-linear boundary value problem * parametrization technique Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0084/gmj-2016-0084.xml

Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions

KAUST Repository

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

2016-01-01

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

Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions

KAUST Repository

Ruggeri, Fabrizio

2015-01-07

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

Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions

KAUST Repository

Ruggeri, Fabrizio

2016-01-06

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

Integral boundary-value problem for impulsive fractional functional differential equations with infinite delay

Directory of Open Access Journals (Sweden)

Archana Chauhan

2012-12-01

Full Text Available In this article, we establish a general framework for finding solutions for impulsive fractional integral boundary-value problems. Then, we prove the existence and uniqueness of solutions by applying well known fixed point theorems. The obtained results are illustrated with an example for their feasibility.

Numerical Analysis of Forth-Order Boundary Value Problems in Fluid Mechanics and Mathematics

DEFF Research Database (Denmark)

Hosseinzadeh, E.; Barari, Amin; Fouladi, F.

2011-01-01

In this paper He's variational iteration method is used to solve some examples of linear and non-linear forth-order boundary value problems. The first problem compared with homotopy analysis method solution and the other ones with the exact solution. The results show the high accuracy and speed o...

Numerical analysis of fourth-order boundary value problems in fluid mechanics and mathematics

DEFF Research Database (Denmark)

Hosseinzadeh, Elham; Barari, Amin; Fouladi, Fama

2010-01-01

In this paper He's variational iteration method is used to solve some examples of linear and non-linear forth-order boundary value problems. The first problem compared with homotopy analysis method solution and the other ones with the exact solution. The results show the high accuracy and speed o...

Geopotential coefficient determination and the gravimetric boundary value problem: A new approach

Science.gov (United States)

Sjoeberg, Lars E.

1989-01-01

New integral formulas to determine geopotential coefficients from terrestrial gravity and satellite altimetry data are given. The formulas are based on the integration of data over the non-spherical surface of the Earth. The effect of the topography to low degrees and orders of coefficients is estimated numerically. Formulas for the solution of the gravimetric boundary value problem are derived.

Influence of the characteristics of atmospheric boundary layer on the vertical distribution of air pollutant in China's Yangtze River Delta

Science.gov (United States)

Wang, Chenggang; Cao, Le

2016-04-01

Air pollution occurring in the atmospheric boundary layer is a kind of weather phenomenon which decreases the visibility of the atmosphere and results in poor air quality. Recently, the occurrence of the heavy air pollution events has become more frequent all over Asia, especially in Mid-Eastern China. In December 2015, the most severe air pollution in recorded history of China occurred in the regions of Yangtze River Delta and Beijing-Tianjin-Hebei. More than 10 days of severe air pollution (Air Quality Index, AQI>200) appeared in many large cities of China such as Beijing, Tianjin, Shijiazhuang and Baoding. Thus, the research and the management of the air pollution has attracted most attentions in China. In order to investigate the formation, development and dissipation of the air pollutions in China, a field campaign has been conducted between January 1, 2015 and January 28, 2015 in Yangtze River Delta of China, aiming at a intensive observation of the vertical structure of the air pollutants in the atmospheric boundary layer during the time period with heavy pollution. In this study, the observation data obtained in the field campaign mentioned above is analyzed. The characteristics of the atmospheric boundary layer and the vertical distribution of air pollutants in the city Dongshan located in the center of Lake Taihu are shown and discussed in great detail. It is indicated that the stability of the boundary layer is the strongest during the nighttime and the early morning of Dongshan. Meanwhile, the major air pollutants, PM2.5 and PM10 in the boundary layer, reach their maximum values, 177.1μg m-3 and 285μg m-3 respectively. The convective boundary layer height in the observations ranges from approximately 700m to 1100m. It is found that the major air pollutants tend to be confined in a relatively shallow boundary layer, which represents that the boundary layer height is the dominant factor for controlling the vertical distribution of the air pollutants. In

A radial distribution function-based open boundary force model for multi-centered molecules

KAUST Repository

Neumann, Philipp

2014-06-01

We derive an expression for radial distribution function (RDF)-based open boundary forcing for molecules with multiple interaction sites. Due to the high-dimensionality of the molecule configuration space and missing rotational invariance, a computationally cheap, 1D approximation of the arising integral expressions as in the single-centered case is not possible anymore. We propose a simple, yet accurate model invoking standard molecule- and site-based RDFs to approximate the respective integral equation. The new open boundary force model is validated for ethane in different scenarios and shows very good agreement with data from periodic simulations. © World Scientific Publishing Company.

The influence of the engine load on value and temperature distribution in the valve seats of turbo diesel engine

Directory of Open Access Journals (Sweden)

Aleksander HORNIK

2009-01-01

Full Text Available In this paper was presented the numerical computations of the influence of engine load on value and temperature distribution of characteristic surfaces of the heat transfer of the valve seats in Turbo diesel engine at the beginning phase of its work. The computations were performed by means of a two-zone combustion model, the boundary of III kind conditions and the finite elements method (FEM by adaptation of the COSMOS/M program.

The nonlocal boundary value problems for strongly singular higher-order nonlinear functional-differential equations

Czech Academy of Sciences Publication Activity Database

Mukhigulashvili, Sulkhan

-, č. 35 (2015), s. 23-50 ISSN 1126-8042 Institutional support: RVO:67985840 Keywords : higher order functional differential equations * Dirichlet boundary value problem * strong singularity Subject RIV: BA - General Mathematics http://ijpam.uniud.it/online_issue/201535/03-Mukhigulashvili.pdf

Evolution of grain boundary character distributions in alloy 825 tubes during high temperature annealing: Is grain boundary engineering achieved through recrystallization or grain growth?

International Nuclear Information System (INIS)

Bai, Qin; Zhao, Qing; Xia, Shuang; Wang, Baoshun; Zhou, Bangxin; Su, Cheng

2017-01-01

Grain boundary engineering (GBE) of nickel-based alloy 825 tubes was carried out with different cold drawing deformations by using a draw-bench on a factory production line and subsequent annealing at various temperatures. The microstructure evolution of alloy 825 during thermal-mechanical processing (TMP) was characterized by means of the electron backscatter diffraction (EBSD) technique to study the TMP effects on the grain boundary network and the evolution of grain boundary character distributions during high temperature annealing. The results showed that the proportion of ∑ 3 n coincidence site lattice (CSL) boundaries of alloy 825 tubes could be increased to > 75% by the TMP of 5% cold drawing and subsequent annealing at 1050 °C for 10 min. The microstructures of the partially recrystallized samples and the fully recrystallized samples suggested that the proportion of low ∑ CSL grain boundaries depended on the annealing time. The frequency of low ∑ CSL grain boundaries increases rapidly with increasing annealing time associating with the formation of large-size highly-twinned grains-cluster microstructure during recrystallization. However, upon further increasing annealing time, the frequency of low ∑ CSL grain boundaries decreased markedly during grain growth. So it is concluded that grain boundary engineering is achieved through recrystallization rather than grain growth. - Highlights: •The grain boundary engineering (GBE) is applicable to 825 tubes. •GBE is achieved through recrystallization rather than grain growth. •The low ∑ CSL grain boundaries in 825 tubes can be increased to > 75%.

On Existence of Solutions to the Caputo Type Fractional Order Three-Point Boundary Value Problems

Directory of Open Access Journals (Sweden)

B.M.B. Krushna

2016-10-01

Full Text Available In this paper, we establish the existence of solutions to the fractional order three-point boundary value problems by utilizing Banach contraction principle and Schaefer's fixed point theorem.

Distribution of convection potential around the polar cap boundary as a function of the interplanetary magnetic field

International Nuclear Information System (INIS)

Lu, G.; Reiff, P.H.; Karty, J.L.; Hairston, M.R.; Heelis, R.A.

1989-01-01

Plasma flow data from the AE-C, AE-D and DE 2 satellites have been used to systematically study the distribution of the convection potential around the polar cap boundary under a variety of different interplanetary magnetic field (IMF) conditions. For either a garden hose (B x B y x B y >0) orientation of the IMF, the potential distribution is mainly affected by the sign of B y . In the northern hemisphere, the zero potential line (which separates the dusk convection cell from the dawn cell) on the dayside shifts duskward as B y changes from positive to negative. But in the southern hemisphere, a dawnward shift has been found, although the uncertainties are large. The typical range of displacement is about ±1.5 hours MLT. Note that this shift is in the opposite direction from most simple schematic models of ionospheric flow; this reflects the fact that the polar cap boundary is typically more poleward than the flow reversal associated with the region 1 current system, which shifts in the opposite direction. Thus the enhanced flow region typically crosses noon. In most cases a sine wave is an adequate representation of the distribution of potential around the boundary. However, in a few cases the data favors (at the 80% confidence level) a steeper gradient near noon, more indicative of a throat. The potential drop at the duskside boundary is almost greater than at the dawnside boundary. A slight duskward shift of the patterns observed as the IMF changes from garden hose to ortho-garden hose conditions. Analytic equipotential contours, given the potential function as a boundary condition, are constructed for several IMF conditions

Boundary curves of individual items in the distribution of total depressive symptom scores approximate an exponential pattern in a general population.

Science.gov (United States)

Tomitaka, Shinichiro; Kawasaki, Yohei; Ide, Kazuki; Akutagawa, Maiko; Yamada, Hiroshi; Furukawa, Toshiaki A; Ono, Yutaka

2016-01-01

Previously, we proposed a model for ordinal scale scoring in which individual thresholds for each item constitute a distribution by each item. This lead us to hypothesize that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores follow a common mathematical model, which is expressed as the product of the frequency of the total depressive symptom scores and the probability of the cumulative distribution function of each item threshold. To verify this hypothesis, we investigated the boundary curves of the distribution of total depressive symptom scores in a general population. Data collected from 21,040 subjects who had completed the Center for Epidemiologic Studies Depression Scale (CES-D) questionnaire as part of a national Japanese survey were analyzed. The CES-D consists of 20 items (16 negative items and four positive items). The boundary curves of adjacent item scores in the distribution of total depressive symptom scores for the 16 negative items were analyzed using log-normal scales and curve fitting. The boundary curves of adjacent item scores for a given symptom approximated a common linear pattern on a log normal scale. Curve fitting showed that an exponential fit had a markedly higher coefficient of determination than either linear or quadratic fits. With negative affect items, the gap between the total score curve and boundary curve continuously increased with increasing total depressive symptom scores on a log-normal scale, whereas the boundary curves of positive affect items, which are not considered manifest variables of the latent trait, did not exhibit such increases in this gap. The results of the present study support the hypothesis that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores commonly follow the predicted mathematical model, which was verified to approximate an exponential mathematical pattern.

Boundary curves of individual items in the distribution of total depressive symptom scores approximate an exponential pattern in a general population

Directory of Open Access Journals (Sweden)

Shinichiro Tomitaka

2016-10-01

Full Text Available Background Previously, we proposed a model for ordinal scale scoring in which individual thresholds for each item constitute a distribution by each item. This lead us to hypothesize that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores follow a common mathematical model, which is expressed as the product of the frequency of the total depressive symptom scores and the probability of the cumulative distribution function of each item threshold. To verify this hypothesis, we investigated the boundary curves of the distribution of total depressive symptom scores in a general population. Methods Data collected from 21,040 subjects who had completed the Center for Epidemiologic Studies Depression Scale (CES-D questionnaire as part of a national Japanese survey were analyzed. The CES-D consists of 20 items (16 negative items and four positive items. The boundary curves of adjacent item scores in the distribution of total depressive symptom scores for the 16 negative items were analyzed using log-normal scales and curve fitting. Results The boundary curves of adjacent item scores for a given symptom approximated a common linear pattern on a log normal scale. Curve fitting showed that an exponential fit had a markedly higher coefficient of determination than either linear or quadratic fits. With negative affect items, the gap between the total score curve and boundary curve continuously increased with increasing total depressive symptom scores on a log-normal scale, whereas the boundary curves of positive affect items, which are not considered manifest variables of the latent trait, did not exhibit such increases in this gap. Discussion The results of the present study support the hypothesis that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores commonly follow the predicted mathematical model, which was verified to approximate an

Initial boundary value problems of nonlinear wave equations in an exterior domain

International Nuclear Information System (INIS)

Chen Yunmei.

1987-06-01

In this paper, we investigate the existence and uniqueness of the global solutions to the initial boundary value problems of nonlinear wave equations in an exterior domain. When the space dimension n >= 3, the unique global solution of the above problem is obtained for small initial data, even if the nonlinear term is fully nonlinear and contains the unknown function itself. (author). 10 refs

Existence of positive solutions for a multi-point four-order boundary-value problem

Directory of Open Access Journals (Sweden)

Le Xuan Truong

2011-10-01

Full Text Available The article shows sufficient conditions for the existence of positive solutions to a multi-point boundary-value problem for a fourth-order differential equation. Our main tools are the Guo-Krasnoselskii fixed point theorem and the monotone iterative technique. We also show that the set of positive solutions is compact.

Remark on periodic boundary-value problem for second-order linear ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Dosoudilová, M.; Lomtatidze, Alexander

2018-01-01

Roč. 2018, č. 13 (2018), s. 1-7 ISSN 1072-6691 Institutional support: RVO:67985840 Keywords : second-order linear equation * periodic boundary value problem * unique solvability Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.954, year: 2016 https://ejde.math.txstate.edu/Volumes/2018/13/abstr.html

Improvement of corrosion resistance in austenitic stainless steel by grain boundary character distribution control

International Nuclear Information System (INIS)

Wang, Yun; Kaneda, Junya; Kasahara, Shigeki; Shigenaka, Naoto

2012-01-01

Strauss test, Coriou test and Huey test were conducted on a Type 316L austenitic stainless steel. Improvement in grain boundary corrosion resistance was verified after raising low Σ coincidence site lattice (CSL) grain boundary (GB) frequency by controlling grain boundary character distribution (GBCD). During crevice corrosion test under gamma-ray irradiation, initiation frequency of GB corrosion after GBCD controlled specimens decreased to 1/10 of GBCD uncontrolled counterpart along with lower depth of corrosion. Stress corrosion cracking (SCC) propagation rate of GBCD controlled specimen decreased to less than 1/2 of GBCD uncontrolled specimen in high temperature and high pressure water. Based on these results, we expect that GBCD control will improve corrosion resistance of austenitic material in a wide range of application and environment. (author)

Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm

Directory of Open Access Journals (Sweden)

Omar Abu Arqub

2012-01-01

Full Text Available In this paper, the continuous genetic algorithm is applied for the solution of singular two-point boundary value problems, where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values. The proposed technique might be considered as a variation of the finite difference method in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. This novel approach possesses main advantages; it can be applied without any limitation on the nature of the problem, the type of singularity, and the number of mesh points. Numerical examples are included to demonstrate the accuracy, applicability, and generality of the presented technique. The results reveal that the algorithm is very effective, straightforward, and simple.

Appling Laplace Adomian decomposition method for delay differential equations with boundary value problems

Science.gov (United States)

Yousef, Hamood Mohammed; Ismail, Ahmad Izani

2017-11-01

In this paper, Laplace Adomian decomposition method (LADM) was applied to solve Delay differential equations with Boundary Value Problems. The solution is in the form of a convergent series which is easy to compute. This approach is tested on two test problem. The findings obtained exhibit the reliability and efficiency of the proposed method.

Boundary value problemfor multidimensional fractional advection-dispersion equation

Directory of Open Access Journals (Sweden)

Khasambiev Mokhammad Vakhaevich

2015-05-01

Full Text Available In recent time there is a very great interest in the study of differential equations of fractional order, in which the unknown function is under the symbol of fractional derivative. It is due to the development of the theory of fractional integro-differential theory and application of it in different fields.The fractional integrals and derivatives of fractional integro-differential equations are widely used in modern investigations of theoretical physics, mechanics, and applied mathematics. The fractional calculus is a very powerful tool for describing physical systems, which have a memory and are non-local. Many processes in complex systems have nonlocality and long-time memory. Fractional integral operators and fractional differential operators allow describing some of these properties. The use of the fractional calculus will be helpful for obtaining the dynamical models, in which integro-differential operators describe power long-time memory by time and coordinates, and three-dimensional nonlocality for complex medium and processes.Differential equations of fractional order appear when we use fractal conception in physics of the condensed medium. The transfer, described by the operator with fractional derivatives at a long distance from the sources, leads to other behavior of relatively small concentrations as compared with classic diffusion. This fact redefines the existing ideas about safety, based on the ideas on exponential velocity of damping. Fractional calculus in the fractal theory and the systems with memory have the same importance as the classic analysis in mechanics of continuous medium.In recent years, the application of fractional derivatives for describing and studying the physical processes of stochastic transfer is very popular too. Many problems of filtration of liquids in fractal (high porous medium lead to the need to study boundary value problems for partial differential equations in fractional order.In this paper the

Classical boundary-value problem in Riemannian quantum gravity and self-dual Taub-NUT-(anti)de Sitter geometries

International Nuclear Information System (INIS)

Akbar, M.M.; D'Eath, P.D.

2003-01-01

The classical boundary-value problem of the Einstein field equations is studied with an arbitrary cosmological constant, in the case of a compact (S 3 ) boundary given a biaxial Bianchi-IX positive-definite three-metric, specified by two radii (a,b). For the simplest, four-ball, topology of the manifold with this boundary, the regular classical solutions are found within the family of Taub-NUT-(anti)de Sitter metrics with self-dual Weyl curvature. For arbitrary choice of positive radii (a,b), we find that there are three solutions for the infilling geometry of this type. We obtain exact solutions for them and for their Euclidean actions. The case of negative cosmological constant is investigated further. For reasonable squashing of the three-sphere, all three infilling solutions have real-valued actions which possess a 'cusp catastrophe' structure with a non-self-intersecting 'catastrophe manifold' implying that the dominant contribution comes from the unique real positive-definite solution on the ball. The positive-definite solution exists even for larger deformations of the three-sphere, as long as a certain inequality between a and b holds. The action of this solution is proportional to -a 3 for large a (∼b) and hence larger radii are favoured. The same boundary-value problem with more complicated interior topology containing a 'bolt' is investigated in a forthcoming paper

The Method of Subsuper Solutions for Weighted p(r-Laplacian Equation Boundary Value Problems

Directory of Open Access Journals (Sweden)

Zhimei Qiu

2008-10-01

Full Text Available This paper investigates the existence of solutions for weighted p(r-Laplacian ordinary boundary value problems. Our method is based on Leray-Schauder degree. As an application, we give the existence of weak solutions for p(x-Laplacian partial differential equations.

Convolution of Distribution-Valued Functions. Applications.

OpenAIRE

BARGETZ, CHRISTIAN

2011-01-01

In this article we examine products and convolutions of vector-valued functions. For nuclear normal spaces of distributions Proposition 25 in [31,p. 120] yields a vector-valued product or convolution if there is a continuous product or convolution mapping in the range of the vector-valued functions. For specific spaces, we generalize this result to hypocontinuous bilinear maps at the expense of generality with respect to the function space. We consider holomorphic, meromorphic and differentia...

Positive solutions for a nonlinear periodic boundary-value problem with a parameter

Directory of Open Access Journals (Sweden)

Jingliang Qiu

2012-08-01

Full Text Available Using topological degree theory with a partially ordered structure of space, sufficient conditions for the existence and multiplicity of positive solutions for a second-order nonlinear periodic boundary-value problem are established. Inspired by ideas in Guo and Lakshmikantham [6], we study the dependence of positive periodic solutions as a parameter approaches infinity, $$ lim_{lambdao +infty}|x_{lambda}|=+infty,quadhbox{or}quad lim_{lambdao+infty}|x_{lambda}|=0. $$

Existence of Positive Solutions to a Boundary Value Problem for a Delayed Nonlinear Fractional Differential System

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Chen Yuming

2011-01-01

Full Text Available Though boundary value problems for fractional differential equations have been extensively studied, most of the studies focus on scalar equations and the fractional order between 1 and 2. On the other hand, delay is natural in practical systems. However, not much has been done for fractional differential equations with delays. Therefore, in this paper, we consider a boundary value problem of a general delayed nonlinear fractional system. With the help of some fixed point theorems and the properties of the Green function, we establish several sets of sufficient conditions on the existence of positive solutions. The obtained results extend and include some existing ones and are illustrated with some examples for their feasibility.

B-spline solution of a singularly perturbed boundary value problem arising in biology

International Nuclear Information System (INIS)

Lin Bin; Li Kaitai; Cheng Zhengxing

2009-01-01

We use B-spline functions to develop a numerical method for solving a singularly perturbed boundary value problem associated with biology science. We use B-spline collocation method, which leads to a tridiagonal linear system. The accuracy of the proposed method is demonstrated by test problems. The numerical result is found in good agreement with exact solution.

Uniqueness in some higher order elliptic boundary value problems in n dimensional domains

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C.-P. Danet

2011-07-01

Full Text Available We develop maximum principles for several P functions which are defined on solutions to equations of fourth and sixth order (including a equation which arises in plate theory and bending of cylindrical shells. As a consequence, we obtain uniqueness results for fourth and sixth order boundary value problems in arbitrary n dimensional domains.

Trans-boundary movement of mercury in the Northeast Asian region predicted by CAMQ-Hg from anthropogenic emissions distribution

Science.gov (United States)

Sung, Jin-Ho; Roy, Debananda; Oh, Joo-Sung; Back, Seung-Ki; Jang, Ha-Na; Kim, Seong-Heon; Seo, Yong-Chil; Kim, Jeong-Hun; Lee, Chong Bum; Han, Young-Ji

2018-05-01

The percentage contribution of trans-boundary mercury (Hg) from China at different locations in South Korea was estimated from Hg anthropogenic emission distributions using the Hg dispersion model, CMAQ-Hg. This investigation quantifies the trans-boundary Hg emissions as contribution ratios. In addition, the long-range transportation frequency is also calculated, to verify inflow cases from China. The seasonal distribution of the Hg contribution ratio was found to be highest in winter (40%), followed by fall (16%). Seasonal observations of Hg inflow frequencies were estimated as 40%, 25%, 21%, and 4% in winter, fall, summer, and spring, respectively, at the same location. Such results would be produced by the wind generally blowing from the west and north-west with a speed of 5.0 m/s and 4.5 m/s, respectively, during winter and fall, around the study area. This study made an effort to quantify the trans-boundary Hg transport and to plot Hg anthropogenic emissions distribution in the region.

Student Solutions Manual to Boundary Value Problems and Partial Differential Equations

CERN Document Server

Powers, David L

2005-01-01

This student solutions manual accompanies the text, Boundary Value Problems and Partial Differential Equations, 5e. The SSM is available in print via PDF or electronically, and provides the student with the detailed solutions of the odd-numbered problems contained throughout the book.Provides students with exercises that skillfully illustrate the techniques used in the text to solve science and engineering problemsNearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercisesMany exercises based on current engineering applications

Experimental data on heat flux distribution from a volumetrically heated pool with frozen boundaries

International Nuclear Information System (INIS)

Helle, Maria; Kymaelaeinen, Olli; Tuomisto, Harri

1999-01-01

The COPO II experiments are confirmatory experiments and a continuation project to the earlier COPO I experiments. As in COPO 1, a molten corium pool on the lower head of a RPV is simulated by a two - dimensional slice of it in linear scale 1:2. The corium is simulated by water-zinc sulfate solution with volumetric Joule heating. The heat flux distribution on the boundaries and the temperature distribution in the pool are measured. The major new feature in COPO II is the cooling arrangement which is based on circulation of liquid nitrogen on the outside of the pool boundaries. The use of liquid nitrogen leads to formation of ice on the inside of boundaries. Two geometrically different versions of the COPO II facility have been constructed: one with a tori-spherical bottom shape, simulating the RPV of a VVER-440 reactor as COPO I, and another one with semicircular bottom simulating a western PWR such as AP600. The modified Rayleigh number in the COPO II experiments corresponds to the one in a prototypic corium pool (∼ 10 15 ). This paper reports results from the COPO II-Lo and COPO II-AP experiments with homogenous pool. Results indicate that the upward heat fluxes are in agreement with the results of the COPO I experiments. Also, as expected, the time averaged upward heat flux profile was relatively flat. On the other hand, the heat fluxes at the side and bottom boundaries of the pool were slightly higher in COPO II-Lo than in COPO I. In COPO II-AP, the average heat transfer coefficients to the curved boundary were higher than predicted by Jahn's and Mayinger's correlation, but slightly lower than in BALI experiments. (authors)

Positive solutions of three-point boundary-value problems for p-Laplacian singular differential equations

Directory of Open Access Journals (Sweden)

George N. Galanis

2005-10-01

Full Text Available In this paper we prove the existence of positive solutions for the three-point singular boundary-value problem$$ -[phi _{p}(u']'=q(tf(t,u(t,quad 0boundary-value problem remains away from the origin for the case where the nonlinearity is sublinear and so we avoid its singularity at $u=0$.

A simple finite element method for boundary value problems with a Riemann–Liouville derivative

KAUST Repository

Jin, Bangti; Lazarov, Raytcho; Lu, Xiliang; Zhou, Zhi

2016-01-01

© 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-¹ in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and ^L2(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.

A simple finite element method for boundary value problems with a Riemann–Liouville derivative

KAUST Repository

Jin, Bangti

2016-02-01

© 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-¹ in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and ^L2(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.

Validation and Spatiotemporal Distribution of GEOS-5-Based Planetary Boundary Layer Height and Relative Humidity in China

Science.gov (United States)

Si, Yidan; Li, Shenshen; Chen, Liangfu; Yu, Chao; Wang, Zifeng; Wang, Yang; Wang, Hongmei

2018-04-01

Few studies have specifically focused on the validation and spatiotemporal distribution of planetary boundary layer height (PBLH) and relative humidity (RH) data in China. In this analysis, continuous PBLH and surface-level RH data simulated from GEOS-5 between 2004 and 2012, were validated against ground-based observations. Overall, the simulated RH was consistent with the statistical data from meteorological stations, with a correlation coefficient of 0.78 and a slope of 0.9. However, the simulated PBLH was underestimated compared to LIDAR data by a factor of approximately two, which was primarily because of poor simulation in late summer and early autumn. We further examined the spatiotemporal distribution characteristics of two factors in four regions—North China, South China, Northwest China, and the Tibetan Plateau. The results showed that the annual PBLH trends in all regions were fairly moderate but sensitive to solar radiation and precipitation, which explains why the PBLH values were ranked in order from largest to smallest as follows: Tibetan Plateau, Northwest China, North China, and South China. Strong seasonal variation of the PBLH exhibited high values in summer and low values in winter, which was also consistent with the turbulent vertical exchange. Not surprisingly, the highest RH in South China and the lowest RH in desert areas of Northwest China (less than 30%). Seasonally, South China exhibited little variation, whereas Northwest China exhibited its highest humidity in winter and lowest humidity in spring, the maximum values in the other regions were obtained from July to September.

Chaotic oscillations of the Klein-Gordon equation with distributed energy pumping and van der Pol boundary regulation and distributed time-varying coefficients

Directory of Open Access Journals (Sweden)

Bo Sun

2014-09-01

Full Text Available Consider the Klein-Gordon equation with variable coefficients, a van der Pol cubic nonlinearity in one of the boundary conditions and a spatially distributed antidamping term, we use a variable-substitution technique together with the analogy with the 1-dimensional wave equation to prove that for the Klein-Gordon equation chaos occurs for a class of equations and boundary conditions when system parameters enter a certain regime. Chaotic and nonchaotic profiles of solutions are illustrated by computer graphics.

Uniqueness in the inverse boundary value problem for piecewise homogeneous anisotropic elasticity

OpenAIRE

Cârstea, Cătălin I.; Honda, Naofumi; Nakamura, Gen

2016-01-01

Consider a three dimensional piecewise homogeneous anisotropic elastic medium $\\Omega$ which is a bounded domain consisting of a finite number of bounded subdomains $D_\\alpha$, with each $D_\\alpha$ a homogeneous elastic medium. One typical example is a finite element model with elements with curvilinear interfaces for an ansiotropic elastic medium. Assuming the $D_\\alpha$ are known and Lipschitz, we are concerned with the uniqueness in the inverse boundary value problem of identifying the ani...

Beyond a climate-centric view of plant distribution: edaphic variables add value to distribution models.

Science.gov (United States)

Beauregard, Frieda; de Blois, Sylvie

2014-01-01

Both climatic and edaphic conditions determine plant distribution, however many species distribution models do not include edaphic variables especially over large geographical extent. Using an exceptional database of vegetation plots (n = 4839) covering an extent of ∼55,000 km2, we tested whether the inclusion of fine scale edaphic variables would improve model predictions of plant distribution compared to models using only climate predictors. We also tested how well these edaphic variables could predict distribution on their own, to evaluate the assumption that at large extents, distribution is governed largely by climate. We also hypothesized that the relative contribution of edaphic and climatic data would vary among species depending on their growth forms and biogeographical attributes within the study area. We modelled 128 native plant species from diverse taxa using four statistical model types and three sets of abiotic predictors: climate, edaphic, and edaphic-climate. Model predictive accuracy and variable importance were compared among these models and for species' characteristics describing growth form, range boundaries within the study area, and prevalence. For many species both the climate-only and edaphic-only models performed well, however the edaphic-climate models generally performed best. The three sets of predictors differed in the spatial information provided about habitat suitability, with climate models able to distinguish range edges, but edaphic models able to better distinguish within-range variation. Model predictive accuracy was generally lower for species without a range boundary within the study area and for common species, but these effects were buffered by including both edaphic and climatic predictors. The relative importance of edaphic and climatic variables varied with growth forms, with trees being more related to climate whereas lower growth forms were more related to edaphic conditions. Our study identifies the potential

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

Science.gov (United States)

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.

Inverse Boundary Value Problem for Non-linear Hyperbolic Partial Differential Equations

OpenAIRE

Nakamura, Gen; Vashisth, Manmohan

2017-01-01

In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\\geq 3$. This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we have the usual linear isotropic wave equation with the speed $\\sqrt{\\gamma(x)}$ at each point $x$ in a given spacial domain. For any small solution $u=u(t,x)$ of this non-linear equation, we have the linear isotr...

Partial differential equations & boundary value problems with Maple

CERN Document Server

Articolo, George A

2009-01-01

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

Correspondence between the ULF wave power spatial distribution and auroral oval boundaries

Directory of Open Access Journals (Sweden)

Kozyreva O.V.

2016-06-01

Full Text Available The world-wide spatial distribution of the wave power in the Pc5 band during magnetic storms has been compared with auroral oval boundaries. The poleward and equatorward auroral oval boundaries are estimated using either the British Antarctic Survey database containing IMAGE satellite UV observations of the aurora or the OVATION model based on the DMSP particle data. The “epicenter” of the spectral power of broadband Pc5 fluctuations during the storm growth phase is mapped inside the auroral oval. During the storm recovery phase, the spectral power of narrowband Pc5 waves, both in the dawn and dusk sectors, is mapped inside the auroral oval or around its equatorward boundary. This observational result confirms previously reported effects: the spatial/temporal variations of the Pc5 wave power in the morning/pre-noon sector are closely related to the dynamics of the auroral electrojet and magnetospheric field-aligned currents. At the same time, narrowband Pc5 waves demonstrate typical resonant features in the amplitude-phase latitudinal structure. Thus, the location of the auroral oval or its equatorward boundary is the preferred latitude for magnetospheric field-line Alfven resonator excitation. This effect is not taken into account by modern theories of ULF Pc5 waves, but it could be significant for the development of more adequate models.

Layer potentials and boundary-value problems for second order elliptic operators with data in Besov spaces

CERN Document Server

Barton, Ariel

2016-01-01

This monograph presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable t-independent coefficients in spaces of fractional smoothness, in Besov and weighted L^p classes. The authors establish: (1) Mapping properties for the double and single layer potentials, as well as the Newton potential; (2) Extrapolation-type solvability results: the fact that solvability of the Dirichlet or Neumann boundary value problem at any given L^p space automatically assures their solvability in an extended range of Besov spaces; (3) Well-posedness for the non-homogeneous boundary value problems. In particular, the authors prove well-posedness of the non-homogeneous Dirichlet problem with data in Besov spaces for operators with real, not necessarily symmetric, coefficients.

The SMM Model as a Boundary Value Problem Using the Discrete Diffusion Equation

Science.gov (United States)

Campbell, Joel

2007-01-01

A generalized single step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.

Theorems on differential inequalities and periodic boundary value problem for second-order ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Lomtatidze, Alexander

2016-01-01

Roč. 67, č. 1 (2016), s. 1-129 ISSN 1512-0015 Institutional support: RVO:67985840 Keywords : periodic boundary value problem * positive solution * singular equation Subject RIV: BA - General Mathematics http://rmi.tsu.ge/jeomj/memoirs/vol67/abs67-1.htm

Existence of positive solutions for nonlocal second-order boundary value problem with variable parameter in Banach spaces

Directory of Open Access Journals (Sweden)

Zhang Peiguo

2011-01-01

Full Text Available Abstract By obtaining intervals of the parameter λ, this article investigates the existence of a positive solution for a class of nonlinear boundary value problems of second-order differential equations with integral boundary conditions in abstract spaces. The arguments are based upon a specially constructed cone and the fixed point theory in cone for a strict set contraction operator. MSC: 34B15; 34B16.

An Issue of Boundary Value for Velocity and Training Overhead Using Cooperative MIMO Technique in Wireless Sensor Network

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M. R. Islam

2011-06-01

Full Text Available A boundary value of velocity of data gathering node (DGN and a critical value for training overhead beyond which the cooperative communication in wireless sensor network will not be feasible is proposed in this paper. Multiple Input Multiple Outputs (MIMO cooperative communication is taken as an application. The performance in terms of energy efficiency and delay for a combination of two transmitting and two receiving antennas is analyzed. The results show that a set of critical value of velocity and training overhead pair is present for the long haul communication from the sensors to the data gathering node. Later a graphical relation between boundary value of training overhead and velocity is simulated. A mathematical relation between velocity and training overhead is also developed. The effects of several parameters on training overhead and velocity are analyzed.

Positive Solutions of Three-Order Delayed Periodic Boundary Value Problems

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Na Wang

2017-01-01

Full Text Available Our main purpose is to consider the existence of positive solutions for three-order two-point boundary value problem in the following form: u′′′(t+ρ3u(t=f(t,u(t-τ,  0≤t≤2π,  u(i(0=u(i(2π,  i=1,2,  u(t=σ,  -τ≤t≤0, where σ,ρ, and τ are given constants satisfying τ∈(0,π/2. Some inequality conditions on ρ3u-f(t,u guaranteeing the existence and nonexistence of positive solutions are presented. Our discussion is based on the fixed point theorem in cones.

Homotopy Analysis Method for Boundary-Value Problem of Turbo Warrant Pricing under Stochastic Volatility

Directory of Open Access Journals (Sweden)

Hoi Ying Wong

2013-01-01

Full Text Available Turbo warrants are liquidly traded financial derivative securities in over-the-counter and exchange markets in Asia and Europe. The structure of turbo warrants is similar to barrier options, but a lookback rebate will be paid if the barrier is crossed by the underlying asset price. Therefore, the turbo warrant price satisfies a partial differential equation (PDE with a boundary condition that depends on another boundary-value problem (BVP of PDE. Due to the highly complicated structure of turbo warrants, their valuation presents a challenging problem in the field of financial mathematics. This paper applies the homotopy analysis method to construct an analytic pricing formula for turbo warrants under stochastic volatility in a PDE framework.

A Hartman–Nagumo inequality for the vector ordinary -Laplacian and applications to nonlinear boundary value problems

Directory of Open Access Journals (Sweden)

Ureña Antonio J

2002-01-01

Full Text Available A generalization of the well-known Hartman–Nagumo inequality to the case of the vector ordinary -Laplacian and classical degree theory provide existence results for some associated nonlinear boundary value problems.

The focal boundary value problem for strongly singular higher-order nonlinear functional-differential equations

Czech Academy of Sciences Publication Activity Database

Mukhigulashvili, Sulkhan; Půža, B.

2015-01-01

Roč. 2015, January (2015), s. 17 ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : higher order nonlinear functional-differential equations * two-point right-focal boundary value problem * strong singularity Subject RIV: BA - General Mathematics Impact factor: 0.642, year: 2015 http://link.springer.com/article/10.1186%2Fs13661-014-0277-1

Solvability of fractional multi-point boundary-value problems with p-Laplacian operator at resonance

Directory of Open Access Journals (Sweden)

Tengfei Shen

2014-02-01

Full Text Available In this article, we consider the multi-point boundary-value problem for nonlinear fractional differential equations with $p$-Laplacian operator: $$\\displaylines{ D_{0^+}^\\beta \\varphi_p (D_{0^+}^\\alpha u(t = f(t,u(t,D_{0^+}^{\\alpha - 2} u(t,D_{0^+}^{\\alpha - 1} u(t, D_{0^+}^\\alpha u(t,\\quad t \\in (0,1, \\cr u(0 = u'(0=D_{0^+}^\\alpha u(0 = 0,\\quad D_{0^+}^{\\alpha - 1} u(1 = \\sum_{i = 1}^m {\\sigma_i D_{0^+}^{\\alpha - 1} u(\\eta_i } , }$$ where $2 < \\alpha \\le 3$, $0 < \\beta \\le 1$, $3 < \\alpha + \\beta \\le 4$, $\\sum_{i = 1}^m {\\sigma_i } = 1$, $D_{0^+}^\\alpha$ is the standard Riemann-Liouville fractional derivative. $\\varphi_{p}(s=|s|^{p-2}s$ is p-Laplacians operator. The existence of solutions for above fractional boundary value problem is obtained by using the extension of Mawhin's continuation theorem due to Ge, which enrich konwn results. An example is given to illustrate the main result.

A comparison of grain boundary evolution during grain growth in fcc metals

International Nuclear Information System (INIS)

Brons, J.G.; Thompson, G.B.

2013-01-01

Grain growth of Cu and Ni thin films, subjected to in situ annealing within a transmission electron microscope, has been quantified using a precession-enhanced electron diffraction technique. The orientation of each grain and its misorientation with respect to its neighboring grains were calculated. The Cu underwent grain growth that maintained a monomodal grain size distribution, with its low-angle grain boundaries being consumed, and the Ni exhibited grain size distributions in stages, from monomodal to bimodal to monomodal. The onset of Ni’s abnormal grain growth was accompanied by a sharp increase in the Σ3 and Σ9 boundary fractions, which is attributed to simulation predictions of their increased mobility. These Σ3 and Σ9 fractions then dropped to their room temperature values during the third stage of grain growth. In addition to the Σ3 and Σ9 boundaries, the Σ5 and Σ7 boundaries also underwent an increase in total boundary fraction with increasing temperature in both metals

Comparison of turbulence in a transitional boundary layer to turbulence in a developed boundary layer*

Science.gov (United States)

Park, G. I.; Wallace, J.; Wu, X.; Moin, P.

2010-11-01

Using a recent DNS of a flat-plate boundary layer, statistics of turbulence in transition at Reθ= 500 where spots merge (distributions of the mean velocity, rms velocity and vorticity fluctuations, Reynolds shear stress, kinetic energy production and dissipation rates and enstrophy) have been compared to these statistics for the developed boundary layer turbulence at Reθ= 1850. When the distributions in the transitional region, determined in narrow planes 0.03 Reθ wide, exclude regions and times when the flow is not turbulent, they closely resemble those in the developed turbulent state at the higher Reynolds number, especially in the buffer and sublayers. The skin friction coefficient, determined in this conditional manner in the transitional flow is, of course, much larger than that obtained by including both turbulent and non-turbulent information there, and is consistent with a value obtained by extrapolating from the developed turbulent region. We are attempting to perform this data analysis even further upstream in the transitioning flow at Reθ= 300 where the turbulent spots are individuated. These results add further evidence to support the view that the structure of a developed turbulent boundary layer is little different from its structure in its embryonic form in turbulent spots. *CTR 2010 Summer Program research.

Customer value and financial services distribution channels

OpenAIRE

Chakrabarty, Anita

2017-01-01

This research effort seeks to investigate the co-creation of customer value in distribution channels of financial services as perceived by customers. In financial services, an in-depth investigation of customer value is necessary because of its recognised strategic imperative for competitive advantage (Woodruff, 1997). The Service Dominant Logic further demonstrates the importance of customer value as the basis of customers’ evaluations of products or service offerings (Vargo and Lusch, 2004)...

Analytic solution of boundary-value problems for nonstationary model kinetic equations

International Nuclear Information System (INIS)

Latyshev, A.V.; Yushkanov, A.A.

1993-01-01

A theory for constructing the solutions of boundary-value problems for non-stationary model kinetic equations is constructed. This theory was incorrectly presented equation, separation of the variables is used, this leading to a characteristic equation. Eigenfunctions are found in the space of generalized functions, and the eigenvalue spectrum is investigated. An existence and uniqueness theorem for the expansion of the Laplace transform of the solution with respect to the eigenfunctions is proved. The proof is constructive and gives explicit expressions for the expansion coefficients. An application to the Rayleigh problem is obtained, and the corresponding result of Cercignani is corrected

Three-Field Modelling of Nonlinear Nonsmooth Boundary Value Problems and Stability of Differential Mixed Variational Inequalities

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J. Gwinner

2013-01-01

Full Text Available The purpose of this paper is twofold. Firstly we consider nonlinear nonsmooth elliptic boundary value problems, and also related parabolic initial boundary value problems that model in a simplified way steady-state unilateral contact with Tresca friction in solid mechanics, respectively, stem from nonlinear transient heat conduction with unilateral boundary conditions. Here a recent duality approach, that augments the classical Babuška-Brezzi saddle point formulation for mixed variational problems to twofold saddle point formulations, is extended to the nonsmooth problems under consideration. This approach leads to variational inequalities of mixed form for three coupled fields as unknowns and to related differential mixed variational inequalities in the time-dependent case. Secondly we are concerned with the stability of the solution set of a general class of differential mixed variational inequalities. Here we present a novel upper set convergence result with respect to perturbations in the data, including perturbations of the associated nonlinear maps, the nonsmooth convex functionals, and the convex constraint set. We employ epiconvergence for the convergence of the functionals and Mosco convergence for set convergence. We impose weak convergence assumptions on the perturbed maps using the monotonicity method of Browder and Minty.

Feasibility of estimating generalized extreme-value distribution of floods

International Nuclear Information System (INIS)

Ferreira de Queiroz, Manoel Moises

2004-01-01

Flood frequency analysis by generalized extreme-value probability distribution (GEV) has found increased application in recent years, given its flexibility in dealing with the three asymptotic forms of extreme distribution derived from different initial probability distributions. Estimation of higher quantiles of floods is usually accomplished by extrapolating one of the three inverse forms of GEV distribution fitted to the experimental data for return periods much higher than those actually observed. This paper studies the feasibility of fitting GEV distribution by moments of linear combinations of higher order statistics (LH moments) using synthetic annual flood series with varying characteristics and lengths. As the hydrologic events in nature such as daily discharge occur with finite values, their annual maximums are expected to follow the asymptotic form of the limited GEV distribution. Synthetic annual flood series were thus obtained from the stochastic sequences of 365 daily discharges generated by Monte Carlo simulation on the basis of limited probability distribution underlying the limited GEV distribution. The results show that parameter estimation by LH moments of this distribution, fitted to annual flood samples of less than 100-year length derived from initial limited distribution, may indicate any form of extreme-value distribution, not just the limited form as expected, and with large uncertainty in fitted parameters. A frequency analysis, on the basis of GEV distribution and LH moments, of annual flood series of lengths varying between 13 and 73 years observed at 88 gauge stations on Parana River in Brazil, indicated all the three forms of GEV distribution.(Author)

METHOD OF GREEN FUNCTIONS IN MATHEMATICAL MODELLING FOR TWO-POINT BOUNDARY-VALUE PROBLEMS

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E. V. Dikareva

2015-01-01

Full Text Available Summary. In many applied problems of control, optimization, system theory, theoretical and construction mechanics, for problems with strings and nods structures, oscillation theory, theory of elasticity and plasticity, mechanical problems connected with fracture dynamics and shock waves, the main instrument for study these problems is a theory of high order ordinary differential equations. This methodology is also applied for studying mathematical models in graph theory with different partitioning based on differential equations. Such equations are used for theoretical foundation of mathematical models but also for constructing numerical methods and computer algorithms. These models are studied with use of Green function method. In the paper first necessary theoretical information is included on Green function method for multi point boundary-value problems. The main equation is discussed, notions of multi-point boundary conditions, boundary functionals, degenerate and non-degenerate problems, fundamental matrix of solutions are introduced. In the main part the problem to study is formulated in terms of shocks and deformations in boundary conditions. After that the main results are formulated. In theorem 1 conditions for existence and uniqueness of solutions are proved. In theorem 2 conditions are proved for strict positivity and equal measureness for a pair of solutions. In theorem 3 existence and estimates are proved for the least eigenvalue, spectral properties and positivity of eigenfunctions. In theorem 4 the weighted positivity is proved for the Green function. Some possible applications are considered for a signal theory and transmutation operators.

Monotone methods for solving a boundary value problem of second order discrete system

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Wang Yuan-Ming

1999-01-01

Full Text Available A new concept of a pair of upper and lower solutions is introduced for a boundary value problem of second order discrete system. A comparison result is given. An existence theorem for a solution is established in terms of upper and lower solutions. A monotone iterative scheme is proposed, and the monotone convergence rate of the iteration is compared and analyzed. The numerical results are given.

Existence and Estimates of Positive Solutions for Some Singular Fractional Boundary Value Problems

Directory of Open Access Journals (Sweden)

Habib Mâagli

2014-01-01

fractional boundary value problem:Dαu(x=−a(xuσ(x, x∈(0,1 with the conditions limx→0+⁡x2−αu(x=0, u(1=0, where 1<α≤2, σ∈(−1,1, and a is a nonnegative continuous function on (0,1 that may be singular at x=0 or x=1. We also give the global behavior of such a solution.

Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds. I - Pressure distribution

Science.gov (United States)

Messiter, A. F.

1980-01-01

Asymptotic solutions are derived for the pressure distribution in the interaction of a weak normal shock wave with a turbulent boundary layer. The undisturbed boundary layer is characterized by the law of the wall and the law of the wake for compressible flow. In the limiting case considered, for 'high' transonic speeds, the sonic line is very close to the wall. Comparisons with experiment are shown, with corrections included for the effect of longitudinal wall curvature and for the boundary-layer displacement effect in a circular pipe.

The effect of wall temperature distribution on streaks in compressible turbulent boundary layer

Science.gov (United States)

Zhang, Zhao; Tao, Yang; Xiong, Neng; Qian, Fengxue

2018-05-01

The thermal boundary condition at wall is very important for the compressible flow due to the coupling of the energy equation, and a lot of research works about it were carried out in past decades. In most of these works, the wall was assumed as adiabatic or uniform isothermal surface; the flow over a thermal wall with some special temperature distribution was seldom studied. Lagha studied the effect of uniform isothermal wall on the streaks, and pointed out that higher the wall temperature is, the longer the streak (POF, 2011, 23, 015106). So, we designed streamwise stripes of wall temperature distribution on the compressible turbulent boundary layer at Mach 3.0 to learn the effect on the streaks by means of direct numerical simulation in this paper. The mean wall temperature is equal to the adiabatic case approximately, and the width of the temperature stripes is in the same order as the width of the streaks. The streak patterns in near-wall region with different temperature stripes are shown in the paper. Moreover, we find that there is a reduction of friction velocity with the wall temperature stripes when compared with the adiabatic case.

Effects of various forces on the distribution of particles at the boundary of a dusty plasma

International Nuclear Information System (INIS)

Liu, J.; Ma, J.X.

1997-01-01

The distribution and suspension of dust particles under the action of electrostatic, gravitational, ion-drag and neutral collision forces are investigated near the boundary of a dusty plasma. It is shown that the competition among the forces results in spatial oscillations (multi-layer) of the particle distribution. For sub-micron grains the ion-drag has a significant effect on the grain dynamics while for micrometer sized grains the gravity quickly dominates over other forces. The effect of the neutral gas flux is to enhance or diminish that of the gravity while the effect of the neutral viscosity is to shift the profile toward the wall. Under the force balance, the particles are suspended in a narrow region with sharp boundaries within the sheath. copyright 1997 American Institute of Physics

A new Ellipsoidal Gravimetric-Satellite Altimetry Boundary Value Problem; Case study: High Resolution Geoid of Iran

Science.gov (United States)

Ardalan, A.; Safari, A.; Grafarend, E.

2003-04-01

A new ellipsoidal gravimetric-satellite altimetry boundary value problem has been developed and successfully tested. This boundary value problem has been constructed for gravity observables of the type (i) gravity potential (ii) gravity intensity (iii) deflection of vertical and (iv) satellite altimetry data. The developed boundary value problem is enjoying the ellipsoidal nature and as such can take advantage of high precision GPS observations in the set-up of the problem. The highlights of the solution are as follows: begin{itemize} Application of ellipsoidal harmonic expansion up to degree/order and ellipsoidal centrifugal field for the reduction of global gravity and isostasy effects from the gravity observable at the surface of the Earth. Application of ellipsoidal Newton integral on the equal area map projection surface for the reduction of residual mass effects within a radius of 55 km around the computational point. Ellipsoidal harmonic downward continuation of the residual observables from the surface of the earth down to the surface of reference ellipsoid using the ellipsoidal height of the observation points derived from GPS. Restore of the removed effects at the application points on the surface of reference ellipsoid. Conversion of the satellite altimetry derived heights of the water bodies into potential. Combination of the downward continued gravity information with the potential equivalent of the satellite altimetry derived heights of the water bodies. Application of ellipsoidal Bruns formula for converting the potential values on the surface of the reference ellipsoid into the geoidal heights (i.e. ellipsoidal heights of the geoid) with respect to the reference ellipsoid. Computation of the high-resolution geoid of Iran has successfully tested this new methodology!

Beyond a climate-centric view of plant distribution: edaphic variables add value to distribution models.

Directory of Open Access Journals (Sweden)

Frieda Beauregard

Full Text Available Both climatic and edaphic conditions determine plant distribution, however many species distribution models do not include edaphic variables especially over large geographical extent. Using an exceptional database of vegetation plots (n = 4839 covering an extent of ∼55,000 km2, we tested whether the inclusion of fine scale edaphic variables would improve model predictions of plant distribution compared to models using only climate predictors. We also tested how well these edaphic variables could predict distribution on their own, to evaluate the assumption that at large extents, distribution is governed largely by climate. We also hypothesized that the relative contribution of edaphic and climatic data would vary among species depending on their growth forms and biogeographical attributes within the study area. We modelled 128 native plant species from diverse taxa using four statistical model types and three sets of abiotic predictors: climate, edaphic, and edaphic-climate. Model predictive accuracy and variable importance were compared among these models and for species' characteristics describing growth form, range boundaries within the study area, and prevalence. For many species both the climate-only and edaphic-only models performed well, however the edaphic-climate models generally performed best. The three sets of predictors differed in the spatial information provided about habitat suitability, with climate models able to distinguish range edges, but edaphic models able to better distinguish within-range variation. Model predictive accuracy was generally lower for species without a range boundary within the study area and for common species, but these effects were buffered by including both edaphic and climatic predictors. The relative importance of edaphic and climatic variables varied with growth forms, with trees being more related to climate whereas lower growth forms were more related to edaphic conditions. Our study

On sign constant solutions of certain boundary value problems for second-order functional differential equations

Czech Academy of Sciences Publication Activity Database

Lomtatidze, Alexander; Vodstrčil, Petr

2005-01-01

Roč. 84, č. 2 (2005), s. 197-209 ISSN 0003-6811 Institutional research plan: CEZ:AV0Z10190503 Keywords : second order linear functional differential equations * nonnegative solution * two-point boundary value problem Subject RIV: BA - General Mathematics http://www.tandfonline.com/doi/full/10.1080/00036810410001724427

β-distribution for Reynolds stress and turbulent heat flux in relaxation turbulent boundary layer of compression ramp

Science.gov (United States)

Hu, YanChao; Bi, WeiTao; Li, ShiYao; She, ZhenSu

2017-12-01

A challenge in the study of turbulent boundary layers (TBLs) is to understand the non-equilibrium relaxation process after sep-aration and reattachment due to shock-wave/boundary-layer interaction. The classical boundary layer theory cannot deal with the strong adverse pressure gradient, and hence, the computational modeling of this process remains inaccurate. Here, we report the direct numerical simulation results of the relaxation TBL behind a compression ramp, which reveal the presence of intense large-scale eddies, with significantly enhanced Reynolds stress and turbulent heat flux. A crucial finding is that the wall-normal profiles of the excess Reynolds stress and turbulent heat flux obey a β-distribution, which is a product of two power laws with respect to the wall-normal distances from the wall and from the boundary layer edge. In addition, the streamwise decays of the excess Reynolds stress and turbulent heat flux also exhibit power laws with respect to the streamwise distance from the corner of the compression ramp. These results suggest that the relaxation TBL obeys the dilation symmetry, which is a specific form of self-organization in this complex non-equilibrium flow. The β-distribution yields important hints for the development of a turbulence model.

Closed form solution to a second order boundary value problem and its application in fluid mechanics

International Nuclear Information System (INIS)

Eldabe, N.T.; Elghazy, E.M.; Ebaid, A.

2007-01-01

The Adomian decomposition method is used by many researchers to investigate several scientific models. In this Letter, the modified Adomian decomposition method is applied to construct a closed form solution for a second order boundary value problem with singularity

Boundary effects in quantum field theory

International Nuclear Information System (INIS)

Deutsch, D.; Candelas, P.

1979-01-01

Electromagnetic and scalar fields are quantized in the region near an arbitrary smooth boundary, and the renormalized expectation value of the stress-energy tensor is calculated. The energy density is found to diverge as the boundary is approached. For nonconformally invariant fields it varies, to leading order, as the inverse fourth power of the distance from the boundary. For conformally invariant fields the coefficient of this leading term is zero, and the energy density varies as the inverse cube of the distance. An asymptotic series for the renormalized stress-energy tensor is developed as far as the inverse-square term in powers of the distance. Some criticisms are made of the usual approach to this problem, which is via the ''renormalized mode sum energy,'' a quantity which is generically infinite. Green's-function methods are used in explicit calculations, and an iterative scheme is set up to generate asymptotic series for Green's functions near a smooth boundary. Contact is made with the theory of the asymptotic distribution of eigenvalues of the Laplacian operator. The method is extended to nonflat space-times and to an example with a nonsmooth boundary

Boundary and sub-boundary hardening in high-Cr ferritic steels during long-term creep at 650 C

Energy Technology Data Exchange (ETDEWEB)

Abe, F. [National Institute for Materials Science (NIMS) (Japan)

2008-07-01

The sub-boundary hardening is shown to be the most important strengthening mechanism in creep of the 9% Cr steel base metal and welded joints. The addition of boron reduces the coarsening rate of M{sub 23}C{sub 6} carbides along boundaries near prior austenite grain boundaries during creep, enhancing the sub-boundary hardening. This improves long-term creep strength. The enhancement of boundary and subboundary hardening by fine distribution of precipitates along boundaries is significantly reduced in fine-grained region of Ac{sub 3} HAZ simulated specimens of conventional steels P92 and P122. In NIMS 9% Cr boron steel welded joints, the grain size and distribution of carbonitrides are substantially the same between the HAZ and base metal, where fine carbonitrides are distributed along the lath and block boundaries as well as along prior austenite grain boundaries. This is essential for the suppression of Type IV fracture in NIMS 9% Cr boron steel welded joints. (orig.)

Estimation of expected value for lognormal and gamma distributions

International Nuclear Information System (INIS)

White, G.C.

1978-01-01

Concentrations of environmental pollutants tend to follow positively skewed frequency distributions. Two such density functions are the gamma and lognormal. Minimum variance unbiased estimators of the expected value for both densities are available. The small sample statistical properties of each of these estimators were compared for its own distribution, as well as the other distribution to check the robustness of the estimator. Results indicated that the arithmetic mean provides an unbiased estimator when the underlying density function of the sample is either lognormal or gamma, and that the achieved coverage of the confidence interval is greater than 75 percent for coefficients of variation less than two. Further Monte Carlo simulations were conducted to study the robustness of the above estimators by simulating a lognormal or gamma distribution with the expected value of a particular observation selected from a uniform distribution before the lognormal or gamma observation is generated. Again, the arithmetic mean provides an unbiased estimate of expected value, and the coverage of the confidence interval is greater than 75 percent for coefficients of variation less than two

Acoustic scattering on spheroidal shapes near boundaries

Science.gov (United States)

Miloh, Touvia

2016-11-01

A new expression for the Lamé product of prolate spheroidal wave functions is presented in terms of a distribution of multipoles along the axis of the spheroid between its foci (generalizing a corresponding theorem for spheroidal harmonics). Such an "ultimate" singularity system can be effectively used for solving various linear boundary-value problems governed by the Helmholtz equation involving prolate spheroidal bodies near planar or other boundaries. The general methodology is formally demonstrated for the axisymmetric acoustic scattering problem of a rigid (hard) spheroid placed near a hard/soft wall or inside a cylindrical duct under an axial incidence of a plane acoustic wave.

Performance improvement of extended boundary node method for solving elliptic boundary-value problems

International Nuclear Information System (INIS)

Saitoh, Ayumu; Kamitani, Atsushi; Takayama, Teruou; Nakamura, Hiroaki

2016-01-01

The extended boundary-node method (X-BNM) with the hierarchical-matrix (H-matrix) method has been developed and its performance has been investigated numerically. The results of computations show that the solver speed of the X-BNM with the H-matrix method is much faster than that of the standard X-BNM for the case where the number of boundary nodes exceeds a certain limit. Furthermore, the accuracy of the X-BNM with the H-matrix method is almost equal to that of the standard X-BNM. From these results, it is found that the H-matrix method is useful as the acceleration technique of the X-BNM. (author)

An initial boundary value problem for modeling a piezoelectric dipolar body

Science.gov (United States)

Marin, Marin; Öchsner, Andreas

2018-03-01

This study deals with the first initial boundary value problem in elasticity of piezoelectric dipolar bodies. We consider the most general case of an anisotropic and inhomogeneous elastic body having a dipolar structure. For two different types of restrictions imposed on the problem data, we prove two results regarding the uniqueness of solution, by using a different but accessible method. Then, the mixed problem is transformed in a temporally evolutionary equation on a Hilbert space, conveniently constructed based on the problem data. With the help of a known result from the theory of semigroups of operators, the existence and uniqueness of the weak solution for this equation are proved.

Extension Theory and Krein-type Resolvent Formulas for Nonsmooth Boundary Value Problems

DEFF Research Database (Denmark)

Abels, Helmut; Grubb, Gerd; Wood, Ian Geoffrey

2014-01-01

The theory of selfadjoint extensions of symmetric operators, and more generally the theory of extensions of dual pairs, was implemented some years ago for boundary value problems for elliptic operators on smooth bounded domains. Recently, the questions have been taken up again for nonsmooth domains....... In the present work we show that pseudodifferential methods can be used to obtain a full characterization, including Kreĭn resolvent formulas, of the realizations of nonselfadjoint second-order operators on

Tangential boundary values of Laplace transforms. Applications to Muntz-Szasz type approximation

Science.gov (United States)

Sedletskii, A. M.

2003-02-01

We consider the Laplace transforms (LT) of functions in L^q(\\mathbb R_+), 1, with a slowly varying weight. We prove that if the weight satisfies certain conditions, then each LT of this class has tangential boundary values almost everywhere on the imaginary axis, and the structure of the corresponding neighbourhoods depends on the weight only. This result is applied to distinguish a wide class of weighted L^p spaces on the half-line such that the Szasz condition is not necessary for the completeness of the system \\exp(-\\lambda_n t) in these spaces.

Variational Homotopy Perturbation Method for Solving Higher Dimensional Initial Boundary Value Problems

Directory of Open Access Journals (Sweden)

Muhammad Aslam Noor

2008-01-01

Full Text Available We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method (VHPM. We use this method for solving higher dimensional initial boundary value problems with variable coefficients. The developed algorithm is quite efficient and is practically well suited for use in these problems. The proposed scheme finds the solution without any discritization, transformation, or restrictive assumptions and avoids the round-off errors. Several examples are given to check the reliability and efficiency of the proposed technique.

BOUNDARY VALUE PROBLEM FOR A LOADED EQUATION ELLIPTIC-HYPERBOLIC TYPE IN A DOUBLY CONNECTED DOMAIN

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O.Kh. Abdullaev

2014-06-01

Full Text Available We study the existence and uniqueness of the solution of one boundary value problem for the loaded elliptic-hyperbolic equation of the second order with two lines of change of type in double-connected domain. Similar results have been received by D.M.Kuryhazov, when investigated domain is one-connected.

Dynamic Phase Boundary Estimation in Two-phase Flows Based on Electrical Impedance Tomography

International Nuclear Information System (INIS)

Lee, Jeong Seong; Muhammada, Nauman Malik; Kim, Kyung Youn; Kim, Sin

2008-01-01

For the dynamic visualization of the phase boundary in two-phase flows, the electrical impedance tomography (EIT) technique is introduced. In EIT, a set of predetermined electrical currents is injected through the electrodes placed on the boundary of the flow passage and the induced electrical potentials are measured on the electrodes. With the relationship between the injected currents and the induced voltages, the electrical conductivity distribution across the flow domain is estimated through the image reconstruction algorithm where the conductivity distribution corresponds to the phase distribution. In the application of EIT to two-phase flows where there are only two conductivity values, the conductivity distribution estimation problem can be transformed into the boundary estimation problem. This paper considers phase boundary estimation with EIT in annular two-phase flows. As the image reconstruction algorithm, the unscented Kalman filter (UKF) is adopted since from the control theory it is reported that the UKF shows better performance than the extended Kalman filter (EKF) that has been commonly used. For the present problem, the formulation of UKF algorithm involved its incorporation in the adopted image reconstruction algorithm. Also, phantom experiments have been conducted to evaluate the improvement reported by UKF

Generalised functions method in the boundary value problems of elastodynamics by stationary running loads

International Nuclear Information System (INIS)

Alexeyeva, L.A.

2001-01-01

Investigation of diffraction processes of seismic waves on underground tunnels and pipelines with use of mathematical methods is related to solving boundary value problems (BVP) for hyperbolic system of differential equations in domains with cylindrical cavities when seismic disturbances propagate along boundaries with subsonic or transonic speeds. Also such classes of problems appear when it's necessary to study the behavior of underground constructions and Stress-strain State of environment. But in this case the velocities of running loads are less than velocities of wave propagation in surrounding medium. At present similar problems were solved only for constructions of circular cylindrical form with use of methods of full and not full dividing of variables. For cylindrical constructions of complex cross section strong mathematical theories for solving these problems were absent.(author)

Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations

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Domoshnitsky Alexander

2009-01-01

Full Text Available We obtain the maximum principles for the first-order neutral functional differential equation where , and are linear continuous operators, and are positive operators, is the space of continuous functions, and is the space of essentially bounded functions defined on . New tests on positivity of the Cauchy function and its derivative are proposed. Results on existence and uniqueness of solutions for various boundary value problems are obtained on the basis of the maximum principles.

Existence of positive solutions for boundary value problems of fractional functional differential equations

Directory of Open Access Journals (Sweden)

Chuanzhi Bai

2010-06-01

Full Text Available This paper deals with the existence of positive solutions for a boundary value problem involving a nonlinear functional differential equation of fractional order $\\alpha$ given by $ D^{\\alpha} u(t + f(t, u_t = 0$, $t \\in (0, 1$, $2 < \\alpha \\le 3$, $ u^{\\prime}(0 = 0$, $u^{\\prime}(1 = b u^{\\prime}(\\eta$, $u_0 = \\phi$. Our results are based on the nonlinear alternative of Leray-Schauder type and Krasnosel'skii fixed point theorem.

Inference for exponentiated general class of distributions based on record values

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Samah N. Sindi

2017-09-01

Full Text Available The main objective of this paper is to suggest and study a new exponentiated general class (EGC of distributions. Maximum likelihood, Bayesian and empirical Bayesian estimators of the parameter of the EGC of distributions based on lower record values are obtained. Furthermore, Bayesian prediction of future records is considered. Based on lower record values, the exponentiated Weibull distribution, its special cases of distributions and exponentiated Gompertz distribution are applied to the EGC of distributions.  

Multiple and sign-changing solutions for discrete Robin boundary value problem with parameter dependence

Directory of Open Access Journals (Sweden)

Long Yuhua

2017-12-01

Full Text Available In this paper, we study second-order nonlinear discrete Robin boundary value problem with parameter dependence. Applying invariant sets of descending flow and variational methods, we establish some new sufficient conditions on the existence of sign-changing solutions, positive solutions and negative solutions of the system when the parameter belongs to appropriate intervals. In addition, an example is given to illustrate our results.

Solvability conditions for non-local boundary value problems for two-dimensional half-linear differential systems

Czech Academy of Sciences Publication Activity Database

Kiguradze, I.; Šremr, Jiří

2011-01-01

Roč. 74, č. 17 (2011), s. 6537-6552 ISSN 0362-546X Institutional research plan: CEZ:AV0Z10190503 Keywords : half-linear differential system * non-local boundary value problem * solvability Subject RIV: BA - General Mathematics Impact factor: 1.536, year: 2011 http://www.sciencedirect.com/science/article/pii/S0362546X11004573

On alternative q-Weibull and q-extreme value distributions: Properties and applications

Science.gov (United States)

Zhang, Fode; Ng, Hon Keung Tony; Shi, Yimin

2018-01-01

Tsallis statistics and Tsallis distributions have been attracting a significant amount of research work in recent years. Importantly, the Tsallis statistics, q-distributions have been applied in different disciplines. Yet, a relationship between some existing q-Weibull distributions and q-extreme value distributions that is parallel to the well-established relationship between the conventional Weibull and extreme value distributions through a logarithmic transformation has not be established. In this paper, we proposed an alternative q-Weibull distribution that leads to a q-extreme value distribution via the q-logarithm transformation. Some important properties of the proposed q-Weibull and q-extreme value distributions are studied. Maximum likelihood and least squares estimation methods are used to estimate the parameters of q-Weibull distribution and their performances are investigated through a Monte Carlo simulation study. The methodologies and the usefulness of the proposed distributions are illustrated by fitting the 2014 traffic fatalities data from The National Highway Traffic Safety Administration.

Rare and common macroinvertebrates: definition of distribution classes and their boundaries

NARCIS (Netherlands)

Nijboer, R.C.; Verdonschot, P.F.M.

2004-01-01

Rarity of macroinvertebrates can be used in assessing the ecological quality or conservation value of freshwaters. To select target species for nature conservation and to compare rarity or commonness between regions a classification of species distributions is needed. A distribution classification

Renormalization of boundary conditions for distribution functions of quasiparticles obeying quantum statistics at interfaces between crystalline grains

International Nuclear Information System (INIS)

Grendel, M.

1981-01-01

Boundary conditions for distribution functions of quasiparticles scattered by an interface between two crystalline grains are presented. Contrary to former formulations where Maxwell-Boltzmann statistics was considered, the present boundary conditions take into account the quantum statistics (Fermi-Dirac or Bose-Einstein) of quasiparticles. Provided that small deviations only from thermodynamic equilibrium are present, the boundary conditions are linearized, and then their ''renormalization'' is investigated in case of elastic scattering. The final results of the renormalization, which are obtained for a simplified model of an interface, sugo.est that the portion of the Fermi (Bose)-quasiparticles reflected or transmitted specularly is decreased (increased) in comparison with the case of quasiparticles obeying Maxwell-Boltzmann statistics. (author)

The boundary value problem for discrete analytic functions

KAUST Repository

Skopenkov, Mikhail

2013-06-01

This paper is on further development of discrete complex analysis introduced by R.Isaacs, J.Ferrand, R.Duffin, and C.Mercat. We consider a graph lying in the complex plane and having quadrilateral faces. A function on the vertices is called discrete analytic, if for each face the difference quotients along the two diagonals are equal.We prove that the Dirichlet boundary value problem for the real part of a discrete analytic function has a unique solution. In the case when each face has orthogonal diagonals we prove that this solution uniformly converges to a harmonic function in the scaling limit. This solves a problem of S.Smirnov from 2010. This was proved earlier by R.Courant-K.Friedrichs-H.Lewy and L.Lusternik for square lattices, by D.Chelkak-S.Smirnov and implicitly by P.G.Ciarlet-P.-A.Raviart for rhombic lattices.In particular, our result implies uniform convergence of the finite element method on Delaunay triangulations. This solves a problem of A.Bobenko from 2011. The methodology is based on energy estimates inspired by alternating-current network theory. © 2013 Elsevier Ltd.

Sufficient condition for existence of solutions for higher-order resonance boundary value problem with one-dimensional p-Laplacian

Directory of Open Access Journals (Sweden)

Liu Yang

2007-10-01

Full Text Available By using coincidence degree theory of Mawhin, existence results for some higher order resonance multipoint boundary value problems with one dimensional p-Laplacian operator are obtained.

Effects of thermo-mechanical iterations on the grain boundary character distribution of Pb-Ca-Sn-Al alloy

International Nuclear Information System (INIS)

Wang Weiguo; Guo Hong

2007-01-01

Recrystallized Pb-0.05%Ca-1.5%Sn-0.026%Al (mass fraction) alloy, with an averaged grain size of 20-30 μm, special grain boundary (Σ1-Σ29) fraction of less than 40% and the general high angle boundary (HAB) network of fully connected, was subjected to 1-4 cycles of thermo-mechanical processing (TMP) of rolling at ambient temperature followed by annealing at 270 deg. C (0.9T m ). Electron back-scatter diffraction (EBSD) techniques were employed to determine the grain boundary character distribution (GBCD) of the processed samples. The results indicated that 1-, 3- and 4-cycle TMP has very strong but nearly identical effects on the GBCD, the fraction of special boundaries enhanced to 80%, and the connectivity of general high angle boundary (HABs) network is interrupted sufficiently by the so-called special boundaries; However, 2-cycle TMP exerts slight impacts on the GBCD, the fraction of special boundaries is only increased to 59.2% and the connectivity of HABs network is not interrupted substantially. Further discussion pointed out the effects of 1-, 3- and 4-cycle TMP might be attributed to the migration and interactions of incoherent Σ3 (Σ3 ic ) and its variants Σ9 and Σ27 boundaries, while that of 2-cycle TMP may be caused by an enhanced recrystallization

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

Science.gov (United States)

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.

Positive solutions for second-order boundary-value problems with phi-Laplacian

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Diana-Raluca Herlea

2016-02-01

Full Text Available This article concerns the existence, localization and multiplicity of positive solutions for the boundary-value problem $$\\displaylines{ \\big(\\phi(u' \\big '+f(t,u =0, \\cr u(0 - a u'(0 = u'(1= 0, }$$ where $f:[0,1]\\times \\mathbb{R}_{+}\\to \\mathbb{R}_{+}$ is a continuous function and $\\phi :\\mathbb{R}\\to (-b,b$ is an increasing homeomorphism with $\\phi (0=0$. We obtain existence, localization and multiplicity results of positive solutions using Krasnosel'skii fixed point theorem in cones, and a weak Harnack type inequality. Concerning systems, the localization is established by the vector version of Krasnosel'skii theorem, where the compression-expansion conditions are expressed on components.

A symmetric solution of a multipoint boundary value problem at resonance

Directory of Open Access Journals (Sweden)

2006-01-01

Full Text Available We apply a coincidence degree theorem of Mawhin to show the existence of at least one symmetric solution of the nonlinear second-order multipoint boundary value problem u ″ ( t = f ( t , u ( t , | u ′ ( t | , t ∈ ( 0 , 1 , u ( 0 = ∑ i = 1 n μ i u ( ξ i , u ( 1 − t = u ( t , t ∈ ( 0 , 1 ] , where 0 < ξ 1 < ξ 2 < … ≤ ξ n 1 / 2 , ∑ i = 1 n μ i = 1 , f : [ 0 , 1 ] × ℝ 2 → ℝ with f ( t , x , y = f ( 1 − t , x , y , ( t , x , y ∈ [ 0 , 1 ] × ℝ 2 , satisfying the Carathéodory conditions.

Boundary Value Problems for a Super-Sublinear Asymmetric Oscillator: The Exact Number of Solutions

Directory of Open Access Journals (Sweden)

Armands Gritsans

2013-01-01

Full Text Available Properties of asymmetric oscillator described by the equation (i, where and , are studied. A set of such that the problem (i, (ii, and (iii have a nontrivial solution, is called α-spectrum. We give full description of α-spectra in terms of solution sets and solution surfaces. The exact number of nontrivial solutions of the two-parameter Dirichlet boundary value problem (i, and (ii is given.

Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's

Science.gov (United States)

Cai, Wei; Wang, Jian-Zhong

1993-01-01

We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.

Tangential boundary values of Laplace transforms. Applications to Muntz-Szasz type approximation

Energy Technology Data Exchange (ETDEWEB)

Sedletskii, A M [M.V. Lomonosov Moscow State University, Moscow (Russian Federation)

2003-02-28

We consider the Laplace transforms (LT) of functions in L{sup q}(R{sub +}), 1boundary values almost everywhere on the imaginary axis, and the structure of the corresponding neighbourhoods depends on the weight only. This result is applied to distinguish a wide class of weighted L{sup p} spaces on the half-line such that the Szasz condition is not necessary for the completeness of the system exp(-{lambda}{sub n}t) in these spaces.

Optimization of b-value distribution for biexponential diffusion-weighted MR imaging of normal prostate.

Science.gov (United States)

Jambor, Ivan; Merisaari, Harri; Aronen, Hannu J; Järvinen, Jukka; Saunavaara, Jani; Kauko, Tommi; Borra, Ronald; Pesola, Marko

2014-05-01

To determine the optimal b-value distribution for biexponential diffusion-weighted imaging (DWI) of normal prostate using both a computer modeling approach and in vivo measurements. Optimal b-value distributions for the fit of three parameters (fast diffusion Df, slow diffusion Ds, and fraction of fast diffusion f) were determined using Monte-Carlo simulations. The optimal b-value distribution was calculated using four individual optimization methods. Eight healthy volunteers underwent four repeated 3 Tesla prostate DWI scans using both 16 equally distributed b-values and an optimized b-value distribution obtained from the simulations. The b-value distributions were compared in terms of measurement reliability and repeatability using Shrout-Fleiss analysis. Using low noise levels, the optimal b-value distribution formed three separate clusters at low (0-400 s/mm2), mid-range (650-1200 s/mm2), and high b-values (1700-2000 s/mm2). Higher noise levels resulted into less pronounced clustering of b-values. The clustered optimized b-value distribution demonstrated better measurement reliability and repeatability in Shrout-Fleiss analysis compared with 16 equally distributed b-values. The optimal b-value distribution was found to be a clustered distribution with b-values concentrated in the low, mid, and high ranges and was shown to improve the estimation quality of biexponential DWI parameters of in vivo experiments. Copyright © 2013 Wiley Periodicals, Inc.

Sharp Boundary Inversion of 2D Magnetotelluric Data using Bayesian Method.

Science.gov (United States)

Zhou, S.; Huang, Q.

2017-12-01

Normally magnetotelluric(MT) inversion method cannot show the distribution of underground resistivity with clear boundary, even if there are obviously different blocks. Aiming to solve this problem, we develop a Bayesian structure to inverse 2D MT sharp boundary data, using boundary location and inside resistivity as the random variables. Firstly, we use other MT inversion results, like ModEM, to analyze the resistivity distribution roughly. Then, we select the suitable random variables and change its data format to traditional staggered grid parameters, which can be used to do finite difference forward part. Finally, we can shape the posterior probability density(PPD), which contains all the prior information and model-data correlation, by Markov Chain Monte Carlo(MCMC) sampling from prior distribution. The depth, resistivity and their uncertainty can be valued. It also works for sensibility estimation. We applied the method to a synthetic case, which composes two large abnormal blocks in a trivial background. We consider the boundary smooth and the near true model weight constrains that mimic joint inversion or constrained inversion, then we find that the model results a more precise and focused depth distribution. And we also test the inversion without constrains and find that the boundary could also be figured, though not as well. Both inversions have a good valuation of resistivity. The constrained result has a lower root mean square than ModEM inversion result. The data sensibility obtained via PPD shows that the resistivity is the most sensible, center depth comes second and both sides are the worst.

The Value of Transparency in Distributed Solar PV Markets

Energy Technology Data Exchange (ETDEWEB)

OShaughnessy, Eric J [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Zamzam, Ahmed S [National Renewable Energy Laboratory (NREL), Golden, CO (United States)

2017-12-01

Market transparency refers to the degree of customer awareness of product options and fair market prices for a given good. In The Value of Transparency in Distributed Solar PV Markets, we use residential solar photovoltaic (PV) quote data to study the value of transparency in distributed solar PV markets. We find that improved market transparency results in lower installation offer prices. Further, the results of this study suggest that PV customers benefit from gaining access to more PV quotes.

Record values from a family of J-shaped distributions

Directory of Open Access Journals (Sweden)

Ahmad A. Zghoul

2013-05-01

Full Text Available A family of J-shaped distributions has applications in life testing modeling. In this paper we study record values from this family of distributions. Based on lower records, recurrence relations and bounds as well as expressions for moments and product moments of record values are obtained, the maximum likelihood estimator of the shape parameter is derived and shown to be consistent, sufficient, complete and UMVU estimator. In addition, an application in reliability is given.

Boundary layer turbulence in transitional and developed states

Science.gov (United States)

Park, George Ilhwan; Wallace, James M.; Wu, Xiaohua; Moin, Parviz

2012-03-01

Using the recent direct numerical simulations by Wu and Moin ["Transitional and turbulent boundary layer with heat transfer," Phys. Fluids 22, 85 (2010)] of a flat-plate boundary layer with a passively heated wall, statistical properties of the turbulence in transition at Reθ ≈ 300, from individual turbulent spots, and at Reθ ≈ 500, where the spots merge (distributions of the mean velocity, Reynolds stresses, kinetic energy production, and dissipation rates, enstrophy and its components) have been compared to these statistical properties for the developed boundary layer turbulence at Reθ = 1840. When the distributions in the transitional regions are conditionally averaged so as to exclude locations and times when the flow is not turbulent, they closely resemble the distributions in the developed turbulent state at the higher Reynolds number, especially in the buffer layer. Skin friction coefficients, determined in this conditional manner at the two Reynolds numbers in the transitional flow are, of course, much larger than when their values are obtained by including both turbulent and non-turbulent information there, and the conditional averaged values are consistent with the 1/7th power law approximation. An octant analysis based on the combinations of signs of the velocity and temperature fluctuations, u, v, and θ shows that the momentum and heat fluxes are predominantly of the mean gradient type in both the transitional and developed regions. The fluxes appear to be closely associated with vortices that transport momentum and heat toward and away from the wall in both regions of the flow. The results suggest that there may be little fundamental difference between the nonlinear processes involved in the formation of turbulent spots that appear in transition and those that sustain the turbulence when it is developed. They also support the view that the transport processes and the vortical structures that drive them in developed and transitional boundary

Existence of global solutions to free boundary value problems for bipolar Navier-Stokes-Possion systems

Directory of Open Access Journals (Sweden)

Jian Liu

2013-09-01

Full Text Available In this article, we consider the free boundary value problem for one-dimensional compressible bipolar Navier-Stokes-Possion (BNSP equations with density-dependent viscosities. For general initial data with finite energy and the density connecting with vacuum continuously, we prove the global existence of the weak solution. This extends the previous results for compressible NS [27] to NSP.

Existence of solutions for a fourth-order boundary value problem on the half-line via critical point theory

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Mabrouk Briki

2016-05-01

Full Text Available In this paper, a fourth-order boundary value problem on the half-line is considered and existence of solutions is proved using a minimization principle and the mountain pass theorem.

Singular boundary perturbations of distributed systems

DEFF Research Database (Denmark)

Pedersen, Michael

1990-01-01

Some problems arising in real-life control applications are addressed--namely, problems concerning non-smooth control inputs on the boundary of the spatial domain. The classical variational approach is extended, and sufficient conditions are given for the solutions to continuous functions of time...

A Novel Approach to Calculation of Reproducing Kernel on Infinite Interval and Applications to Boundary Value Problems

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Jing Niu

2013-01-01

reproducing kernel on infinite interval is obtained concisely in polynomial form for the first time. Furthermore, as a particular effective application of this method, we give an explicit representation formula for calculation of reproducing kernel in reproducing kernel space with boundary value conditions.

Value-based distributed generator placements for service quality improvements

Energy Technology Data Exchange (ETDEWEB)

Teng, Jen-Hao; Chen, Chi-Fa [Department of Electrical Engineering, I-Shou University, No. 1, Section 1, Syuecheng Road, Dashu Township, Kaohsiung Country 840 (Taiwan); Liu, Yi-Hwa [Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei (Taiwan); Chen, Chia-Yen [Department of Computer Science, The University of Auckland (New Zealand)

2007-03-15

Distributed generator (DG) resources are small, self-contained electric generating plants that can provide power to homes, businesses or industrial facilities in distribution feeders. They can be used to reduce power loss and improve service reliability. However, the values of DGs are largely dependent on their types, sizes and locations as they were installed in distribution feeders. A value-based method is proposed in this paper to enhance the reliability and obtain the benefits for DG placement. The benefits of DG placement described in this paper include power cost saving, power loss reduction, and reliability enhancement. The costs of DG placement include the investment, maintenance and operating costs. The proposed value-based method tries to find the best tradeoff between the costs and benefits of DG placement and then find the optimal types of DG and their corresponding locations and sizes in distribution feeders. The derived formulations are solved by a genetic algorithm based method. Test results show that with proper types, sizes and installation site selection, DG placement can be used to improve system reliability, reduce customer interruption costs and save power cost; as well as enabling electric utilities to obtain the maximal economical benefits. (author)

On Impulsive Boundary Value Problems of Fractional Differential Equations with Irregular Boundary Conditions

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Guotao Wang

2012-01-01

Full Text Available We study nonlinear impulsive differential equations of fractional order with irregular boundary conditions. Some existence and uniqueness results are obtained by applying standard fixed-point theorems. For illustration of the results, some examples are discussed.

Existence of solutions to fractional boundary-value problems with a parameter

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Ya-Ning Li

2013-06-01

Full Text Available This article concerns the existence of solutions to the fractional boundary-value problem $$displaylines{ -frac{d}{dt} ig(frac{1}{2} {}_0D_t^{-eta}+ frac{1}{2}{}_tD_{T}^{-eta}igu'(t=lambda u(t+abla F(t,u(t,quad hbox{a.e. } tin[0,T], cr u(0=0,quad u(T=0. }$$ First for the eigenvalue problem associated with it, we prove that there is a sequence of positive and increasing real eigenvalues; a characterization of the first eigenvalue is also given. Then under different assumptions on the nonlinearity F(t,u, we show the existence of weak solutions of the problem when $lambda$ lies in various intervals. Our main tools are variational methods and critical point theorems.

On some boundary value problems in quantum statistical mechanics

International Nuclear Information System (INIS)

Angelescu, N.

1978-01-01

The following two topics of equilibrium quantum statistical mechanics are discussed in this thesis: (i) the independence of the thermodynamic limit of grand-canonical pressure on the boundary conditions; (ii) the magnetic properties of free quantum gases. Problem (i) is handled with a functional integration technique. Wiener-type conditional measures are constructed for a given domain and a general class of mixed conditions on its boundary, these measures are used to write down Feynman-Kac formulae for the kernels of exp(-βH), where H is the Hamiltonian of N interacting particles in the given domain. These measures share the property that they assign the same mass as the usual Wiener measure to any set of trajectories not intersecting the boundary. Local estimates on the kernels of exp(-βH) are derived, which imply independence of the pressure on the boundary conditions in the thermodynamic limit. Problem (ii) has a historical development: since Landau's work (1930), much discussion has been devoted to the influence of the finite size on the susceptibility. In finite volume, Dirichlet boundary conditions are imposed, on the ground that they ensure gauge invariance. The thermodynamic limit of the pressure is proved, using again functional integration. The functional measure is now complex but absolutely continuous with respect to Wiener measure, so the usual local estimates hold true. The controversy in the literature was concentrated on the commutativity of the operations of H-derivation and thermodynamic limit, so the existence of this limit for the zero-field susceptibility and its surface term are proved separately, demonstrating this commutativity. The proof relies on the following result of independent interest: the perturbation theory of self-adjoint trace-class semigroups is trace-class convergent and analytic. (author)

The significance of a grassy field boundary for the spatial distribution of carabids within two cereal fields

NARCIS (Netherlands)

Saska, P.; Vodde, M.; Heijerman, Th.; Westerman, P.R.; Werf, van der W.

2007-01-01

This paper investigated how distance from the field edge affects overall activity-density, species richness and distribution of individual carabid (Coleoptera: Carabidae) species. Carabid beetles were sampled using pitfall traps at six different locations: grassy field boundary, 0 (field edge), 4,

Two-dimensional boundary-value problem for ion-ion diffusion

International Nuclear Information System (INIS)

Tuszewski, M.; Lichtenberg, A.J.

1977-01-01

Like-particle diffusion is usually negligible compared with unlike-particle diffusion because it is two orders higher in spatial derivatives. When the ratio of the ion gyroradius to the plasma transverse dimension is of the order of the fourth root of the mass ratio, previous one-dimensional analysis indicated that like-particle diffusion is significant. A two-dimensional boundary-value problem for ion-ion diffusion is investigated. Numerical solutions are found with models for which the nonlinear partial differential equation reduces to an ordinary fourth-order differential equation. These solutions indicate that the ion-ion losses are higher by a factor of six for a slab geometry, and by a factor of four for circular geometry, than estimated from dimensional analysis. The solutions are applied to a multiple mirror experiment stabilized with a quadrupole magnetic field which generates highly elliptical flux surfaces. It is found that the ion-ion losses dominate the electron-ion losses and that these classical radial losses contribute to a significant decrease of plasma lifetime, in qualitiative agreement with the experimental results

Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method

Science.gov (United States)

Sohaib, Muhammad; Haq, Sirajul; Mukhtar, Safyan; Khan, Imad

2018-03-01

An efficient method is proposed to approximate sixth order boundary value problems. The proposed method is based on Legendre wavelet in which Legendre polynomial is used. The mechanism of the method is to use collocation points that converts the differential equation into a system of algebraic equations. For validation two test problems are discussed. The results obtained from proposed method are quite accurate, also close to exact solution, and other different methods. The proposed method is computationally more effective and leads to more accurate results as compared to other methods from literature.

Two-point boundary value and Cauchy formulations in an axisymmetrical MHD equilibrium problem

International Nuclear Information System (INIS)

Atanasiu, C.V.; Subbotin, A.A.

1999-01-01

In this paper we present two equilibrium solvers for axisymmetrical toroidal configurations, both based on the expansion in poloidal angle method. The first one has been conceived as a two-point boundary value solver in a system of coordinates with straight field lines, while the second one uses a well-conditioned Cauchy formulation of the problem in a general curvilinear coordinate system. In order to check the capability of our moment methods to describe equilibrium accurately, a comparison of the moment solutions with analytical solutions obtained for a Solov'ev equilibrium has been performed. (author)

Value Assessment of Distribution Network Reconfiguration: A Danish Case Study

DEFF Research Database (Denmark)

Vaskantiras, Georgios; You, Shi

2016-01-01

. This paper presents a case study-based analysis to explore the potential value of reconfiguration in detail. The study is performed using a 10kV distribution grid of Denmark, while reconfiguration is applied to minimize the energy losses under both normal and post-fault conditions. The results show......Distribution network reconfiguration is a mechanism that can improve the distribution system performance from multiple perspectives. In the context of smart grid wherein the degrees of automation and intelligence are high, the potential value of network reconfiguration can be significant...

On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation

Science.gov (United States)

Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich

2018-01-01

The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.

Modified quasi-boundary value method for Cauchy problems of elliptic equations with variable coefficients

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Hongwu Zhang

2011-08-01

Full Text Available In this article, we study a Cauchy problem for an elliptic equation with variable coefficients. It is well-known that such a problem is severely ill-posed; i.e., the solution does not depend continuously on the Cauchy data. We propose a modified quasi-boundary value regularization method to solve it. Convergence estimates are established under two a priori assumptions on the exact solution. A numerical example is given to illustrate our proposed method.

Electrical Resistance Imaging of Bubble Boundary in Annular Two-Phase Flows Using Unscented Kalman Filter

International Nuclear Information System (INIS)

Lee, Jeong Seong; Chung, Soon Il; Ljaz, Umer Zeeshan; Khambampati, Anil Kumar; Kim, Kyung Youn; Kim, Sin Kim

2007-01-01

For the visualization of the phase boundary in annular two-phase flows, the electrical resistance tomography (ERT) technique is introduced. In ERT, a set of predetermined electrical currents is injected trough the electrodes placed on the boundary of the flow passage and the induced electrical potentials are measured on the electrode. With the relationship between the injected currents and the induced voltages, the electrical conductivity distribution across the flow domain is estimated through the image reconstruction algorithm. In this, the conductivity distribution corresponds to the phase distribution. In the application of ERT to two-phase flows where there are only two conductivity values, the conductivity distribution estimation problem can be transformed into the boundary estimation problem. This paper considers a bubble boundary estimation with ERT in annular two-phase flows. As the image reconstruction algorithm, the unscented Kalman filter (UKF) is adopted since from the control theory it is reported that the UKF shows better performance than the extended Kalman filter (EKF) that has been commonly used. We formulated the UKF algorithm to be incorporate into the image reconstruction algorithm for the present problem. Also, phantom experiments have been conducted to evaluate the improvement by UKF

The Boundary Function Method. Fundamentals

Science.gov (United States)

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.

Einstein boundary conditions in relation to constraint propagation for the initial-boundary value problem of the Einstein equations

International Nuclear Information System (INIS)

Frittelli, Simonetta; Gomez, Roberto

2004-01-01

We show how the use of the normal projection of the Einstein tensor as a set of boundary conditions relates to the propagation of the constraints, for two representations of the Einstein equations with vanishing shift vector: the Arnowitt-Deser-Misner formulation, which is ill posed, and the Einstein-Christoffel formulation, which is symmetric hyperbolic. Essentially, the components of the normal projection of the Einstein tensor that act as nontrivial boundary conditions are linear combinations of the evolution equations with the constraints that are not preserved at the boundary, in both cases. In the process, the relationship of the normal projection of the Einstein tensor to the recently introduced 'constraint-preserving' boundary conditions becomes apparent

Analysis of stress fields and elastic energies in the vicinity of nanograin boundaries using the disclination approach

Science.gov (United States)

Sukhanov, Ivan I.; Ditenberg, Ivan A.

2017-12-01

The paper provides a theoretical analysis of elastic stresses and elastic energy distribution in nanostructured metal materials in the vicinity of nanograin boundaries with a high partial disclination density. The analysis demonstrates the stress field distribution in disclination grain boundary configurations as a function of nanograin size, taking into account the superposition of these stresses in screening the disclination pile-ups. It is found that the principal stress tensor components reach maximum values only in disclination planes P ≈ E/25 and that the stress gradients peak at nodal points ∂P/∂x ≈ 0.08E nm-1. The shear stress components are localized within the physical grain size, and the specific elastic energy distribution for such configurations reveals characteristic local maxima which can be the cause for physical broadening of nanograin boundaries.

Characterization of distributions by conditional expectation of record values

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A.H. Khan

2016-01-01

Full Text Available A family of continuous probability distributions has been characterized by two conditional expectations of record statistics conditioned on a non-adjacent record value. Besides various deductions, this work extends the result of Lee [8] in which Pareto distribution has been characterized.

Existence and nonexistence results for a singular boundary value problem arising in the theory of epitaxial growth

Czech Academy of Sciences Publication Activity Database

Escudero, C.; Hakl, Robert; Peral, I.; Torres, P.J.

2014-01-01

Roč. 37, č. 6 (2014), s. 793-807 ISSN 0170-4214 Institutional support: RVO:67985840 Keywords : singular boundary value problem * epitaxial growth * radial solution Subject RIV: BA - General Mathematics Impact factor: 0.918, year: 2014 http://onlinelibrary.wiley.com/doi/10.1002/mma.2836/full

Southern limits of distribution of the intertidal gobies Chaenogobius annularis and C. gulosus support the existence of a biogeographic boundary in southern Japan (Teleostei, Perciformes, Gobiidae

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Atsunobu Murase

2017-12-01

Full Text Available Understanding the distributional patterns of individual animal groups with respect to coastal topology and the local physical environment provides essential foundational frameworks for marine zoogeography. In the northwestern Pacific waters of Japan, the distributional pattern of some cool-temperate species of marine fishes suggests the existence of a biogeographic boundary corresponding to a long sandy shore on the eastern coast of Kyushu, southern Japan. The existence of this hypothetical biogeographic boundary was tested by mapping the southern distributional limit of two species of cool-temperate intertidal gobies, Chaenogobius annularis and C. gulosus, which are endemic to East Asia and common in rock pools within their range in the Japanese Archipelago. Distribution and abundance were assessed by survey of museum collections from south-east Kyushu (i.e., the entire coasts of Kagoshima and Miyazaki prefectures; and a quantitative survey of the abundance of these gobies in rock pools at various sites around the hypothesized boundary on the eastern coast of Kyushu, including the subtropical Tanega-shima Island. The museum collection survey showed different distribution patterns between the two species: C. annularis was distributed along the entire coasts of south-east Kyushu including subtropical islands, whereas C. gulosus was distributed along these coasts, including one site on a subtropical island, except for an area south of the hypothesized boundary on the eastern coast of Kyushu. The density and occurrence rates of C. annularis in rock pools decreased with latitude, it being absent from a subtropical island, and C. gulosus was not detected from sites south of the hypothesized boundary. The qualitative survey showed that the southernmost records of C. annularis and C. gulosus were the adjacent subtropical islands (Yaku-shima and Tanega-shima islands respectively, although the quantitative survey suggested that their normal range of

Existence of Positive Solutions to a Singular Semipositone Boundary Value Problem of Nonlinear Fractional Differential Systems

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Xiaofeng Zhang

2017-12-01

Full Text Available In this paper, we consider the existence of positive solutions to a singular semipositone boundary value problem of nonlinear fractional differential equations. By applying the fixed point index theorem, some new results for the existence of positive solutions are obtained. In addition, an example is presented to demonstrate the application of our main results.

On Perturbation Solutions for Axisymmetric Bending Boundary Values of a Deep Thin Spherical Shell

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Rong Xiao

2014-01-01

Full Text Available On the basis of the general theory of elastic thin shells and the Kirchhoff-Love hypothesis, a fundamental equation for a thin shell under the moment theory is established. In this study, the author derives Reissner’s equation with a transverse shear force Q1 and the displacement component w. These basic unknown quantities are derived considering the axisymmetry of the deep, thin spherical shell and manage to constitute a boundary value question of axisymmetric bending of the deep thin spherical shell under boundary conditions. The asymptotic solution is obtained by the composite expansion method. At the end of this paper, to prove the correctness and accuracy of the derivation, an example is given to compare the numerical solution by ANSYS and the perturbation solution. Meanwhile, the effects of material and geometric parameters on the nonlinear response of axisymmetric deep thin spherical shell under uniform external pressure are also analyzed in this paper.

Improved polycrystalline Ni{sub 54}Mn{sub 16}Fe{sub 9}Ga{sub 21} high-temperature shape memory alloy by γ phase distributing along grain boundaries

Energy Technology Data Exchange (ETDEWEB)

Yang, Shuiyuan; Zhang, Fan; Zhang, Kaixin; Huang, Yangyang; Wang, Cuiping; Liu, Xingjun [Xiamen Univ. (China). Fujian Key Laboratory of Materials Genome

2016-09-15

In this study, the shape recovery and mechanical properties of Ni{sub 54}Mn{sub 16}Fe{sub 9}Ga{sub 21} high-temperature shape memory alloy are improved simultaneously. This results from the low, about 4.4%, volume fraction of γ phase being almost completely distributed along grain boundaries. The recovery strain gradually increases with the increase in residual strain with a shape recovery rate of above 68%, up to a maximum value of 5.3%. The compressive fracture strain of Ni{sub 54}Mn{sub 16}Fe{sub 9}Ga{sub 21} alloy is about 35%. The results further reveal that when applying a high compression deformation two types of cracks form and propagate either within martensite grains (type I) or along the boundaries between martensite phase and γ phase (type II) in the present two-phase alloy.

An efficient computer based wavelets approximation method to solve Fuzzy boundary value differential equations

Science.gov (United States)

Alam Khan, Najeeb; Razzaq, Oyoon Abdul

2016-03-01

In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.

Localizing value of pain distribution patterns in cervical spondylosis.

Science.gov (United States)

Bunyaratavej, Krishnapundha; Montriwiwatnchai, Peerapong; Siwanuwatn, Rungsak; Khaoroptham, Surachai

2015-04-01

Prospective observational study. To investigate the value of pain distribution in localizing appropriate surgical levels in patients with cervical spondylosis. Previous studies have investigated the value of pain drawings in its correlation with various features in degenerative spine diseases including surgical outcome, magnetic resonance imaging findings, discographic study, and psychogenic issues. However, there is no previous study on the value of pain drawings in identifying symptomatic levels for the surgery in cervical spondylosis. The study collected data from patients with cervical spondylosis who underwent surgical treatment between August 2009 and July 2012. Pain diagrams drawn separately by each patient and physician were collected. Pain distribution patterns among various levels of surgery were analyzed by the chi-square test. Agreement between different pairs of data, including pain diagrams drawn by each patient and physician, intra-examiner agreement on interpretation of pain diagrams, inter-examiner agreement on interpretation of pain diagrams, interpretation of pain diagram by examiners and actual surgery, was analyzed by Kappa statistics. The study group consisted of 19 men and 28 women with an average age of 55.2 years. Average duration of symptoms was 16.8 months. There was no difference in the pain distribution pattern at any level of surgery. The agreement between pain diagram drawn by each patient and physician was moderate. Intra-examiner agreement was moderate. There was slight agreement of inter-examiners, examiners versus actual surgery. Pain distribution pattern by itself has limited value in identifying surgical levels in patients with cervical spondylosis.

The first and second e of the extreme value distribution.

NARCIS (Netherlands)

Montfort, van M.A.J.; Otten, A.

1991-01-01

In the peak over threshold model resulting in the Extreme-value distribution, type I, (EV1) the first e of the distribution function is based on the Poisson number of exceedances, and the second e arises from the Exponentially distributed magnitudes. This paper, on the one hand, generalises the

Variational Iteration Method for Fifth-Order Boundary Value Problems Using He's Polynomials

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Muhammad Aslam Noor

2008-01-01

Full Text Available We apply the variational iteration method using He's polynomials (VIMHP for solving the fifth-order boundary value problems. The proposed method is an elegant combination of variational iteration and the homotopy perturbation methods and is mainly due to Ghorbani (2007. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discritization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed technique solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method.

Identification of Climate Change with Generalized Extreme Value (GEV) Distribution Approach

International Nuclear Information System (INIS)

Rahayu, Anita

2013-01-01

Some events are difficult to avoid and gives considerable influence to humans and the environment is extreme weather and climate change. Many of the problems that require knowledge about the behavior of extreme values and one of the methods used are the Extreme Value Theory (EVT). EVT used to draw up reliable systems in a variety of conditions, so as to minimize the risk of a major disaster. There are two methods for identifying extreme value, Block Maxima with Generalized Extreme Value (GEV) distribution approach and Peaks over Threshold (POT) with Generalized Pareto Distribution (GPD) approach. This research in Indramayu with January 1961-December 2003 period, the method used is Block Maxima with GEV distribution approach. The result showed that there is no climate change in Indramayu with January 1961-December 2003 period.

Thin-film superconducting rings in the critical state: the mixed boundary value approach

Science.gov (United States)

Brambilla, Roberto; Grilli, Francesco

2015-02-01

In this paper, we describe the critical state of a thin superconducting ring (and of a perfectly conducting ring as a limiting case) as a mixed boundary value problem. The disc is characterized by a three-part boundary division of the positive real axis, so this work is an extension of the procedure used in a previous work of ours for describing superconducting discs and strips, which are characterized by a two-part boundary division of the real axis. Here, we present the mathematical tools to solve this kind of problems—the Erdélyi-Kober operators—in a frame that can be immediately used. Contrary to the two-part problems considered in our previous work, three-part problems do not generally have analytical solutions and the numerical work takes on a significant heaviness. Nevertheless, this work is remunerated by three clear advantages: firstly, all the cases are afforded in the same way, without the necessity of any brilliant invention or ability; secondly, in the case of superconducting rings, the penetration of the magnetic field in the internal/external rims is a result of the method itself and does not have to be imposed, as it is commonly done with other methods presented in the literature; thirdly, the method can be extended to investigate even more complex cases (four-part problems). In this paper, we consider the cases of rings in uniform field and with transport current, with or without flux trapping in the hole and the case without net current, corresponding to a cut ring (washer), as used in some SQUID applications.

Localizing Value of Pain Distribution Patterns in Cervical Spondylosis

OpenAIRE

Bunyaratavej, Krishnapundha; Montriwiwatnchai, Peerapong; Siwanuwatn, Rungsak; Khaoroptham, Surachai

2015-01-01

Study Design Prospective observational study. Purpose To investigate the value of pain distribution in localizing appropriate surgical levels in patients with cervical spondylosis. Overview of Literature Previous studies have investigated the value of pain drawings in its correlation with various features in degenerative spine diseases including surgical outcome, magnetic resonance imaging findings, discographic study, and psychogenic issues. However, there is no previous study on the value o...

Nonlinear fractional differential equations and inclusions of arbitrary order and multi-strip boundary conditions

Directory of Open Access Journals (Sweden)

Bashir Ahmad

2012-06-01

Full Text Available We study boundary value problems of nonlinear fractional differential equations and inclusions of order $q in (m-1, m]$, $m ge 2$ with multi-strip boundary conditions. Multi-strip boundary conditions may be regarded as the generalization of multi-point boundary conditions. Our problem is new in the sense that we consider a nonlocal strip condition of the form: $$ x(1=sum_{i=1}^{n-2}alpha_i int^{eta_i}_{zeta_i} x(sds, $$ which can be viewed as an extension of a multi-point nonlocal boundary condition: $$ x(1=sum_{i=1}^{n-2}alpha_i x(eta_i. $$ In fact, the strip condition corresponds to a continuous distribution of the values of the unknown function on arbitrary finite segments $(zeta_i,eta_i$ of the interval $[0,1]$ and the effect of these strips is accumulated at $x=1$. Such problems occur in the applied fields such as wave propagation and geophysics. Some new existence and uniqueness results are obtained by using a variety of fixed point theorems. Some illustrative examples are also discussed.

measurements of distribution coefficients and lipophilicity values

African Journals Online (AJOL)

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octanol and water, followed by measuring the distribution of the solute in ... Instrumentation and apparatus: HPLC-UV-DAD and HPLC–ESI-MS experiments .... process in the determination of KD and log P values for the HFSLM extracts. ..... Perrin, D.D.; Dempsey, B. Buffers for pH and Metal Ion Control, Chapman and Hall:.

Generalised extreme value distributions provide a natural hypothesis for the shape of seed mass distributions.

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Will Edwards

Full Text Available Among co-occurring species, values for functionally important plant traits span orders of magnitude, are uni-modal, and generally positively skewed. Such data are usually log-transformed "for normality" but no convincing mechanistic explanation for a log-normal expectation exists. Here we propose a hypothesis for the distribution of seed masses based on generalised extreme value distributions (GEVs, a class of probability distributions used in climatology to characterise the impact of event magnitudes and frequencies; events that impose strong directional selection on biological traits. In tests involving datasets from 34 locations across the globe, GEVs described log10 seed mass distributions as well or better than conventional normalising statistics in 79% of cases, and revealed a systematic tendency for an overabundance of small seed sizes associated with low latitudes. GEVs characterise disturbance events experienced in a location to which individual species' life histories could respond, providing a natural, biological explanation for trait expression that is lacking from all previous hypotheses attempting to describe trait distributions in multispecies assemblages. We suggest that GEVs could provide a mechanistic explanation for plant trait distributions and potentially link biology and climatology under a single paradigm.

Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity

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Mitsuhiro Nakao

2014-01-01

Full Text Available We prove the existence and uniqueness of a global decaying solution to the initial boundary value problem for the quasilinear wave equation with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a 'loan' method and use a difference inequality on the energy.

Influence of Last Glacial Maximum boundary conditions on the global water isotope distribution in an atmospheric general circulation model

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T. Tharammal

2013-03-01

Full Text Available To understand the validity of δ18O proxy records as indicators of past temperature change, a series of experiments was conducted using an atmospheric general circulation model fitted with water isotope tracers (Community Atmosphere Model version 3.0, IsoCAM. A pre-industrial simulation was performed as the control experiment, as well as a simulation with all the boundary conditions set to Last Glacial Maximum (LGM values. Results from the pre-industrial and LGM simulations were compared to experiments in which the influence of individual boundary conditions (greenhouse gases, ice sheet albedo and topography, sea surface temperature (SST, and orbital parameters were changed each at a time to assess their individual impact. The experiments were designed in order to analyze the spatial variations of the oxygen isotopic composition of precipitation (δ18Oprecip in response to individual climate factors. The change in topography (due to the change in land ice cover played a significant role in reducing the surface temperature and δ18Oprecip over North America. Exposed shelf areas and the ice sheet albedo reduced the Northern Hemisphere surface temperature and δ18Oprecip further. A global mean cooling of 4.1 °C was simulated with combined LGM boundary conditions compared to the control simulation, which was in agreement with previous experiments using the fully coupled Community Climate System Model (CCSM3. Large reductions in δ18Oprecip over the LGM ice sheets were strongly linked to the temperature decrease over them. The SST and ice sheet topography changes were responsible for most of the changes in the climate and hence the δ18Oprecip distribution among the simulations.

A boundary-value inverse model and its application to the calculation of tidal oscillation systems in the Western South Atlantic Ocean

International Nuclear Information System (INIS)

Miranda-Alonso, S.

1991-01-01

A Cauchy-Riemann problem is solved for the case of the linearized equations for long waves. The initial-values are amplitudes and phases measured at the coast. No boundary values are made use of. This inverse-problem is solved by starting the calculations at the coast and continuing outwards to the open ocean in a rectangular areas with one side at the coast and the other three at the open ocean. The initial values were expanded into the complex plane to get a platform to perform with the calculations. This non-well-posed problem was solved by means of two different mathematical techniques for comparison. The results produced with the inverse model were compared with those produced with a 'classical' model initialized at the three open boundaries with the results of the inverse model. The oscillating systems produced by both models were quite similar, giving validity to this invese modeling approach which should be a useful technique to solve problems when only initial values are known. (orig.)

Application of power series to the solution of the boundary value problem for a second order nonlinear differential equation

International Nuclear Information System (INIS)

Semenova, V.N.

2016-01-01

A boundary value problem for a nonlinear second order differential equation has been considered. A numerical method has been proposed to solve this problem using power series. Results of numerical experiments have been presented in the paper [ru

The Laplace equation boundary value problems on bounded and unbounded Lipschitz domains

CERN Document Server

Medková, Dagmar

2018-01-01

This book is devoted to boundary value problems of the Laplace equation on bounded and unbounded Lipschitz domains. It studies the Dirichlet problem, the Neumann problem, the Robin problem, the derivative oblique problem, the transmission problem, the skip problem and mixed problems. It also examines different solutions - classical, in Sobolev spaces, in Besov spaces, in homogeneous Sobolev spaces and in the sense of non-tangential limit. It also explains relations between different solutions. The book has been written in a way that makes it as readable as possible for a wide mathematical audience, and includes all the fundamental definitions and propositions from other fields of mathematics. This book is of interest to research students, as well as experts in partial differential equations and numerical analysis.

Existence of Positive Solutions for a Coupled System of (p, q-Laplacian Fractional Higher Order Boundary Value Problems

Directory of Open Access Journals (Sweden)

K.R. Prasad

2015-11-01

Full Text Available In this paper, we establish the existence of at least three positive solutions for a system of (p,q-Laplacian fractional order two-point boundary value problems by applying five functionals fixed point theorem under suitable conditions on a cone in a Banach space.

Initial-boundary value problems for multi-term time-fractional diffusion equations with x-dependent coefficients

OpenAIRE

Li, Zhiyuan; Huang, Xinchi; Yamamoto, Masahiro

2018-01-01

In this paper, we discuss an initial-boundary value problem (IBVP) for the multi-term time-fractional diffusion equation with x-dependent coefficients. By means of the Mittag-Leffler functions and the eigenfunction expansion, we reduce the IBVP to an equivalent integral equation to show the unique existence and the analyticity of the solution for the equation. Especially, in the case where all the coefficients of the time-fractional derivatives are non-negative, by the Laplace and inversion L...

Fermat collocation method for the solutions of nonlinear system of second order boundary value problems

Directory of Open Access Journals (Sweden)

Salih Yalcinbas

2016-01-01

Full Text Available In this study, a numerical approach is proposed to obtain approximate solutions of nonlinear system of second order boundary value problem. This technique is essentially based on the truncated Fermat series and its matrix representations with collocation points. Using the matrix method, we reduce the problem system of nonlinear algebraic equations. Numerical examples are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and produces accurate results.

Quantifying liquid boundary and vapor distributions in a fuel spray by rainbow schlieren deflectometry.

Science.gov (United States)

Taber Wanstall, C; Agrawal, Ajay K; Bittle, Joshua A

2017-10-20

The rainbow schlieren deflectometry (RSD) technique is used to determine the liquid boundary and the fuel volume fraction distributions in the vapor region of a high-pressure fuel spray. Experiments were conducted in a constant pressure flow vessel, whereby a customized single-hole common-rail diesel injector is used to introduce n-heptane fuel into a coflow of low-speed ambient air at two different test conditions. Only the quasi-steady period of the fuel spray is considered, and multiple injections are performed to acquire statistically significant data at an image acquisition rate of 20 kHz. An algorithm to identify the liquid boundary using intensity recorded by the RSD images is presented. The results are compared against measurements obtained by the Mie scattering technique. Results demonstrate that the RSD can be a powerful optical diagnostics technique to simultaneously quantify both the vapor and liquid regions in the high-pressure fuel sprays.

Magnetostatic calculation of fringing field for the Rogowski pole boundary with floating snake

Energy Technology Data Exchange (ETDEWEB)

Chen, Yan; Ming-Wu, Fan [Institute of Atomic Energy, Peking (China)

1984-01-01

A boundary integral method has been used to calculate the fringing field distribution of Rogowski pole boundary with floating snake for QMG2 type of QDDD magnetic spectrograph and the experimental EFB is nearly reproduced from BIM calculation. As a further criteria, a calculation for clamped Rogowski pole but without snake is also performed and the calculated EFB shows perfect identity with the experiment. For evaluating the effect of snake quantitatively, this work also predicts the EFB values for two different positions of snake.

Effect of Grain Orientation and Boundary Distributions on Hydrogen-Induced Cracking in Low-Carbon-Content Steels

Science.gov (United States)

Masoumi, Mohammad; Coelho, Hana Livia Frota; Tavares, Sérgio Souto Maior; Silva, Cleiton Carvalho; de Abreu, Hamilton Ferreira Gomes

2017-08-01

Hydrogen-induced cracking (HIC) causes considerable economic losses in a wide range of steels exposed to corrosive environments. The effect of crystallographic texture and grain boundary distributions tailored by rolling at 850 °C in three different steels with a body-centered cube structure was investigated on HIC resistance. The x-ray and electron backscattered diffraction techniques were used to characterize texture evolutions during the rolling process. The findings revealed a significant improvement against HIC based on texture engineering. In addition, increasing the number of {111} and {110} grains, associated with minimizing the number of {001} grains in warm-rolled samples, reduced HIC susceptibility. Moreover, the results showed that boundaries associated with low {hkl} indexing and denser packing planes had more resistance against crack propagation.

Lower and Upper Solutions Method for Positive Solutions of Fractional Boundary Value Problems

Directory of Open Access Journals (Sweden)

R. Darzi

2013-01-01

Full Text Available We apply the lower and upper solutions method and fixed-point theorems to prove the existence of positive solution to fractional boundary value problem D0+αut+ft,ut=0, 0

Productivity and value added distribution in family-owned businesses

Directory of Open Access Journals (Sweden)

Jose Luis Gallizo Larraz

2017-01-01

Full Text Available Objective: Identify similarities and/or differences in the distribution of Value Added characterizing family businesses as opposed to non-family held firms, and analyse productivity by linking the distribution of the wealth generated by the company to a variety of related agents or stakeholders (employees, providers of loan capital, and shareholders. Design/methodology: A data series consisting of VA distribution in a sample of 8,609 Spanish companies, of which 5,109 are family firms and another 3,500 companies which are not, for the period comprising 2008 to 2013 was employed for this study. The data from the financial statements pertaining to these companies was taken from the SABI system (a privately-funded database analysing the financials of Spanish and Portuguese firms, operated by INFORMA, SA, selecting only those companies that employ standardized financial reporting practices. Findings and results: The work shows the existence of significant differences between family and non-family businesses in the distribution of value added among the different stakeholders. Given that, although both types of company spend most of the value added to remunerate staff, the family company spends a higher proportion thereof on self-financing as compared to non-family businesses, which spend a higher percentage on the remuneration of firm ownership. On the other hand, the lower labour productivity of family businesses is apparent, a result that can be explained both by the lower staff monetary remuneration, as well as the use of production technologies that are also less capital-intensive. Limitations: The study included only medium and large companies. These are companies that report financial statements offering more disaggregated data (through use of the standard forms. This owes to the legal requirement of these companies to file a cash flow statement, a necessary source for deriving information on dividends paid by the company. Added value: This is

The energetic ion substorm injection boundary

International Nuclear Information System (INIS)

Lopez, R.E.; Sibeck, D.G.; McEntire, R.W.; Krimigis, S.M.

1990-01-01

The substorm injection boundary model has enjoyed considerable success in explaining plasma signatures in the near-geosynchronous region. However, the injection boundary has remained primarily a phenomenological model. In this paper the authors examine 167 dispersionless energetic ion injections which were observed by AMPTE CCE. The radial and local time distribution of the events as a function of Kp is qualitatively similar to that envisioned in the injection boundary model of Mauk and McIlwain (1974). They argue that particles observed during dispersionless injections are locally energized during the disruption of the cross-tail current sheet. Therefore they identify the injection boundary, as derived from the spatial distribution of dispersionless injections, with the earthward edge of the region of the magnetotail which undergoes current sheet disruption during the substorm expansion phase. The authors show that this qualitative model for the generation of the injection boundary can provide an explanation for the dispersionless nature, the double spiral shape, and the Kp dependence of the boundary

Boundary and sub-boundary hardening in tempered martensitic 9Cr steel during long-term creep at 650 C

Energy Technology Data Exchange (ETDEWEB)

Abe, Fujio [National Institute for Materials Science, Sengen, Tsukuba (Japan)

2010-07-01

The boundary and sub-boundary hardening is shown to be the most important strengthening mechanism in creep of the 9% Cr steel base metal and welded joints. The addition of boron reduces the coarsening rate of M{sub 23}C{sub 6} carbides along boundaries near prior austenite grain boundaries during creep, enhancing the boundary and sub-boundary hardening. This improves long-term creep strength of base metal. The enhancement of boundary and sub-boundary hardening is significantly reduced in fine-grained region of Ac{sub 3} HAZ simulated specimens of conventional steel P92. In NIMS 9Cr boron steel welded joints, the grain size and distribution of carbonitrides are substantially the same between the HAZ and base metal, where fine carbonitrides are distributed along the lath and block boundaries as well as along prior austenite grain boundaries. This is essential for the suppression of Type IV fracture in NIMS 9% Cr boron steel welded joints. Newly alloy-designed 9Cr steel with 160 ppm boron and 85 ppm nitrogen exhibits much higher creep rupture strength of base metal than P92 and also no Tpe-IV fracture in welded joints at 650 C. (orig.)

Determination of grain boundary mobility during recrystallization by statistical evaluation of electron backscatter diffraction measurements

International Nuclear Information System (INIS)

Basu, I.; Chen, M.; Loeck, M.; Al-Samman, T.; Molodov, D.A.

2016-01-01

One of the key aspects influencing microstructural design pathways in metallic systems is grain boundary motion. The present work introduces a method by means of which direct measurement of grain boundary mobility vs. misorientation dependence is made possible. The technique utilizes datasets acquired by means of serial electron backscatter diffraction (EBSD) measurements. The experimental EBSD measurements are collectively analyzed, whereby datasets were used to obtain grain boundary mobility and grain aspect ratio with respect to grain boundary misorientation. The proposed method is further validated using cellular automata (CA) simulations. Single crystal aluminium was cold rolled and scratched in order to nucleate random orientations. Subsequent annealing at 300 °C resulted in grains growing, in the direction normal to the scratch, into a single deformed orientation. Growth selection was observed, wherein the boundaries with misorientations close to Σ7 CSL orientation relationship (38° 〈111〉) migrated considerably faster. The obtained boundary mobility distribution exhibited a non-monotonic behavior with a maximum corresponding to misorientation of 38° ± 2° about 〈111〉 axes ± 4°, which was 10–100 times higher than the mobility values of random high angle boundaries. Correlation with the grain aspect ratio values indicated a strong growth anisotropy displayed by the fast growing grains. The observations have been discussed in terms of the influence of grain boundary character on grain boundary motion during recrystallization. - Highlights: • Statistical microstructure method to measure grain boundary mobility during recrystallization • Method implementation independent of material or crystal structure • Mobility of the Σ7 boundaries in 5N Al was calculated as 4.7 × 10"–"8 m"4/J ⋅ s. • Pronounced growth selection in the recrystallizing nuclei in Al • Boundary mobility values during recrystallization 2–3 orders of magnitude

Experimental study of boundary-layer transition on an airfoil induced by periodically passing wake

Energy Technology Data Exchange (ETDEWEB)

Jeon, W.P. [Center for Turbulence and Flow Control Research Institute of Advanced Machinery and Design, Seoul National University (Korea); Park, T.C.; Kang, S.H. [School of Mechanical and Aerospace Engineering, Seoul National University (Korea)

2002-02-01

Hot-wire measurements are performed in boundary-layer flows developing on a NACA 0012 airfoil over which wakes pass periodically. The periodic wakes are generated by rotating circular cylinders clockwise or counterclockwise around the airfoil. The time- and phase-averaged mean streamwise velocities and turbulence fluctuations are measured to investigate the phenomena of wake-induced transition. Especially, the phase-averaged wall shear stresses are evaluated using a computational Preston tube method. The passing wakes significantly change the pressure distribution on the airfoil, which has influence on the transition process of the boundary layer. The orientation of the passing wake alters the pressure distribution in a different manner. Due to the passing wake, the turbulent patches are generated inside the laminar boundary layer on the airfoil, and the boundary layer becomes temporarily transitional. The patches propagate downstream at a speed smaller than the free-stream velocity and merge together further downstream. Relatively high values of phase-averaged turbulence fluctuations in the outer part of the boundary layer indicate the possibility that breakdown occurs in the outer layer away from the wall. It is confirmed that the phase-averaged mean velocity profile has two dips in the outer region of the transitional boundary layer for each passing cycle. (orig.)

EXISTENCE OF POSITIVE SOLUTION TO TWO-POINT BOUNDARY VALUE PROBLEM FOR A SYSTEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

Institute of Scientific and Technical Information of China (English)

无

2009-01-01

In this paper, we consider a two-point boundary value problem for a system of second order ordinary differential equations. Under some conditions, we show the existence of positive solution to the system of second order ordinary differential equa-tions.

Polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains

CERN Document Server

Gazzola, Filippo; Sweers, Guido

2010-01-01

This monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for linear problems, after a brief summary of the existence theory and Lp and Schauder estimates, the focus is on positivity or - since, in contrast to second order equations, a general form of a comparison principle does not exist - on “near positivity.” The required kernel estimates are also presented in detail. As for nonlinear problems, several techniques well-known from second order equations cannot be utilized and have to be replaced by new and different methods. Subcritical, critical and supercritical nonlinearities are discussed and various existence and nonexistence results are proved. The interplay with the positivity topic from the first part is emphasized and, moreover, a far-reaching Gidas-Ni-Nirenbe...

An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems

Directory of Open Access Journals (Sweden)

Mohammad Maleki

2012-01-01

Full Text Available An adaptive pseudospectral method is presented for solving a class of multiterm fractional boundary value problems (FBVP which involve Caputo-type fractional derivatives. The multiterm FBVP is first converted into a singular Volterra integrodifferential equation (SVIDE. By dividing the interval of the problem to subintervals, the unknown function is approximated using a piecewise interpolation polynomial with unknown coefficients which is based on shifted Legendre-Gauss (ShLG collocation points. Then the problem is reduced to a system of algebraic equations, thus greatly simplifying the problem. Further, some additional conditions are considered to maintain the continuity of the approximate solution and its derivatives at the interface of subintervals. In order to convert the singular integrals of SVIDE into nonsingular ones, integration by parts is utilized. In the method developed in this paper, the accuracy can be improved either by increasing the number of subintervals or by increasing the degree of the polynomial on each subinterval. Using several examples including Bagley-Torvik equation the proposed method is shown to be efficient and accurate.

Response of Non-Linear Shock Absorbers-Boundary Value Problem Analysis

Science.gov (United States)

Rahman, M. A.; Ahmed, U.; Uddin, M. S.

2013-08-01

A nonlinear boundary value problem of two degrees-of-freedom (DOF) untuned vibration damper systems using nonlinear springs and dampers has been numerically studied. As far as untuned damper is concerned, sixteen different combinations of linear and nonlinear springs and dampers have been comprehensively analyzed taking into account transient terms. For different cases, a comparative study is made for response versus time for different spring and damper types at three important frequency ratios: one at r = 1, one at r > 1 and one at r <1. The response of the system is changed because of the spring and damper nonlinearities; the change is different for different cases. Accordingly, an initially stable absorber may become unstable with time and vice versa. The analysis also shows that higher nonlinearity terms make the system more unstable. Numerical simulation includes transient vibrations. Although problems are much more complicated compared to those for a tuned absorber, a comparison of the results generated by the present numerical scheme with the exact one shows quite a reasonable agreement

Bubble boundary estimation in an annulus two-phase flow using electrical impedance tomography

International Nuclear Information System (INIS)

Lee, Jeong Seong

2008-02-01

For the visualization of the phase boundary in an annulus two-phase flows, the electrical impedance tomography (EIT) technique is introduced. In EIT, a set of predetermined electrical currents is injected trough the electrodes placed on the boundary of the flow passage and the induced electrical potentials are measured on the electrode. With the relationship between the injected currents and the induced voltages, the electrical conductivity distribution across the flow domain is estimated through the image reconstruction algorithm. In this, the conductivity distribution corresponds to the phase distribution. In the application of EIT to two-phase flows where there are only two conductivity values, the conductivity distribution estimation problem can be transformed into the boundary estimation problem. This paper considers a bubble boundary estimation with EIT in an annulus two-phase flows. And in many industrial cases there are a priori known internal structures inside the vessels which could be used as internal electrodes in tomographical imaging. In this paper internal electrodes were considered in electrical impedance tomography. As the image reconstruction algorithm, the unscented Kalman filter (UKF) is adopted since from the control theory it is reported that the UKF shows better performance than the extended Kalman filter (EKF) that has been commonly used. The UKF algorithm was formulated to be incorporate into the image reconstruction algorithm for the present problem. Also, phantom experiments have been conducted to evaluate the improvement by UKF

The Initial and Neumann Boundary Value Problem for a Class Parabolic Monge-Ampère Equation

Directory of Open Access Journals (Sweden)

Juan Wang

2013-01-01

Full Text Available We consider the existence, uniqueness, and asymptotic behavior of a classical solution to the initial and Neumann boundary value problem for a class nonlinear parabolic equation of Monge-Ampère type. We show that such solution exists for all times and is unique. It converges eventually to a solution that satisfies a Neumann type problem for nonlinear elliptic equation of Monge-Ampère type.

Triple Positive Solutions of a Nonlocal Boundary Value Problem for Singular Differential Equations with p-Laplacian

Directory of Open Access Journals (Sweden)

Jufang Wang

2013-01-01

Full Text Available We establish the existence of triple positive solutions of an m-point boundary value problem for the nonlinear singular second-order differential equations of mixed type with a p-Laplacian operator by Leggett-William fixed point theorem. At last, we give an example to demonstrate the use of the main result of this paper. The conclusions in this paper essentially extend and improve the known results.

Forecasting Value-at-Risk under Different Distributional Assumptions

Directory of Open Access Journals (Sweden)

Manuela Braione

2016-01-01

Full Text Available Financial asset returns are known to be conditionally heteroskedastic and generally non-normally distributed, fat-tailed and often skewed. These features must be taken into account to produce accurate forecasts of Value-at-Risk (VaR. We provide a comprehensive look at the problem by considering the impact that different distributional assumptions have on the accuracy of both univariate and multivariate GARCH models in out-of-sample VaR prediction. The set of analyzed distributions comprises the normal, Student, Multivariate Exponential Power and their corresponding skewed counterparts. The accuracy of the VaR forecasts is assessed by implementing standard statistical backtesting procedures used to rank the different specifications. The results show the importance of allowing for heavy-tails and skewness in the distributional assumption with the skew-Student outperforming the others across all tests and confidence levels.

Numeric treatment of nonlinear second order multi-point boundary value problems using ANN, GAs and sequential quadratic programming technique

Directory of Open Access Journals (Sweden)

Zulqurnain Sabir

2014-06-01

Full Text Available In this paper, computational intelligence technique are presented for solving multi-point nonlinear boundary value problems based on artificial neural networks, evolutionary computing approach, and active-set technique. The neural network is to provide convenient methods for obtaining useful model based on unsupervised error for the differential equations. The motivation for presenting this work comes actually from the aim of introducing a reliable framework that combines the powerful features of ANN optimized with soft computing frameworks to cope with such challenging system. The applicability and reliability of such methods have been monitored thoroughly for various boundary value problems arises in science, engineering and biotechnology as well. Comprehensive numerical experimentations have been performed to validate the accuracy, convergence, and robustness of the designed scheme. Comparative studies have also been made with available standard solution to analyze the correctness of the proposed scheme.

A Direct Approach to Determine the External Disturbing Gravity Field by Applying Green Integral with the Ground Boundary Value

Directory of Open Access Journals (Sweden)

TIAN Jialei

2015-11-01

Full Text Available By using the ground as the boundary, Molodensky problem usually gets the solution in form of series. Higher order terms reflect the correction between a smooth surface and the ground boundary. Application difficulties arise from not only computational complexity and stability maintenance, but also data-intensiveness. Therefore, in this paper, starting from the application of external gravity disturbance, Green formula is used on digital terrain surface. In the case of ignoring the influence of horizontal component of the integral, the expression formula of external disturbance potential determined by boundary value consisted of ground gravity anomalies and height anomaly difference are obtained, whose kernel function is reciprocal of distance and Poisson core respectively. With this method, there is no need of continuation of ground data. And kernel function is concise, and suitable for the stochastic computation of external disturbing gravity field.

Solution of a Problem Linear Plane Elasticity with Mixed Boundary Conditions by the Method of Boundary Integrals

Directory of Open Access Journals (Sweden)

Nahed S. Hussein

2014-01-01

Full Text Available A numerical boundary integral scheme is proposed for the solution to the system of …eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.

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

Science.gov (United States)

Biala, T A; Jator, S N

2015-01-01

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

A magnetostatic calculation of fringing field for the Rogowski pole boundary with floating snake

International Nuclear Information System (INIS)

Yan Chen; Fan Ming-Wu

1984-01-01

A boundary integral method has been used to calculate the fringing field distribution of Rogowski pole boundary with floating snake for QMG2 type of QDDD magnetic spectrograph and the experimental EFB is nearly reproduced from BIM calculation. As a further criteria, a calculation for clamped Rogowski pole but without snake is also performed and the calculated EFB shows perfect identity with the experiment. For evaluating the effect of snake quantitatively, this work also predicts the EFB values for two different positions of snake

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

Science.gov (United States)

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

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

Research on the Automatic Fusion Strategy of Fixed Value Boundary Based on the Weak Coupling Condition of Grid Partition

Science.gov (United States)

Wang, X. Y.; Dou, J. M.; Shen, H.; Li, J.; Yang, G. S.; Fan, R. Q.; Shen, Q.

2018-03-01

With the continuous strengthening of power grids, the network structure is becoming more and more complicated. An open and regional data modeling is used to complete the calculation of the protection fixed value based on the local region. At the same time, a high precision, quasi real-time boundary fusion technique is needed to seamlessly integrate the various regions so as to constitute an integrated fault computing platform which can conduct transient stability analysis of covering the whole network with high accuracy and multiple modes, deal with the impact results of non-single fault, interlocking fault and build “the first line of defense” of the power grid. The boundary fusion algorithm in this paper is an automatic fusion algorithm based on the boundary accurate coupling of the networking power grid partition, which takes the actual operation mode for qualification, complete the boundary coupling algorithm of various weak coupling partition based on open-loop mode, improving the fusion efficiency, truly reflecting its transient stability level, and effectively solving the problems of too much data, too many difficulties of partition fusion, and no effective fusion due to mutually exclusive conditions. In this paper, the basic principle of fusion process is introduced firstly, and then the method of boundary fusion customization is introduced by scene description. Finally, an example is given to illustrate the specific algorithm on how it effectively implements the boundary fusion after grid partition and to verify the accuracy and efficiency of the algorithm.

Weak values of a quantum observable and the cross-Wigner distribution

International Nuclear Information System (INIS)

Gosson, Maurice A. de; Gosson, Serge M. de

2012-01-01

We study the weak values of a quantum observable from the point of view of the Wigner formalism. The main actor here is the cross-Wigner transform of two functions, which is in disguise the cross-ambiguity function familiar from radar theory and time-frequency analysis. It allows us to express weak values using a complex probability distribution. We suggest that our approach seems to confirm that the weak value of an observable is, as conjectured by several authors, due to the interference of two wavefunctions, one coming from the past, and the other from the future. -- Highlights: ► Application of the cross-Wigner transform to a redefinition of the weak value of a quantum observable. ► Phase space approach to weak values, associated with a complex probability distribution. ► Opens perspectives for the study of retrodiction.

Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology

Directory of Open Access Journals (Sweden)

Suheel Abdullah Malik

2014-01-01

Full Text Available We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA, interior point algorithm (IPA, and active set algorithm (ASA. The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.

From boundaries to boundary work: middle managers creating inter-organizational change.

Science.gov (United States)

Oldenhof, Lieke; Stoopendaal, Annemiek; Putters, Kim

2016-11-21

Purpose In healthcare, organizational boundaries are often viewed as barriers to change. The purpose of this paper is to show how middle managers create inter-organizational change by doing boundary work: the dual act of redrawing boundaries and coordinating work in new ways. Design/methodology/approach Theoretically, the paper draws on the concept of boundary work from Science and Technology Studies. Empirically, the paper is based on an ethnographic investigation of middle managers that participate in a Dutch reform program across health, social care, and housing. Findings The findings show how middle managers create a sense of urgency for inter-organizational change by emphasizing "fragmented" service provision due to professional, sectoral, financial, and geographical boundaries. Rather than eradicating these boundaries, middle managers change the status quo gradually by redrawing composite boundaries. They use boundary objects and a boundary-transcending vocabulary emphasizing the need for societal gains that go beyond production targets of individual organizations. As a result, work is coordinated in new ways in neighborhood teams and professional expertise is being reconfigured. Research limitations/implications Since boundary workers create incremental change, it is necessary to follow their work for a longer period to assess whether boundary work contributes to paradigm change. Practical implications Organizations should pay attention to conditions for boundary work, such as legitimacy of boundary workers and the availability of boundary spaces that function as communities of practice. Originality/value By shifting the focus from boundaries to boundary work, this paper gives valuable insights into "how" boundaries are redrawn and embodied in objects and language.

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

Science.gov (United States)

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

Inter-particle gap distribution and spectral rigidity of the totally asymmetric simple exclusion process with open boundaries

International Nuclear Information System (INIS)

Krbalek, Milan; Hrabak, Pavel

2011-01-01

We consider the one-dimensional totally asymmetric simple exclusion process (TASEP model) with open boundary conditions and present the analytical computations leading to the exact formula for distance clearance distribution, i.e. probability density for a clear distance between subsequent particles of the model. The general relation is rapidly simplified for the middle part of the one-dimensional lattice. Both the analytical formulas and their approximations are compared with the numerical representation of the TASEP model. Such a comparison is presented for particles occurring in the internal part as well as in the boundary part of the lattice. Furthermore, we introduce the pertinent estimation for the so-called spectral rigidity of the model. The results obtained are sequentially discussed within the scope of vehicular traffic theory.

Ground State Solutions for a Class of Fractional Differential Equations with Dirichlet Boundary Value Condition

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Zhigang Hu

2014-01-01

Full Text Available In this paper, we apply the method of the Nehari manifold to study the fractional differential equation (d/dt((1/2 0Dt-β(u′(t+(1/2 tDT-β(u′(t=  f(t,u(t, a.e. t∈[0,T], and u0=uT=0, where  0Dt-β, tDT-β are the left and right Riemann-Liouville fractional integrals of order 0≤β<1, respectively. We prove the existence of a ground state solution of the boundary value problem.

Boundary value problems of the circular cylinders in the strain-gradient theory of linear elasticity

International Nuclear Information System (INIS)

Kao, B.G.

1979-11-01

Three boundary value problems in the strain-gradient theory of linear elasticity are solved for circular cylinders. They are the twisting of circular cylinder, uniformly pressuring of concentric circular cylinder, and pure-bending of simply connected cylinder. The comparisons of these solutions with the solutions in classical elasticity and in couple-stress theory reveal the differences in the stress fields as well as the apparent stress fields due to the influences of the strain-gradient. These aspects of the strain-gradient theory could be important in modeling the failure behavior of structural materials

Exact multiplicity results for quasilinear boundary-value problems with cubic-like nonlinearities

Directory of Open Access Journals (Sweden)

Idris Addou

2000-01-01

Full Text Available We consider the boundary-value problem $$displaylines{ -(varphi_p (u'' =lambda f(u mbox{ in }(0,1 cr u(0 = u(1 =0,, }$$ where $p>1$, $lambda >0$ and $varphi_p (x =| x|^{p-2}x$. The nonlinearity $f$ is cubic-like with three distinct roots 0=a less than b less than c. By means of a quadrature method, we provide the exact number of solutions for all $lambda >0$. This way we extend a recent result, for $p=2$, by Korman et al. cite{KormanLiOuyang} to the general case $p>1$. We shall prove that when 1less than $pleq 2$ the structure of the solution set is exactly the same as that studied in the case $p=2$ by Korman et al. cite{KormanLiOuyang}, and strictly different in the case $p>2$.

Calpionellid distribution and microfacies across the Jurassic/ Cretaceous boundary in western Cuba (Sierra de los Órganos)

Science.gov (United States)

López-Martínez, Rafael; Barragán, Ricardo; Reháková, Daniela; Cobiella-Reguera, Jorge Luis

2013-06-01

A detailed bed-by-bed sampled stratigraphic section of the Guasasa Formation in the Rancho San Vicente area of the "Sierra de los Órganos", western Cuba, provides well-supported evidence about facies and calpionellid distribution across the Jurassic/Cretaceous boundary. These new data allowed the definition of an updated and sound calpionellid biozonation scheme for the section. In this scheme, the drowning event of a carbonate platform displayed by the facies of the San Vicente Member, the lowermost unit of the section, is dated as Late Tithonian, Boneti Subzone. The Jurassic/Cretaceous boundary was recognized within the facies of the overlying El Americano Member on the basis of the acme of Calpionella alpina Lorenz. The boundary is placed nearly six meters above the contact between the San Vicente and the El Americano Members, in a facies linked to a sea-level drop. The recorded calpionellid bioevents should allow correlations of the Cuban biozonation scheme herein proposed, with other previously published schemes from distant areas of the Tethyan Domain.

Distributions of p-values smaller than .05 in psychology: what is going on?

Science.gov (United States)

van Aert, Robbie C.M.; Nuijten, Michèle B.; Wicherts, Jelte M.; van Assen, Marcel A.L.M.

2016-01-01

Previous studies provided mixed findings on pecularities in p-value distributions in psychology. This paper examined 258,050 test results across 30,710 articles from eight high impact journals to investigate the existence of a peculiar prevalence of p-values just below .05 (i.e., a bump) in the psychological literature, and a potential increase thereof over time. We indeed found evidence for a bump just below .05 in the distribution of exactly reported p-values in the journals Developmental Psychology, Journal of Applied Psychology, and Journal of Personality and Social Psychology, but the bump did not increase over the years and disappeared when using recalculated p-values. We found clear and direct evidence for the QRP “incorrect rounding of p-value” (John, Loewenstein & Prelec, 2012) in all psychology journals. Finally, we also investigated monotonic excess of p-values, an effect of certain QRPs that has been neglected in previous research, and developed two measures to detect this by modeling the distributions of statistically significant p-values. Using simulations and applying the two measures to the retrieved test results, we argue that, although one of the measures suggests the use of QRPs in psychology, it is difficult to draw general conclusions concerning QRPs based on modeling of p-value distributions. PMID:27077017

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

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Michael Eydenberg

2009-07-01

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

Boundary curves of individual items in the distribution of total depressive symptom scores approximate an exponential pattern in a general population

OpenAIRE

Tomitaka, Shinichiro; Kawasaki, Yohei; Ide, Kazuki; Akutagawa, Maiko; Yamada, Hiroshi; Furukawa, Toshiaki A.; Ono, Yutaka

2016-01-01

[Background]Previously, we proposed a model for ordinal scale scoring in which individual thresholds for each item constitute a distribution by each item. This lead us to hypothesize that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores follow a common mathematical model, which is expressed as the product of the frequency of the total depressive symptom scores and the probability of the cumulative distribution function of each item th...

Description of internal flow problems by a boundary integral method with dipole panels

International Nuclear Information System (INIS)

Krieg, R.; Hailfinger, G.

1979-01-01

In reactor safety studies the failure of single components is postulated or sudden accident loadings are assumed and the consequences are investigated. Often as a first consequence highly transient three dimensional flow problems occur. In contrast to classical flow problems, in most of the above cases the fluid velocities are relatively small whereas the accelerations assume high values. As a consequence both, viscosity effects and dynamic pressures which are proportional to the square of the fluid velocities are usually negligible. For cases, where the excitation times are considerably longer than the times necessary for a wave to traverse characteristic regions of the fluid field, also the fluid compressibility is negligible. Under these conditions boundary integral methods are an appropriate tool to deal with the problem. Flow singularities are distributed over the fluid boundaries in such a way that pressure and velocity fields are obtained which satisfy the boundary conditions. In order to facilitate the numerical treatment the fluid boundaries are approximated by a finite number of panels with uniform singularity distributions on each of them. Consequently the pressure and velocity field of the given problem may be obtained by superposition of the corresponding fields due to these panels with their singularity intensities as unknown factors. Then satisfying the boundary conditions in so many boundary points as panels have been introduced, yields a system of linear equations which in general allows for a unique determination of the unknown intensities. (orig./RW)

Blurring Boundaries

DEFF Research Database (Denmark)

Neergaard, Ulla; Nielsen, Ruth

2010-01-01

of welfare functions into EU law both from an internal market law and a constitutional law perspective. The main problem areas covered by the Blurring Boundaries project were studied in sub-projects on: 1) Internal market law and welfare services; 2) Fundamental rights and non-discrimination law aspects......; and 3) Services of general interest. In the Blurring Boundaries project, three aspects of the European Social Model have been particularly highlighted: the constitutionalisation of the European Social Model, its multi-level legal character, and the clash between market access justice at EU level...... and distributive justice at national level....

Molecular dynamics study of the role of symmetric tilt grain boundaries on the helium distribution in nickel

Science.gov (United States)

Torres, E.; Pencer, J.

2018-04-01

Helium impurities, from either direct implantation or transmutation reactions, have been associated with embrittlement in nickel-based alloys. Helium has very low solubility in nickel, and has been found to aggregate at lattice defects such as vacancies, dislocations, and grain boundaries. The retention and precipitation of helium in nickel-based alloys have deleterious effects on the material mechanical properties. However, the underlying mechanisms that lead to helium effects in the host metal are not fully understood. In the present work, we investigate the role of symmetric tilt grain boundary (STGB) structures on the distribution of helium in nickel using molecular dynamics simulations. We investigate the family of STGBs specific to the 〈 110 〉 tilt axis. The present results indicate that accumulation of helium at the grain boundary may be modulated by details of grain boundary geometry. A plausible correlation between the grain boundary energy and misorientation with the accumulation and mobility of helium is proposed. Small clusters with up to 6 helium atoms show significant interstitial mobility in the nickel bulk, but also become sites for nucleation and grow of more stable helium clusters. High-energy GBs are found mainly populated with small helium clusters. The high mobility of small clusters along the GBs indicates the role of these GBs as fast two-dimensional channels for diffusion. In contrast, the accumulation of helium in large helium clusters at low-energy STGB creates a favorable environment for the formation of large helium bubbles, indicating a potential role for low-energy STGB in promoting helium-induced GB embrittlement.

Optimal boundary control and boundary stabilization of hyperbolic systems

CERN Document Server

Gugat, Martin

2015-01-01

This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary.  The wave equation is used as a typical example of a linear system, through which the author explores initial boundary value problems, concepts of exact controllability, optimal exact control, and boundary stabilization.  Nonlinear systems are also covered, with the Korteweg-de Vries and Burgers Equations serving as standard examples.  To keep the presentation as accessible as possible, the author uses the case of a system with a state that is defined on a finite space interval, so that there are only two boundary points where the system can be controlled.  Graduate and post-graduate students as well as researchers in the field will find this to be an accessible introduction to problems of optimal control and stabilization.

Studying the active deformation of distributed plate boundaries by integration of GNSS networks

Science.gov (United States)

D'Agostino, Nicola; Avallone, Antonio; Cecere, Gianpaolo; D'Anastasio, Elisabetta

2013-04-01

In the last decade GNSS networks installed for different purposes have proliferated in Italy and now provide a large amount of data available to geophysical studies. In addition to the existing regional and nation-wide scientific GNSS networks developed by ASI (http://geodaf.mt.asi.it), INGV (http://ring.gm.ingv.it) and OGS (http://crs.inogs.it/frednet), a large number (> 400) of continuously-operating GPS stations have been installed in the framework of regional and national networks, both publicly-operated and commercial, developed to provide real-time positioning capability to surveyors. Although the quality of the data and metadata associated to these stations is generally lower with respect to the "scientific" CGPS stations, the increased density and redundancy in crustal motion information, resulting in more than 500 stations with more than 2.5 years of observations, significantly increase the knowledge of the active deformation of the Italian territory and provides a unique image of the crustal deformation field. The obtained GPS velocity field is analysed and various features ranging from the definition of strain distribution and microplate kinematics within the plate boundary, to the evaluation of tectonic strain accumulation on active faults are presented in this work. Undeforming, aseismic regions (Sardinia, Southern Apulia) provide test sites to evaluate the lower bound on the accuracy achievable to measure tectonic deformation. Integration of GNSS networks significantly improves the resolution of the strain rate field in Central Italy showing that active deformation is concentrated in a narrow belt along the crest of the Apennines, consistently with the distribution of the largest historical and recent earthquakes. Products derived from dense GPS velocity and strain rate fields include map of earthquake potential developed under the assumption that the rate of seismic moment accumulation measured from geodesy distributes into earthquake sizes that

A boundary value problem for a third order hyperbolic equation with degeneration of order inside the domain

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Ruzanna Kh. Makaova

2017-12-01

Full Text Available In this paper we study the boundary value problem for a degenerating third order equation of hyperbolic type in a mixed domain. The equation under consideration in the positive part of the domain coincides with the Hallaire equation, which is a pseudoparabolic type equation. Moreover, in the negative part of the domain it coincides with a degenerating hyperbolic equation of the first kind, the particular case of the Bitsadze–Lykov equation. The existence and uniqueness theorem for the solution is proved. The uniqueness of the solution to the problem is proved with the Tricomi method. Using the functional relationships of the positive and negative parts of the domain on the degeneration line, we arrive at the convolution type Volterra integral equation of the 2nd kind with respect to the desired solution by a derivative trace. With the Laplace transform method, we obtain the solution of the integral equation in its explicit form. At last, the solution to the problem under study is written out explicitly as the solution of the second boundary-value problem in the positive part of the domain for the Hallaire equation and as the solution to the Cauchy problem in the negative part of the domain for a degenerate hyperbolic equation of the first kind.

Spectral combination of spherical gravitational curvature boundary-value problems

Science.gov (United States)

PitoÅák, Martin; Eshagh, Mehdi; Šprlák, Michal; Tenzer, Robert; Novák, Pavel

2018-04-01

Four solutions of the spherical gravitational curvature boundary-value problems can be exploited for the determination of the Earth's gravitational potential. In this article we discuss the combination of simulated satellite gravitational curvatures, i.e., components of the third-order gravitational tensor, by merging these solutions using the spectral combination method. For this purpose, integral estimators of biased- and unbiased-types are derived. In numerical studies, we investigate the performance of the developed mathematical models for the gravitational field modelling in the area of Central Europe based on simulated satellite measurements. Firstly, we verify the correctness of the integral estimators for the spectral downward continuation by a closed-loop test. Estimated errors of the combined solution are about eight orders smaller than those from the individual solutions. Secondly, we perform a numerical experiment by considering the Gaussian noise with the standard deviation of 6.5× 10-17 m-1s-2 in the input data at the satellite altitude of 250 km above the mean Earth sphere. This value of standard deviation is equivalent to a signal-to-noise ratio of 10. Superior results with respect to the global geopotential model TIM-r5 are obtained by the spectral downward continuation of the vertical-vertical-vertical component with the standard deviation of 2.104 m2s-2, but the root mean square error is the largest and reaches 9.734 m2s-2. Using the spectral combination of all gravitational curvatures the root mean square error is more than 400 times smaller but the standard deviation reaches 17.234 m2s-2. The combination of more components decreases the root mean square error of the corresponding solutions while the standard deviations of the combined solutions do not improve as compared to the solution from the vertical-vertical-vertical component. The presented method represents a weight mean in the spectral domain that minimizes the root mean square error

Convergence Analysis of the Preconditioned Group Splitting Methods in Boundary Value Problems

Directory of Open Access Journals (Sweden)

Norhashidah Hj. Mohd Ali

2012-01-01

Full Text Available The construction of a specific splitting-type preconditioner in block formulation applied to a class of group relaxation iterative methods derived from the centred and rotated (skewed finite difference approximations has been shown to improve the convergence rates of these methods. In this paper, we present some theoretical convergence analysis on this preconditioner specifically applied to the linear systems resulted from these group iterative schemes in solving an elliptic boundary value problem. We will theoretically show the relationship between the spectral radiuses of the iteration matrices of the preconditioned methods which affects the rate of convergence of these methods. We will also show that the spectral radius of the preconditioned matrices is smaller than that of their unpreconditioned counterparts if the relaxation parameter is in a certain optimum range. Numerical experiments will also be presented to confirm the agreement between the theoretical and the experimental results.

Uncertainties of the 50-year wind from short time series using generalized extreme value distribution and generalized Pareto distribution

DEFF Research Database (Denmark)

Larsén, Xiaoli Guo; Mann, Jakob; Rathmann, Ole

2015-01-01

This study examines the various sources to the uncertainties in the application of two widely used extreme value distribution functions, the generalized extreme value distribution (GEVD) and the generalized Pareto distribution (GPD). The study is done through the analysis of measurements from...... as a guideline for applying GEVD and GPD to wind time series of limited length. The data analysis shows that, with reasonable choice of relevant parameters, GEVD and GPD give consistent estimates of the return winds. For GEVD, the base period should be chosen in accordance with the occurrence of the extreme wind...

Empirically testing the relationship between income distribution, perceived value of money and pay satisfaction

Directory of Open Access Journals (Sweden)

Azman Ismail

2009-07-01

Full Text Available Compensation management literature highlights that income has three major features: salary, bonus and allowance. If the level and/or amount of income are distributed to employees based on proper rules this may increase pay satisfaction. More importantly, a thorough investigation in this area reveals that the effect of income distribution on pay satisfaction is not consistent if perceived value of money is present in organizations. The nature of this relationship is less emphasized in pay distribution literature. Therefore, this study was conducted to measure the effect of the perceived value of money and income distribution on pay satisfaction using 136 usable questionnaires gathered from employees who have worked in one city based local authority in Sabah, Malaysia (MSLAUTHORITY. Outcomes of hierarchical regression analysis showed that the interaction between perceived value of money and income distribution significantly correlated with pay satisfaction. This result confirms that perceived value of money does act as a moderating variable in the income distribution model of the organizational sample. In addition, discussion and implications of this study are elaborated.

Comparative analysis of sustainable value distribution for stakeholders in the mining industry

Science.gov (United States)

Lorenc, Sylwia; Kustra, Arkadiusz

2018-01-01

The objective of this article is the analysis and comparison of the value distribution process that takes place in enterprises for stakeholders. The following coal mining enterprises are subject of this work: JSW S.A., KGHM S.A., and LW Bogdanka S.A, for which the directions of value distribution in the years 2011-2016 were presented. The article defines the main groups of the partnerships' stakeholders, such as the owners, staff, suppliers, equity providers, the country budget and the local governments' budgets. The sustainable value benchmark was defined as the benefits received by the stakeholders through the allocation of financial surplus. The value defined for the abovementioned stakeholders was assessed according to the Free Cash Flow (FCF) methodology.

Effects of temperature distribution on boundary layer stability for a circular cone at Mach 10

Science.gov (United States)

Rigney, Jeffrey M.

A CFD analysis was conducted on a circular cone at 3 degrees angle of attack at Mach 10 using US3D and STABL 3D to determine the effect of wall temperature on the stability characteristics that lead to laminar-to-turbulent transition. Wall temperature distributions were manipulated while all other flow inputs and geometric qualities were held constant. Laminar-to-turbulent transition was analyzed for isothermal and adiabatic wall conditions, a simulated short-duration wind tunnel case, and several hot-nose temperature distributions. For this study, stability characteristics include maximum N-factor growth and the corresponding frequency range, disturbance spatial amplification rate and the corresponding modal frequency, and stability neutral point location. STABL 3D analysis indicates that temperature distributions typical of those in short-duration hypersonic wind tunnels do not result in any significant difference on the stability characteristics, as compared to an isothermal wall boundary condition. Hypothetical distributions of much greater temperatures at and past the nose tip do show a trend of dampening of second-mode disturbances, most notably on the leeward ray. The most pronounced differences existed between the isothermal and adiabatic cases.

Efficient Closed Form Cut-Off Planes and Propagation Planes Characteristics for Dielectric Slab Loaded Boundary Value Problems

OpenAIRE

Zafar, Junaid

2012-01-01

The geometrical relationship between the cut-off and propagating planes of any waveguide system is a prerequisite for any design process. The characterization of cut-off planes and optimisation are challenging for numerical methods, closed-form solutions are always preferred. In this paper Maxwells coupled field equations are used to characterise twin E-plane and H-plane slab loaded boundary value problems. The single mode bandwidths and dispersion characteristics of these structures are pres...

An Existence Principle for Nonlocal Difference Boundary Value Problems with φ-Laplacian and Its Application to Singular Problems

Directory of Open Access Journals (Sweden)

Svatoslav Stanêk

2008-03-01

Full Text Available The paper presents an existence principle for solving a large class of nonlocal regular discrete boundary value problems with the φ-Laplacian. Applications of the existence principle to singular discrete problems are given.

Two approximations of the present value distribution of a disability annuity

Science.gov (United States)

Spreeuw, Jaap

2006-02-01

The distribution function of the present value of a cash flow can be approximated by means of a distribution function of a random variable, which is also the present value of a sequence of payments, but with a simpler structure. The corresponding random variable has the same expectation as the random variable corresponding to the original distribution function and is a stochastic upper bound of convex order. A sharper upper bound can be obtained if more information about the risk is available. In this paper, it will be shown that such an approach can be adopted for disability annuities (also known as income protection policies) in a three state model under Markov assumptions. Benefits are payable during any spell of disability whilst premiums are only due whenever the insured is healthy. The quality of the two approximations is investigated by comparing the distributions obtained with the one derived from the algorithm presented in the paper by Hesselager and Norberg [Insurance Math. Econom. 18 (1996) 35-42].

Comments on the comparison of global methods for linear two-point boundary value problems

International Nuclear Information System (INIS)

de Boor, C.; Swartz, B.

1977-01-01

A more careful count of the operations involved in solving the linear system associated with collocation of a two-point boundary value problem using a rough splines reverses results recently reported by others in this journal. In addition, it is observed that the use of the technique of ''condensation of parameters'' can decrease the computer storage required. Furthermore, the use of a particular highly localized basis can also reduce the setup time when the mesh is irregular. Finally, operation counts are roughly estimated for the solution of certain linear system associated with two competing collocation methods; namely, collocation with smooth splines and collocation of the equivalent first order system with continuous piecewise polynomials

Multiple Positive Solutions of a Nonlinear Four-Point Singular Boundary Value Problem with a p-Laplacian Operator on Time Scales

Directory of Open Access Journals (Sweden)

Shihuang Hong

2009-01-01

Full Text Available We present sufficient conditions for the existence of at least twin or triple positive solutions of a nonlinear four-point singular boundary value problem with a p-Laplacian dynamic equation on a time scale. Our results are obtained via some new multiple fixed point theorems.

RANGE AND DISTRIBUTION OF TECHNETIUM KD VALUES IN THE SRS SUBSURFACE ENVIRONMENT

International Nuclear Information System (INIS)

Kaplan, D.

2008-01-01

Performance assessments (PAs) are risk calculations used to estimate the amount of low-level radioactive waste that can be disposed at DOE sites. Distribution coefficients (K d values) are input parameters used in PA calculations to provide a measure of radionuclide sorption to sediment; the greater the K d value, the greater the sorption and the slower the estimated movement of the radionuclide through sediment. Understanding and quantifying K d value variability is important for estimating the uncertainty of PA calculations. Without this information, it is necessary to make overly conservative estimates about the possible limits of K d values, which in turn may increase disposal costs. Finally, technetium is commonly found to be amongst the radionuclides posing potential risk at waste disposal locations because it is believed to be highly mobile in its anionic form (pertechnetate, TcO 4 - ), it exists in relatively high concentrations in SRS waste, and it has a long half-life (213,000 years). The objectives of this laboratory study were to determine under SRS environmental conditions: (1) whether and to what extent TcO 4 - sorbs to sediments, (2) the range of Tc K d values, (3) the distribution (normal or log-normal) of Tc K d values, and (4) how strongly Tc sorbs to SRS sediments through desorption experiments. Objective 3, to identify the Tc K d distribution is important because it provides a statistical description that influences stochastic modeling of estimated risk. The approach taken was to collect 26 sediments from a non-radioactive containing sediment core collected from E-Area, measure Tc K d values and then perform statistical analysis to describe the measured Tc K d values. The mean K d value was 3.4 ± 0.5 mL/g and ranged from -2.9 to 11.2 mL/g. The data did not have a Normal distribution (as defined by the Shapiro-Wilk's Statistic) and had a 95-percentile range of 2.4 to 4.4 mL/g. The E-Area subsurface is subdivided into three hydrostratigraphic

Comparative analysis of sustainable value distribution for stakeholders in the mining industry

Directory of Open Access Journals (Sweden)

Lorenc Sylwia

2018-01-01

Full Text Available The objective of this article is the analysis and comparison of the value distribution process that takes place in enterprises for stakeholders. The following coal mining enterprises are subject of this work: JSW S.A., KGHM S.A., and LW Bogdanka S.A, for which the directions of value distribution in the years 2011-2016 were presented. The article defines the main groups of the partnerships’ stakeholders, such as the owners, staff, suppliers, equity providers, the country budget and the local governments’ budgets. The sustainable value benchmark was defined as the benefits received by the stakeholders through the allocation of financial surplus. The value defined for the abovementioned stakeholders was assessed according to the Free Cash Flow (FCF methodology.

Einstein boundary conditions for the 3+1 Einstein equations

International Nuclear Information System (INIS)

Frittelli, Simonetta; Gomez, Roberto

2003-01-01

In the 3+1 framework of the Einstein equations for the case of a vanishing shift vector and arbitrary lapse, we calculate explicitly the four boundary equations arising from the vanishing of the projection of the Einstein tensor along the normal to the boundary surface of the initial-boundary value problem. Such conditions take the form of evolution equations along (as opposed to across) the boundary for certain components of the extrinsic curvature and for certain space derivatives of the three-metric. We argue that, in general, such boundary conditions do not follow necessarily from the evolution equations and the initial data, but need to be imposed on the boundary values of the fundamental variables. Using the Einstein-Christoffel formulation, which is strongly hyperbolic, we show how three of the boundary equations up to linear combinations should be used to prescribe the values of some incoming characteristic fields. Additionally, we show that the fourth one imposes conditions on some outgoing fields

Boundary-value problems in ODE

Science.gov (United States)

Tanriverdi, Tanfer

In this thesis we discuss two problems. The first problem is that of Fanno flow in a tube. In [10] the authors have discussed the mathematics of the Fanno model in much more detail than had been previously been done. The analysis in [10] indicates that the Fanno model becomes relevant, if t indicates the unscaled time and t=et , only when t is at least of order O(e- 1) . Indeed, two most important time scales are when t=O(e-1) and t=O(e- 2) . The authors, in the former case, set t=e- 1t1 (t1=t),x=e -11, and obtain the equation math> 62u6t 21- 62u 6x21=- 2u6 2u6t21 , ( 0.0.1) where u is the velocity of the gas, with p=1,6x1=0 (x1=0). One can follow the solution along the characteristic x1=t1 , and to match with the inviscid behaviour when t1-->0 , u=2+t1 (x1=t1). (0.0.2) In the region t=O(e2) , the authors set t=e2t2, x=e2x2,h= x2t2. For small e , the BC (0.0.02) now becomes u=t2 (x2=t 2), (0.0.3) so that (0.0.1) now has a similarity solution of the form u=t2g( h), u2=e- 1u, and (h2- 1)g'' +4hg'+2g=2g(g+hg' ),' =/ (0.0.4) with g(h)-->2 ash-->1- ,from(0.0.3) (0.0.5) g(h)-->∞ ash-->0- ,(fromthe pressure). ( 0.0.6) In a recent paper [11] the authors discuss the existence of a solution of (0.0.4)-(0.0.6) by using a two dimensional topological shooting method. We also discuss the existence of a solution of (0.0.4)-(0.0.6) by using a shooting method. We first turn the nonlinear ode (0.0.4) into an integral equation and then shoot from the singularity at ∞. The second problem arises when one considers eigenfunction expansions associated with second order ordinary differential equations, as Titchmarsh does in his book. One is concerned with the solutions of the equation - d2ydx2+ q(x)y=ly, (0.0.7) along with certain boundary conditions, where q(x)=-( n2- /)sech 2(x), n=n+/. The problem (0.0.7) has an application in the study of discrete reaction-diffusion equations. Our purpose in this problem is to look in some detail at the equation (0.0.7). We first use contour

Secondary recrystallization in non-sag W filament wires -- On the possible role of relative grain boundary character distribution

International Nuclear Information System (INIS)

Samajdar, I.; Watte, P.; Mertens, F.

1999-01-01

Non-Sag tungsten (W) wire is indispensable for the lighting industry. For the necessary creep resistance, large elongated grains are considered as the desired microstructure. These large grains are obtained by primary and secondary recrystallization. In the present study an effort has been made to characterize and to understand the origin of such large elongated grains. In secondary recrystallization, often called abnormal grain growth, a few of the grains grow massive. The mechanisms of normal and abnormal grain growth are essentially the same, involving high angle boundary migration and driven by the reduction of surface energy. The abnormal grain growth can be visualized as a growth advantage for a few of the grains or growth disadvantage for the majority. Such an advantage/disadvantage may be caused by (1) differences in grain size and/or (2) differences in grain boundary character distribution (GBCD). In other words, a grain may grow massive if it has large size and/or possibilities of more favorable (i.e., of higher mobility) grain boundaries with the matrix grains

Existence and Uniqueness of Solutions for a Discrete Fractional Mixed Type Sum-Difference Equation Boundary Value Problem

Directory of Open Access Journals (Sweden)

Weidong Lv

2015-01-01

Full Text Available By means of Schauder’s fixed point theorem and contraction mapping principle, we establish the existence and uniqueness of solutions to a boundary value problem for a discrete fractional mixed type sum-difference equation with the nonlinear term dependent on a fractional difference of lower order. Moreover, a suitable choice of a Banach space allows the solutions to be unbounded and two representative examples are presented to illustrate the effectiveness of the main results.

Numerical continuation methods for dynamical systems path following and boundary value problems

CERN Document Server

Krauskopf, Bernd; Galan-Vioque, Jorge

2007-01-01

Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel''s 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects ...

Nonlinear observer-based Lyapunov boundary control of distributed heat transfer mechanisms for membrane distillation plant

KAUST Repository

Eleiwi, Fadi

2016-09-19

This paper presents a nonlinear observer-based Lyapunov control for a membrane distillation (MD) process. The control considers the inlet temperatures of the feed and the permeate solutions as inputs, transforming it to boundary control process, and seeks to maintain the temperature difference along the membrane boundaries around a sufficient level to promote water production. MD process is modeled with advection diffusion equation model in two dimensions, where the diffusion and convection heat transfer mechanisms are best described. Model analysis, effective order reduction and parameters physical interpretation, are provided. Moreover, a nonlinear observer has been designed to provide the control with estimates of the temperature evolution at each time instant. In addition, physical constraints are imposed on the control to have an acceptable range of feasible inputs, and consequently, better energy consumption. Numerical simulations for the complete process with real membrane parameter values are provided, in addition to detailed explanations for the role of the controller and the observer. (C) 2016 Elsevier Ltd. All rights reserved.

Contrasting the surface ocean distribution of bromoform and methyl iodide; implications for boundary layer physics, chemistry and climate

Energy Technology Data Exchange (ETDEWEB)

Palmer, C J, E-mail: carl.j.palmer@gmail.co [Department of Oceanography, University of Cape Town, 7701 (South Africa)

2010-08-15

Bromoform and methyl iodide are both methane-like hydrocarbons with a halogen atom replacing one or more of the hydrogen atoms. Both of these compounds occur naturally in the environment as a result of their production from seaweed and kelp. They are of interest to climate science as a result of their catalytic destruction of boundary layer ozone (a potent greenhouse gas) and, specifically for methyl iodide, the proposed role in the formation of new cloud condensation nuclei with implications for climate. In this paper, the currently available data on the distribution of bromoform and methyl iodide are analysed and contrasted to show that the concentrations of bromoform and methyl iodide do not correlate, that, in contrast to bromoform, the parameterization of sea surface methyl iodide concentrations demands only the sea surface temperature, and that the pelagic distribution of methyl iodide appears to follow the solar zenith angle. These three observations together suggest that, while the pelagic source of bromoform is mostly biogenic, the source of methyl iodide is photochemical. This has implications for the understanding of planetary boundary layer chemistry and potential organohalogen mediated feedbacks to climate.

Contrasting the surface ocean distribution of bromoform and methyl iodide; implications for boundary layer physics, chemistry and climate

International Nuclear Information System (INIS)

Palmer, C J

2010-01-01

Bromoform and methyl iodide are both methane-like hydrocarbons with a halogen atom replacing one or more of the hydrogen atoms. Both of these compounds occur naturally in the environment as a result of their production from seaweed and kelp. They are of interest to climate science as a result of their catalytic destruction of boundary layer ozone (a potent greenhouse gas) and, specifically for methyl iodide, the proposed role in the formation of new cloud condensation nuclei with implications for climate. In this paper, the currently available data on the distribution of bromoform and methyl iodide are analysed and contrasted to show that the concentrations of bromoform and methyl iodide do not correlate, that, in contrast to bromoform, the parameterization of sea surface methyl iodide concentrations demands only the sea surface temperature, and that the pelagic distribution of methyl iodide appears to follow the solar zenith angle. These three observations together suggest that, while the pelagic source of bromoform is mostly biogenic, the source of methyl iodide is photochemical. This has implications for the understanding of planetary boundary layer chemistry and potential organohalogen mediated feedbacks to climate.

A boundary element model for investigating the effects of eye tumor on the temperature distribution inside the human eye.

Science.gov (United States)

Ooi, E H; Ang, W T; Ng, E Y K

2009-08-01

A three-dimensional boundary element model of the human eye is developed to investigate the thermal effects of eye tumor on the ocular temperature distribution. The human eye is modeled as comprising several regions which have different thermal properties. The tumor is one of these regions. The thermal effects of the tumor are simulated by taking it to have a very high metabolic heat generation and blood perfusion rate. Inside the tumor, the steady state temperature is governed by the Pennes bioheat equation. Elsewhere, in normal tissues of the eye, the temperature satisfies the Laplace's equation. To compute the temperature on the corneal surface, the surface boundary of each region is divided into triangular elements.

On non-equilibrium states in QFT model with boundary interaction

International Nuclear Information System (INIS)

Bazhanov, Vladimir V.; Lukyanov, Sergei L.; Zamolodchikov, Alexander B.

1999-01-01

We prove that certain non-equilibrium expectation values in the boundary sine-Gordon model coincide with associated equilibrium-state expectation values in the systems which differ from the boundary sine-Gordon in that certain extra boundary degrees of freedom (q-oscillators) are added. Applications of this result to actual calculation of non-equilibrium characteristics of the boundary sine-Gordon model are also discussed

Boundary value problems for multi-term fractional differential equations

Science.gov (United States)

Daftardar-Gejji, Varsha; Bhalekar, Sachin

2008-09-01

Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind.

Variations in plasma wave intensity with distance along the electron foreshock boundary at Venus

Science.gov (United States)

Crawford, G. K.; Strangeway, R. J.; Russell, C. T.

1991-01-01

Plasma waves are observed in the solar wind upstream of the Venus bow shock by the Pioneer Venus Orbiter. These wave signatures occur during periods when the interplanetary magnetic field through the spacecraft position intersects the bow shock, thereby placing the spacecraft in the foreshock region. Wave intensity is analyzed as a function of distance along the electron foreshock boundary. It is found that the peak wave intensity may increase along the foreshock boundary from the tangent point to a maximum value at several Venus radii, then decrease in intensity with subsequent increase in distance. These observations could be associated with the instability process: the instability of the distribution function increasing with distance from the tangent point to saturation at the peak. Thermalization of the beam for distances beyond this point could reduce the distribution function instability resulting in weaker wave signatures.

Unsteady magnetohydrodynamic thermal and diffusion boundary layer from a horizontal circular cylinder

Directory of Open Access Journals (Sweden)

Boričić Aleksandar Z.

2016-01-01

Full Text Available The unsteady 2-D dynamic, thermal, and diffusion magnetohydrodynamic laminar boundary layer flow over a horizontal cylinder of incompressible and electrical conductivity fluid, in mixed convection in the presence of heat source or sink and chemical reactions. The present magnetic field is homogenous and perpendicular to the body surface. It is assumed that induction of outer magnetic field is a function of longitudinal co-ordinate outer electric field is neglected and magnetic Reynolds number is significantly lower than one, i. e. considered the problem is in approximation without induction. Fluid electrical conductivity is constant. Free stream velocity, temperature, and concentration on the body are functions of longitudinal co-ordinate. The developed governing boundary layer equations and associated boundary conditions are made dimensionless using a suitable similarity transformation and similarity parameters. System of non-dimensionless equations is solved using the implicit finite difference three-diagonal and iteration method. Numerical results are obtained and presented for different Prandtl, Eckart, and Schmidt numbers, and values: magnetic parameter, temperature, and diffusion parameters, buoyancy temperature parameters, thermal parameter, and chemical reaction parameter. Variation of velocity profiles, temperature and diffusion distributions, and many integral and differential characteristics, boundary layer, are evaluated numerically for different values of the magnetic field. Transient effects of velocity, temperature and diffusion are analyzed. A part of obtained results is given in the form of figures and corresponding conclusions.

Boundary conditions for the solar burst phenomenons stablished from the statistical behaviour in the hard X-ray range

International Nuclear Information System (INIS)

Correia, E.

1983-01-01

A review on the statistical studies of solar burst parameters at X-rays and microwaves, as well as an analysis of the limits caused by instrumental sensitivity and their effect on the form of the distributions and on the establishment of boundary conditions for solar flare phenomena are presented. A study on the statistical behaviour of events observed with high sensitivity at hard X-rays with the HXRBS experiment (SMM) was performed. Maxima have been formed in the parameters distribution, which may be related to intrinsic characteristics of the source-regions. This result seems to confirm searly studies which indicated the influence of the sensitivity limits. Assuming the maxima of the distributions as real, it was possible to establish boundary conditions for the mechanisms of primary energy release. The principal condition establishes that solar bursts can be interpreted as a superposition of primary explosions. The statistical analysis permitted the estimate of a value for the amount of energy in a primary explosion, making use of adjustments of Poisson functions. The value found is consistent with values derived directly from ultra-fast time structures observed in bursts. Assuming an empirical pulse shape for the primary burst and the superposition condition, simulations of bursts have been successfully obtained. (Author) [pt

Instantaneous fluctuation velocity and skewness distributions upstream of transition onset

International Nuclear Information System (INIS)

Hernon, D.; Walsh, E.J.; McEligot, D.M.

2007-01-01

The development of streamwise orientated disturbances through the boundary layer thickness prior to transition onset for zero-pressure gradient boundary layer flow under the influence %Tu = 4.2 is presented. The analysis concentrates on the development of the maximum positive and negative of the fluctuation velocity in order to gain further insight into the transition process. The average location of the peak negative fluctuation velocity over a range of Reynolds numbers was measured in the upper portion of the boundary layer at y/δ ∼ 0.6, whereas the location of the peak positive value was measured at y/δ ∼ 0.3. The disturbance magnitude of the negative fluctuation velocity increased beyond that of the positive as transition onset approached. The distribution and disturbance magnitude of the maximum positive and negative fluctuation velocities indicate that the initiation of transition may occur on the low-speed components of the flow that are lifted up to the upper region of the boundary layer. This is in qualitative agreement with recent direct numerical simulations on the breakdown of the flow on the lifted low-speed streaks near the boundary layer edge. The results presented in this investigation also demonstrate the increased physical insight gained by examining the distributions of the maximum positive and negative of the streamwise fluctuation velocity component associated with the low- and high-speed streaks, compared to time-averaged values, in determining what structures cause the breakdown to turbulence

Pressure effect on grain boundary diffusion

International Nuclear Information System (INIS)

Smirnova, E.S.; Chuvil'deev, V.N.

1997-01-01

The influence of hydrostatic pressure on grain boundary diffusion and grain boundary migration in metallic materials is theoretically investigated. The model is suggested that permits describing changes in activation energy of grain boundary self-diffusion and diffusion permeability of grain boundaries under hydrostatic pressure. The model is based on the ideas about island-type structure of grain boundaries as well as linear relationship of variations in grain boundary free volume to hydrostatic pressure value. Comparison of theoretical data with experimental ones for a number of metals and alloys (α-Zr, Sn-Ge, Cu-In with Co, In, Al as diffusing elements) shows a qualitative agreement

A new boundary control scheme for simultaneous achievement of H-mode and radiative cooling (SHC boundary)

International Nuclear Information System (INIS)

Ohyabu, N.

1995-05-01

We have proposed a new boundary control scheme (SHC boundary), which could allow simultaneous achievement of the H-mode type confinement improvement and radiative cooling with wide heat flux distribution. In our proposed configuration, a low m island layer sharply separates a plasma confining region from an open 'ergodic' boundary. The degree of openness in the ergodic boundary must be high enough to make the plasma pressure constant along the field line, which in turn separates low density plasma just outside the plasma confining region (the key external condition for achieving a good H-mode discharge) from very high density, cold radiative plasma near the wall (required for effective edge radiative cooling). Examples of such proposed SHC boundaries for Heliotron typed devices and tokamaks are presented. (author)

Boundary organizations to boundary chains: Prospects for advancing climate science application

Directory of Open Access Journals (Sweden)

Christine J. Kirchhoff

2015-01-01

Full Text Available Adapting to climate change requires the production and use of climate information to inform adaptation decisions. By facilitating sustained interaction between science producers, boundary organizations narrow the gap between science and decision-making and foster the co-production of actionable knowledge. While traditional boundary organization approaches focused on intense one-on-one interactions between producers and users increases usability, this approach requires significant time and resources. Forming “boundary chains”, linking complimentary boundary organizations together, may reduce those costs. In this paper, we use longitudinal observations of a boundary chain, interviews and surveys to explore: (1 how producer-user interactions increase understanding and information usability and (2 if and how efficiencies in climate information production, dissemination and use arise as a result of the boundary chain. We find that forming and sustaining an effective boundary chain requires not only interest, commitment and investment from every link in the chain but also a level of non-overlapping mutual dependency and complementary skill sets. In this case, GLISA’s strength in producing scientific information and their credibility as climate scientists and HRWC’s strengths in facilitation, connection with potential information users, and their recognition and reputation in the watershed add value to the boundary chain enabling the boundary chain to accomplish more with greater efficiency than if each organization in the chain tried to work independently. Finally, data show how the boundary chain increased efficiencies in educating potential users about the strengths and limitations of climate science and improving the production, dissemination, and use of climate information.

Positive solutions of a three-point boundary-value problem for differential equations with damping and actively bounded delayed forcing term

Directory of Open Access Journals (Sweden)

George L. Karakostas

2006-08-01

Full Text Available We provide sufficient conditions for the existence of positive solutions of a three-point boundary value problem concerning a second order delay differential equation with damping and forcing term whose the delayed part is an actively bounded function, a meaning introduced in [19]. By writing the damping term as a difference of two factors one can extract more information on the solutions. (For instance, in an application, given in the last section, we can give the exact value of the norm of the solution.

Exact solution of nonsteady thermal boundary layer equation

International Nuclear Information System (INIS)

Dorfman, A.S.

1995-01-01

There are only a few exact solutions of the thermal boundary layer equation. Most of them are derived for a specific surface temperature distribution. The first exact solution of the steady-state boundary layer equation was given for a plate with constant surface temperature and free-stream velocity. The same problem for a plate with polynomial surface temperature distribution was solved by Chapmen and Rubesin. Levy gave the exact solution for the case of a power law distribution of both surface temperature and free-stream velocity. The exact solution of the steady-state boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution was given by the author in two forms: of series and of the integral with an influence function of unheated zone. A similar solution of the nonsteady thermal boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution is presented here. In this case, the coefficients of series depend on time, and in the limit t → ∞ they become the constant coefficients of a similar solution published before. This solution, unlike the one presented here, does not satisfy the initial conditions at t = 0, and, hence, can be used only in time after the beginning of the process. The solution in the form of a series becomes a closed-form exact solution for polynomial surface temperature and a power law free-stream velocity distribution. 7 refs., 2 figs

Necessary and Sufficient Conditions for the Existence of Positive Solution for Singular Boundary Value Problems on Time Scales

Directory of Open Access Journals (Sweden)

Zhang Xuemei

2009-01-01

Full Text Available By constructing available upper and lower solutions and combining the Schauder's fixed point theorem with maximum principle, this paper establishes sufficient and necessary conditions to guarantee the existence of as well as positive solutions for a class of singular boundary value problems on time scales. The results significantly extend and improve many known results for both the continuous case and more general time scales. We illustrate our results by one example.

Boundary vapor contentsin an annular channel

International Nuclear Information System (INIS)

Remizov, O.V.; Shurkin, N.G.; Podgornyj, K.K.; Gal'chenko, Eh.F.; Bukhteev, I.S.

1978-01-01

The work is aimed at the experimental investigation of the worsening of the heat transfer in an annular channel. The experiments have been carried out on the annular channel 32x28x3000 mm with the even distribution of the heat flux along the length at pressures of 6.9-19.6 MPa, flow rate of 350-1000 kg/m 2 s, and specific heat fluxes from 0.18 up to 0.6 MW/m 2 . Heating is external, oneside. Water monodistillate of the following composition has been used as a coolant: pH 9; dry residue - 0.8-1.2 mg/kg, oxygen -10-15 mg/kg. It is found out that the change character of the temperature field of the heating surface of the annular channel at the regime with the worsen of heat emission depends on the ratio of regime parameters. At pressures of 6.9-13.7 MPa and flow rate of 350-500 kg/m 2 s the channel wall temperature rises monotoneously, never reaching its maximum. With pressure rise > 13.7 MPa and mass velocity > 500 kg/m 2 s the temperature of the heat emitting surface reaches its maximum, and then slowly falls. At pressures of 6.9-11.8 MPa the boundary vapor content value within the whole range of mass velocities does not depend on the specific heat flux q. At pressures higher than 13.7 MPa and mass velocities of 350-1000 kg/m 2 s the boundary vapor content depends on q. The heating of the external or internal surface of the annular channel affects the value of the boundary vapor content within the whole range of regime parameters' change under investigation

Experimental Research on Boundary Shear Stress in Typical Meandering Channel

Science.gov (United States)

Chen, Kai-hua; Xia, Yun-feng; Zhang, Shi-zhao; Wen, Yun-cheng; Xu, Hua

2018-06-01

A novel instrument named Micro-Electro-Mechanical System (MEMS) flexible hot-film shear stress sensor was used to study the boundary shear stress distribution in the generalized natural meandering open channel, and the mean sidewall shear stress distribution along the meandering channel, and the lateral boundary shear stress distribution in the typical cross-section of the meandering channel was analysed. Based on the measurement of the boundary shear stress, a semi-empirical semi-theoretical computing approach of the boundary shear stress was derived including the effects of the secondary flow, sidewall roughness factor, eddy viscosity and the additional Reynolds stress, and more importantly, for the first time, it combined the effects of the cross-section central angle and the Reynolds number into the expressions. Afterwards, a comparison between the previous research and this study was developed. Following the result, we found that the semi-empirical semi-theoretical boundary shear stress distribution algorithm can predict the boundary shear stress distribution precisely. Finally, a single factor analysis was conducted on the relationship between the average sidewall shear stress on the convex and concave bank and the flow rate, water depth, slope ratio, or the cross-section central angle of the open channel bend. The functional relationship with each of the above factors was established, and then the distance from the location of the extreme sidewall shear stress to the bottom of the open channel was deduced based on the statistical theory.

LARGE-EDDY SIMULATIONS OF A SEPARATION/REATTACHMENT BUBBLE IN A TURBULENT-BOUNDARY-LAYER SUBJECTED TO A PRESCRIBED UPPER-BOUNDARY, VERTICAL-VELOCITY PROFILE

KAUST Repository

Cheng, Wan

2015-06-30

We describe large-eddy simulations of turbulent boundary-layer flow over a flat plate at high Reynolds number in the presence of an unsteady, three-dimensional flow separation/reattachment bubble. The stretched-vortex subgrid-scale model is used in the main flow domain combined with a wall-model that is a two-dimensional extension of that developed by Chung & Pullin (2009). Flow separation and re-attachment of the incoming boundary layer is induced by prescribing wall-normal velocity distribution on the upper boundary of the flow domain that produces an adverse-favorable stream-wise pressure distribution at the wall. The LES predicts the distribution of mean shear stress along the wall including the interior of the separation bubble. Several properties of the separation/reattachment flow are discussed.

Economic Consequences of Fair Value Accounting and a Change in the Distribution Rule

OpenAIRE

Kochiyama, Takuma

2011-01-01

This research examines the economic consequences of fair value accounting and a change in the distribution rule. In Japan, fair value accounting for financial instruments was mandated from 2001, and unrealized revaluation profits were to be included in income statements. As an institutional correspondence to the change in accounting standards, Japanese Commerce Law implemented the deduction of revaluation profits from distributable profits. However, from 2006, the Japanese Company Act changed...

Multiple positive solutions to nonlinear boundary value problems of a system for fractional differential equations.

Science.gov (United States)

Zhai, Chengbo; Hao, Mengru

2014-01-01

By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a system of fractional boundary value problems given by -D(0+)(ν1)y1(t) = λ1a1(t)f(y1(t), y2(t)), - D(0+)(ν2)y2(t) = λ2a2(t)g(y1(t), y2(t)), where D(0+)(ν) is the standard Riemann-Liouville fractional derivative, ν1, ν2 ∈ (n - 1, n] for n > 3 and n ∈ N, subject to the boundary conditions y1((i))(0) = 0 = y ((i))(0), for 0 ≤ i ≤ n - 2, and [D(0+)(α)y1(t)] t=1 = 0 = [D(0+ (α)y2(t)] t=1, for 1 ≤ α ≤ n - 2, or y1((i))(0) = 0 = y ((i))(0), for 0 ≤ i ≤ n - 2, and [D(0+)(α)y1(t)] t=1 = ϕ1(y1), [D(0+)(α)y2(t)] t=1 = ϕ2(y2), for 1 ≤ α ≤ n - 2, ϕ1, ϕ2 ∈ C([0,1], R). Our results are new and complement previously known results. As an application, we also give an example to demonstrate our result.

Application of extreme value distribution function in the determination of standard meteorological parameters for nuclear power plants

International Nuclear Information System (INIS)

Jiang Haimei; Liu Xinjian; Qiu Lin; Li Fengju

2014-01-01

Based on the meteorological data from weather stations around several domestic nuclear power plants, the statistical results of extreme minimum temperatures, minimum. central pressures of tropical cyclones and some other parameters are calculated using extreme value I distribution function (EV- I), generalized extreme value distribution function (GEV) and generalized Pareto distribution function (GP), respectively. The influence of different distribution functions and parameter solution methods on the statistical results of extreme values is investigated. Results indicate that generalized extreme value function has better applicability than the other two distribution functions in the determination of standard meteorological parameters for nuclear power plants. (authors)

On nonlinear statistical thermodynamics of boundary plasma with postactions

International Nuclear Information System (INIS)

Temko, S.W.; Temko, K.W.; Kuz'min, S.K.

1992-01-01

The authors use the statistical thermodynamics of small systems proposed before their publications for boundary weakly ionized plasma with postaction. Boundary properties of the plasma is taken into account by two ways: (1) suppose that only small number of very quick particles are able to leave the cloud having done entrance into outer medium work; (2) take into account the interaction between particles and inner surface of the cloud. Interactions in the boundary plasma are described by corresponding potential functions. The potential functions are mathematical models of real interactions in boundary plasma. Choosing of potential functions, their numerical parameters, geometrical form and dimensions of the cloud is made by using the methods of optimal experiment planning, maximum likelihood and computer experiment. Free energy of the cloud is a likelihood function. State of boundary plasma with admixtures is described by vector-density of particles distribution. Term ''distribution'' is used here in Sobolev-Schwartc sense. The authors obtain the vector-density of particles distribution in cloud which gives the condition minimum of free energy for every time moment under quasistatistical equilibrium. The system of conditions for free energy conditional minimizing for every time moment includes integral equilibrium equations, ''non-hard normalization'' and additional conditions taken as a result of analyzing physical and physical-chemical nature of boundary plasma. To obtain conditional minimum of free energy it is necessary to solve the system of conditions. First of all they solve equilibrium problem by the authors method. They obtain vector-density of particles distribution in the cloud. Then using method of random walk with postaction between sets of random walk process they build distribution function of random vector-density

Existence and smoothness of solutions to second initial boundary value problems for Schrodinger systems in cylinders with non-smooth bases

Directory of Open Access Journals (Sweden)

Nguyen Manh Hung

2008-03-01

Full Text Available In this paper, we consider the second initial boundary value problem for strongly general Schrodinger systems in both the finite and the infinite cylinders $Q_T, 0

Peary caribou distribution within the Bathurst Island Complex relative to the boundary proposed for Qausuittuq National Park, Nunavut

Directory of Open Access Journals (Sweden)

Kim G. Poole

2015-12-01

Full Text Available How caribou (Rangifer tarandus, including Peary caribou (R. t. pearyi, use their annual ranges varies with changes in abundance. While fidelity to some seasonal ranges is persistent, use of other areas changes. Consequently, understanding changes in seasonal distribution is useful for designing boundaries of protected areas for caribou conservation. A case in point is the proposed Qausuittuq (Northern Bathurst Island National Park for Bathurst Island and its satellite islands in the High Arctic of Canada. Since 1961, Peary caribou have been through three periods of high and low abundance. We examined caribou distribution and composition mapped during nine systematic aerial surveys (1961–2013, unsystematic helicopter surveys (1989–98, and limited radio-collaring from 1994–97 and 2003–06. While migration patterns changed and use of southern Bathurst Island decreased during lows in abundance, use of satellite islands, especially Cameron Island for winter range, persisted during both highs and lows in abundance. The northeast coast of Bathurst Island was used to a greater extent during the rut and during summer at low abundance. We suggest that Park boundaries which include Cameron Island and the northeast coast of Bathurst Island will be more effective in contributing to the persistence of Peary caribou on the Bathurst Island Complex.

An Examination of the Effect of Boundary Layer Ingestion on Turboelectric Distributed Propulsion Systems

Science.gov (United States)

Felder, James L.; Kim, Huyn Dae; Brown, Gerald V.; Chu, Julio

2011-01-01

A Turboelectric Distributed Propulsion (TeDP) system differs from other propulsion systems by the use of electrical power to transmit power from the turbine to the fan. Electrical power can be efficiently transmitted over longer distances and with complex topologies. Also the use of power inverters allows the generator and motors speeds to be independent of one another. This decoupling allows the aircraft designer to place the core engines and the fans in locations most advantageous for each. The result can be very different installation environments for the different devices. Thus the installation effects on this system can be quite different than conventional turbofans where the fan and core both see the same installed environments. This paper examines a propulsion system consisting of two superconducting generators, each driven by a turboshaft engine located so that their inlets ingest freestream air, superconducting electrical transmission lines, and an array of superconducting motor driven fan positioned across the upper/rear fuselage area of a hybrid wing body aircraft in a continuous nacelle that ingests all of the upper fuselage boundary layer. The effect of ingesting the boundary layer on the design of the system with a range of design pressure ratios is examined. Also the impact of ingesting the boundary layer on off-design performance is examined. The results show that when examining different design fan pressure ratios it is important to recalculate of the boundary layer mass-average Pt and MN up the height for each inlet height during convergence of the design point for each fan design pressure ratio examined. Correct estimation of off-design performance is dependent on the height of the column of air measured from the aircraft surface immediately prior to any external diffusion that will flow through the fan propulsors. The mass-averaged Pt and MN calculated for this column of air determine the Pt and MN seen by the propulsor inlet. Since the height

The values of the parameters of some multilayer distributed RC null networks

Science.gov (United States)

Huelsman, L. P.; Raghunath, S.

1974-01-01

In this correspondence, the values of the parameters of some multilayer distributed RC notch networks are determined, and the usually accepted values are shown to be in error. The magnitude of the error is illustrated by graphs of the frequency response of the networks.

Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations

Czech Academy of Sciences Publication Activity Database

Dilna, N.; Rontó, András

2010-01-01

Roč. 60, č. 3 (2010), s. 327-338 ISSN 0139-9918 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : non-linear boundary value-problem * functional differential equation * non-local condition * unique solvability * differential inequality Subject RIV: BA - General Mathematics Impact factor: 0.316, year: 2010 http://link.springer.com/article/10.2478%2Fs12175-010-0015-9

Temperature and species measurement in a quenching boundary layer on a flat-flame burner

Energy Technology Data Exchange (ETDEWEB)

Fuyuto, Takayuki; Fujikawa, Taketoshi; Akihama, Kazuhiro [Toyota Central Research and Development Labs., Inc., Nagakute, Aichi (Japan); Kronemayer, Helmut [University of Duisburg-Essen, IVG, Institute for Combustion and Gasdynamics, Duisburg (Germany); BASF SE, Ludwigshafen (Germany); Lewerich, Burkhard; Dreier, Thomas; Schulz, Christof [University of Duisburg-Essen, IVG, Institute for Combustion and Gasdynamics, Duisburg (Germany); Bruebach, Jan [Technical University Darmstadt, EKT, Institute for Energy and Powerplant Technology, Darmstadt (Germany)

2010-10-15

A detailed understanding of transport phenomena and reactions in near-wall boundary layers of combustion chambers is essential for further reducing pollutant emissions and improving thermal efficiencies of internal combustion engines. In a model experiment, the potential of laser-induced fluorescence (LIF) was investigated for measurements inside the boundary layer connected to flame-wall interaction at atmospheric pressure. Temperature and species distributions were measured in the quenching boundary layer formed close to a cooled metal surface located parallel to the flow of a premixed methane/air flat flame. Multi-line NO-LIF thermometry provided gas-phase temperature distributions. In addition, flame species OH, CH{sub 2}O and CO were monitored by single-photon (OH, CH{sub 2}O) and two-photon (CO) excitation LIF, respectively. The temperature dependence of the OH-LIF signal intensities was corrected for using the measured gas-phase temperature distributions. The spatial line-pair resolution of the imaging system was 22 {mu}m determined by imaging microscopic line pairs printed on a resolution target. The experimental results show the expected flame quenching behavior in the boundary layer and they reveal the potential and limitations of the applied diagnostics techniques. Limitations in spatial resolution are attributed to refraction of fluorescence radiation propagating through steep temperature gradients in the boundary layer. For the present experimental arrangements, the applied diagnostics techniques are applicable as close to the wall as 200 {mu}m with measurement precision then exceeding the 15-25% limit for species detection, with estimates of double this value for the case of H{sub 2}CO due to the unknown effect of the Boltzmann fraction corrections not included in the data evaluation process. Temperature measurements are believed to be accurate within 50 K in the near-wall zone, which amounts to roughly 10% at the lower temperatures encountered in

Antiperiodic Boundary Value Problems for Second-Order Impulsive Ordinary Differential Equations

Directory of Open Access Journals (Sweden)

2009-02-01

Full Text Available We consider a second-order ordinary differential equation with antiperiodic boundary conditions and impulses. By using Schaefer's fixed-point theorem, some existence results are obtained.

Random walks in the quarter plane algebraic methods, boundary value problems, applications to queueing systems and analytic combinatorics

CERN Document Server

Fayolle, Guy; Malyshev, Vadim

2017-01-01

This monograph aims to promote original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes arise in numerous applications and are of interest in several areas of mathematical research, such as Stochastic Networks, Analytic Combinatorics, and Quantum Physics. This second edition consists of two parts. Part I is a revised upgrade of the first edition (1999), with additional recent results on the group of a random walk. The theoretical approach given therein has been developed by the authors since the early 1970s. By using Complex Function Theory, Boundary Value Problems, Riemann Surfaces, and Galois Theory, completely new methods are proposed for solving functional equations of two complex variables, which can also be applied to characterize the Transient Behavior of the walks, as well as to find explicit solutions to the one-dimensional Quantum Three-Body Problem, or to tackle a new class of Integrable Systems. Part II borrows spec...

Response of a Hypersonic Boundary Layer to Freestream Pulse Acoustic Disturbance

Directory of Open Access Journals (Sweden)

Zhenqing Wang

2014-01-01

Full Text Available The response of hypersonic boundary layer over a blunt wedge to freestream pulse acoustic disturbance was investigated. The stability characteristics of boundary layer for freestream pulse wave and continuous wave were analyzed comparatively. Results show that freestream pulse disturbance changes the thermal conductivity characteristics of boundary layer. For pulse wave, the number of main disturbance clusters decreases and the frequency band narrows along streamwise. There are competition and disturbance energy transfer among different modes in boundary layer. The dominant mode of boundary layer has an inhibitory action on other modes. Under continuous wave, the disturbance modes are mainly distributed near fundamental and harmonic frequencies, while under pulse wave, the disturbance modes are widely distributed in different modes. For both pulse and continuous waves, most of disturbance modes slide into a lower-growth or decay state in downstream, which is tending towards stability. The amplitude of disturbance modes in boundary layer under continuous wave is considerably larger than pulse wave. The growth rate for the former is also considerably larger than the later the disturbance modes with higher growth are mainly distributed near fundamental and harmonic frequencies for the former, while the disturbance modes are widely distributed in different frequencies for the latter.

Response of a hypersonic boundary layer to freestream pulse acoustic disturbance.

Science.gov (United States)

Wang, Zhenqing; Tang, Xiaojun; Lv, Hongqing

2014-01-01

The response of hypersonic boundary layer over a blunt wedge to freestream pulse acoustic disturbance was investigated. The stability characteristics of boundary layer for freestream pulse wave and continuous wave were analyzed comparatively. Results show that freestream pulse disturbance changes the thermal conductivity characteristics of boundary layer. For pulse wave, the number of main disturbance clusters decreases and the frequency band narrows along streamwise. There are competition and disturbance energy transfer among different modes in boundary layer. The dominant mode of boundary layer has an inhibitory action on other modes. Under continuous wave, the disturbance modes are mainly distributed near fundamental and harmonic frequencies, while under pulse wave, the disturbance modes are widely distributed in different modes. For both pulse and continuous waves, most of disturbance modes slide into a lower-growth or decay state in downstream, which is tending towards stability. The amplitude of disturbance modes in boundary layer under continuous wave is considerably larger than pulse wave. The growth rate for the former is also considerably larger than the later the disturbance modes with higher growth are mainly distributed near fundamental and harmonic frequencies for the former, while the disturbance modes are widely distributed in different frequencies for the latter.

Analytical model for advective-dispersive transport involving flexible boundary inputs, initial distributions and zero-order productions

Science.gov (United States)

Chen, Jui-Sheng; Li, Loretta Y.; Lai, Keng-Hsin; Liang, Ching-Ping

2017-11-01

A novel solution method is presented which leads to an analytical model for the advective-dispersive transport in a semi-infinite domain involving a wide spectrum of boundary inputs, initial distributions, and zero-order productions. The novel solution method applies the Laplace transform in combination with the generalized integral transform technique (GITT) to obtain the generalized analytical solution. Based on this generalized analytical expression, we derive a comprehensive set of special-case solutions for some time-dependent boundary distributions and zero-order productions, described by the Dirac delta, constant, Heaviside, exponentially-decaying, or periodically sinusoidal functions as well as some position-dependent initial conditions and zero-order productions specified by the Dirac delta, constant, Heaviside, or exponentially-decaying functions. The developed solutions are tested against an analytical solution from the literature. The excellent agreement between the analytical solutions confirms that the new model can serve as an effective tool for investigating transport behaviors under different scenarios. Several examples of applications, are given to explore transport behaviors which are rarely noted in the literature. The results show that the concentration waves resulting from the periodically sinusoidal input are sensitive to dispersion coefficient. The implication of this new finding is that a tracer test with a periodic input may provide additional information when for identifying the dispersion coefficients. Moreover, the solution strategy presented in this study can be extended to derive analytical models for handling more complicated problems of solute transport in multi-dimensional media subjected to sequential decay chain reactions, for which analytical solutions are not currently available.

Pressure gradient effect at distributed excitation of 3D TS waves by freestream and wall disturbances

Directory of Open Access Journals (Sweden)

Borodulin Vladimir

2017-01-01

Full Text Available The present work is a continuation of previous experiments (carried out in the Blasius boundary layer and devoted to quantitative investigation of influence of an adverse pressure gradient on two efficient mechanisms of excitation of 3D TS instability waves due to a distributed boundary layer receptivity to free-stream vortices. These mechanisms are associated with distributed scattering of 3D amplified free-stream vortices both on the natural boundary-layer nonuniformity (on smooth surface and on 2D surface nonuniformities (waviness. The corresponding detailed hotwire measurements were carried out in a self-similar boundary layer with Hartree parameter βH = –0.115 in a wide range of the problem parameters. Complex values of quantitative characteristics of the physical phenomenon under study (the distributed receptivity coefficients are evaluated by based on the obtained experimental data. It is found that the adverse pressure gradient leads to reduction of efficiency of the investigated vortexroughness receptivity mechanism.

New formulations on the finite element method for boundary value problems with internal/external boundary layers

International Nuclear Information System (INIS)

Pereira, Luis Carlos Martins

1998-06-01

New Petrov-Galerkin formulations on the finite element methods for convection-diffusion problems with boundary layers are presented. Such formulations are based on a consistent new theory on discontinuous finite element methods. Existence and uniqueness of solutions for these problems in the new finite element spaces are demonstrated. Some numerical experiments shows how the new formulation operate and also their efficacy. (author)

Phase boundary in compatible and incompatible polymer blends studied by micro indentation test and microscopic observations

International Nuclear Information System (INIS)

Mina, M. F.; Akhtar, F.; Haque, M.E.

2003-10-01

The phase boundary of incompatible polymer blends such as poly (methyl methacrylate) (PMMA)/natural rubber (NR) and polyestyrene (PS)/NR as well as compatible blends such as PMMA/NR/epoxidizer NR (compatibilizer) and PS/NR/styrene-butadiene-styrene (SBS) block copolymer (compatibilizer) was studied by means of microhardness (H) technique and microscopy. Solution grown films of neat PMMA, PS and blended films of PMMA/NR, PS/NR, PMMA/NR/ENR and PS/NR/SBS were cast using a common solvent (toluene). While the neat PMMA and PS provide constant hardness values of 178 and 173 MPa, respectively, the binary (incompatible) and the ternary (compatible) blends show a conspicuous H-decrease (PMMA/NR=140 MPa, PS/NR=167 MPa, PMMA/NR/ENR=109 MPa and PS/NR/SBS=127 MPa). Scanning electron microscopy and optical microscopy reveal clear difference of the phase boundary of compatible (smooth boundary) and incompatible (sharp boundary) blends. Besides, the compatibilizer blends are characterised by the thinnest phase boundary (30 μm), which is found about 60 μm in the incompatible blends, showing a final hardness value that demonstrates the compatibilizer to be smoothly distributed in the interface between the two blend components. Results highlight that microindentation technique, in combination with microscopic observations, is a sensitive tool for studying the breadth and quality of the interphase boundary in non- or compatibilized polymer blends and other inhomogeneous materials. (author)

Magnetohydrodynamic boundary layer flow past a porous substrate with Beavers-Joseph boundary condition

International Nuclear Information System (INIS)

Jat, R.N.; Chaudhary, Santosh

2009-01-01

The flow of an electrically conducting fluid past a porous substrate attached to the flat plate with Beavers-Joseph boundary condition under the influence of a uniform transverse magnetic field has been studied. Taking suitable similar variables, the momentum equation is transformed to ordinary differential equation and solved by standard techniques. The energy equation is solved by considering two boundary layers, one in the porous substrate and the other above the porous substrate. The velocity and temperature distributions along with Nusselt number are discussed numerically and presented through graphs. (author)

Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique

Directory of Open Access Journals (Sweden)

Omar Abu Arqub

2014-01-01

Full Text Available The purpose of this paper is to present a new kind of analytical method, the so-called residual power series, to predict and represent the multiplicity of solutions to nonlinear boundary value problems of fractional order. The present method is capable of calculating all branches of solutions simultaneously, even if these multiple solutions are very close and thus rather difficult to distinguish even by numerical techniques. To verify the computational efficiency of the designed proposed technique, two nonlinear models are performed, one of them arises in mixed convection flows and the other one arises in heat transfer, which both admit multiple solutions. The results reveal that the method is very effective, straightforward, and powerful for formulating these multiple solutions.

Practice of value-based distribution reliability assessment (VBDRA) at Scarborough Public Utilities

International Nuclear Information System (INIS)

Chen, R-L.

1995-01-01

The development of value-based distribution reliability assessment (VBDRA) at Scarborough Public Utilities was described. Load point reliability indices, customer interruption costs (CIC), continuity and service reliability, accuracy of CIC, and the aspects of application of VBDRA were addressed. The application of VBDRA to a long-term rebuild plan for 4.16 kV distribution system was described. The importance of a cost-benefit analysis for implementation of VBDRA was emphasized. In the case of the Scarborough Public Utilities Commission the enhanced feeder reliability assessment was found to influence the allocation of funding to where it provided the most value to customers. 14 refs., 3 tabs., 3 figs

Additive recovery at lateral boundaries of grains under electronic exposure

International Nuclear Information System (INIS)

Plotnikov, S.V.; Postnikov, D.V.

2000-01-01

The experimental investigation of additive re-distribution under electronic beam revealed a recovery of the additive at grain boundaries. Additive accumulation mainly takes place at the boundaries that are perpendicular to material surface, whereas there is no an observed recovery of additive at the boundaries that are parallel to the surface. To construe the processes of additive recovery at grain boundaries, we may use the kinetic diffusion equation describing the mass transfer processes in the presence of temperature gradients and non-equilibrium vacancies. The additive recovery is caused by spot fault gradients near the grain boundary. The grain boundary is an intensive run-off region of vacancies. Therefore, the average vacancy distribution profile near the grain boundary changes its pattern. The above case indicates that there are two additive fluxes. One of them is vectored perpendicular to the surface, and the other one is parallel to it, i.e. it is vectored to the grain boundary. A study of the perpendicular and parallel boundaries shows that there is no additive settling at the boundaries that are parallel to the surface, since the general flux is vectored to the parallel boundaries. There is no such kind of phenomenon at the grain boundaries that are perpendicular to the surface. Besides, the perpendicular boundaries are more effective run-off regions for vacancies, since there is a slower build-up of the region with vacancies due to displacement of the vacancies to the surface

Boundary layer development on turbine airfoil suction surfaces

Science.gov (United States)

Sharma, O. P.; Wells, R. A.; Schlinker, R. H.; Bailey, D. A.

1981-01-01

The results of a study supported by NASA under the Energy Efficient Engine Program, conducted to investigate the development of boundary layers under the influence of velocity distributions that simulate the suction sides of two state-of-the-art turbine airfoils, are presented. One velocity distribution represented a forward loaded airfoil ('squared-off' design), while the other represented an aft loaded airfoil ('aft loaded' design). These velocity distributions were simulated in a low-speed, high-aspect-ratio wind tunnel specifically designed for boundary layer investigations. It is intended that the detailed data presented in this paper be used to develop improved turbulence model suitable for application to turbine airfoil design.

Rearranging social space: Boundary-making and boundary-work in a joint forest management project, Andhra Pradesh, India

Directory of Open Access Journals (Sweden)

Saito-Jensen Moeko

2010-01-01

Full Text Available Since the 1990s, there has been an increasing trend in developing countries to shift from state driven approaches to Community-based Natural Resource Management (CBNRM. In order to ensure sustainability of resources, the need for creating and maintaining clear resource use boundaries has been emphasised, both theoretically and in practice. However, there has been less attention to the varied social consequences for involved villages (whose inhabitants can access resources within the new boundaries and for excluded villages (whose inhabitants are prevented from accessing resources due to these boundaries. Drawing on a case study of three villages affected by the Joint Forest Management project in Andhra Pradesh, India, this article shows how resource use boundaries interact with social categories such as caste, gender and livelihood occupation in ways that facilitate asymmetric distribution of costs and benefits among local people. The article calls for more consultative processes in constituting new resources use boundaries and for flexible interventions to reconcile conflicts arising from boundary-making.

77 FR 5454 - Modifications to Minimum Present Value Requirements for Partial Annuity Distribution Options...

Science.gov (United States)

2012-02-03

... Modifications to Minimum Present Value Requirements for Partial Annuity Distribution Options Under Defined... guidance relating to the minimum present value requirements applicable to certain defined benefit pension plans. These proposed regulations would change the regulations regarding the minimum present value...

The Value of Transparency in Distributed Solar PV Markets

Energy Technology Data Exchange (ETDEWEB)

OShaughnessy, Eric J. [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Margolis, Robert M. [National Renewable Energy Laboratory (NREL), Golden, CO (United States)

2017-10-09

Distributed solar photovoltaic (PV) markets are relatively non-transparent: PV price and product information is not readily available, searching for this information is costly (in terms of time and effort), and customers are mostly unfamiliar with the new technology. Quote aggregation, where third-party companies collect PV quotes on behalf of customers, may be one way to increase PV market transparency. In this paper, quote aggregation data are analyzed to study the value of transparency for distributed solar PV markets. The results suggest that easier access to more quotes results in lower prices. We find that installers tend to offer lower prices in more competitive market environments. We supplement the empirical analysis with key findings from interviews of residential PV installers.

Easy boundary definition for EGUN

International Nuclear Information System (INIS)

Becker, R.

1989-01-01

The relativistic electron optics program EGUN has reached a broad distribution, and many users have asked for an easier way of boundary input. A preprocessor to EGUN has been developed that accepts polygonal input of boundary points, and offers features such as rounding off of corners, shifting and squeezing of electrodes and simple input of slanted Neumann boundaries. This preprocessor can either be used on a PC that is linked to a mainframe using the FORTRAN version of EGUN, or in connection with the version EGNc, which also runs on a PC. In any case, direct graphic response on the PC greatly facilitates the creation of correct input files for EGUN. (orig.)

Easy boundary definition for EGUN

Science.gov (United States)

Becker, R.

1989-06-01

The relativistic electron optics program EGUN [1] has reached a broad distribution, and many users have asked for an easier way of boundary input. A preprocessor to EGUN has been developed that accepts polygonal input of boundary points, and offers features such as rounding off of corners, shifting and squeezing of electrodes and simple input of slanted Neumann boundaries. This preprocessor can either be used on a PC that is linked to a mainframe using the FORTRAN version of EGUN, or in connection with the version EGNc, which also runs on a PC. In any case, direct graphic response on the PC greatly facilitates the creation of correct input files for EGUN.

Easy boundary definition for EGUN

Energy Technology Data Exchange (ETDEWEB)

Becker, R. (Frankfurt Univ. (Germany, F.R.). Inst. fuer Angewandte Physik)

1989-06-01

The relativistic electron optics program EGUN has reached a broad distribution, and many users have asked for an easier way of boundary input. A preprocessor to EGUN has been developed that accepts polygonal input of boundary points, and offers features such as rounding off of corners, shifting and squeezing of electrodes and simple input of slanted Neumann boundaries. This preprocessor can either be used on a PC that is linked to a mainframe using the FORTRAN version of EGUN, or in connection with the version EGNc, which also runs on a PC. In any case, direct graphic response on the PC greatly facilitates the creation of correct input files for EGUN. (orig.).

Investigating the distribution of the value of travel time savings

DEFF Research Database (Denmark)

Fosgerau, Mogens

2006-01-01

The distribution of the value of travel time savings (VTTS) is investigated employing various nonparametric techniques to a large dataset originating from a stated choice experiment. The data contain choices between a fast and more expensive alternative and a slow and less expensive alternative....... Increasing the implicit price of time leads to an increased share of respondents who decline to pay to save time. But a significant proportion of respondents, 13%, remain willing to pay to save time at the highest price of time in the design. This means that the right tail of the VTTS distribution...

Boundary-value problems in cosmological dynamics

Science.gov (United States)

Nusser, Adi

2008-08-01

The dynamics of cosmological gravitating system is governed by the Euler and the Poisson equations. Tiny fluctuations near the big bang singularity are amplified by gravitational instability into the observed structure today. Given the current distribution of galaxies and assuming initial homogeneity, dynamic reconstruction methods have been developed to derive the cosmic density and velocity fields back in time. The reconstruction method described here is based on a least action principle formulation of the dynamics of collisionless particles (representing galaxies). Two observational data sets will be considered. The first is the distribution of galaxies which is assumed to be an fair tracer of the mass density field of the dark matter. The second set is measurements of the peculiar velocities (deviations from pure Hubble flow) of galaxies. Given the first data set, the reconstruction method recovers the associated velocity field which can then be compared with the second data set. This comparison constrains the nature of the dark matter and the relation between mass and light in the Universe.

Weak values of a quantum observable and the cross-Wigner distribution.

Science.gov (United States)

de Gosson, Maurice A; de Gosson, Serge M

2012-01-09

We study the weak values of a quantum observable from the point of view of the Wigner formalism. The main actor here is the cross-Wigner transform of two functions, which is in disguise the cross-ambiguity function familiar from radar theory and time-frequency analysis. It allows us to express weak values using a complex probability distribution. We suggest that our approach seems to confirm that the weak value of an observable is, as conjectured by several authors, due to the interference of two wavefunctions, one coming from the past, and the other from the future.

Proton isotropy boundaries as measured on mid- and low-altitude satellites

Directory of Open Access Journals (Sweden)

N. Yu. Ganushkina

2005-07-01

Full Text Available Polar CAMMICE MICS proton pitch angle distributions with energies of 31-80 keV were analyzed to determine the locations where anisotropic pitch angle distributions (perpendicular flux dominating change to isotropic distributions. We compared the positions of these mid-altitude isotropic distribution boundaries (IDB for different activity conditions with low-altitude isotropic boundaries (IB observed by NOAA 12. Although the obtained statistical properties of IDBs were quite similar to those of IBs, a small difference in latitudes, most pronounced on the nightside and dayside, was found. We selected several events during which simultaneous observations in the same local time sector were available from Polar at mid-altitudes, and NOAA or DMSP at low-altitudes. Magnetic field mapping using the Tsyganenko T01 model with the observed solar wind input parameters showed that the low- and mid-altitude isotropization boundaries were closely located, which leads us to suggest that the Polar IDB and low-altitude IBs are related. Furthermore, we introduced a procedure to control the difference between the observed and model magnetic field to reduce the large scatter in the mapping. We showed that the isotropic distribution boundary (IDB lies in the region where Rc/ρ~6, that is at the boundary of the region where the non-adiabatic pitch angle scattering is strong enough. We therefore conclude that the scattering in the large field line curvature regions in the nightside current sheet is the main mechanism producing isotropization for the main portion of proton population in the tail current sheet. This mechanism controls the observed positions of both IB and IDB boundaries. Thus, this tail region can be probed, in its turn, with observations of these isotropy boundaries. Keywords. Magnetospheric physics (Energetic particles, Precipitating; Magnetospheric configuration and dynamics; Magnetotail

Proton isotropy boundaries as measured on mid- and low-altitude satellites

Directory of Open Access Journals (Sweden)

N. Yu. Ganushkina

2005-07-01

Full Text Available Polar CAMMICE MICS proton pitch angle distributions with energies of 31-80 keV were analyzed to determine the locations where anisotropic pitch angle distributions (perpendicular flux dominating change to isotropic distributions. We compared the positions of these mid-altitude isotropic distribution boundaries (IDB for different activity conditions with low-altitude isotropic boundaries (IB observed by NOAA 12. Although the obtained statistical properties of IDBs were quite similar to those of IBs, a small difference in latitudes, most pronounced on the nightside and dayside, was found. We selected several events during which simultaneous observations in the same local time sector were available from Polar at mid-altitudes, and NOAA or DMSP at low-altitudes. Magnetic field mapping using the Tsyganenko T01 model with the observed solar wind input parameters showed that the low- and mid-altitude isotropization boundaries were closely located, which leads us to suggest that the Polar IDB and low-altitude IBs are related. Furthermore, we introduced a procedure to control the difference between the observed and model magnetic field to reduce the large scatter in the mapping. We showed that the isotropic distribution boundary (IDB lies in the region where R_c/ρ~6, that is at the boundary of the region where the non-adiabatic pitch angle scattering is strong enough. We therefore conclude that the scattering in the large field line curvature regions in the nightside current sheet is the main mechanism producing isotropization for the main portion of proton population in the tail current sheet. This mechanism controls the observed positions of both IB and IDB boundaries. Thus, this tail region can be probed, in its turn, with observations of these isotropy boundaries.

Keywords. Magnetospheric physics (Energetic particles, Precipitating; Magnetospheric configuration and dynamics; Magnetotail

Normal cranial bone marrow MR imaging pattern with age-related ADC value distribution

International Nuclear Information System (INIS)

Li Qi; Pan Shinong; Yin Yuming; Li Wei; Chen Zhian; Liu Yunhui; Wu Zhenhua; Guo Qiyong

2011-01-01

Objective: To determine MRI appearances of normal age-related cranial bone marrow and the relationship between MRI patterns and apparent diffusion coefficient (ADC) values. Methods: Five hundred subjects were divided into seven groups based on ages. Cranial bone marrow MRI patterns were performed based on different thickness of the diploe and signal intensity distribution characteristics. ADC values of the frontal, parietal, occipital and temporal bones on DWI were measured and calculated. Correlations between ages and ADC values, between patterns and ADC values, as well as the distribution of ADC values were analyzed. Results: Normal cranial bone marrow was divided into four types and six subtypes, Type I, II, III and IV, which had positive correlation with age increasing (χ 2 = 266.36, P 0.05). In addition, there was significant negative correlation between the ADC values and MRI patterns in the normal parietal and occipital bones (r = -0.691 and -0.750, P < 0.01). Conclusion: The combination of MRI features and ADC values changes in different cranial bones showed significant correlation with age increasing. Familiar with the MRI appearance of the normal bone marrow conversion pattern in different age group and their ADC value will aid the diagnosis and differential of the cranial bone pathology.

Multiplicity results for classes of one-dimensional p-Laplacian boundary-value problems with cubic-like nonlinearities

Directory of Open Access Journals (Sweden)

Idris Addou

2000-07-01

Full Text Available We study boundary-value problems of the type $$displaylines{ -(varphi_{p}( u' ' =lambda f( u ,hbox{ in }(0,1 cr u( 0 =u( 1 =0, }$$ where $p>1$, $varphi_{p}( x =left| x ight| ^{p-2}x$, and $lambda >0$. We provide multiplicity results when $f$ behaves like a cubic with three distinct roots, at which it satisfies Lipschitz-type conditions involving a parameter $q>1$. We shall show how changes in the position of $q$ with respect to $p$ lead to different behavior of the solution set. When dealing with sign-changing solutions, we assume that $f$ is {it half-odd}; a condition generalizing the usual oddness. We use a quadrature method.

Necessary and Sufficient Conditions for the Existence of Positive Solution for Singular Boundary Value Problems on Time Scales

Directory of Open Access Journals (Sweden)

Meiqiang Feng

2009-01-01

Full Text Available By constructing available upper and lower solutions and combining the Schauder's fixed point theorem with maximum principle, this paper establishes sufficient and necessary conditions to guarantee the existence of Cld[0,1]𝕋 as well as CldΔ[0,1]𝕋 positive solutions for a class of singular boundary value problems on time scales. The results significantly extend and improve many known results for both the continuous case and more general time scales. We illustrate our results by one example.

Fundamental solutions and dual boundary element methods for fracture in plane Cosserat elasticity.

Science.gov (United States)

Atroshchenko, Elena; Bordas, Stéphane P A

2015-07-08

In this paper, both singular and hypersingular fundamental solutions of plane Cosserat elasticity are derived and given in a ready-to-use form. The hypersingular fundamental solutions allow to formulate the analogue of Somigliana stress identity, which can be used to obtain the stress and couple-stress fields inside the domain from the boundary values of the displacements, microrotation and stress and couple-stress tractions. Using these newly derived fundamental solutions, the boundary integral equations of both types are formulated and solved by the boundary element method. Simultaneous use of both types of equations (approach known as the dual boundary element method (BEM)) allows problems where parts of the boundary are overlapping, such as crack problems, to be treated and to do this for general geometry and loading conditions. The high accuracy of the boundary element method for both types of equations is demonstrated for a number of benchmark problems, including a Griffith crack problem and a plate with an edge crack. The detailed comparison of the BEM results and the analytical solution for a Griffith crack and an edge crack is given, particularly in terms of stress and couple-stress intensity factors, as well as the crack opening displacements and microrotations on the crack faces and the angular distributions of stresses and couple-stresses around the crack tip.

Integral Method of Boundary Characteristics: Neumann Condition

Science.gov (United States)

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.

Velocity Distributions in Inelastic Granular Gases with Continuous Size Distributions

International Nuclear Information System (INIS)

Li Rui; Li Zhi-Hao; Zhang Duan-Ming

2011-01-01

We study by numerical simulation the property of velocity distributions of granular gases with a power-law size distribution, driven by uniform heating and boundary heating. It is found that the form of velocity distribution is primarily controlled by the restitution coefficient η and q, the ratio between the average number of heatings and the average number of collisions in the system. Furthermore, we show that uniform and boundary heating can be understood as different limits of q, with q ≫ 1 and q ≤ 1, respectively. (general)

Temperature and stress distribution in pressure vessel by the boundary element method

International Nuclear Information System (INIS)

Alujevic, A.; Apostolovic, D.

1990-01-01

The aim of this paper is to demonstrate the applicability of boundary element method for the solution of temperatures and thermal stresses in the body of reactor pressure vessel of the NPP Krsko . In addition to the theory of boundary elements for thermo-elastic continua (2D, 3D) results are given of a numerically evaluated meridional cross-section. (author)

Distributed Multimedia Technologies and Value Chain Structuring

DEFF Research Database (Denmark)

Hjarup, Søren

2001-01-01

to an altered knowledge-formation on markets and demand-situations, as well as on suppliers' provisions and optimised value chain structuring. These socio-economic impacts have been analysed from an economic theoretical perspective, where a communication model has been introduced emphasising knowledge...... for product presentations and alterations. Present impacts and future implications from applied DMM-technologies have been analysed within the realm of the Danish textile and clothing industry. Businesses within this industry have specialised and become dependent on extensive levels of communication with both...... national and international contractors. DMM-technologies have become widely applied within production-processes and impact the international distribution of labour. In addition, the case shows that there are evident potentials in impacting the businesses and their decision taking. Potentials relate...

Improving Modeling of Extreme Events using Generalized Extreme Value Distribution or Generalized Pareto Distribution with Mixing Unconditional Disturbances

OpenAIRE

Suarez, R

2001-01-01

In this paper an alternative non-parametric historical simulation approach, the Mixing Unconditional Disturbances model with constant volatility, where price paths are generated by reshuffling disturbances for S&P 500 Index returns over the period 1950 - 1998, is used to estimate a Generalized Extreme Value Distribution and a Generalized Pareto Distribution. An ordinary back-testing for period 1999 - 2008 was made to verify this technique, providing higher accuracy returns level under upper ...

Boundary conditions for the diffusion equation in radiative transfer

International Nuclear Information System (INIS)

Haskell, R.C.; Svaasand, L.O.; Tsay, T.; Feng, T.; McAdams, M.S.; Tromberg, B.J.

1994-01-01

Using the method of images, we examine the three boundary conditions commonly applied to the surface of a semi-infinite turbid medium. We find that the image-charge configurations of the partial-current and extrapolated-boundary conditions have the same dipole and quadrupole moments and that the two corresponding solutions to the diffusion equation are approximately equal. In the application of diffusion theory to frequency-domain photon-migration (FDPM) data, these two approaches yield values for the scattering and absorption coefficients that are equal to within 3%. Moreover, the two boundary conditions can be combined to yield a remarkably simple, accurate, and computationally fast method for extracting values for optical parameters from FDPM data. FDPM data were taken both at the surface and deep inside tissue phantoms, and the difference in data between the two geometries is striking. If one analyzes the surface data without accounting for the boundary, values deduced for the optical coefficients are in error by 50% or more. As expected, when aluminum foil was placed on the surface of a tissue phantom, phase and modulation data were closer to the results for an infinite-medium geometry. Raising the reflectivity of a tissue surface can, in principle, eliminate the effect of the boundary. However, we find that phase and modulation data are highly sensitive to the reflectivity in the range of 80--100%, and a minimum value of 98% is needed to mimic an infinite-medium geometry reliably. We conclude that noninvasive measurements of optically thick tissue require a rigorous treatment of the tissue boundary, and we suggest a unified partial-current--extrapolated boundary approach

Observing grain boundaries in CVD-grown monolayer transition metal dichalcogenides

KAUST Repository

Ly, Thuchue

2014-11-25

Two-dimensional monolayer transition metal dichalcogenides (TMdCs), driven by graphene science, revisit optical and electronic properties, which are markedly different from bulk characteristics. These properties are easily modified due to accessibility of all the atoms viable to ambient gases, and therefore, there is no guarantee that impurities and defects such as vacancies, grain boundaries, and wrinkles behave as those of ideal bulk. On the other hand, this could be advantageous in engineering such defects. Here, we report a method of observing grain boundary distribution of monolayer TMdCs by a selective oxidation. This was implemented by exposing directly the TMdC layer grown on sapphire without transfer to ultraviolet light irradiation under moisture-rich conditions. The generated oxygen and hydroxyl radicals selectively functionalized defective grain boundaries in TMdCs to provoke morphological changes at the boundary, where the grain boundary distribution was observed by atomic force microscopy and scanning electron microscopy. This paves the way toward the investigation of transport properties engineered by defects and grain boundaries. (Figure Presented).

Boundary values as Hamiltonian variables. II. Graded structures

International Nuclear Information System (INIS)

Soloviev, Vladimir O.

2002-01-01

It is shown that the new formula for the field theory Poisson brackets arises naturally in the proposed extension of the formal variational calculus incorporating divergences. The linear spaces of local functionals, evolutionary vector fields, functional forms, multi-vectors and differential operators become graded with respect to divergences. The bilinear operations, such as the action of vector fields onto functionals, the commutator of vector fields, the interior product of forms and vectors and the Schouten-Nijenhuis bracket are compatible with the grading. A definition of the adjoint graded operator is proposed and antisymmetric operators are constructed with the help of boundary terms. The fulfilment of the Jacobi identity for the new Poisson brackets is shown to be equivalent to vanishing of the Schouten-Nijenhuis bracket of the Poisson bivector with itself

Distributions of p-values smaller than .05 in Psychology: What is going on?

NARCIS (Netherlands)

Hartgerink, Chris H J; Van Aert, Robbie C M; Nuijten, Michèle B.; Wicherts, Jelte M.; Van Assen, Marcel A L M

2016-01-01

Previous studies provided mixed findings on pecularities in p-value distributions in psychology. This paper examined 258,050 test results across 30,710 articles from eight high impact journals to investigate the existence of a peculiar prevalence of p-values just below .05 (i.e., a bump) in the

Distributions of p-values smaller than .05 in psychology : What is going on?

NARCIS (Netherlands)

Hartgerink, C.H.J.; van Aert, R.C.M.; Nuijten, M.B.; Wicherts, J.M.; van Assen, M.A.L.M.

2016-01-01

Previous studies provided mixed findings on pecularities in p-value distributions in psychology. This paper examined 258,050 test results across 30,710 articles from eight high impact journals to investigate the existence of a peculiar prevalence of p-values just below .05 (i.e., a bump) in the

Temperature distribution in a uniformly moving medium

International Nuclear Information System (INIS)

Mitchell, Joseph D; Petrov, Nikola P

2009-01-01

We apply several physical ideas to determine the steady temperature distribution in a medium moving with uniform velocity between two infinite parallel plates. We compute it in the coordinate frame moving with the medium by integration over the 'past' to account for the influence of an infinite set of instantaneous point sources of heat in past moments as seen by an observer moving with the medium. The boundary heat flux is simulated by appropriately distributed point heat sources on the inner side of an adiabatically insulating boundary. We make an extensive use of the Green functions with an emphasis on their physical meaning. The methodology used in this paper is of great pedagogical value as it offers an opportunity for students to see the connection between powerful mathematical techniques and their physical interpretation in an intuitively clear physical problem. We suggest several problems and a challenging project that can be easily incorporated in undergraduate or graduate courses

Absorbing boundary conditions for Einstein's field equations

Energy Technology Data Exchange (ETDEWEB)

Sarbach, Olivier [Instituto de Fisica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Edificio C-3, Cd. Universitaria. C. P. 58040 Morelia, Michoacan (Mexico)

2007-11-15

A common approach for the numerical simulation of wave propagation on a spatially unbounded domain is to truncate the domain via an artificial boundary, thus forming a finite computational domain with an outer boundary. Absorbing boundary conditions must then be specified at the boundary such that the resulting initial-boundary value problem is well posed and such that the amount of spurious reflection is minimized. In this article, we review recent results on the construction of absorbing boundary conditions in General Relativity and their application to numerical relativity.

Existence of solutions to boundary value problems arising from the fractional advection dispersion equation

Directory of Open Access Journals (Sweden)

Lingju Kong

2013-04-01

Full Text Available We study the existence of multiple solutions to the boundary value problem $$displaylines{ frac{d}{dt}Big(frac12{}_0D_t^{-eta}(u'(t+frac12{}_tD_T^{-eta}(u'(t Big+lambda abla F(t,u(t=0,quad tin [0,T],cr u(0=u(T=0, }$$ where $T>0$, $lambda>0$ is a parameter, $0leqeta<1$, ${}_0D_t^{-eta}$ and ${}_tD_T^{-eta}$ are, respectively, the left and right Riemann-Liouville fractional integrals of order $eta$, $F: [0,T]imesmathbb{R}^Nomathbb{R}$ is a given function. Our interest in the above system arises from studying the steady fractional advection dispersion equation. By applying variational methods, we obtain sufficient conditions under which the above equation has at least three solutions. Our results are new even for the special case when $eta=0$. Examples are provided to illustrate the applicability of our results.

Principal Component Analysis for Normal-Distribution-Valued Symbolic Data.

Science.gov (United States)

Wang, Huiwen; Chen, Meiling; Shi, Xiaojun; Li, Nan

2016-02-01

This paper puts forward a new approach to principal component analysis (PCA) for normal-distribution-valued symbolic data, which has a vast potential of applications in the economic and management field. We derive a full set of numerical characteristics and variance-covariance structure for such data, which forms the foundation for our analytical PCA approach. Our approach is able to use all of the variance information in the original data than the prevailing representative-type approach in the literature which only uses centers, vertices, etc. The paper also provides an accurate approach to constructing the observations in a PC space based on the linear additivity property of normal distribution. The effectiveness of the proposed method is illustrated by simulated numerical experiments. At last, our method is applied to explain the puzzle of risk-return tradeoff in China's stock market.

Grain boundaries in Ni3Al. 2

International Nuclear Information System (INIS)

Kung, H.; Sass, S.L.

1992-01-01

This paper discusses the dislocation structure of small angle tilt and twist boundaries in ordered Ni 3 Al, with and without boron, investigated using transmission electron microscopy. Dislocation with Burgers vectors that correspond to anti-phase boundary (APB)-coupled superpartials were found in small angle twist boundaries in both boron-free and boron-doped Ni 3 Al, and a small angle tilt boundary in boron-doped Ni 3 Al. The boundary structures are in agreement with theoretical models proposed by Marcinkowski and co-workers. The APB energy determined from the dissociation of the grain boundary dislocations was lower than values reported for isolated APBs in Ni 3 Al. For small angle twist boundaries the presence of boron reduced the APB energy at the interface until it approached zero. This is consistent with the structure of these boundaries containing small regions of increased compositional disorder in the first atomic plane next to the interface

Probability distributions in conservative energy exchange models of multiple interacting agents

International Nuclear Information System (INIS)

Scafetta, Nicola; West, Bruce J

2007-01-01

Herein we study energy exchange models of multiple interacting agents that conserve energy in each interaction. The models differ regarding the rules that regulate the energy exchange and boundary effects. We find a variety of stochastic behaviours that manifest energy equilibrium probability distributions of different types and interaction rules that yield not only the exponential distributions such as the familiar Maxwell-Boltzmann-Gibbs distribution of an elastically colliding ideal particle gas, but also uniform distributions, truncated exponential distributions, Gaussian distributions, Gamma distributions, inverse power law distributions, mixed exponential and inverse power law distributions, and evolving distributions. This wide variety of distributions should be of value in determining the underlying mechanisms generating the statistical properties of complex phenomena including those to be found in complex chemical reactions

Additive recovery of lateral boundaries of grains under electronic exposure

International Nuclear Information System (INIS)

Postnikov, D.V.; Plotnikov, S.V.

2002-01-01

The experimental investigation of additive re-distribution under electronic beam revealed a recovery of the additive at grain boundaries. Additive accumulation mainly takes place at the boundaries that are perpendicular to material surface, whereas there is no an observed recovery of additive at the boundaries that are parallel to the surface. The additive recovery is caused by spot fault gradients near the grain boundary. The grain boundary is an intensive run-off region of vacancies. Therefore, the average vacancy distribution profile near the grain boundary changes its pattern. The above case indicates that there are two additive fluxes. One of them is vectored perpendicular to the surface, and the other one is parallel to it, i. e. it is vectored to the grain boundary. A study of the perpendicular and parallel boundaries shows that there is no additive settling at the boundaries that are parallel to the surface, since the general flux is vectored to the parallel boundaries. There is no such kind of phenomenon at the grain boundaries that are perpendicular to the surface. Besides, the perpendicular boundaries are more effective run-off regions for vacancies, since there is a slower build-up of the region with vacancies due to displacement of the vacancies to the surface. To compute concentration of vacancies we will consider a grain of the surface as a model. The computations indicate the presence of vacancy gradients vectored to the surface and grain boundaries, which are perpendicular to the surface. Comparison of the experimental and theoretical outcomes shows a good agreement between the theoretical model and actual processes occurring under the exposure. This theory disclose wide potentials for application of diffusion processes in alloys

Boundary effects in a quasi-two-dimensional driven granular fluid.

Science.gov (United States)

Smith, N D; Smith, M I

2017-12-01

The effect of a confining boundary on the spatial variations in granular temperature of a driven quasi-two-dimensional layer of particles is investigated experimentally. The radial drop in the relative granular temperature ΔT/T exhibits a maximum at intermediate particle numbers which coincides with a crossover from kinetic to collisional transport of energy. It is also found that at low particle numbers, the distributions of radial velocities are increasingly asymmetric as one approaches the boundary. The radial and tangential granular temperatures split, and in the tails of the radial velocity distribution there is a higher population of fast moving particles traveling away rather than towards the boundary.

Boundary-layer height detection with a ceilometer at a coastal site in western Denmark

DEFF Research Database (Denmark)

Hannesdóttir, Ásta; Hansen, Aksel Walle

in atmospheric transport- and dispersion models. A new method of filtering clouds from the ceilometer data is presented. This allows for the inclusion of more than half of the data in the subsequent analysis, as the presence of clouds would otherwise complicate the boundary-layer height estimations. The boundary....... The boundary-layer height estimates are then used to analyse the daily evolution of the boundary layer and to perform monthly and annual frequency distributions of the boundary-layer height. For westerly winds bi-modal distributions are often found, which may be separated by different criteria, while...

Generic short-time propagation of sharp-boundaries wave packets

Science.gov (United States)

Granot, E.; Marchewka, A.

2005-11-01

A general solution to the "shutter" problem is presented. The propagation of an arbitrary initially bounded wave function is investigated, and the general solution for any such function is formulated. It is shown that the exact solution can be written as an expression that depends only on the values of the function (and its derivatives) at the boundaries. In particular, it is shown that at short times (t << 2mx2/hbar, where x is the distance to the boundaries) the wave function propagation depends only on the wave function's values (or its derivatives) at the boundaries of the region. Finally, we generalize these findings to a non-singular wave function (i.e., for wave packets with finite-width boundaries) and suggest an experimental verification.

BSLIC: SLIC Superpixels Based on Boundary Term

Directory of Open Access Journals (Sweden)

Hai Wang

2017-02-01

Full Text Available A modified method for better superpixel generation based on simple linear iterative clustering (SLIC is presented and named BSLIC in this paper. By initializing cluster centers in hexagon distribution and performing k-means clustering in a limited region, the generated superpixels are shaped into regular and compact hexagons. The additional cluster centers are initialized as edge pixels to improve boundary adherence, which is further promoted by incorporating the boundary term into the distance calculation of the k-means clustering. Berkeley Segmentation Dataset BSDS500 is used to qualitatively and quantitatively evaluate the proposed BSLIC method. Experimental results show that BSLIC achieves an excellent compromise between boundary adherence and regularity of size and shape. In comparison with SLIC, the boundary adherence of BSLIC is increased by at most 12.43% for boundary recall and 3.51% for under segmentation error.

Boundary conditions for the gravitational field

International Nuclear Information System (INIS)

Winicour, Jeffrey

2012-01-01

A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the harmonic formulation of Einstein's equations and a tetrad formulation of the Einstein-Bianchi system. However, a universal approach valid for other formulations is not in hand. In particular, there is no satisfactory boundary theory for the 3+1 formulations which have been highly successful in binary black hole simulation. I discuss the underlying problems that make the initial-boundary-value problem much more complicated than the Cauchy problem. I review the progress that has been made and the important open questions that remain. Science is a differential equation. Religion is a boundary condition. (Alan Turing, quoted in J D Barrow, 'Theories of Everything') (topical review)

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

Science.gov (United States)

Beshtokov, M. Kh.

2016-10-01

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

Boundary condition effect on response modification factor of X-braced steel frames

Directory of Open Access Journals (Sweden)

Walid A. Attia

2018-04-01

Full Text Available Design of the structures to resist seismic force depends on the theory of dissipation in elastic energy that already exists in response modification factor “R-factor”. The main problem in codes gives a constant value for R-factor, since change in boundary conditions of building change in behavior of braced steel frame structures and that effects on R-factor. This study is an attempt to assess overstrength, ductility and response modification factor of X-braced steel frame under change in boundary conditions, as change in the direction of strong axis of column and connection support type of column besides variation in storey and bays numbers to be 21 frames and each frame has 8 different boundary conditions as sum of 168 cases for analysis. These frames were analyzed by using nonlinear static “pushover” analysis. As results of this study change in support type and direction of strong axis of column give large change in value of R-factor; the minimum value was 4.37 and maximum value 10.97. Minimum value is close to code value that’s mean the code is more conservative in suggesting of R-factor and gives a large factor of safety. Change in the location of bracing gives change in value of R-factor for all boundary conditions. Change in direction of strong axis of columns and support type didn’t give change in value of fundamental period, all boundary conditions. Keywords: Response modification factor, Ductility reduction factor, Overstrength factor, Boundary conditions, Brace frame, Nonlinear static analysis “Pushover”

Periodic Boundary Conditions in the ALEGRA Finite Element Code

International Nuclear Information System (INIS)

Aidun, John B.; Robinson, Allen C.; Weatherby, Joe R.

1999-01-01

This document describes the implementation of periodic boundary conditions in the ALEGRA finite element code. ALEGRA is an arbitrary Lagrangian-Eulerian multi-physics code with both explicit and implicit numerical algorithms. The periodic boundary implementation requires a consistent set of boundary input sets which are used to describe virtual periodic regions. The implementation is noninvasive to the majority of the ALEGRA coding and is based on the distributed memory parallel framework in ALEGRA. The technique involves extending the ghost element concept for interprocessor boundary communications in ALEGRA to additionally support on- and off-processor periodic boundary communications. The user interface, algorithmic details and sample computations are given

A three-point Taylor algorithm for three-point boundary value problems

NARCIS (Netherlands)

J.L. López; E. Pérez Sinusía; N.M. Temme (Nico)

2011-01-01

textabstractWe consider second-order linear differential equations $\\varphi(x)y''+f(x)y'+g(x)y=h(x)$ in the interval $(-1,1)$ with Dirichlet, Neumann or mixed Dirichlet-Neumann boundary conditions given at three points of the interval: the two extreme points $x=\\pm 1$ and an interior point

Geochemistry and magnetic sediment distribution at the western boundary upwelling system of southwest Atlantic

Science.gov (United States)

Cruz, Anna P. S.; Barbosa, Catia F.; Ayres-Neto, Arthur; Munayco, Pablo; Scorzelli, Rosa B.; Amorim, Nívea Santos; Albuquerque, Ana L. S.; Seoane, José C. S.

2018-02-01

In order to investigate the chemical and magnetic characteristics of sediments of the western boundary upwelling system of Southwest Atlantic we analyzed magnetic susceptibility, grain size distribution, total organic carbon, heavy mineral abundance, Fe associated with Mössbauer spectra, and Fe and Mn of pore water to evaluate the deposition patterns of sediments. Four box-cores were collected along a cross-shelf transect. Brazil Current and coastal plume exert a primary control at the inner and outer shelf cores, which exhibited similar depositional patterns characterized by a high abundance of heavy minerals (mean 0.21% and 0.08%, respectively) and very fine sand, whereas middle shelf cores presented low abundances of heavy minerals (mean 0.03%) and medium silt. The inner shelf was dominated by sub-angular grains, while in middle and outer shelf cores well-rounded grains were found. The increasing Fe3+:Fe2+ ratio from the inner to the outer shelf reflects farther distance to the sediment source. The outer shelf presented well-rounded minerals, indicating abrasive processes as a result of transport by the Brazil Current from the source areas. In the middle shelf, cold-water intrusion of the South Atlantic Central Water contributes to the primary productivity, resulting in higher deposition of fine sediment and organic carbon accumulation. The high input of organic carbon and the decreased grain size are indicative of changes in the hydrodynamics and primary productivity fueled by the western boundary upwelling system, which promotes loss of magnetization due to the induction of diagenesis of iron oxide minerals.

Vertical distribution of ozone and VOCs in the low boundary layer of Mexico City

Directory of Open Access Journals (Sweden)

E. Velasco

2008-06-01

Full Text Available The evolution of ozone (O₃ and 13 volatile organic compounds (VOCs in the boundary layer of Mexico City was investigated during 2000–2004 to improve our understanding of the complex interactions between those trace gases and meteorological variables, and their influence on the air quality of a polluted megacity. A tethered balloon, fitted with electrochemical and meteorological sondes, was used to obtain detailed vertical profiles of O₃ and meteorological parameters up to 1000 m above ground during part of the diurnal cycle (02:00–18:00 h. VOCs samples were collected up to 200 m by pumping air to canisters with a Teflon tube attached to the tether line. Overall, features of these profiles were found to be consistent with the formation of an upper residual layer during nighttime carrying over a fraction of the O₃ from the previous day that contributes to the background concentration in surrounding regions. At the same time the release of heat stored in the urban surface forms a shallow unstable layer close to the ground, where the nocturnal emissions are trapped. After sunrise an O₃ balance is determined by photochemical production, entrainment from the upper residual layer and destruction by titration with nitric oxide, delaying the ground-level O₃ rise by 2 h. The subsequent evolution of the conductive boundary layer and vertical distribution of pollutants are discussed in terms of the energy balance, the presence of turbulence and the atmospheric stability.

Twin Positive Solutions of a Nonlinear m-Point Boundary Value Problem for Third-Order p-Laplacian Dynamic Equations on Time Scales

Directory of Open Access Journals (Sweden)

Wei Han

2008-01-01

Full Text Available Several existence theorems of twin positive solutions are established for a nonlinear m-point boundary value problem of third-order p-Laplacian dynamic equations on time scales by using a fixed point theorem. We present two theorems and four corollaries which generalize the results of related literature. As an application, an example to demonstrate our results is given. The obtained conditions are different from some known results.

Observation of universality for high pT distribution at LHC energies

Science.gov (United States)

Tabassam, U.; Ali, Y.; Ullah, S.; Ajaz, M.; Ali, Q.; Suleymanov, M.; Bhatti, A. S.; Suleymanov, R.

We have studied the distributions of the yield of primary charged particles produced in the asymmetric p-Pb collisions at sNN = 5.02TeV for the three pseudorapidity regions: 0.3 Heavy ion jet interaction generator (HIJING) and Ultra relativistic quantum molecular dynamics (UrQMD) models are used to produce simulated data and the results are compared with the CMS and ATLAS data. The comparison of models and data shows the existence of high pT area with boundary values that depend upon pseudorapidity (η). At high pT values, the behavior of the distributions shows some universality, which does not depend upon the models. The reason of the universality could be the string dynamics for the parton hadronization at high pT values.

Interactions of impurities with a moving grain boundary

Energy Technology Data Exchange (ETDEWEB)

Bauer, C L [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA)

1975-01-01

Most theories developed to explain interaction of impurities with a moving grain boundary involve a uniform excess impurity concentration distributed along a planar grain boundary. As boundary velocity increases, the excess impurities exert a net drag force on the boundary until a level is reached whereat the drag force no longer can balance the driving force and breakaway of the boundary from these impurities occurs. In this investigation, assumptions of a uniform lateral impurity profile and a planar grain boundary shape are relaxed by allowing both forward and lateral diffusion of impurities in the vicinity of a grain boundary. It is found that the two usual regions (drag of impurities by, and breakaway of a planar grain boundary) are separated by an extensive region wherein a uniform lateral impurity profile and a planar grain boundary shape are unstable. It is suspected that, in this unstable region, grain boundaries assume a spectrum of more complex morphologies and that elucidation of these morphologies can provide the first definitive description of the breakaway process and insight to more complex phenomena such as solid-solution strengthening, grain growth and secondary recrystallization.

Effects of K and Ca doping on twin boundary energy of cupperate superconductors

Science.gov (United States)

Khoshnevisan, Bahram; Mohammadi, Mahnaz

2016-04-01

Ab-initio calculations under GGA approximation have been employed to find out the effect Ba substitution by K and Ca on the structural and electronic properties twined and untwined YBCO system. In this regard, the twin boundary energy, γ, and impact of the substitution on the boundary's charge distribution have been of special consideration. Our results show that despite the structural changes the presence of K (Ca) modifies substantially density of levels at the Fermi level, which could be responsible for empirical reports of decreasing the critical temperature (Tc) by increasing the K(Ca) content. Although, the K doping reduces the γ value in YBa2-xKxCu3O7 system, after calcium doping it remains more or less unchanged. In addition, reduction of the carrier density occurs at twin boundary in CuO2 layer for the substituted system with respect to the untwined YBCO system. Our results would be noticeable in conjunction with the experimentally reported twinned and alkali substituted superconductive properties of the YBCO samples.

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

Science.gov (United States)

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.

A Value Chain Analysis of ghost nets in the Arafura Sea: identifying trans-boundary stakeholders, intervention points and livelihood trade-offs.

Science.gov (United States)

Butler, J R A; Gunn, R; Berry, H L; Wagey, G A; Hardesty, B D; Wilcox, C

2013-07-15

Lost or discarded fishing nets are a significant component of marine debris which has trans-boundary impacts in large marine ecosystems. Such 'ghost nets' cause the by-catch of marine fauna and require retrieval from coastlines where they wash up. Identifying the causes of discarded nets and feasible intervention points requires analysis of a complex value chain and the stakeholders within it, yet no studies have attempted this. In this paper we combine Value Chain Analysis, commonly applied to understand value-adding for a commodity, with elements of Life Cycle Assessment and social network analysis to examine the drivers, stakeholders, economic, environmental and social costs and benefits in the life of a trawl net. We use the Arafura Sea as a case study, which is shared by Indonesia, Papua New Guinea and Australia, and is the focus of a Trans-boundary Diagnostic Assessment (TDA) within the Arafura-Timor Seas Ecosystem Action program (ATSEA). We follow a trawl net through four sub-systems: manufacture of webbing in South Korea, fishing and loss by an Indonesian vessel, retrieval as ghost net on the northern Australian coastline by Indigenous rangers, and disposal or re-cycling as 'GhostNet Art' by Indigenous artists. Primary stakeholders along the value chain incur economic and social benefits, and economic and environmental costs. There is an anomaly in the chain between Indonesian fishermen and Indigenous rangers, artists and communities due to the lack of market linkages between these primary stakeholders. The first 'nexus of influence' where reductions in net losses and environmental costs can be achieved is through interactions between GhostNets Australia, the World Wide Fund for Nature and the Australian Government, which can influence Indonesian fishery management institutions and fishing crews. The second nexus is via the international art market which by publicising GhostNet Art can raise awareness amongst fish consumers about the impacts of ghost nets

On non-linear boundary value problems and parametrisation at multiple nodes

Czech Academy of Sciences Publication Activity Database

Rontó, András; Rontó, M.; Varha, J.

2016-01-01

Roč. 2016, Č. 80 (2016), s. 1-18 ISSN 1417-3875 Institutional support: RVO:67985840 Keywords : non-local boundary conditions * parametrisation * successive approximations * interval division Subject RIV: BA - General Mathematics Impact factor: 0.926, year: 2016 http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5302

Tokamak plasma boundary layer model

International Nuclear Information System (INIS)

Volkov, T.F.; Kirillov, V.D.

1983-01-01

A model has been developed for the limiter layer and for the boundary region of the plasma column in a tokamak to facilitate analytic calculations of the thickness of the limiter layers, the profiles and boundary values of the temperature and the density under various conditions, and the difference between the electron and ion temperatures. This model can also be used to analyze the recycling of neutrals, the energy and particle losses to the wall and the limiter, and other characteristics

Value distribution assessment of geothermal development in Lake County, CA

Energy Technology Data Exchange (ETDEWEB)

Churchman, C.W.; Nelson, H.G.; Eacret, K.

1977-10-01

A value distribution assessment is defined as the determination of the distribution of benefits and costs of a proposed or actual development, with the intent of comparing such a development with alternative plans. Included are not only the social and economic effects, but also people's perceptions of their roles and how they are affected by the proposed or actual development. Discussion is presented under the following section headings: on morality and ethics; the vanishing community; case study of pre-development planning--Lake County; methodology for research; Lake County geothermal energy resource; decision making; Planning Commission hearing; communication examples; benefit tracing; response to issues raised by the report of the State Geothermal Task Force; and, conclusions and recommendations. (JGB)

Electrical properties of grain boundaries in polycrystalline materials under intrinsic or low doping

International Nuclear Information System (INIS)

Chowdhury, M H; Kabir, M Z

2011-01-01

An analytical model is developed to study the electrical properties (electric field and potential distributions, potential energy barrier height and polarization phenomenon) of polycrystalline materials at intrinsic or low doping for detector and solar cell applications by considering an arbitrary amount of grain boundary charge and a finite width of grain boundary region. The general grain boundary model is also applicable to highly doped polycrystalline materials. The electric field and potential distributions are obtained by solving Poisson's equation in both depleted grains and grain boundary regions. The electric field and potential distributions across the detector are analysed under various doping, trapping and applied biases. The electric field collapses, i.e. a nearly zero-average electric field region exists in some part of the biased detector at high trapped charge densities at the grain boundaries. The model explains the conditions of existence of a zero-average field region, i.e. the polarization mechanisms in polycrystalline materials. The potential energy barrier at the grain boundary exists if the electric field changes its sign at the opposite side of the grain boundary. The energy barrier does not exist in all grain boundaries in the low-doped polycrystalline detector and it never exists in intrinsic polycrystalline detectors under applied bias condition provided that there is no charge trapping in the grain.