Electromagnetic wave theory for boundary-value problems an advanced course on analytical methods
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 numerical solution of a singular boundary value problem arising in boundary layer theory.
Hu, Jiancheng
2016-01-01
In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors.
Boundary value problems on the half line in the theory of colloids
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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.
Asymptotic Solution of the Theory of Shells Boundary Value Problem
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I. V. Andrianov
2007-01-01
Full Text Available This paper provides a state-of-the-art review of asymptotic methods in the theory of plates and shells. Asymptotic methods of solving problems related to theory of plates and shells have been developed by many authors. The main features of our paper are: (i it is devoted to the fundamental principles of asymptotic approaches, and (ii it deals with both traditional approaches, and less widely used, new approaches. The authors have paid special attention to examples and discussion of results rather than to burying the ideas in formalism, notation, and technical details.
Muskhelishvili, N I
2011-01-01
Singular integral equations play important roles in physics and theoretical mechanics, particularly in the areas of elasticity, aerodynamics, and unsteady aerofoil theory. They are highly effective in solving boundary problems occurring in the theory of functions of a complex variable, potential theory, the theory of elasticity, and the theory of fluid mechanics.This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values. Its coverage includes such topics as the Hölder condition, Hilbert and Riemann-Hilbert 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
Discrete quintic spline for boundary value problem in plate deflation theory
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.
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
A review on application of MHD theory to plasma boundary problems in tokamaks
International Nuclear Information System (INIS)
Itoh, Kimitaka.
1992-08-01
A survey is made on the problems of the edge plasmas, to which the analyses based on the MHD theory have been successfully applied. Also discussed are the efforts to extend the model equation to more general (and important as well) problems such as H-mode physics. An overview is first made on the advantages of the MHD picture, and the necessary supplementary physics are examined. Next, one- and two-dimensional models of the spatial structure of the edge plasma is discussed. The results on the stationary structure, both analytical and numerical, are reviewed: Typical example as well as the scaling law are shown. The instabilities associated with edge plasma is next reviewed. The surface kink mode, ballooning mode, interchange mode, resistive interchange mode and thermal instability are discussed. Role of the geometry such as the location of the X-point is studied. Influences of the atomic processes, and those of the radial electric field are also discussed. The analysis of the H-mode transition physics is finally discussed. The boundary plasma is a nonlinear media which possesses the possibility for bifurcation in which the radial electric field plays a key role. The model of the ion viscosity is also studied. Transition physics is developed. Analysis on the self-generating oscillation is shown and the relation with ELMs is discussed. After reviewing these problems, several comments are made to what directions the study can be deepened. (author) 53 refs
On inverse and direct free boundary problems in the theory of plasma equilibrium in a Tokamak
International Nuclear Information System (INIS)
Demidov, A.; Petrova, V.; Silantiev, V.
1996-01-01
Theorems of existence of simply connected 'plasma' domain for the cylindrical case of the Grad-Shafranov equation Δu = F(u) are given. For the inverse problem upper and lower estimates of normal derivative of u on the boundary of the 'plasma' domain are obtained. (author)
Analytic theory of curvature effects for wave problems with general boundary conditions
DEFF Research Database (Denmark)
Willatzen, Morten; Gravesen, Jens; Voon, L. C. Lew Yan
2010-01-01
A formalism based on a combination of differential geometry and perturbation theory is used to obtain analytic expressions for confined eigenmode changes due to general curvature effects. In cases of circular-shaped and helix-shaped structures, where alternative analytic solutions can be found......, the perturbative solution is shown to yield the same result. The present technique allows the generalization of earlier results to arbitrary boundary conditions. The power of the method is illustrated using examples based on Maxwell’s and Schrödinger’s equations for applications in photonics and nanoelectronics....
International Nuclear Information System (INIS)
Akhiezer, A.I.; Shul'ga, N.F.
1991-01-01
The process of relativistic particle radiation in an external field has been studied in the semi-classical approximation rather extensively. The main problem arising in the studies is in expressing the formula of the quantum theory of radiation in terms of classical quantities, for example of the classical trajectories. However, it still remains unclear how the particle trajectory is assigned, that is which particular initial or boundary conditions determine the trajectory in semi-classical approximation quantum theory of radiation. We shall try to solve this problem. Its importance comes from the fact that in some cases one and the same boundary conditions may give rise to two or more trajectories. We demonstrate that this fact must necessarily be taken into account on deriving the classical limit for the formulae of the quantum theory of radiation, since it leads to a specific interference effect in radiation. The method we used to deal with the problem is similar to the method employed by Fock to analyze the problem of a canonical transformation in classical and quantum mechanics. (author)
Energy Technology Data Exchange (ETDEWEB)
Jamet, P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1967-07-01
This report gives a general presentation of barrier theory for finite difference operators, with its applications to some boundary value problems. (author) [French] Ce rapport est un expose synthetique de la theorie des barrieres pour les operateurs aux differences finies et ses applications a certaines classes de problemes lineaires elliptiques du 'type de Dirichlet'. (auteur)
Schlichting (Deceased), Hermann
2017-01-01
This new edition of the near-legendary textbook by Schlichting and revised by Gersten presents a comprehensive overview of boundary-layer theory and its application to all areas of fluid mechanics, with particular emphasis on the flow past bodies (e.g. aircraft aerodynamics). The new edition features an updated reference list and over 100 additional changes throughout the book, reflecting the latest advances on the subject.
Directory of Open Access Journals (Sweden)
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.
Boundary-value problems with free boundaries for elliptic systems of equations
Monakhov, V N
1983-01-01
This book is concerned with certain classes of nonlinear problems for elliptic systems of partial differential equations: boundary-value problems with free boundaries. The first part has to do with the general theory of boundary-value problems for analytic functions and its applications to hydrodynamics. The second presents the theory of quasiconformal mappings, along with the theory of boundary-value problems for elliptic systems of equations and applications of it to problems in the mechanics of continuous media with free boundaries: problems in subsonic gas dynamics, filtration theory, and problems in elastico-plasticity.
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
Separable boundary-value problems in physics
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
Fourier analysis and boundary value problems
Gonzalez-Velasco, Enrique A
1996-01-01
Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.Key Features* Topics are covered from a historical perspective with biographical information on key contributors to the field* The text contains more than 500 exercises* Includes practical applicati...
Boundary conditions in conformal and integrable theories
Petkova, V B
2000-01-01
The study of boundary conditions in rational conformal field theories is not only physically important. It also reveals a lot on the structure of the theory ``in the bulk''. The same graphs classify both the torus and the cylinder partition functions and provide data on their hidden ``quantum symmetry''. The Ocneanu triangular cells -- the 3j-symbols of these symmetries, admit various interpretations and make a link between different problems.
Numerical Methods for Free Boundary Problems
1991-01-01
About 80 participants from 16 countries attended the Conference on Numerical Methods for Free Boundary Problems, held at the University of Jyviiskylii, Finland, July 23-27, 1990. The main purpose of this conference was to provide up-to-date information on important directions of research in the field of free boundary problems and their numerical solutions. The contributions contained in this volume cover the lectures given in the conference. The invited lectures were given by H.W. Alt, V. Barbu, K-H. Hoffmann, H. Mittelmann and V. Rivkind. In his lecture H.W. Alt considered a mathematical model and existence theory for non-isothermal phase separations in binary systems. The lecture of V. Barbu was on the approximate solvability of the inverse one phase Stefan problem. K-H. Hoff mann gave an up-to-date survey of several directions in free boundary problems and listed several applications, but the material of his lecture is not included in this proceedings. H.D. Mittelmann handled the stability of thermo capi...
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.
Problems of matter-antimatter boundary layers
International Nuclear Information System (INIS)
Lehnert, B.
1975-01-01
This paper outlines the problems of the quasi-steady matter-antimatter boundary layers discussed in Klein-Alfven's cosmological theory, and a crude model of the corresponding ambiplasma balance is presented: (i) at interstellar particle densities, no well-defined boundary layer can exist in presence of neutral gas, nor can such a layer be sustained in an unmagnetized fully ionized ambiplasma. (ii) Within the limits of applicability of the present model, sharply defined boundary layers are under certain conditions found to exist in a magnetized ambiplasma. Thus, at beta values less than unity, a steep pressure drop of the low-energy components of matter and antimatter can be balanced by a magnetic field and the electric currents in the ambiplasma. (iii) The boundary layer thickness is of the order of 2x 0 approximately 10/BT 0 sup(1/4) meters, where B is the magnetic field strength in MKS units and T 0 the characteristic temperature of the low-energy components in the layer. (Auth.)
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
Problems in equilibrium theory
Aliprantis, Charalambos D
1996-01-01
In studying General Equilibrium Theory the student must master first the theory and then apply it to solve problems. At the graduate level there is no book devoted exclusively to teaching problem solving. This book teaches for the first time the basic methods of proof and problem solving in General Equilibrium Theory. The problems cover the entire spectrum of difficulty; some are routine, some require a good grasp of the material involved, and some are exceptionally challenging. The book presents complete solutions to two hundred problems. In searching for the basic required techniques, the student will find a wealth of new material incorporated into the solutions. The student is challenged to produce solutions which are different from the ones presented in the book.
Boundary value problems and partial differential equations
Powers, David L
2005-01-01
Boundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, (Clarkson) has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering.* CD with animations and graphics of solutions, additional exercises and chapter review questions* Nearly 900 exercises ranging in difficulty* Many fully worked examples
Effective Field Theory on Manifolds with Boundary
Albert, Benjamin I.
In the monograph Renormalization and Effective Field Theory, Costello made two major advances in rigorous quantum field theory. Firstly, he gave an inductive position space renormalization procedure for constructing an effective field theory that is based on heat kernel regularization of the propagator. Secondly, he gave a rigorous formulation of quantum gauge theory within effective field theory that makes use of the BV formalism. In this work, we extend Costello's renormalization procedure to a class of manifolds with boundary and make preliminary steps towards extending his formulation of gauge theory to manifolds with boundary. In addition, we reorganize the presentation of the preexisting material, filling in details and strengthening the results.
International Nuclear Information System (INIS)
Adler, S.L.; Wilczek, F.
1992-11-01
Members of the Institute have worked on a number of problems including the following: acceleration algorithms for the Monte Carlo analysis of lattice field, and gauge and spin theories, based on changes of variables specific to lattices of dimension 2 ell ; construction of quaternionic generalizations of complex quantum mechanics and field theory; wave functions for paired Hall states; black hole quantum mechanics; generalized target-space duality in curved string backgrounds; gauge symnmetry algebra of the N = 2 string; two-dimensional quantum gravity and associated string theories; organizing principles from which the signal processing of neural networks in the retina and cortex can be deduced; integrable systems of KdV type; and a theory for Kondo insulators
Boundary Value Problems Arising in Kalman Filtering
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Sinem Ertürk
2009-01-01
Full Text Available The classic Kalman filtering equations for independent and correlated white noises are ordinary differential equations (deterministic or stochastic with the respective initial conditions. Changing the noise processes by taking them to be more realistic wide band noises or delayed white noises creates challenging partial differential equations with initial and boundary conditions. In this paper, we are aimed to give a survey of this connection between Kalman filtering and boundary value problems, bringing them into the attention of mathematicians as well as engineers dealing with Kalman filtering and boundary value problems.
Boundary Value Problems Arising in Kalman Filtering
Directory of Open Access Journals (Sweden)
Bashirov Agamirza
2008-01-01
Full Text Available The classic Kalman filtering equations for independent and correlated white noises are ordinary differential equations (deterministic or stochastic with the respective initial conditions. Changing the noise processes by taking them to be more realistic wide band noises or delayed white noises creates challenging partial differential equations with initial and boundary conditions. In this paper, we are aimed to give a survey of this connection between Kalman filtering and boundary value problems, bringing them into the attention of mathematicians as well as engineers dealing with Kalman filtering and boundary value problems.
Directory of Open Access Journals (Sweden)
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.
A Boundary Value Problem for Introductory Physics?
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…
Solution of moving boundary problems with implicit boundary condition
International Nuclear Information System (INIS)
Moyano, E.A.
1990-01-01
An algorithm that solves numerically a model for studying one dimensional moving boundary problems, with implicit boundary condition, is described. Landau's transformation is used, in order to work with a fixed number of nodes at each instant. Then, it is necessary to deal with a parabolic partial differential equation, whose diffusive and convective terms have variable coefficients. The partial differential equation is implicitly discretized, using Laasonen's scheme, always stable, instead of employing Crank-Nicholson sheme, as it has been done by Ferris and Hill. Fixed time and space steps (Δt, Δξ) are used, and the iteration is made with variable positions of the interface, i.e. varying δs until a boundary condition is satisfied. The model has the same features of the oxygen diffusion in absorbing tissue. It would be capable of estimating time variant radiation treatments of cancerous tumors. (Author) [es
Boundary value problems and dichotomic stability
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.
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.)
Boundary conditions in rational conformal field theories
International Nuclear Information System (INIS)
Behrend, Roger E.; Pearce, Paul A.; Petkova, Valentina B.; Zuber, Jean-Bernard
2000-01-01
We develop further the theory of Rational Conformal Field Theories (RCFTs) on a cylinder with specified boundary conditions emphasizing the role of a triplet of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that solving Cardy's equation, expressing consistency of a RCFT on a cylinder, is equivalent to finding integer valued matrix representations of the Verlinde algebra. These matrices allow us to naturally associate a graph G to each RCFT such that the conformal boundary conditions are labelled by the nodes of G. This approach is carried to completion for sl(2) theories leading to complete sets of conformal boundary conditions, their associated cylinder partition functions and the A-D-E classification. We also review the current status for WZW sl(3) theories. Finally, a systematic generalisation of the formalism of Cardy-Lewellen is developed to allow for multiplicities arising from more general representations of the Verlinde algebra. We obtain information on the bulk-boundary coefficients and reproduce the relevant algebraic structures from the sewing constraints
Antireflective Boundary Conditions for Deblurring Problems
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Marco Donatelli
2010-01-01
Full Text Available This survey paper deals with the use of antireflective boundary conditions for deblurring problems where the issues that we consider are the precision of the reconstruction when the noise is not present, the linear algebra related to these boundary conditions, the iterative and noniterative regularization solvers when the noise is considered, both from the viewpoint of the computational cost and from the viewpoint of the quality of the reconstruction. In the latter case, we consider a reblurring approach that replaces the transposition operation with correlation. For many of the considered items, the anti-reflective algebra coming from the given boundary conditions is the optimal choice. Numerical experiments corroborating the previous statement and a conclusion section end the paper.
International Nuclear Information System (INIS)
Adler, S.L.; Wilczek, F.
1993-11-01
Areas of emphasis include acceleration algorithms for the Monte Carlo analysis of lattice field and gauge theories, quaternionic generalizations of complex quantum mechanics and field theory, application of the renormalization group to the QCD phase transition, the quantum Hall effect, and black holes. Other work involved string theory, statistical properties of energy levels in integrable quantum systems, baryon asymmetry and the electroweak phase transition, anisotropies of the cosmic microwave background, and theory of superconductors
Trace expansions for mixed boundary problems
Energy Technology Data Exchange (ETDEWEB)
Seeley, Robert T
2002-01-01
We discuss the heat trace expansion for a mixed boundary problem for the Laplace operator acting on sections of some bundle V over a manifold M of dimension d. The boundary is divided in two parts N{sub D} and N{sub N}, intersecting in a smooth submanifold {sigma}. Dirichlet conditions are imposed on N{sub D} - {sigma}, and Neumann conditions on N{sub N} - {sigma}. It turns out that it is also necessary to impose a condition along {sigma}. We then obtain an expansion of the trace of the heat operator with these boundary conditions, containing integrals of the usual terms over the interior and the two parts of the boundary, together with integrals over {sigma} of terms that are 'global' in certain operators on a semicircle. The first nonzero such term is computed; it involves the zeta function of an operator on the semicircle, and depends on the boundary condition along {sigma}. We find that no logarithmic terms occur in the expansion.
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
The Boundary Element Method Applied to the Two Dimensional Stefan Moving Boundary Problem
1991-03-15
Unc), - ( UGt )t - (UG,,),,] - (UG), If we integrate this equation with respect to r from 0 to t - c and with respect to and ij on the region 11(r...and others. "Moving Boundary Problems in Phase Change Mod- els," SIGNUM Newsletter, 20: 8-12 (1985). 21. Stefan, J. "Ober einige Probleme der Theorie ...ier Wirmelcitung," S.-B. \\Vein. Akad. Mat. Natur., 98: 173-484 (1889). 22.-. "flber (lie Theorie der Eisbildung insbesondere fiber die lisbildung im
Group invariance in engineering boundary value problems
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...
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.
Adaptive boundary conditions for exterior flow problems
Boenisch, V; Wittwer, S
2003-01-01
We consider the problem of solving numerically the stationary incompressible Navier-Stokes equations in an exterior domain in two dimensions. This corresponds to studying the stationary fluid flow past a body. The necessity to truncate for numerical purposes the infinite exterior domain to a finite domain leads to the problem of finding appropriate boundary conditions on the surface of the truncated domain. We solve this problem by providing a vector field describing the leading asymptotic behavior of the solution. This vector field is given in the form of an explicit expression depending on a real parameter. We show that this parameter can be determined from the total drag exerted on the body. Using this fact we set up a self-consistent numerical scheme that determines the parameter, and hence the boundary conditions and the drag, as part of the solution process. We compare the values of the drag obtained with our adaptive scheme with the results from using traditional constant boundary conditions. Computati...
DEFF Research Database (Denmark)
Christensen, Ole
2014-01-01
We discuss various problems in frame theory that have been open for some years. A short discussion of frame theory is also provided, but it only contains the information that is necessary in order to understand the open problems and their role.......We discuss various problems in frame theory that have been open for some years. A short discussion of frame theory is also provided, but it only contains the information that is necessary in order to understand the open problems and their role....
Mixed Boundary Value Problem on Hypersurfaces
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R. DuDuchava
2014-01-01
Full Text Available The purpose of the present paper is to investigate the mixed Dirichlet-Neumann boundary value problems for the anisotropic Laplace-Beltrami equation divC(A∇Cφ=f on a smooth hypersurface C with the boundary Γ=∂C in Rn. A(x is an n×n bounded measurable positive definite matrix function. The boundary is decomposed into two nonintersecting connected parts Γ=ΓD∪ΓN and on ΓD the Dirichlet boundary conditions are prescribed, while on ΓN the Neumann conditions. The unique solvability of the mixed BVP is proved, based upon the Green formulae and Lax-Milgram Lemma. Further, the existence of the fundamental solution to divS(A∇S is proved, which is interpreted as the invertibility of this operator in the setting Hp,#s(S→Hp,#s-2(S, where Hp,#s(S is a subspace of the Bessel potential space and consists of functions with mean value zero.
The entropic boundary law in BF theory
Livine, Etera R.; Terno, Daniel R.
2009-01-01
We compute the entropy of a closed bounded region of space for pure 3d Riemannian gravity formulated as a topological BF theory for the gauge group SU(2) and show its holographic behavior. More precisely, we consider a fixed graph embedded in space and study the flat connection spin network state without and with particle-like topological defects. We regularize and compute exactly the entanglement for a bipartite splitting of the graph and show it scales at leading order with the number of vertices on the boundary (or equivalently with the number of loops crossing the boundary). More generally these results apply to BF theory with any compact gauge group in any space-time dimension.
Diamagnetic boundary layers: a kinetic theory
International Nuclear Information System (INIS)
Lemaire, J.; Burlaga, L.F.
1976-01-01
A kinetic theory for boundary layers associated with MHD tangential 'discontinuities' in a collisionless magnetized plasma such as those observed in the solar wind is presented. The theory consists of finding self-consistent solutions of Vlasov's equation and Maxwell's equation for stationary, one-dimensional boundary layers separating two Maxwellian plasma states. Layers in which the current is carried by electrons are found to have a thickness of the order of a few electron gyroradii, but the drift speed of the current-carrying electrons is found to exceed the Alfven speed, and accordingly such layers are not stable. Several types of layers, in which the current is carried by protons are discussed; in particular, cases in which the magnetic field intensity and/or direction changed across the layer were considered. In every case, the thickness was of the order of a few proton gyroradii and the field changed smoothly , although the characteristics depended somewhat on the boundary conditions. The drift speed was always less than the Alfven speed, consistent with stability of such structures. The results are consistent with the observations of boundary layers in the solar wind near 1 AU. (Auth.)
Moving-Boundary Problems Associated with Lyopreservation
Gruber, Christopher Andrew
The work presented in this Dissertation is motivated by research into the preservation of biological specimens by way of vitrification, a technique known as lyopreservation. The operative principle behind lyopreservation is that a glassy material forms as a solution of sugar and water is desiccated. The microstructure of this glass impedes transport within the material, thereby slowing metabolism and effectively halting the aging processes in a biospecimen. This Dissertation is divided into two segments. The first concerns the nature of diffusive transport within a glassy state. Experimental studies suggest that diffusion within a glass is anomalously slow. Scaled Brownian motion (SBM) is proposed as a mathematical model which captures the qualitative features of anomalously slow diffusion while minimizing computational expense. This model is applied to several moving-boundary problems and the results are compared to a more well-established model, fractional anomalous diffusion (FAD). The virtues of SBM are based on the model's relative mathematical simplicity: the governing equation under FAD dynamics involves a fractional derivative operator, which precludes the use of analytical methods in almost all circumstances and also entails great computational expense. In some geometries, SBM allows similarity solutions, though computational methods are generally required. The use of SBM as an approximation to FAD when a system is "nearly classical'' is also explored. The second portion of this Dissertation concerns spin-drying, which is an experimental approach to biopreservation in a laboratory setting. A biospecimen is adhered to a glass wafer and this substrate is covered with sugar solution and rapidly spun on a turntable while water is evaporated from the film surface. The mathematical model for the spin-drying process includes diffusion, viscous fluid flow, and evaporation, among other contributions to the dynamics. Lubrication theory is applied to the model and an
Energy Technology Data Exchange (ETDEWEB)
Schlichting, Hermann [Technische Univ. Braunschweig (Germany). Inst. fuer Stroemungsmechanik; Gersten, Klaus [Bochum Univ. (Germany). Lehrstuhl fuer Thermodynamik und Stroemungsmechanik
2017-03-01
This new edition of the near-legendary textbook by Schlichting and revised by Gersten presents a comprehensive overview of boundary-layer theory and its application to all areas of fluid mechanics, with particular emphasis on the flow past bodies (e.g. aircraft aerodynamics). The new edition features an updated reference list and over 100 additional changes throughout the book, reflecting the latest advances on the subject.
Riemann surfaces with boundaries and string theory
International Nuclear Information System (INIS)
Morozov, A.Yu.; Roslyj, A.A.
1989-01-01
A consideration of the cutting and joining operations for Riemann surfaces permits one to express the functional integral on a Riemann surface in terms of integrals over its pieces which are suarfaces with boundaries. This yields an expression for the determinant of the Laplacian on a Riemann surface in terms of Krichever maps for its pieces. Possible applications of the methods proposed to a study of the string perturbation theory in terms of an universal moduli space are mentioned
Boundary operators in effective string theory
Energy Technology Data Exchange (ETDEWEB)
Hellerman, Simeon [Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo,Kashiwa, Chiba 277-8582 (Japan); Swanson, Ian [Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo,Kashiwa, Chiba 277-8582 (Japan)
2017-04-13
Various universal features of relativistic rotating strings depend on the organization of allowed local operators on the worldsheet. In this paper, we study the set of Neumann boundary operators in effective string theory, which are relevant for the controlled study of open relativistic strings with freely moving endpoints. Relativistic open strings are thought to encode the dynamics of confined quark-antiquark pairs in gauge theories in the planar approximation. Neumann boundary operators can be organized by their behavior under scaling of the target space coordinates X{sup μ}, and the set of allowed X-scaling exponents is bounded above by +1/2 and unbounded below. Negative contributions to X-scalings come from powers of a single invariant, or “dressing' operator, which is bilinear in the embedding coordinates. In particular, we show that all Neumann boundary operators are dressed by quarter-integer powers of this invariant, and we demonstrate how this rule arises from various ways of regulating the short-distance singularities of the effective theory.
Asymptotic boundary value problems for evolution inclusions
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
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.
On the solvability of initial boundary value problems for nonlinear ...
African Journals Online (AJOL)
In this paper, we study the initial boundary value problems for a non-linear time dependent Schrödinger equation with Dirichlet and Neumann boundary conditions, respectively. We prove the existence and uniqueness of solutions of the initial boundary value problems by using Galerkin's method. Keywords: Initial boundary ...
Grain Boundaries From Theory to Engineering
Priester, Louisette
2013-01-01
Grain boundaries are a main feature of crystalline materials. They play a key role in determining the properties of materials, especially when grain size decreases and even more so with the current improvements of processing tools and methods that allow us to control various elements in a polycrystal. This book presents the theoretical basis of the study of grain boundaries and aims to open up new lines of research in this area. The treatment is light on mathematical approaches while emphasizing practical examples; the issues they raise are discussed with reference to theories. The general approach of the book has two main goals: to lead the reader from the concept of ‘ideal’ to ‘real’ grain boundaries; to depart from established knowledge and address the opportunities emerging through "grain boundary engineering", the control of morphological and crystallographic features that affect material properties. The book is divided in three parts: I ‘From interganular order to disorder’ deals wit...
The use of MACSYMA for solving elliptic boundary value problems
Thejll, Peter; Gilbert, Robert P.
1990-01-01
A boundary method is presented for the solution of elliptic boundary value problems. An approach based on the use of complete systems of solutions is emphasized. The discussion is limited to the Dirichlet problem, even though the present method can possibly be adapted to treat other boundary value problems.
Bifurcation of solutions to Hamiltonian boundary value problems
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.
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)
Parallel algorithms for boundary value problems
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.
Positive solutions for a fourth order boundary value problem
Directory of Open Access Journals (Sweden)
Bo Yang
2005-02-01
Full Text Available We consider a boundary value problem for the beam equation, in which the boundary conditions mean that the beam is embedded at one end and free at the other end. Some new estimates to the positive solutions to the boundary value problem are obtained. Some sufficient conditions for the existence of at least one positive solution for the boundary value problem are established. An example is given at the end of the paper to illustrate the main results.
Unsolved problems in number theory
Guy, Richard K
1994-01-01
Unsolved Problems in Number Theory contains discussions of hundreds of open questions, organized into 185 different topics. They represent numerous aspects of number theory and are organized into six categories: prime numbers, divisibility, additive number theory, Diophantine equations, sequences of integers, and miscellaneous. To prevent repetition of earlier efforts or duplication of previously known results, an extensive and up-to-date collection of references follows each problem. In the second edition, not only extensive new material has been added, but corrections and additions have been included throughout the book.
State-dependent impulses boundary value problems on compact interval
Rachůnková, Irena
2015-01-01
This book offers the reader a new approach to the solvability of boundary value problems with state-dependent impulses and provides recently obtained existence results for state dependent impulsive problems with general linear boundary conditions. It covers fixed-time impulsive boundary value problems both regular and singular and deals with higher order differential equations or with systems that are subject to general linear boundary conditions. We treat state-dependent impulsive boundary value problems, including a new approach giving effective conditions for the solvability of the Dirichlet problem with one state-dependent impulse condition and we show that the depicted approach can be extended to problems with a finite number of state-dependent impulses. We investigate the Sturm–Liouville boundary value problem for a more general right-hand side of a differential equation. Finally, we offer generalizations to higher order differential equations or differential systems subject to general linear boundary...
Free boundary problems in PDEs and particle systems
Carinci, Gioia; Giardinà, Cristian; Presutti, Errico
2016-01-01
In this volume a theory for models of transport in the presence of a free boundary is developed. Macroscopic laws of transport are described by PDE's. When the system is open, there are several mechanisms to couple the system with the external forces. Here a class of systems where the interaction with the exterior takes place in correspondence of a free boundary is considered. Both continuous and discrete models sharing the same structure are analysed. In Part I a free boundary problem related to the Stefan Problem is worked out in all details. For this model a new notion of relaxed solution is proposed for which global existence and uniqueness is proven. It is also shown that this is the hydrodynamic limit of the empirical mass density of the associated particle system. In Part II several other models are discussed. The expectation is that the results proved for the basic model extend to these other cases. All the models discussed in this volume have an interest in problems arising in several research fields...
Elasticity problems in domains with nonsmooth boundaries
International Nuclear Information System (INIS)
Esparza, David
2001-01-01
In the present work we study the behaviour of elastic stress fields in domains with non-regular boundaries. We consider three-dimensional problems in elastic media with thin conical defects (inclusions or cavities) and analyse the stress singularity at their vertices. To construct asymptotic expansions for the stress and displacement fields in terms of a small parameter ε related to the 'thickness' of the defect, we employ a technique based on the work by Kondrat'ev, Maz'ya, Nazarov and Plamenevskii. We first study the stress distribution in an elastic body with a thin conical notch. We derive an asymptotic representation for the stress singularity exponent by reducing the original problem to a spectral problem for a 9x9 matrix. The elements of this matrix are found to depend upon the geometry of the cross-section of the notch and the elastic properties of the medium. We specify the sets of eigenvalues and the corresponding eigenvectors for a circular, elliptical, 'triangular' and 'square' cross-section, and show that the strongest singularity is associated with the 'triangular' cross-section, and is generated by a non-axisymmetric load. We then analyse the stress distribution near a thin conical inclusion which is allowed to slide freely along its axis. We derive the representation for the stress singularity exponent for the case of a circular conical inclusion whose elastic properties differ from those of the medium. In the last chapter we study the stress distribution in the vicinity of a thin 'coated' conical inclusion. We show that a soft thin coating (perfectly bonded to the inclusion and the surrounding material) can be replaced by a so-called linear interface at which the normal displacement is discontinuous, and the stresses are proportional to the 'jump' in the normal displacement across the coating. We analyse the effect of the properties of the coating on the stress singularity exponent and compare the results with those for a perfectly bonded
Heat Kernel Asymptotics of Zaremba Boundary Value Problem
Energy Technology Data Exchange (ETDEWEB)
Avramidi, Ivan G. [Department of Mathematics, New Mexico Institute of Mining and Technology (United States)], E-mail: iavramid@nmt.edu
2004-03-15
The Zaremba boundary-value problem is a boundary value problem for Laplace-type second-order partial differential operators acting on smooth sections of a vector bundle over a smooth compact Riemannian manifold with smooth boundary but with discontinuous boundary conditions, which include Dirichlet boundary conditions on one part of the boundary and Neumann boundary conditions on another part of the boundary. We study the heat kernel asymptotics of Zaremba boundary value problem. The construction of the asymptotic solution of the heat equation is described in detail and the heat kernel is computed explicitly in the leading approximation. Some of the first nontrivial coefficients of the heat kernel asymptotic expansion are computed explicitly.
Boundary-value problems in ODE
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
Unitarity problems in 3D gravity theories
Alkac, Gokhan; Basanisi, Luca; Kilicarslan, Ercan; Tekin, Bayram
2017-07-01
We revisit the problem of the bulk-boundary unitarity clash in 2 +1 -dimensional gravity theories, which has been an obstacle in providing a viable dual two-dimensional conformal field theory for bulk gravity in anti-de Sitter (AdS) spacetime. Chiral gravity, which is a particular limit of cosmological topologically massive gravity (TMG), suffers from perturbative log-modes with negative energies inducing a nonunitary logarithmic boundary field theory. We show here that any f (R ) extension of TMG does not improve the situation. We also study the perturbative modes in the metric formulation of minimal massive gravity—originally constructed in a first-order formulation—and find that the massive mode has again negative energy except in the chiral limit. We comment on this issue and also discuss a possible solution to the problem of negative-energy modes. In any of these theories, the infinitesimal dangerous deformations might not be integrable to full solutions; this suggests a linearization instability of AdS spacetime in the direction of the perturbative log-modes.
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)
Potential Theory Surveys and Problems
Lukeš, Jaroslav; Netuka, Ivan; Veselý, Jiří
1988-01-01
The volume comprises eleven survey papers based on survey lectures delivered at the Conference in Prague in July 1987, which covered various facets of potential theory, including its applications in other areas. The survey papers deal with both classical and abstract potential theory and its relations to partial differential equations, stochastic processes and other branches such as numerical analysis and topology. A collection of problems from potential theory, compiled on the occasion of the conference, is included, with additional commentaries, in the second part of this volume.
Boundary states in c=-2 logarithmic conformal field theory
International Nuclear Information System (INIS)
Bredthauer, Andreas; Flohr, Michael
2002-01-01
Starting from first principles, a constructive method is presented to obtain boundary states in conformal field theory. It is demonstrated that this method is well suited to compute the boundary states of logarithmic conformal field theories. By studying the logarithmic conformal field theory with central charge c=-2 in detail, we show that our method leads to consistent results. In particular, it allows to define boundary states corresponding to both, indecomposable representations as well as their irreducible subrepresentations
Collection of problems in transport theory
International Nuclear Information System (INIS)
Kaper, H.G.
1975-01-01
Problems presented are: (1) definition of transport operators; (2) relation between the integro-differential and integral form of the transport equation; (3) asymptotic behavior of the scalar density near curved boundaries and interfaces; (4) singularities at a corner; (5) regularity of the solution of the transport equation; (7) transport equations on a manifold; (8) numerical analysis; (9) cubature; (10) point spectrum of the transport operator; (11) convergence of the multigroup approximation; (12) convergence of discrete ordinates approximations; (13) the finite double-norm property; (14) convergence of discrete ordinates approximation. The presentation of the problems is intended to direct attention to gaps in the existing knowledge of transport theory and to stimulate research into new areas of transport theory
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.
Boundary effects in super-Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Shah, Mushtaq B.; Ganai, Prince A. [National Institute of Technology, Department of Physics, Srinagar, Kashmir (India); Faizal, Mir [University of British Columbia-Okanagan, Irving K. Barber School of Arts and Sciences, Kelowna, BC (Canada); University of Lethbridge, Department of Physics and Astronomy, Alberta (Canada); Zaz, Zaid [University of Kashmir, Department of Electronics and Communication Engineering, Srinagar, Kashmir (India); Bhat, Anha [National Institute of Technology, Department of Metallurgical and Materials Engineering, Srinagar, Kashmir (India); Masood, Syed [International Islamic University, Department of Physics, Islamabad (Pakistan)
2017-05-15
In this paper, we shall analyze a three dimensional supersymmetry theory with N = 2 supersymmetry. We will analyze the quantization of this theory, in the presence of a boundary. The effective Lagrangian used in the path integral quantization of this theory, will be given by the sum of the gauge fixing term and the ghost term with the original classical Lagrangian. Even though the supersymmetry of this effective Lagrangian will also be broken due to the presence of a boundary, it will be demonstrated that half of the supersymmetry of this theory can be preserved by adding a boundary Lagrangian to the effective bulk Lagrangian. The supersymmetric transformation of this new boundary Lagrangian will exactly cancel the boundary term generated from the supersymmetric transformation of the effective bulk Lagrangian. We will analyze the Slavnov-Taylor identity for this N = 2 Yang-Mills theory with a boundary. (orig.)
Boundary effects in super-Yang-Mills theory
International Nuclear Information System (INIS)
Shah, Mushtaq B.; Ganai, Prince A.; Faizal, Mir; Zaz, Zaid; Bhat, Anha; Masood, Syed
2017-01-01
In this paper, we shall analyze a three dimensional supersymmetry theory with N = 2 supersymmetry. We will analyze the quantization of this theory, in the presence of a boundary. The effective Lagrangian used in the path integral quantization of this theory, will be given by the sum of the gauge fixing term and the ghost term with the original classical Lagrangian. Even though the supersymmetry of this effective Lagrangian will also be broken due to the presence of a boundary, it will be demonstrated that half of the supersymmetry of this theory can be preserved by adding a boundary Lagrangian to the effective bulk Lagrangian. The supersymmetric transformation of this new boundary Lagrangian will exactly cancel the boundary term generated from the supersymmetric transformation of the effective bulk Lagrangian. We will analyze the Slavnov-Taylor identity for this N = 2 Yang-Mills theory with a boundary. (orig.)
A two-dimensional embedded-boundary method for convection problems with moving boundaries
Y.J. Hassen (Yunus); B. Koren (Barry)
2010-01-01
htmlabstractIn this work, a two-dimensional embedded-boundary algorithm for convection problems is presented. A moving body of arbitrary boundary shape is immersed in a Cartesian finite-volume grid, which is fixed in space. The boundary surface is reconstructed in such a way that only certain fluxes
Uniqueness of solution to a stationary boundary kinetic problem
International Nuclear Information System (INIS)
Zhykharsky, A.V.
1992-01-01
The paper treats the question of uniqueness of solution to the boundary kinetic problem. This analysis is based on the accurate solutions to the stationary one-dimensional boundary kinetic problem for the limited plasma system. In the paper a simplified problem statement is used (no account is taken of the external magnetic field, a simplest form of boundary conditions is accepted) which, however, covers all features of the problem considered. Omitting the details of the conclusion we will write a set of Vlasov stationary kinetic equations for the cases of plane, cylindrical and spherical geometry of the problem. (author) 1 ref
METHOD OF GREEN FUNCTIONS IN MATHEMATICAL MODELLING FOR TWO-POINT BOUNDARY-VALUE PROBLEMS
Directory of Open Access Journals (Sweden)
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.
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
Boundary Hamiltonian Theory for Gapped Topological Orders
Hu, Yuting; Wan, Yidun; Wu, Yong-Shi
2017-06-01
We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by (bi-) modules over Frobenius algebras.
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.
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
State space approach to mixed boundary value problems.
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.
A Duality Approach for the Boundary Variation of Neumann Problems
DEFF Research Database (Denmark)
Bucur, Dorin; Varchon, Nicolas
2002-01-01
In two dimensions, we study the stability of the solution of an elliptic equation with Neumann boundary conditions for nonsmooth perturbations of the geometric domain. Using harmonic conjugates, we relate this problem to the shape stability of the solution of an elliptic equation with Dirichlet b...... boundary conditions. As a particular case, we prove the stability of the solution under a topological constraint ( uniform number of holes), which is analogous to Sverak's result for Dirichlet boundary conditions....
A duality approach or the boundary variation of Neumann problems
DEFF Research Database (Denmark)
Bucur, D.; Varchon, Nicolas
2002-01-01
In two dimensions, we study the stability of the solution of an elliptic equation with Neumann boundary conditions for nonsmooth perturbations of the geometric domain. Using harmonic conjugates, we relate this problem to the shape stability of the solution of an elliptic equation with Dirichlet b...... boundary conditions. As a particular case, we prove the stability of the solution under a topological constraint ( uniform number of holes), which is analogous to Sverak's result for Dirichlet boundary conditions....
Twisted boundary conditions: a non-perturbative probe for pure non-abelian gauge theories
International Nuclear Information System (INIS)
Baal, P. van.
1984-01-01
In this thesis the author describes a pure non-abelian gauge theory on the hypertorus with gauge group SU(N). To test the flux tube picture he has studied the large distance limit of this theory, leading to a large coupling constant. To tackle this problem, he describes two approaches, in both of which twisted boundary conditions play an important role. (Auth.)
Boundary Value Problems and Approximate Solutions
African Journals Online (AJOL)
Tadesse
Department of Mathematics, College of Natural and Computational Scineces, Mekelle ..... In this section, the Variational Iteration Method is applied to different forms of .... Some problems in non-Newtonian fluid mechanics, Ph.D. thesis, Wales.
The boundary value problem for discrete analytic functions
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.
Stability of boundary layer flow based on energy gradient theory
Dou, Hua-Shu; Xu, Wenqian; Khoo, Boo Cheong
2018-05-01
The flow of the laminar boundary layer on a flat plate is studied with the simulation of Navier-Stokes equations. The mechanisms of flow instability at external edge of the boundary layer and near the wall are analyzed using the energy gradient theory. The simulation results show that there is an overshoot on the velocity profile at the external edge of the boundary layer. At this overshoot, the energy gradient function is very large which results in instability according to the energy gradient theory. It is found that the transverse gradient of the total mechanical energy is responsible for the instability at the external edge of the boundary layer, which induces the entrainment of external flow into the boundary layer. Within the boundary layer, there is a maximum of the energy gradient function near the wall, which leads to intensive flow instability near the wall and contributes to the generation of turbulence.
On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation
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.
Determination of free boundary problem of flow through porous media
International Nuclear Information System (INIS)
Tavares Junior, H.M.; Souza, A.J. de
1989-01-01
This paper deals with a free boundary problem of flow through porous media, which is solved by simplicial method conbined with mesh refinement. Variational method on fixed domain is utilized. (author)
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.
APPLICATION OF BOUNDARY INTEGRAL EQUATION METHOD FOR THERMOELASTICITY PROBLEMS
Directory of Open Access Journals (Sweden)
Vorona Yu.V.
2015-12-01
Full Text Available Boundary Integral Equation Method is used for solving analytically the problems of coupled thermoelastic spherical wave propagation. The resulting mathematical expressions coincide with the solutions obtained in a conventional manner.
On a non-linear pseudodifferential boundary value problem
International Nuclear Information System (INIS)
Nguyen Minh Chuong.
1989-12-01
A pseudodifferential boundary value problem for operators with symbols taking values in Sobolev spaces and with non-linear right-hand side was studied. Existence and uniqueness theorems were proved. (author). 11 refs
Boundary effects on quantum field theories
International Nuclear Information System (INIS)
Lee, Tae Hoon
1991-01-01
Quantum field theory in the S 1 *R 3 space-time is simply described by the imaginary time formalism. We generalize Schwinger-DeWitt proper-time technique which is very useful in zero temperature field theories to this case. As an example we calculate the one-loop effective potential of the finite temperature scala field theory by this technique.(Author)
Classically integrable boundary conditions for affine Toda field theories
International Nuclear Information System (INIS)
Bowcock, P.; Corrigan, E.; Dorey, P.E.; Rietdijk, R.H.
1995-01-01
Boundary conditions compatible with classical integrability are studied both directly, using an approach based on the explicit construction of conserved quantities, and indirectly by first developing a generalisation of the Lax pair idea. The latter approach is closer to the spirit of earlier work by Sklyanin and yields a complete set of conjectures for permissible boundary conditions for any affine Toda field theory. (orig.)
International Nuclear Information System (INIS)
Ishimoto, Yukitaka
2004-01-01
Amongst conformal field theories, there exist logarithmic conformal field theories such as c p,1 models. We have investigated c p,q models with a boundary in search of logarithmic theories and have found logarithmic solutions of two-point functions in the context of the Coulomb gas picture. We have also found the relations between coefficients in the two-point functions and correlation functions of logarithmic boundary operators, and have confirmed the solutions in [hep-th/0003184]. Other two-point functions and boundary operators have also been studied in the free boson construction of boundary CFT with SU(2) k symmetry in regard to logarithmic theories. This paper is based on a part of D. Phil. Thesis [hep-th/0312160]. (author)
Mixed global anomalies and boundary conformal field theories
Numasawa, Tokiro; Yamaguchi, Satoshi
2017-01-01
We consider the relation of mixed global gauge gravitational anomalies and boundary conformal field theory in WZW models for simple Lie groups. The discrete symmetries of consideration are the centers of the simple Lie groups. These mixed anomalies prevent to gauge them i.e, take the orbifold by the center. The absence of anomalies impose conditions on the levels of WZW models. Next, we study the conformal boundary conditions for the original theories. We consider the existence of a conformal...
Sewing constraints for conformal field theories on surfaces with boundaries
International Nuclear Information System (INIS)
Lewellen, D.C.
1992-01-01
In a conformal field theory, correlation functions on any Riemann surface are in principle unambiguously defined by sewing together three-point functions on the sphere, provided that the four-point functions on the sphere are crossing symmetric, and the one-point functions on the torus are modular covariant. In this work we extend Sonoda's proof of this result to conformal field theories defined on surfaces with boundaries. Four additional sewing constraints arise; three on the half-plane and one on the cylinder. These relate the various OPE coefficients in the theory (bulk, boundary, and bulk-boundary) to one another. In rational theories these relations can be expressed in terms of data arising solely within the bulk theory: The matrix S which implements modular transformations on the characters, and the matrices implementing duality transformations on the four-point conformal-block functions. As an example we solve these relations for the boundary and bulk-boundary structure constants in the Ising model with all possible conformally invariant boundary conditions. The role of the basic sewing constraints in the construction of open string theories is discussed. (orig.)
Turbulent Boundary Layers - Experiments, Theory and Modelling
1980-01-01
anemometry, London, Academic Press, 1976. 7. H.R.E. van Maanen, K. van der Molen and J. Blom, "Reduction of ambiguity noise in laser-Doppler...Raumfahrttechnik Hochschule der Bundeswehr München 8014 Neubiberg — Germany Professor Dr J.L. Van Ingen Dept. of Aerospace Engineering Delft...proximity to a solid boundary. J.Fluid Mech.12, 388 - 397, 1962. (21) Van Thin N., Messungen mit einem Hitzdraht in einer turbulenten Strömung in der
Boundary value problems and Fourier expansions
MacCluer, Charles R
2004-01-01
Based on modern Sobolev methods, this text for advanced undergraduates and graduate students is highly physical in its orientation. It integrates numerical methods and symbolic manipulation into an elegant viewpoint that is consonant with implementation by digital computer. The first five sections form an informal introduction that develops students' physical and mathematical intuition. The following section introduces Hilbert space in its natural environment, and the next six sections pose and solve the standard problems. The final seven sections feature concise introductions to selected topi
Effect of elastic boundaries in hydrostatic problems
Volobuev, A. N.; Tolstonogov, A. P.
2010-03-01
The possibility and conditions of use of the Bernoulli equation for description of an elastic pipeline were considered. It is shown that this equation is identical in form to the Bernoulli equation used for description of a rigid pipeline. It has been established that the static pressure entering into the Bernoulli equation is not identical to the pressure entering into the impulse-momentum equation. The hydrostatic problem on the pressure distribution over the height of a beaker with a rigid bottom and elastic walls, filled with a liquid, was solved.
Discontinuous Sturm-Liouville Problems with Eigenvalue Dependent Boundary Condition
Energy Technology Data Exchange (ETDEWEB)
Amirov, R. Kh., E-mail: emirov@cumhuriyet.edu.tr; Ozkan, A. S., E-mail: sozkan@cumhuriyet.edu.tr [Cumhuriyet University, Department of Mathematics Faculty of Art and Science (Turkey)
2014-12-15
In this study, an inverse problem for Sturm-Liouville differential operators with discontinuities is studied when an eigenparameter appears not only in the differential equation but it also appears in the boundary condition. Uniqueness theorems of inverse problems according to the Prüfer angle, the Weyl function and two different eigenvalues sets are proved.
Parametrices and exact paralinearization of semi-linear boundary problems
DEFF Research Database (Denmark)
Johnsen, Jon
2008-01-01
The subject is parametrices for semi-linear problems, based on parametrices for linear boundary problems and on non-linearities that decompose into solution-dependent linear operators acting on the solutions. Non-linearities of product type are shown to admit this via exact paralinearization...... of homogeneous distributions, tensor products and halfspace extensions have been revised. Examples include the von Karman equation....
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) + ...
Twisted boundary states in c=1 coset conformal field theories
International Nuclear Information System (INIS)
Ishikawa, Hiroshi; Yamaguchi, Atsushi
2003-01-01
We study the mutual consistency of twisted boundary conditions in the coset conformal field theory G/H. We calculate the overlap of the twisted boundary states of G/H with the untwisted ones, and show that the twisted boundary states are consistently defined in the charge-conjugation modular invariant. The overlap of the twisted boundary states is expressed by the branching functions of a twisted affine Lie algebra. As a check of our argument, we study the diagonal coset theory so(2n) 1 +so(2n) 1 /so(2n) 2 , which is equivalent to the orbifold S 1 /Z 2 at a particular radius. We construct the boundary states twisted by the automorphisms of the unextended Dynkin diagram of so(2n), and show their mutual consistency by identifying their counterpart in the orbifold. For the triality of so(8), the twisted states of the coset theory correspond to neither the Neumann nor the Dirichlet boundary states of the orbifold and yield conformal boundary states that preserve only the Virasoro algebra. (author)
Bayesian decision theory : A simple toy problem
van Erp, H.R.N.; Linger, R.O.; van Gelder, P.H.A.J.M.
2016-01-01
We give here a comparison of the expected outcome theory, the expected utility theory, and the Bayesian decision theory, by way of a simple numerical toy problem in which we look at the investment willingness to avert a high impact low probability event. It will be found that for this toy problem
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.
A finite difference method for free boundary problems
Fornberg, Bengt
2010-04-01
Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems. © 2009 Elsevier B.V. All rights reserved.
Modified Differential Transform Method for Two Singular Boundary Values Problems
Directory of Open Access Journals (Sweden)
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.
Positive solutions and eigenvalues of nonlocal boundary-value problems
Directory of Open Access Journals (Sweden)
Jifeng Chu
2005-07-01
Full Text Available We study the ordinary differential equation $x''+lambda a(tf(x=0$ with the boundary conditions $x(0=0$ and $x'(1=int_{eta}^{1}x'(sdg(s$. We characterize values of $lambda$ for which boundary-value problem has a positive solution. Also we find appropriate intervals for $lambda$ so that there are two positive solutions.
Uniqueness in some higher order elliptic boundary value problems in n dimensional domains
Directory of Open Access Journals (Sweden)
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.
Heading off boundary problems: clinical supervision as risk management.
Walker, R; Clark, J J
1999-11-01
The effective management of risk in clinical practice includes steps to limit harm to clients resulting from ethical violations or professional misconduct. Boundary problems constitute some of the most damaging ethical violations. The authors propose an active use of clinical supervision to anticipate and head off possible ethical violations by intervening when signs of boundary problems appear. The authors encourage a facilitative, Socratic method, rather than directive approaches, to help supervisees maximize their learning about ethical complexities. Building on the idea of a slippery slope, in which seemingly insignificant acts can lead to unethical patterns of behavior, the authors discuss ten cues to potential boundary problems, including strong feelings about a client; extended sessions with clients; gift giving between clinician and client; loans, barter, and sale of goods; clinician self-disclosures; and touching and sex. The authors outline supervisory interventions to be made when the cues are detected.
Problems and Perspectives of Life Management Theory
Hirata, Michinori
2001-01-01
This paper examines the problems of life management theory and shows the directions of researches in this field. I examine the directions of research in home management theory, which is antecedents of life management theory. There are three directions of research in home management theory. The first direction is to make clear the problems of people's family lives in terms of time use, money expenditure, family relations and so on. The second direction is to examine the home management itself....
Applying Lakatos' Theory to the Theory of Mathematical Problem Solving.
Nunokawa, Kazuhiko
1996-01-01
The relation between Lakatos' theory and issues in mathematics education, especially mathematical problem solving, is investigated by examining Lakatos' methodology of a scientific research program. (AIM)
The Dirichlet problem with L2-boundary data for elliptic linear equations
Chabrowski, Jan
1991-01-01
The Dirichlet problem has a very long history in mathematics and its importance in partial differential equations, harmonic analysis, potential theory and the applied sciences is well-known. In the last decade the Dirichlet problem with L2-boundary data has attracted the attention of several mathematicians. The significant features of this recent research are the use of weighted Sobolev spaces, existence results for elliptic equations under very weak regularity assumptions on coefficients, energy estimates involving L2-norm of a boundary data and the construction of a space larger than the usual Sobolev space W1,2 such that every L2-function on the boundary of a given set is the trace of a suitable element of this space. The book gives a concise account of main aspects of these recent developments and is intended for researchers and graduate students. Some basic knowledge of Sobolev spaces and measure theory is required.
Boundary-layer theory, strong-coupling series, and large-order behavior
International Nuclear Information System (INIS)
Bender, Carl M.; Pelster, Axel; Weissbach, Florian
2002-01-01
The introduction of a lattice converts a singular boundary-layer problem in the continuum into a regular perturbation problem. However, the continuum limit of the discrete problem is extremely nontrivial and is not completely understood. This article examines two singular boundary-layer problems taken from mathematical physics, the instanton problem and the Blasius equation, and in each case examines two strategies, Pade resummation and variational perturbation theory, to recover the solution to the continuum problem from the solution to the associated discrete problem. Both resummation procedures produce good and interesting results for the two cases, but the results still deviate from the exact solutions. To understand the discrepancy a comprehensive large-order behavior analysis of the strong-coupling lattice expansions for each of the two problems is done
Nonlinear Elliptic Boundary Value Problems at Resonance with Nonlinear Wentzell Boundary Conditions
Directory of Open Access Journals (Sweden)
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.
Inverse problems in linear transport theory
International Nuclear Information System (INIS)
Dressler, K.
1988-01-01
Inverse problems for a class of linear kinetic equations are investigated. The aim is to identify the scattering kernel of a transport equation (corresponding to the structure of a background medium) by observing the 'albedo' part of the solution operator for the corresponding direct initial boundary value problem. This means to get information on some integral operator in an integrodifferential equation through on overdetermined boundary value problem. We first derive a constructive method for solving direct halfspace problems and prove a new factorization theorem for the solutions. Using this result we investigate stationary inverse problems with respect to well posedness (e.g. reduce them to classical ill-posed problems, such as integral equations of first kind). In the time-dependent case we show that a quite general inverse problem is well posed and solve it constructively. (orig.)
Boundary value problem for Caputo-Hadamard fractional differential equations
Directory of Open Access Journals (Sweden)
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.
Bibliography on moving boundary problems with key word index
International Nuclear Information System (INIS)
Wilson, D.G.; Solomon, A.D.; Trent, J.S.
1979-10-01
This bibliography concentrates mainly on time-dependent moving-boundary problems of heat and mass transfer. The bibliography is in two parts, a list of the references ordered by last name of the first author and a key word index to the titles. Few references from before 1965 are included
Boundary conditions for free surface inlet and outlet problems
Taroni, M.; Breward, C. J. W.; Howell, P. D.; Oliver, J. M.
2012-01-01
We investigate and compare the boundary conditions that are to be applied to free-surface problems involving inlet and outlets of Newtonian fluid, typically found in coating processes. The flux of fluid is a priori known at an inlet, but unknown
Fourth-order discrete anisotropic boundary-value problems
Directory of Open Access Journals (Sweden)
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.
Bibliography on moving boundary problems with key word index
Energy Technology Data Exchange (ETDEWEB)
Wilson, D.G.; Solomon, A.D.; Trent, J.S.
1979-10-01
This bibliography concentrates mainly on time-dependent moving-boundary problems of heat and mass transfer. The bibliography is in two parts, a list of the references ordered by last name of the first author and a key word index to the titles. Few references from before 1965 are included. (RWR)
Operator approximant problems arising from quantum theory
Maher, Philip J
2017-01-01
This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.
Reconstruction of boundary conditions from internal conditions using viability theory
Hofleitner, Aude; Claudel, Christian G.; Bayen, Alexandre M.
2012-01-01
This article presents a method for reconstructing downstream boundary conditions to a HamiltonJacobi partial differential equation for which initial and upstream boundary conditions are prescribed as piecewise affine functions and an internal condition is prescribed as an affine function. Based on viability theory, we reconstruct the downstream boundary condition such that the solution of the Hamilton-Jacobi equation with the prescribed initial and upstream conditions and reconstructed downstream boundary condition satisfies the internal value condition. This work has important applications for estimation in flow networks with unknown capacity reductions. It is applied to urban traffic, to reconstruct signal timings and temporary capacity reductions at intersections, using Lagrangian sensing such as GPS devices onboard vehicles.
Reconstruction of boundary conditions from internal conditions using viability theory
Hofleitner, Aude
2012-06-01
This article presents a method for reconstructing downstream boundary conditions to a HamiltonJacobi partial differential equation for which initial and upstream boundary conditions are prescribed as piecewise affine functions and an internal condition is prescribed as an affine function. Based on viability theory, we reconstruct the downstream boundary condition such that the solution of the Hamilton-Jacobi equation with the prescribed initial and upstream conditions and reconstructed downstream boundary condition satisfies the internal value condition. This work has important applications for estimation in flow networks with unknown capacity reductions. It is applied to urban traffic, to reconstruct signal timings and temporary capacity reductions at intersections, using Lagrangian sensing such as GPS devices onboard vehicles.
An initial boundary value problem for modeling a piezoelectric dipolar body
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.
IMPSOR, 3-D Boundary Problems Solution for Thermal Conductivity Calculation
International Nuclear Information System (INIS)
Wilson, D.G.; Williams, M.A.
1994-01-01
1 - Description of program or function: IMPSOR implements finite difference methods for multidimensional moving boundary problems with Dirichlet or Neumann boundary conditions. The geometry of the spatial domain is a rectangular parallelepiped with dimensions specified by the user. Dirichlet or Neumann boundary conditions may be specified on each face of the box independently. The user defines the initial and boundary conditions as well as the thermal and physical properties of the problem and several parameters for the numerical method, e.g. degree of implicitness, time-step size. 2 - Method of solution: The spatial domain is partitioned and the governing equation discretized, which yields a nonlinear system of equations at each time-step. This nonlinear system is solved using a successive over-relaxation (SOR) algorithm. For a given node, the previous iteration's temperature and thermal conductivity values are used for advanced points with current values at previous points. This constitutes a Gauss-Seidel iteration. Most of the computing time used by the numerical method is spent in the iterative solution of the nonlinear system. The SOR scheme employed is designed to accommodate vectorization on a Cray X-MP. 3 - Restrictions on the complexity of the problem: Maximum of 70,000 nodes
Zero-energy eigenstates for the Dirac boundary problem
International Nuclear Information System (INIS)
Hortacsu, M.; Rothe, K.D.; Schroer, B.
1980-01-01
As an alternative to the method of spherical compactification for the Dirac operator in instanton background fields we study the correct method of 'box-quantization': the Atiyah-Patodi-Singer spectral boundary condition. This is the only self-adjoint boundary condition which respects the charge conjugation property and the γ 5 symmetry, apart form the usual breaking due to zero modes. We point out the relevance of this approach to the computation of instanton determinants and other problems involving Dirac spinors. (orig.)
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)
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
Atmospheric boundary layers in storms: advanced theory and modelling applications
Directory of Open Access Journals (Sweden)
S. S. Zilitinkevich
2005-01-01
Full Text Available Turbulent planetary boundary layers (PBLs control the exchange processes between the atmosphere and the ocean/land. The key problems of PBL physics are to determine the PBL height, the momentum, energy and matter fluxes at the surface and the mean wind and scalar profiles throughout the layer in a range of regimes from stable and neutral to convective. Until present, the PBLs typical of stormy weather were always considered as neutrally stratified. Recent works have disclosed that such PBLs are in fact very strongly affected by the static stability of the free atmosphere and must be treated as factually stable (we call this type of the PBL "conventionally neutral" in contract to the "truly neutral" PBLs developed against the neutrally stratified free flow. It is common knowledge that basic features of PBLs exhibit a noticeable dependence on the free-flow static stability and baroclinicity. However, the concern of the traditional theory of neural and stable PBLs was almost without exception the barotropic nocturnal PBL, which develops at mid latitudes during a few hours in the night, on the background of a neutral or slightly stable residual layer. The latter separates this type of the PBL from the free atmosphere. It is not surprising that the nature of turbulence in such regimes is basically local and does not depend on the properties of the free atmosphere. Alternatively, long-lived neutral (in fact only conditionally neutral or stable PBLs, which have much more time to grow up, are placed immediately below the stably stratified free flow. Under these conditions, the turbulent transports of momentum and scalars even in the surface layer - far away from the PBL outer boundary - depend on the free-flow Brunt-Väisälä frequency, N. Furthermore, integral measures of the long-lived PBLs (their depths and the resistance law functions depend on N and also on the baroclinic shear, S. In the traditional PBL models both non-local parameters N and S
Asymptotic boundary conditions for dissipative waves: General theory
Hagstrom, Thomas
1990-01-01
An outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.
Asymptotic boundary conditions for dissipative waves - General theory
Hagstrom, Thomas
1991-01-01
An outstanding issue in computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.
Experimental demonstration of the Rayleigh acoustic viscous boundary layer theory.
Castrejón-Pita, J R; Castrejón-Pita, A A; Huelsz, G; Tovar, R
2006-03-01
Amplitude and phase velocity measurements on the laminar oscillatory viscous boundary layer produced by acoustic waves are presented. The measurements were carried out in acoustic standing waves in air with frequencies of 68.5 and 114.5 Hz using laser Doppler anemometry and particle image velocimetry. The results obtained by these two techniques are in good agreement with the predictions made by the Rayleigh viscous boundary layer theory and confirm the existence of a local maximum of the velocity amplitude and its expected location.
Analytic Solution to Shell Boundary – Value Problems
Directory of Open Access Journals (Sweden)
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.
New Theories on Boundary Layer Transition and Turbulence Formation
Directory of Open Access Journals (Sweden)
Chaoqun Liu
2012-01-01
Full Text Available This paper is a short review of our recent DNS work on physics of late boundary layer transition and turbulence. Based on our DNS observation, we propose a new theory on boundary layer transition, which has five steps, that is, receptivity, linear instability, large vortex structure formation, small length scale generation, loss of symmetry and randomization to turbulence. For turbulence generation and sustenance, the classical theory, described with Richardson's energy cascade and Kolmogorov length scale, is not observed by our DNS. We proposed a new theory on turbulence generation that all small length scales are generated by “shear layer instability” through multiple level ejections and sweeps and consequent multiple level positive and negative spikes, but not by “vortex breakdown.” We believe “shear layer instability” is the “mother of turbulence.” The energy transferring from large vortices to small vortices is carried out by multiple level sweeps, but does not follow Kolmogorov's theory that large vortices pass energy to small ones through vortex stretch and breakdown. The loss of symmetry starts from the second level ring cycle in the middle of the flow field and spreads to the bottom of the boundary layer and then the whole flow field.
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)
Energy Technology Data Exchange (ETDEWEB)
Gorenflo, Norbert [Beuth Hochschule fuer Technik Berlin (Germany). Fachbereich II; Kunik, Matthias [Magdeburg Univ. (Germany). Inst. fuer Analysis und Numerik
2009-07-01
We present a new and self-contained theory for mapping properties of the boundary operators for slit diffraction occurring in Sommerfeld's diffraction theory, covering two different cases of the polarisation of the light. This theory is entirely developed in the context of the boundary operators with a Hankel kernel and not based on the corresponding mixed boundary value problem for the Helmholtz equation. For a logarithmic approximation of the Hankel kernel we also study the corresponding mapping properties and derive explicit solutions together with certain regularity results. (orig.)
The vanishing discount problem and viscosity Mather measures. Part 2: boundary value problems
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.
Chiral unitary theory: Application to nuclear problems
Indian Academy of Sciences (India)
Chiral unitary theory: Application to nuclear problems ... Physics Department, Nara Women University, Nara, Japan. 5 ... RCNP, Osaka University, Osaka, Japan ...... We acknowledge partial financial support from the DGICYT under contract ...
Conformal field theories near a boundary in general dimensions
International Nuclear Information System (INIS)
McAvity, D.M.
1995-01-01
The implications of restricted conformal invariance under conformal transformations preserving a plane boundary are discussed for general dimensions d. Calculations of the universal function of a conformal invariant ξ which appears in the two-point function of scalar operators in conformally invariant theories with a plane boundary are undertaken to first order in the ε=4-d expansion for the operator φ 2 in φ 4 theory. The form for the associated functions of ξ for the two-point functions for the basic field φ α and the auxiliary field λ in the N→∞ limit of the O(N) non-linear sigma model for any d in the range 2 α φ β and λλ. Using this method the form of the two-point function for the energy-momentum tensor in the conformal O(N) model with a plane boundary is also found. General results for the sum of the contributions of all derivative operators appearing in the operator product expansion, and also in a corresponding boundary operator expansion, to the two-point functions are also derived making essential use of conformal invariance. (orig.)
Generalised boundary terms for higher derivative theories of gravity
Energy Technology Data Exchange (ETDEWEB)
Teimouri, Ali; Talaganis, Spyridon; Edholm, James [Consortium for Fundamental Physics, Lancaster University,North West Drive, Lancaster, LA1 4YB (United Kingdom); Mazumdar, Anupam [Consortium for Fundamental Physics, Lancaster University,North West Drive, Lancaster, LA1 4YB (United Kingdom); Kapteyn Astronomical Institute, University of Groningen,9700 AV Groningen (Netherlands)
2016-08-24
In this paper we wish to find the corresponding Gibbons-Hawking-York term for the most general quadratic in curvature gravity by using Coframe slicing within the Arnowitt-Deser-Misner (ADM) decomposition of spacetime in four dimensions. In order to make sure that the higher derivative gravity is ghost and tachyon free at a perturbative level, one requires infinite covariant derivatives, which yields a generalised covariant infinite derivative theory of gravity. We will be exploring the boundary term for such a covariant infinite derivative theory of gravity.
Fluid analog model for boundary effects in field theory
International Nuclear Information System (INIS)
Ford, L. H.; Svaiter, N. F.
2009-01-01
Quantum fluctuations in the density of a fluid with a linear phonon dispersion relation are studied. In particular, we treat the changes in these fluctuations due to nonclassical states of phonons and to the presence of boundaries. These effects are analogous to similar effects in relativistic quantum field theory, and we argue that the case of the fluid is a useful analog model for effects in field theory. We further argue that the changes in the mean squared density are, in principle, observable by light scattering experiments.
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, $$ lim_{lambdao +infty}|x_{lambda}|=+infty,quadhbox{or}quad lim_{lambdao+infty}|x_{lambda}|=0. $$
Infinitely many solutions for a fourth-order boundary-value problem
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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.
Two problems in thermal field theory
Indian Academy of Sciences (India)
In this talk, I review recent progress made in two areas of thermal field theory. In par- ticular, I discuss various approaches for the calculation of the quark gluon plasma thermodynamical properties, and the problem of its photon production rate. Keywords. Thermal field theory; quark-gluon plasma. PACS Nos 11.10.Wx; 12.38.
Directory of Open Access Journals (Sweden)
Aqlan Mohammed H.
2016-01-01
Full Text Available We develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration but also yield some new special cases for specific choices of parameters involved in the problems.
Scattering theory some old and new problems
Yafaev, Dmitri R
2000-01-01
Scattering theory is, roughly speaking, perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum. It has its origin in mathematical problems of quantum mechanics and is intimately related to the theory of partial differential equations. Some recently solved problems, such as asymptotic completeness for the Schrödinger operator with long-range and multiparticle potentials, as well as open problems, are discussed. Potentials for which asymptotic completeness is violated are also constructed. This corresponds to a new class of asymptotic solutions of the time-dependent Schrödinger equation. Special attention is paid to the properties of the scattering matrix, which is the main observable of the theory. The book is addressed to readers interested in a deeper study of the subject.
Problems and paradoxes of the Lifshitz theory
International Nuclear Information System (INIS)
Klimchitskaya, G L
2009-01-01
The problems and paradoxes of the Lifshitz theory in application to real dielectric and semiconductor materials are reviewed. It is shown that the inclusion of drift current of conduction electrons into the model of dielectric response results in contradictions with both thermodynamics and experimental data of different experimental groups. Physical reasons why the problems and paradoxes arise are analyzed and found to be connected with the violation of basic applicability condition of the Lifshitz theory, the thermal equilibrium. A recent alternative approach to the resolution of the problems based on the inclusion of screening effects and diffusion current is considered and demonstrated to be thermodynamically and experimentally inconsistent. It is argued that the inclusion of the diffusion current leads to an even deeper violation of thermal equilibrium. Phenomenologically, the Lifshitz theory with role of drift and diffusion currents neglected is shown to be free of problems and in agreement with both thermodynamics and all available experimental data.
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.
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.
Partial differential equations and boundary-value problems with applications
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
Analytic solutions to a family of boundary-value problems for Ginsburg-Landau type equations
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.
Matrix product density operators: Renormalization fixed points and boundary theories
Energy Technology Data Exchange (ETDEWEB)
Cirac, J.I. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Pérez-García, D., E-mail: dperezga@ucm.es [Departamento de Análisis Matemático, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain); ICMAT, Nicolas Cabrera, Campus de Cantoblanco, 28049 Madrid (Spain); Schuch, N. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Verstraete, F. [Department of Physics and Astronomy, Ghent University (Belgium); Vienna Center for Quantum Technology, University of Vienna (Austria)
2017-03-15
We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).
Fifty Years of Boundary-Layer Theory and Experiment
Dryden, Hugh L.
1955-01-01
The year 1954 marked the 50th anniversary of the Prandtl boundary-layer theory from which we may date the beginning of man's understanding of the dynamics of real fluids. A backward look at this aspect of the history of the last 50 years may be instructive. This paper (1) attempts to compress the events of those 50 years into a few thousand words, to tell in this brief space the interesting story of the development of a new concept, its slow acceptance and growth, its spread from group to group within its country of origin, and its diffusion to other countries of the world. The original brief paper of Prandtl (2) was presented at the Third International Mathematical Congress at Heidelberg in 1904 and published in the following year. It was an attempt to explain the d'Alembert paradox, namely, that the neglect of the small friction of air in the theory resulted in the prediction of zero resistance to motion. Prandtl set himself the task of computing the motion of a fluid of small friction, so small that its effect could be neglected everywhere except where large velocity differences were present or a cumulative effect of friction occurred This led to the concept of boundary layer, or transition layer, near the wall of a body immersed in a fluid stream in which the velocity rises from zero to the free-stream value. It is interesting that Prandtl used the term Grenzsehicht (boundary layer) only once and the term Ubergangsschicht (transition layer) seven times in the brief article. Later writers also used Reibungsschicht (friction layer), but most writers today use Grenzschicht (boundary layer).
Numerical treatment of the unsteady hydromagnetic thermal boundary layer problem
International Nuclear Information System (INIS)
Drymonitou, M.A.; Geroyannis, V.S.; Goudas, C.L.
1980-01-01
This paper presents a suitable numerical method for the treatment of the unsteady hydromagnetic thermal boundary layer problem for flows past an infinite porous flat plate, the motion of which is governed by a general time-dependent law, under the influence of a transverse externally set magnetic field. The normal velocity of suction/injection at the plate is also assumed to be time-dependent. The results obtained on the basis of numerical approximations seem to compare favourably with earlier results (Pande et al., 1976; Tokis, 1978). Analytical approximations are given for the cases of a plate (i) generally accelerated and (ii) harmonically oscillating. The direct numerical treatment is obviously advantageous since it allows handling of cases where the known methods for analytical approximations are not applicable. This problem is closely related to the motions and heat transfer occurring locally on the surfaces of stars. (orig.)
Boundary conditions for free surface inlet and outlet problems
Taroni, M.
2012-08-10
We investigate and compare the boundary conditions that are to be applied to free-surface problems involving inlet and outlets of Newtonian fluid, typically found in coating processes. The flux of fluid is a priori known at an inlet, but unknown at an outlet, where it is governed by the local behaviour near the film-forming meniscus. In the limit of vanishing capillary number Ca it is well known that the flux scales with Ca 2/3, but this classical result is non-uniform as the contact angle approaches π. By examining this limit we find a solution that is uniformly valid for all contact angles. Furthermore, by considering the far-field behaviour of the free surface we show that there exists a critical capillary number above which the problem at an inlet becomes over-determined. The implications of this result for the modelling of coating flows are discussed. © 2012 Cambridge University Press.
Problem of ''global color'' in gauge theories
International Nuclear Information System (INIS)
Horvathy, P.A.; Rawnsley, J.H.; UER de Mathematique, Universite de Provence, Marseille, France)
1986-01-01
The problem of ''global color'' (which arose recently in monopole theory) is generalized to arbitrary gauge theories: a subgroup K of the ''unbroken'' gauge group G is implementable iff the gauge bundle reduces to the centralizer of K in G. Equivalent implementations correspond to equivalent reductions. Such an action is an internal symmetry for a given configuration iff the Yang-Mills field reduces also. The case of monopoles is worked out in detail
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)
Mathematical conversations multicolor problems, problems in the theory of numbers, and random walks
Dynkin, E B
2006-01-01
Comprises Multicolor Problems, dealing with map-coloring problems; Problems in the Theory of Numbers, an elementary introduction to algebraic number theory; Random Walks, addressing basic problems in probability theory. 1963 edition.
Infrared problems in field perturbation theory
International Nuclear Information System (INIS)
David, Francois.
1982-12-01
The work presented mainly covers questions related to the presence of ''infrared'' divergences in perturbation expansions of the Green functions of certain massless field theories. It is important to determine the mathematical status of perturbation expansions in field theory in order to define the region in which they are valid. Renormalization and the symmetry of a theory are important factors in infrared problems. The main object of this thesis resides in the mathematical techniques employed: integral representations of the Feynman amplitudes; methods for desingularization, regularization and dimensional renormalization. Nonlinear two dimensional space-time sigma models describing Goldstone's low energy boson dynamics associated with a breaking of continuous symmetry are studied. Random surface models are then investigated followed by infrared divergences in super-renormalizable theories. Finally, nonperturbation effects in massless theories are studied by expanding the two-dimensional nonlinear sigma model in 1/N [fr
Four tails problems for dynamical collapse theories
McQueen, Kelvin J.
2015-02-01
The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many authors dismiss the problem without considering the more severe formulations. Here I distinguish four distinct tails problems. The first (bare tails problem) and second (structured tails problem) exist in the literature. I argue that while the first is a pseudo-problem, the second has not been adequately addressed. The third (multiverse tails problem) reformulates the second to account for recently discovered dynamical consequences of collapse. Finally the fourth (tails problem dilemma) shows that solving the third by replacing the Gaussian with a non-Gaussian collapse function introduces new conflict with relativity theory.
Electromagnetic Field Theory A Collection of Problems
Mrozynski, Gerd
2013-01-01
After a brief introduction into the theory of electromagnetic fields and the definition of the field quantities the book teaches the analytical solution methods of Maxwell’s equations by means of several characteristic examples. The focus is on static and stationary electric and magnetic fields, quasi stationary fields, and electromagnetic waves. For a deeper understanding, the many depicted field patterns are very helpful. The book offers a collection of problems and solutions which enable the reader to understand and to apply Maxwell’s theory for a broad class of problems including classical static problems right up to waveguide eigenvalue problems. Content Maxwell’s Equations - Electrostatic Fields - Stationary Current Distributions – Magnetic Field of Stationary Currents – Quasi Stationary Fields: Eddy Currents - Electromagnetic Waves Target Groups Advanced Graduate Students in Electrical Engineering, Physics, and related Courses Engineers and Physicists Authors Professor Dr.-Ing. Gerd Mrozynski...
Bayesian probability theory and inverse problems
International Nuclear Information System (INIS)
Kopec, S.
1994-01-01
Bayesian probability theory is applied to approximate solving of the inverse problems. In order to solve the moment problem with the noisy data, the entropic prior is used. The expressions for the solution and its error bounds are presented. When the noise level tends to zero, the Bayesian solution tends to the classic maximum entropy solution in the L 2 norm. The way of using spline prior is also shown. (author)
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.
Existence of solutions to boundary value problem of fractional differential equations with impulsive
Directory of Open Access Journals (Sweden)
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.
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.
Lectures on mathematical theory of extremum problems
1972-01-01
The author of this book, Igor' Vladimirovich Girsanov, was one of the first mathematicians to study general extremum problems and to realize the feasibility and desirability of a unified theory of extremal problems, based on a functional analytic approach. He actively advocated this view, and his special course, given at the Faculty of Mechanics and Mathematics of the Moscow State University in 1963 and 1964, was apparently the first systematic exposition of a unified approach to the theory of extremal problems. This approach was based on the ideas of Dubovitskii and Milyutin [1]. The general theory of extremal problems has developed so intensely during the past few years that its basic concepts may now be considered finalized. Nevertheless, as yet the basic results of this new field of mathematics have not been presented in a form accessible to a wide range of readers. (The profound paper of Dubovitskii and Milyutin [2] can hardly be recommended for a first study of the theory, since, in particular, it doe...
An asymptotic problem in renewal theory
Klamkin, M.S.; van Lint, J.H.
1972-01-01
A special problem in renewal theory is considered. The asymptotic behavior of the renewal function was studied by W. L. Smith. Here we show that his result with an exponentially small remainder term follows from a theorem of De Bruijn on Volterra integral equations.
Some formal problems in gauge theories
International Nuclear Information System (INIS)
Magpantay, J.A.
1980-01-01
The concerns of this thesis are the problems due to the extra degrees of freedom in gauge-invariant theories. Since gauge-invariant Lagrangians are singular, Dirac's consistency formalism and Fadeev's extension are first reviewed. A clarification on the origin of primary constraints is given, and some of the open problems in singular Lagrangian theory are discussed. The criteria in choosing a gauge, i.e., attainability, maintainability and Poincare invariance are summarized and applied to various linear gauges. The effects of incomplete removal of all gauge freedom on the criteria for gauge conditions are described. A simple example in point mechanics that contains some of the features of gauge field theories is given. Finally, we describe a method of constructing gauge-invariant variables in various gauge field theories. For the Abelian theory, the gauge-invariant, transverse potential and Dirac's gauge-invariant fermion field was derived. For the non-Abelian case we introduce a local set of basis vectors and gauge transformations are interpreted as rotations of the basis vectors introduced. The analysis leads to the reformulation of local SU(2) field theory in terms of path-dependent U(1) x U(1) x U(1). However, the analysis fails to include the matter fields as of now
The Unknown Component Problem Theory and Applications
Villa, Tiziano; Brayton, Robert K; Mishchenko, Alan; Petrenko, Alexandre; Sangiovanni-Vincentelli, Alberto
2012-01-01
The Problem of the Unknown Component: Theory and Applications addresses the issue of designing a component that, combined with a known part of a system, conforms to an overall specification. The authors tackle this problem by solving abstract equations over a language. The most general solutions are studied when both synchronous and parallel composition operators are used. The abstract equations are specialized to languages associated with important classes of automata used for modeling systems. The book is a blend of theory and practice, which includes a description of a software package with applications to sequential synthesis of finite state machines. Specific topologies interconnecting the components, exact and heuristic techniques, and optimization scenarios are studied. Finally the scope is enlarged to domains like testing, supervisory control, game theory and synthesis for special omega languages. The authors present original results of the authors along with an overview of existing ones.
Partial differential equations & boundary value problems with Maple
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...
Solving fuzzy two-point boundary value problem using fuzzy Laplace transform
Ahmad, Latif; Farooq, Muhammad; Ullah, Saif; Abdullah, Saleem
2014-01-01
A natural way to model dynamic systems under uncertainty is to use fuzzy boundary value problems (FBVPs) and related uncertain systems. In this paper we use fuzzy Laplace transform to find the solution of two-point boundary value under generalized Hukuhara differentiability. We illustrate the method for the solution of the well known two-point boundary value problem Schrodinger equation, and homogeneous boundary value problem. Consequently, we investigate the solutions of FBVPs under as a ne...
A survey of problems in divertor and edge plasma theory
International Nuclear Information System (INIS)
Boozer, A.; Braams, B.; Weitzner, H.; Hazeltine, R.; Houlberg, W.; Oktay, E.; Sadowski, W.; Wootton, A.
1992-01-01
Theoretical physics problems related to divertor design are presented, organized by the region in which they occur. Some of the open questions in edge physics are presented from a theoretician's point of view. After a cursory sketch of the fluid models of the edge plasma and their numerical realization, the following topics are taken up: time-dependent problems, non-axisymmetric effects, anomalous transport in the scrape-off layer, edge kinetic theory, sheath effects and boundary conditions in divertors, electric field effects, atomic and molecular data issues, impurity transport in the divertor region, poloidally localized power dissipation (MARFEs and dense gas targets), helium ash removal, and neutral transport. The report ends with a summary of selected problems of particular significance and a brief bibliography of survey articles and related conference proceedings
Hamiltonian and Algebraic Theories of Gapped Boundaries in Topological Phases of Matter
Cong, Iris; Cheng, Meng; Wang, Zhenghan
2017-10-01
We present an exactly solvable lattice Hamiltonian to realize gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories. We classify the elementary excitations on the boundary, and systematically describe the bulk-to-boundary condensation procedure. We also present the parallel algebraic/categorical structure of gapped boundaries.
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.
Fundamental problems of gauge field theory
International Nuclear Information System (INIS)
Velo, G.; Wightman, A.S.
1986-01-01
As a result of the experimental and theoretical developments of the last two decades, gauge field theory, in one form or another, now provides the standard language for the description of Nature; QCD and the standard model of the electroweak interactions illustrate this point. It is a basic task of mathematical physics to provide a solid foundation for these developments by putting the theory in a physically transparent and mathematically rigorous form. The lecture notes collected in this volume concentrate on the many unsolved problems which arise here, and on the general ideas and methods which have been proposed for their solution. In particular, the use of rigorous renormalization group methods to obtain control over the continuum limit of lattice gauge field theories, the exploration of the extraordinary enigmatic connections between Kac-Moody-Virasoro algebras and string theory, and the systematic use of the theory of local algebras and indefinite metric spaces to classify the charged C* states in gauge field theories are mentioned
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
Krylov Techniques for 3D Problems in Transport Theory
International Nuclear Information System (INIS)
Ruben Panta Pazos
2006-01-01
When solving integral-differential equations by means of numerical methods one has to deal with large systems of linear equations, such as happens in transport theory [10]. Many iterative techniques are now used in Transport Theory in order to solve problems of 2D and 3D dimensions. In this paper, we choose two problems to solve the following transport equation, [Equation] where x: represents the spatial variable, μ: the cosine of the angle, ψ: the angular flux, h(x, μ): is the collision frequency, k(x, μ, μ'): the scattering kernel, q(x, μ): the source. The aim of this work is the straightforward application of the Krylov spaces technique [2] to the governing equation or to its discretizations derived of the discrete ordinates method (choosing a finite number of directions and then approximating the integral term by means of a proper sum). The equation (1) can be written in functional form as [Equation] with ψ in the Hilbert space L 2 ([0,a] x [-1,1])., and q is the source function. The operator derived from a discrete ordinates scheme that approximates the operator [Equation] generates the following subspace [Equation] i.e. the subspace generated by the iterations of order 0, 1, 2,..., m-1 of the source function q. Two methods are specially outstanding, the Lanczos method to solve the problem given by equation (2) with certain boundary conditions, and the conjugate gradient method to solve the same problem with identical boundary conditions. We discuss and accelerate the basic iterative method [8]. An important conclusion is the generation of these methods to solve linear systems in Hilbert spaces, if verify the convergence conditions, which are outlined in this work. The first problem is a cubic domain with two regions, one with a source near the vertex at the origin and the shield region. In this case, the Cartesian planes (specifically 0 < x < L, 0 < y < L, 0 < z < L) are reflexive boundaries and the rest faces of the cube are vacuum boundaries. The
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
International Nuclear Information System (INIS)
Ozgener, B.
1998-01-01
A boundary integral equation (BIE) is developed for the application of the boundary element method to the multigroup neutron diffusion equations. The developed BIE contains no explicit scattering term; the scattering effects are taken into account by redefining the unknowns. Boundary elements of the linear and constant variety are utilised for validation of the developed boundary integral formulation
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.
Mixed problems for linear symmetric hyperbolic systems with characteristic boundary conditions
International Nuclear Information System (INIS)
Secchi, P.
1994-01-01
We consider the initial-boundary value problem for symmetric hyperbolic systems with characteristic boundary of constant multiplicity. In the linear case we give some results about the existence of regular solutions in suitable functions spaces which take in account the loss of regularity in the normal direction to the characteristic boundary. We also consider the equations of ideal magneto-hydrodynamics under perfectly conducting wall boundary conditions and give some results about the solvability of such mixed problem. (author). 16 refs
Directory of Open Access Journals (Sweden)
Volodymyr S. Il'kiv
2016-11-01
Full Text Available We study a problem with integral boundary conditions in the time coordinate for a system of Lame equations of dynamic elasticity theory of an arbitrary dimension. We find necessary and sufficient conditions for the existence and uniqueness of solution in the class of almost periodic functions in the spatial variables. To solve the problem of small denominators arising while constructing solutions, we use the metric approach.
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.
Method of interior boundaries in a mixed problem of acoustic scattering
Directory of Open Access Journals (Sweden)
P. A. Krutitskii
1999-01-01
Full Text Available The mixed problem for the Helmholtz equation in the exterior of several bodies (obstacles is studied in 2 and 3 dimensions. The Dirichlet boundary condition is given on some obstacles and the impedance boundary condition is specified on the rest. The problem is investigated by a special modification of the boundary integral equation method. This modification can be called ‘Method of interior boundaries’, because additional boundaries are introduced inside scattering bodies, where impedance boundary condition is given. The solution of the problem is obtained in the form of potentials on the whole boundary. The density in the potentials satisfies the uniquely solvable Fredholm equation of the second kind and can be computed by standard codes. In fact our method holds for any positive wave numbers. The Neumann, Dirichlet, impedance problems and mixed Dirichlet–Neumann problem are particular cases of our problem.
Fixing the Big Bang Theory's Lithium Problem
Kohler, Susanna
2017-02-01
How did our universe come into being? The Big Bang theory is a widely accepted and highly successful cosmological model of the universe, but it does introduce one puzzle: the cosmological lithium problem. Have scientists now found a solution?Too Much LithiumIn the Big Bang theory, the universe expanded rapidly from a very high-density and high-temperature state dominated by radiation. This theory has been validated again and again: the discovery of the cosmic microwave background radiation and observations of the large-scale structure of the universe both beautifully support the Big Bang theory, for instance. But one pesky trouble-spot remains: the abundance of lithium.The arrows show the primary reactions involved in Big Bang nucleosynthesis, and their flux ratios, as predicted by the authors model, are given on the right. Synthesizing primordial elements is complicated! [Hou et al. 2017]According to Big Bang nucleosynthesis theory, primordial nucleosynthesis ran wild during the first half hour of the universes existence. This produced most of the universes helium and small amounts of other light nuclides, including deuterium and lithium.But while predictions match the observed primordial deuterium and helium abundances, Big Bang nucleosynthesis theory overpredicts the abundance of primordial lithium by about a factor of three. This inconsistency is known as the cosmological lithium problem and attempts to resolve it using conventional astrophysics and nuclear physics over the past few decades have not been successful.In a recent publicationled by Suqing Hou (Institute of Modern Physics, Chinese Academy of Sciences) and advisorJianjun He (Institute of Modern Physics National Astronomical Observatories, Chinese Academy of Sciences), however, a team of scientists has proposed an elegant solution to this problem.Time and temperature evolution of the abundances of primordial light elements during the beginning of the universe. The authors model (dotted lines
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
A Duality Theory for Non-convex Problems in the Calculus of Variations
Bouchitté, Guy; Fragalà, Ilaria
2018-02-01
We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no duality gap. Further, we provide necessary and sufficient optimality conditions, and we show that our duality principle can be reformulated as a min-max result which is quite useful for numerical implementations. As an example, we illustrate the application of our method to a celebrated free boundary problem. The results were announced in Bouchitté and Fragalà (C R Math Acad Sci Paris 353(4):375-379, 2015).
Singular problems in shell theory. Computing and asymptotics
Energy Technology Data Exchange (ETDEWEB)
Sanchez-Palencia, Evariste [Institut Jean Le Rond d' Alembert, Paris (France); Millet, Olivier [La Rochelle Univ. (France). LEPTIAB; Bechet, Fabien [Metz Univ. (France). LPMM
2010-07-01
It is known that deformations of thin shells exhibit peculiarities such as propagation of singularities, edge and internal layers, piecewise quasi inextensional deformations, sensitive problems and others, leading in most cases to numerical locking phenomena under several forms, and very poor quality of computations for small relative thickness. Most of these phenomena have a local and often anisotropic character (elongated in some directions), so that efficient numerical schemes should take them in consideration. This book deals with various topics in this context: general geometric formalism, analysis of singularities, numerical computing of thin shell problems, estimates for finite element approximation (including non-uniform and anisotropic meshes), mathematical considerations on boundary value problems in connection with sensitive problems encountered for very thin shells; and others. Most of numerical computations presented here use an adaptive anisotropic mesh procedure which allows a good computation of the physical peculiarities on one hand, and the possibility to perform automatic computations (without a previous mathematical description of the singularities) on the other. The book is recommended for PhD students, postgraduates and researchers who want to improve their knowledge in shell theory and in particular in the areas addressed (analysis of singularities, numerical computing of thin and very thin shell problems, sensitive problems). The lecture of the book may not be continuous and the reader may refer directly to the chapters concerned. (orig.)
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.
Problems in the theory of point explosions
Korobeinikov, V. P.
The book is concerned with the development of the theory of point explosions, which is relevant to the study of such phenomena as the initiation of detonation, high-power explosions, electric discharges, cosmic explosions, laser blasts, and hypersonic aerodynamics. The discussion covers the principal equations and the statement of problems; linearized non-self-similar one-dimensional problems; spherical, cylindrical, and plane explosions with allowance for counterpressure under conditions of constant initial density; explosions in a combustible mixture of gases; and point explosions in inhomogeneous media with nonsymmetric energy release. Attention is also given to point explosions in an electrically conducting gas with allowance for the effect of the magnetic field and to the propagation of perturbations from solar flares.
On a variational principle for shape optimization and elliptic free boundary problems
Directory of Open Access Journals (Sweden)
Raúl B. González De Paz
2009-02-01
Full Text Available A variational principle for several free boundary value problems using a relaxation approach is presented. The relaxed Energy functional is concave and it is defined on a convex set, so that the minimizing points are characteristic functions of sets. As a consequence of the first order optimality conditions, it is shown that the corresponding sets are domains bounded by free boundaries, so that the equivalence of the solution of the relaxed problem with the solution of several free boundary value problem is proved. Keywords: Calculus of variations, optimization, free boundary problems.
Using complexity science and negotiation theory to resolve boundary-crossing water issues
Islam, Shafiqul; Susskind, Lawrence
2018-07-01
Many water governance and management issues are complex. The complexity of these issues is related to crossing of multiple boundaries: political, social and jurisdictional, as well as physical, ecological and biogeochemical. Resolution of these issues usually requires interactions of many parties with conflicting values and interests operating across multiple boundaries and scales to make decisions. The interdependence and feedback among interacting variables, processes, actors and institutions are hard to model and difficult to forecast. Thus, decision-making related to complex water problems needs be contingent and adaptive. This paper draws on a number of ideas from complexity science and negotiation theory that may make it easier to cope with the complexities and difficulties of managing boundary crossing water disputes. It begins with the Water Diplomacy Framework that was developed and tested over the past several years. Then, it uses three key ideas from complexity science (interdependence and interconnectedness; uncertainty and feedback; emergence and adaptation) and three from negotiation theory (stakeholder identification and engagement; joint fact finding; and value creation through option generation) to show how application of these ideas can help enhance effectiveness of water management.
A finite-volume method for convection problems with embedded moving boundaries
Y.J. Hassen (Yunus); B. Koren (Barry)
2009-01-01
htmlabstractAn accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. Moving interior boundary conditions are embedded in the fixed-grid fluxes in the direct neighborhood of the moving boundaries. Tailor-made limiters are
Mathematical problems in wave propagation theory
1970-01-01
The papers comprising this collection are directly or indirectly related to an important branch of mathematical physics - the mathematical theory of wave propagation and diffraction. The paper by V. M. Babich is concerned with the application of the parabolic-equation method (of Academician V. A. Fok and M. A, Leontovich) to the problem of the asymptotic behavior of eigenfunc tions concentrated in a neighborhood of a closed geodesie in a Riemannian space. The techniques used in this paper have been föund useful in solving certain problems in the theory of open resonators. The topic of G. P. Astrakhantsev's paper is similar to that of the paper by V. M. Babich. Here also the parabolic-equation method is used to find the asymptotic solution of the elasticity equations which describes Love waves concentrated in a neighborhood of some surface ray. The paper of T. F. Pankratova is concerned with finding the asymptotic behavior of th~ eigenfunc tions of the Laplace operator from the exact solution for the surf...
Statistical problems of a galaxies formation theory
International Nuclear Information System (INIS)
Doroshkevich, A.G.; Shandarin, S.F.
1978-01-01
Some problems of galaxies and galaxy clusters formation from random adiabatic disturbances are discussed. Disturbances grow according to the nonlinear theory of gravitational instability. In this theory maxima of the largest characteristic values of a strain tensor have a particular significance as they are just the points of the formation of dense flattened structures - ''pancakes'' which then transform into galaxies and galaxy clusters. It is shown that parameters of a ''pancake'' such as time of the origin, mass, temperature etc. are determined by the lambda 11 largest characteristic value of the strain tensor in the centre of the ''pancake''. The lambda 11 distribution function the rate of mass condensation into ''pancakes'', the rate of production and the spatial density of ''pancakes'' are given. Some statistic properties of a single ''pancake'' such as a mean displacement and dispersion of a displacement in the vicinity of centre of a ''pancake'' were found. The possibility of connection between young galaxies and quasars is discussed in the framework of this theory
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...
CFD simulation of the atmospheric boundary layer: wall function problems
Blocken, B.J.E.; Stathopoulos, T.; Carmeliet, J.
2007-01-01
Accurate Computational Fluid Dynamics (CFD) simulations of atmospheric boundary layer (ABL) flow are essential for a wide variety of atmospheric studies including pollutant dispersion and deposition. The accuracy of such simulations can be seriously compromised when wall-function roughness
Stochastic Theory of Turbulence Mixing by Finite Eddies in the Turbulent Boundary Layer
Dekker, H.; Leeuw, G. de; Maassen van den Brink, A.
1995-01-01
Turbulence mixing is treated by means of a novel formulation of nonlocal K-theory, involving sample paths and a stochastic hypothesis. The theory simplifies for mixing by exchange (strong-eddies) and is then applied to the boundary layer (involving scaling). This maps boundary layer turbulence onto
Order Reduction in High-Order Runge-Kutta Methods for Initial Boundary Value Problems
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...
Gauge hierarchy problem in grand unified theories
International Nuclear Information System (INIS)
Alhendi, H.A.A.
1982-01-01
In grand unification schemes, several mass scales are to be introduced, with some of them much larger than all the others, to cope with experimental observations, in which elementary particles of higher masses require higher energy to observe them than elementary particles of lower masses. There have been controversial arguments in the literature on such hierarchical scale structure, when radiative corrections are taken into account. It has been asserted that the gauge hierarchy depends on the choice of the subtraction point (in the classical field space), of the four-point function at zero external momentum. It also has been asserted that the gauge hierarchy problem whenever it is possible to be maintained in one sector of particles, it also is possible to be maintained in the other sectors. These two problems have been studied in a prototype model, namely an 0(3)-model with two triplets of real scalar Higgs fields. Our analysis shows that, within ordinary perturbation theory, none of these two problems is quite correct
Energy Technology Data Exchange (ETDEWEB)
Galaktionov, V A; Hulshof, J; Vazquez, J L
1997-09-01
We consider a free-boundary problem for the heat equation which arises in the description of premixed equi-diffusional flames in the limit of high activation energy. It consists of the heat equation u{sub t} = {Delta}u, u > 0, posed in an a priori unknown set {Omega} included in Q{sub T} = R{sup N} x (0,T) for some T >0 with boundary conditions on the free lateral boundary {Gamma}intersection between {partial_derivative}{Omega} et Q{sub T} (the flame front): u = 0 and {delta}u/{delta}{nu} = - 1. We impose initial condition u{sub 0}(x) {>=} 0 on the know initial domain {Omega}{sub 0} = interaction between {Omega}-bar et {l_brace} t = 0 {r_brace}. The paper establishes a theory of existence, uniqueness and regularity for radial symmetric solutions having bounded support. We remark that such solutions vanish in finite time (extinction phenomenon). in the paper we analyze the different types of possible extinction behaviour. We also investigate the focusing behaviour for solutions whose support expands in finite time to fill a hole. In all the cases the asymptotic behaviour is shown to be self-similar. (authors) 38 refs.
Ghost problem of quantum field theories with higher derivatives
International Nuclear Information System (INIS)
Gavrielides, A.; Kuo, T.K.; Lee, S.Y.
1976-01-01
Second-order theories, i.e., theories described by Lagrangians quadratic in second derivatives of the fields, are carefully examined and their ghost problems are isolated and clearly exhibited. In particular, theories with gauge symmetry are shown to have precisely the same ghost problems as theories without gauge symmetry. It is also shown that massless theories of the same nature are the limit of massive theories containing ghost states
Spectral combination of spherical gravitational curvature boundary-value problems
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
Energy Technology Data Exchange (ETDEWEB)
Pereira, Luis Carlos Martins
1998-06-15
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)
Vragov’s boundary value problem for an implicit equation of mixed type
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.
Directory of Open Access Journals (Sweden)
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.
Physiological Plausibility and Boundary Conditions of Theories of Risk Sensitivity
DEFF Research Database (Denmark)
Marchiori, Davide; Elqayam, Shira
2012-01-01
dilatation, which in turn positively correlates with a risk aversion behavior. They hypothesize that participants’ attention is increased in decision problems involving losses, which trigger an innate prudent behavior in situations entailing danger and/or hazard. Interestingly, Y&T find that the nature...... of attention is not selective, i.e., when losses are present, participants are shown to devote more attention to the task as a whole rather than to the single negative outcomes, in contrast to Prospect Theory's loss aversion....... and physiological underpinnings of one of the central topics in judgment and decision-making (JDM) research – choice behavior in decisions from experience. Y&T successfully contributes to this goal by demonstrating a novel effect that losses increase experimental participants’ arousal as measured by pupil...
Boundary conformal field theory analysis of the H+3 model
International Nuclear Information System (INIS)
Adorf, Hendrik
2008-01-01
The central topic of this thesis is the study of consistency conditions for the maximally symmetric branes of the H + 3 model. It is carried out by deriving constraints in the form of so-called shift equations and analysing their solutions. This results in explicit expressions for the one point functions in the various brane backgrounds. The brane spectrum becomes organized in certain continuous and discrete series. In the first part, we give an introduction to two dimensional conformal field theory (CFT) in the framework of vertex operator algebras and their modules. As this approach has been developed along with rational CFT, we pay attention to adapt it to the special needs of the nonrational H + 3 model. Part two deals with boundary CFT only. We start with a review of some basic techniques of boundary CFT and the Cardy-Lewellen sewing relations that will be at the heart of all following constructions. Afterwards, we introduce the systematics of brane solutions that we are going to follow. With the distinction between regular and irregular one point functions, we propose a new additional pattern according to which the brane solutions must be organized. We argue that all isospin dependencies must be subjected to the sewing constraints. At this point, the programme to be carried out is established and we are ready to derive the missing 1/2-shift equations for the various types of AdS 2 branes in order to make the list of this kind of equation complete. Then we address the b -2 /2-shift equations. It turns out that their derivation is not straightforward: One needs to extend the initial region of definition of a certain (boundary CFT) two point function to a suitable patch. Therefore, a continuation prescription has to be assumed. The most natural candidate is analytic continuation. We show that it can be carried out, although it is rather technical and involves the use of certain generalized hypergeometric functions in two variables. In this way, we derive a
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.
Information theory and coding solved problems
Ivaniš, Predrag
2017-01-01
This book is offers a comprehensive overview of information theory and error control coding, using a different approach then in existed literature. The chapters are organized according to the Shannon system model, where one block affects the others. A relatively brief theoretical introduction is provided at the beginning of every chapter, including a few additional examples and explanations, but without any proofs. And a short overview of some aspects of abstract algebra is given at the end of the corresponding chapters. The characteristic complex examples with a lot of illustrations and tables are chosen to provide detailed insights into the nature of the problem. Some limiting cases are presented to illustrate the connections with the theoretical bounds. The numerical values are carefully selected to provide in-depth explanations of the described algorithms. Although the examples in the different chapters can be considered separately, they are mutually connected and the conclusions for one considered proble...
ACTUAL PROBLEMS OF THE THEORY OF QUALITY
Directory of Open Access Journals (Sweden)
V. P. Panasyuk
2016-01-01
Full Text Available The aim of the publication is the analysis of the place and the role of scientific categories and application of the concept of «quality» as a threepronged science of quality, quality management, quality assessment in contemporary global processes, as well as applied aspects with regard to the adoption of specific management decisions.Methods. Methodology of interdisciplinary approach to the analysis of the "quality" category is used; the methods of theoretical analysis, synthesis and generalization.Analysis of the «quality» of the concept is carried out in conjunction with the global processes and trends in the economy, the crisis in the world, due to the emerging new technological order. The theoretical foundation that can be laid at the base of the further development of the theory of quality and making the qualitative nature of the reforms in the social sphere and the economic sphere is considered in details.Results. The tendencies, risks, problems and suggestions on the practical application of some or other quality concepts, approaches to enforcement are signified. The author's vision of the future development direction, associated with quality, including in international breaking is given.Scientific novelty consists in determining of qualitology potential applied to solve complex theoretical and practical problems, its place and role among emerging new classification of classical and non-classical sciences. The promising directions of the quality theory in relation to the economy, social sphere, education are identified.Practical significance. The proposed recommendations on use of ideas for management approaches reconsideration, organization of research and training in the field of quality.
Bilinear Inverse Problems: Theory, Algorithms, and Applications
Ling, Shuyang
We will discuss how several important real-world signal processing problems, such as self-calibration and blind deconvolution, can be modeled as bilinear inverse problems and solved by convex and nonconvex optimization approaches. In Chapter 2, we bring together three seemingly unrelated concepts, self-calibration, compressive sensing and biconvex optimization. We show how several self-calibration problems can be treated efficiently within the framework of biconvex compressive sensing via a new method called SparseLift. More specifically, we consider a linear system of equations y = DAx, where the diagonal matrix D (which models the calibration error) is unknown and x is an unknown sparse signal. By "lifting" this biconvex inverse problem and exploiting sparsity in this model, we derive explicit theoretical guarantees under which both x and D can be recovered exactly, robustly, and numerically efficiently. In Chapter 3, we study the question of the joint blind deconvolution and blind demixing, i.e., extracting a sequence of functions [special characters omitted] from observing only the sum of their convolutions [special characters omitted]. In particular, for the special case s = 1, it becomes the well-known blind deconvolution problem. We present a non-convex algorithm which guarantees exact recovery under conditions that are competitive with convex optimization methods, with the additional advantage of being computationally much more efficient. We discuss several applications of the proposed framework in image processing and wireless communications in connection with the Internet-of-Things. In Chapter 4, we consider three different self-calibration models of practical relevance. We show how their corresponding bilinear inverse problems can be solved by both the simple linear least squares approach and the SVD-based approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus allowing for real-time deployment. Explicit theoretical
A problem of atomic diffusion in a moving boundary
International Nuclear Information System (INIS)
Bezerra, M.C.C.
1985-01-01
It is analysed the convergence of a numerical scheme for calculating approximate solutions of a model used for evaluating concentration of atoms in a diffusion process in the walls of nuclear reactors. The ion trapping process is admitted to be reversible and the wall corrosion process is also considered in the model so that must deal with a moving boundary. Some conditions for the motion of the boundary are established in such a way that convergence can be assured in more general settings than those of previous papers. (Author) [pt
Boundary conformal field theory and the worldsheet approach to D-branes
Recknagel, Andreas
2013-01-01
Boundary conformal field theory is concerned with a class of two-dimensional quantum field theories which display a rich mathematical structure and have many applications ranging from string theory to condensed matter physics. In particular, the framework allows discussion of strings and branes directly at the quantum level. Written by internationally renowned experts, this comprehensive introduction to boundary conformal field theory reaches from theoretical foundations to recent developments, with an emphasis on the algebraic treatment of string backgrounds. Topics covered include basic concepts in conformal field theory with and without boundaries, the mathematical description of strings and D-branes, and the geometry of strongly curved spacetime. The book offers insights into string geometry that go beyond classical notions. Describing the theory from basic concepts, and providing numerous worked examples from conformal field theory and string theory, this reference is of interest to graduate students and...
International Nuclear Information System (INIS)
Choi, C. Y.; Park, C. T.; Kim, T. H.; Han, K. N.; Choe, S. H.
1995-01-01
A geometrical inverse heat conduction problem is solved for the development of Infrared Computerized-Axial-Tomography (IR CAT) Scan by using a boundary element method in conjunction with regularization procedure. In this problem, an overspecified temperature condition by infrared scanning is provided on the surface, and is used together with other conditions to solve the position of an unknown boundary (cavity). An auxiliary problem is introduced in the solution of this problem. By defining a hypothetical inner boundary for the auxiliary problem domain, the cavity is located interior to the domain and its position is determined by solving a potential problem. Boundary element method with regularization procedure is used to solve this problem, and the effects of regularization on the inverse solution method are investigated by means of numerical analysis
Projective geometry solved problems and theory review
Fortuna, Elisabetta; Pardini, Rita
2016-01-01
This book starts with a concise but rigorous overview of the basic notions of projective geometry, using straightforward and modern language. The goal is not only to establish the notation and terminology used, but also to offer the reader a quick survey of the subject matter. In the second part, the book presents more than 200 solved problems, for many of which several alternative solutions are provided. The level of difficulty of the exercises varies considerably: they range from computations to harder problems of a more theoretical nature, up to some actual complements of the theory. The structure of the text allows the reader to use the solutions of the exercises both to master the basic notions and techniques and to further their knowledge of the subject, thus learning some classical results not covered in the first part of the book. The book addresses the needs of undergraduate and graduate students in the theoretical and applied sciences, and will especially benefit those readers with a solid grasp of ...
Boundary value problems for multi-term fractional differential equations
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.
A finite difference method for free boundary problems
Fornberg, Bengt
2010-01-01
Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax
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...
String Theory: Big Problem for Small Size
Sahoo, S.
2009-01-01
String theory is the most promising candidate theory for a unified description of all the fundamental forces that exist in nature. It provides a mathematical framework that combines quantum theory with Einstein's general theory of relativity. The typical size of a string is of the order of 10[superscript -33] cm, called the Planck length. But due…
Spline-Interpolation Solution of One Elasticity Theory Problem
Shirakova, Elena A
2011-01-01
The book presents methods of approximate solution of the basic problem of elasticity for special types of solids. Engineers can apply the approximate methods (Finite Element Method, Boundary Element Method) to solve the problems but the application of these methods may not be correct for solids with the certain singularities or asymmetrical boundary conditions. The book is recommended for researchers and professionals working on elasticity modeling. It explains methods of solving elasticity problems for special solids. Approximate methods (Finite Element Method, Boundary Element Method) have b
Solving 1D plasmas and 2D boundary problems using Jack polynomials and functional relations
International Nuclear Information System (INIS)
Fendley, P.; Saleur, H.; Lesage, F.
1995-01-01
The general one-dimensional open-quotes log-sineclose quotes gas is defined by restricting the positive and negative charges of a two-dimensional Coulomb gas to live on a circle. Depending on charge constraints, this problem is equivalent to different boundary field theories. We study the electrically neutral case, which is equivalent to a two-dimensional free boson with an impurity cosine potential. We use two different methods: a perturbative one based on Jack symmetric functions, and a non-perturbative one based on the thermodynamic Bethe ansatz and functional relations. The first method allows us to find an explicit series expression for all coefficients in the virial expansion of the free energy and the experimentally measurable conductance. Some results for correlation functions are also presented. The second method gives an expression for the full free energy, which yields a surprising fluctuation-dissipation relation between the conductance and the free energy
Numerical continuation methods for dynamical systems path following and boundary value problems
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 ...
Quasisolutions of Inverse Boundary-Value Problem of Aerodynamics for Dense Airfoil Grids
Directory of Open Access Journals (Sweden)
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.
Entanglement spectrum and boundary theories with projected entangled-pair states
Energy Technology Data Exchange (ETDEWEB)
Cirac, Ignacio [Max-Planck-Institut fuer Quantenoptik, Garching (Germany); Poilblanc, Didier [Laboratoire de Physique Theorique, C.N.R.S. and Universite de Toulouse, Toulouse (France); Schuch, Norbert [California Institute of Technology, Pasadena, CA (United States); Verstraete, Frank [Vienna Univ. (Austria)
2012-07-01
In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated to their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin system and its boundary using Projected Entangled Pair States (PEPS). This duality associates to every region a Hamiltonian on its boundary, in such a way that the entanglement spectrum of the bulk corresponds to the excitation spectrum of the boundary Hamiltonian. We study various models and find that a gapped bulk phase with local order corresponds to a boundary Hamiltonian with local interactions, whereas critical behavior in the bulk is reflected on a diverging interaction length of the boundary Hamiltonian. Furthermore, topologically ordered states yield non-local Hamiltonians. As our duality also associates a boundary operator to any operator in the bulk, it in fact provides a full holographic framework for the study of quantum many-body systems via their boundary.
Boundary integral equation methods in eigenvalue problems of elastodynamics and thin plates
Kitahara, M
1985-01-01
The boundary integral equation (BIE) method has been used more and more in the last 20 years for solving various engineering problems. It has important advantages over other techniques for numerical treatment of a wide class of boundary value problems and is now regarded as an indispensable tool for potential problems, electromagnetism problems, heat transfer, fluid flow, elastostatics, stress concentration and fracture problems, geomechanical problems, and steady-state and transient electrodynamics.In this book, the author gives a complete, thorough and detailed survey of the method. It pro
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)
A Boundary Value Problem for Hermitian Monogenic Functions
Directory of Open Access Journals (Sweden)
Ricardo Abreu Blaya
2008-02-01
Full Text Available We study the problem of finding a Hermitian monogenic function with a given jump on a given hypersurface in Ã¢Â„Âm,Ã¢Â€Â‰m=2n. Necessary and sufficient conditions for the solvability of this problem are obtained.
Laplace Boundary-Value Problem in Paraboloidal Coordinates
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…
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.
How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems
Cortazar, C.; Elgueta, M.; Rossi, J. D.; Wolanski, N.
2006-01-01
We present a model for nonlocal diffusion with Neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary. We study the limit of this family of nonlocal diffusion operators when a rescaling parameter related to the kernel of the nonlocal operator goes to zero. We prove that the solutions of this family of problems converge to a solution of the heat equation with Neumann boundary conditions.
Renormalization problem in a class of nonrenormalizable theories
International Nuclear Information System (INIS)
Symanzik, K.
1975-08-01
A possible way to approach the simplest nonrenormalizable theory - phi 4 theory in more than four space-time dimensions - is described. The problems of extension to other nonrenormalizable theories are discussed and the conclusions reached so far are compared with the corresponding ones for renormalizable theories. For more details, Comm. Math. Phys. or DESY 75/12 should be consulted. (BJ) [de
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)
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.
Boundary layer studies related to fusion theory. Final report
International Nuclear Information System (INIS)
1981-01-01
The described work studied the boundary between closed and open field lines in EBT geometry, with emphasis on the microstability properties. These properties were established primarily for drift waves in the lower hybrid range of frequencies. The transport due to these modes was evaluated by a self-consistent treatment, using quasilinear models in a plasma diffusion code. The model was benchmarked against the EDT experimental results from ORNL and the sensitivity to transport model established. Viscosity was estimated to be negligible compared with anomalous transport. Drift wave turbulence gave a boundary layer size much more consistent with experiment than either collisional transport or Bohm diffusion
Formulated linear programming problems from game theory and its ...
African Journals Online (AJOL)
Formulated linear programming problems from game theory and its computer implementation using Tora package. ... Game theory, a branch of operations research examines the various concepts of decision ... AJOL African Journals Online.
Numerical Solutions of Fifth Order Boundary Value Problems Using
African Journals Online (AJOL)
Dr A.B.Ahmed
1Department of Mathematics Delta State University, Abraka, Nigeria. 2Department of ..... International Journal of Computational. Mathematics and ... Value Problems using Power Series Approximation Method.Applied. Mathematics,. 7,. 1215-.
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/
On the Nature, Theory, and Modeling of Atmospheric Planetary Boundary Layers
DEFF Research Database (Denmark)
Baklanov, Alexander A.; Grisogono, Branko; Bornstein, Robert
2011-01-01
The gap between our modern understanding of planetary boundary layer physics and its decades-old representations in current operational atmospheric models is widening, which has stimulated this review of the current state of the art and an analysis of the immediate needs in boundary layer theory......, measurements, and modeling....
Positive solutions for a nonlocal boundary-value problem with vector-valued response
Directory of Open Access Journals (Sweden)
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.
Jang, Hae-Won; Ih, Jeong-Guon
2012-04-01
The time domain boundary element method (BEM) is associated with numerical instability that typically stems from the time marching scheme. In this work, a formulation of time domain BEM is derived to deal with all types of boundary conditions adopting a multi-input, multi-output, infinite impulse response structure. The fitted frequency domain impedance data are converted into a time domain expression as a form of an infinite impulse response filter, which can also invoke a modeling error. In the calculation, the response at each time step is projected onto the wave vector space of natural radiation modes, which can be obtained from the eigensolutions of the single iterative matrix. To stabilize the computation, unstable oscillatory modes are nullified, and the same decay rate is used for two nonoscillatory modes. As a test example, a transient sound field within a partially lined, parallelepiped box is used, within which a point source is excited by an octave band impulse. In comparison with the results of the inverse Fourier transform of a frequency domain BEM, the average of relative difference norm in the stabilized time response is found to be 4.4%.
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
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.
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.
Directory of Open Access Journals (Sweden)
Weifeng Wang
2014-01-01
Full Text Available We study an optimal control problem governed by a semilinear parabolic equation, whose control variable is contained only in the boundary condition. An existence theorem for the optimal control is obtained.
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
Variational methods for boundary value problems for systems of elliptic equations
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.
A fast direct solver for boundary value problems on locally perturbed geometries
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.
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
Rethinking the Boundaries of Cognitive Load Theory in Complex Learning
Kalyuga, Slava; Singh, Anne-Marie
2016-01-01
In the traditional framework of cognitive load theory, it is assumed that the acquisition of domain-specific knowledge structures (or schemas) is the only instructional goal, and therefore, the theory is applicable to any instructional task. Accordingly, the basic concepts of intrinsic (productive) and extraneous (unproductive) types of cognitive…
An analogue of Morse theory for planar linear networks and the generalized Steiner problem
International Nuclear Information System (INIS)
Karpunin, G A
2000-01-01
A study is made of the generalized Steiner problem: the problem of finding all the locally minimal networks spanning a given boundary set (terminal set). It is proposed to solve this problem by using an analogue of Morse theory developed here for planar linear networks. The space K of all planar linear networks spanning a given boundary set is constructed. The concept of a critical point and its index is defined for the length function l of a planar linear network. It is shown that locally minimal networks are local minima of l on K and are critical points of index 1. The theorem is proved that the sum of the indices of all the critical points is equal to χ(K)=1. This theorem is used to find estimates for the number of locally minimal networks spanning a given boundary set
A combined analytic-numeric approach for some boundary-value problems
Directory of Open Access Journals (Sweden)
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.
A Boundary Element Solution to the Problem of Interacting AC Fields in Parallel Conductors
Directory of Open Access Journals (Sweden)
Einar M. Rønquist
1984-04-01
Full Text Available The ac fields in electrically insulated conductors will interact through the surrounding electromagnetic fields. The pertinent field equations reduce to the Helmholtz equation inside each conductor (interior problem, and to the Laplace equation outside the conductors (exterior problem. These equations are transformed to integral equations, with the magnetic vector potential and its normal derivative on the boundaries as unknowns. The integral equations are then approximated by sets of algebraic equations. The interior problem involves only unknowns on the boundary of each conductor, while the exterior problem couples unknowns from several conductors. The interior and the exterior problem are coupled through the field continuity conditions. The full set of equations is solved by standard Gaussian elimination. We also show how the total current and the dissipated power within each conductor can be expressed as boundary integrals. Finally, computational results for a sample problem are compared with a finite difference solution.
Fostering Cultural Diversity: Problems of Access and Ethnic Boundary Maintenance
Maria T. Allison
1992-01-01
This presentation explores theoretical reasons for the underutilization of services, discusses types and problems of access which may be both inadvertent and institutionalized, and discusses policy implications of this work. Data suggest that individuals from distinct ethnic populations, particularly Hispanic, African-American, and Native American, tend to underutilize...
On problems with displacement in boundary conditions for hyperbolic equation
Directory of Open Access Journals (Sweden)
Elena A. Utkina
2016-03-01
Full Text Available We consider three problems for hyperbolic equation on a plane in the characteristic domain. In these problems at least one of the conditions of the Goursat problem is replaced by nonlocal condition on the relevant characteristic. Non-local conditions are the linear combinations of the normal derivatives at points on opposite characteristics. In case of replacement of one condition we solve the problem by reduction to the Goursat problem for which it exists and is unique. To find the unknown Goursat condition author receives the integral equation, rewrite it in operational form and finds its unique solvability cases. To prove the unique solvability of the equation, the author shows the continuous linear operator and the fact, that some degree of the resulting operator is a contraction mapping. It is known that in this case the required Goursat condition can be written as Neumann series. We considered in detail only one of the tasks, but for both the unique solvability theorems are formulated. If the two conditions are changed, the uniqueness of the solution on the assumption that it exists, is proved by the method of a priori estimates. For this purpose, the inner product and the norm in $L_2$ are used. As a result, the conditions were obtained for the coefficients of a hyperbolic equation that ensure the uniqueness of the solution. An example is given, confirming that these conditions are essential. Namely, constructed an equation whose coefficients do not satisfy the conditions of the last theorem, given the conditions on the characteristics and nontrivial solution is built.
Dobaczewski, Jacek
2010-06-01
Nuclear structure theory is a domain of physics faced at present with great challenges and opportunities. A larger and larger body of high-precision experimental data has been and continues to be accumulated. Experiments on very exotic short-lived isotopes are the backbone of activity at numerous large-scale facilities. Over the years, tremendous progress has been made in understanding the basic features of nuclei. However, the theoretical description of nuclear systems is still far from being complete and is often not very precise. Many questions, both basic and practical, remain unanswered. The goal of publishing this special focus issue of Journal of Physics G: Nuclear and Particle Physics on Open Problems in Nuclear Structure Theory (OPeNST) is to construct a fundamental inventory thereof, so that the tasks and available options become more clearly exposed and that this will help to stimulate a boost in theoretical activity, commensurate with the experimental progress. The requested format and scope of the articles on OPeNST was quite flexible. The journal simply offered the possibility to provide a forum for the material, which is very often discussed at conferences during the coffee breaks but does not normally have sufficient substance to form regular publications. Nonetheless, very often formulating a problem provides a major step towards its solution, and it may constitute a scientific achievement on its own. Prospective authors were therefore invited to find their own balance between the two extremes of very general problems on the one hand (for example, to solve exactly the many-body equations for a hundred particles) and very specific problems on the other hand (for example, those that one could put in one's own grant proposal). The authors were also asked not to cover results already obtained, nor to limit their presentations to giving a review of the subject, although some elements of those could be included to properly introduce the subject matter
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.
Simulating a singularity-free universe outside the problem boundary in poisson
International Nuclear Information System (INIS)
Halbach, K.; Schlueter, R.
1992-01-01
An exact analytical solution developed from the Dirichlet problem exterior to a circle is employed in the magnetostatics code POISSON to provide a boundary condition option which simulates a singularity-free universe external to the problem domain. Problems with domains of large unequal extents in perpendicular directions are treated by first conformally mapping the exterior of an ellipse onto the exterior of the unit circle. Problems exhibiting symmetry in one or two planes are modeled using a semi or quarter, respectively, in conjunction with the singularity-free rest-of-universe boundary condition
Problems with False Vacua in Supersymmetric Theories
Bajc, Borut; Senjanovic, Goran
2011-01-01
It has been suggested recently that in a consistent theory any Minkowski vacuum must be exactly stable. As a result, a large class of theories that in ordinary treatment would appear sufficiently long-lived, in reality make no sense. In particular, this applies to supersymmetric models in which global supersymmetry is broken in a false vacuum. We show that in any such theory the dynamics of supersymmetry breaking cannot be decoupled from the Planck scale physics. This finding poses an obvious challenge for the idea of low-scale metastable (for example gauge) mediation.
Problems of linear electron (polaron) transport theory in semiconductors
Klinger, M I
1979-01-01
Problems of Linear Electron (Polaron) Transport Theory in Semiconductors summarizes and discusses the development of areas in electron transport theory in semiconductors, with emphasis on the fundamental aspects of the theory and the essential physical nature of the transport processes. The book is organized into three parts. Part I focuses on some general topics in the theory of transport phenomena: the general dynamical theory of linear transport in dissipative systems (Kubo formulae) and the phenomenological theory. Part II deals with the theory of polaron transport in a crystalline semicon
A free boundary problem for a reaction-diffusion system with nonlinear memory
DEFF Research Database (Denmark)
Lin, Zhigui; Ling, Zhi; Pedersen, Michael
2013-01-01
We consider a integro-partial differential equation with a free boundary which appears in the theory of the nuclear dynamics. First, local existence and uniqueness are obtained by using the contraction mapping theorem. Then, the behavior of the free boundary and the blow-up criteria are obtained........ Finally, we examine the long-time behavior of the global solution. We show that the solution is global and fast if the initial data are small....
RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems
Farrell, Patricio
2013-01-01
In this paper, we discuss multiscale radial basis function collocation methods for solving elliptic partial differential equations on bounded domains. The approximate solution is constructed in a multilevel fashion, each level using compactly supported radial basis functions of smaller scale on an increasingly fine mesh. On each level, standard symmetric collocation is employed. A convergence theory is given, which builds on recent theoretical advances for multiscale approximation using compactly supported radial basis functions. We are able to show that the convergence is linear in the number of levels. We also discuss the condition numbers of the arising systems and the effect of simple, diagonal preconditioners, now proving rigorously previous numerical observations. © 2013 Society for Industrial and Applied Mathematics.
Valent, Tullio
1988-01-01
In this book I present, in a systematic form, some local theorems on existence, uniqueness, and analytic dependence on the load, which I have recently obtained for some types of boundary value problems of finite elasticity. Actually, these results concern an n-dimensional (n ~ 1) formal generalization of three-dimensional elasticity. Such a generalization, be sides being quite spontaneous, allows us to consider a great many inter esting mathematical situations, and sometimes allows us to clarify certain aspects of the three-dimensional case. Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality. Note that I concentrate on simultaneous local existence and uniqueness; thus, I do not deal with the more general theory of exis tence. Moreover, I restrict my discussion to compressible elastic bodies and I do not treat unilateral problems. The clever use of the inverse function theorem in finite elasticity made by STOPPELLI [1954, 1957a, 1957b]...
A Review of Methods for Moving Boundary Problems
2009-07-01
the bound- ary value problem for the eikonal equation: ‖∇u‖ = 1 for x ∈ Ω (29) u = 0 for x ∈ Γ (30) ERDC/CHL TR-09-10 8 where ‖ ‖ is the Euclidean norm...Solutions of the eikonal equation can in turn be characterized as steady state solutions of the initial value prob- lem ut + sgn(u0)(‖∇u‖ − 1) = 0...LS using the eikonal equation and use the NCI equation for the LS dynam- ics. The complete system of equations in weak form is ∫ Ω (‖∇u‖ − 1)wdV = 0
Hydrodynamic theory of convective transport across a dynamically stabilized diffuse boundary layer
International Nuclear Information System (INIS)
Gerhauser, H.
1983-09-01
The diffuse boundary layer between miscible liquids is subject to Rayleigh-Taylor instabilities if the heavy fluid is supported by the light one. The resulting rapid interchange of the liquids can be suppressed by enforcing vertical oscillations on the whole system. This dynamic stabilization is incomplete and produces some peculiar novel transport phenomena such as decay off the density profile into several steps, periodic peeling of density sheets of the boundary layer and the appearance of steady vortex flow. The theory presented in this paper identifies the basic mechanism as formation of convective cells leading to enhanced diffusion, and explains previous experimental results with water and ZnJ 2 -solutions. A nonlinear treatment of the stationary convective flow problem gives the saturation amplitude of the ground mode and provides an upper bound for the maximum convective transport. The hydrodynamic model can be used for visualizing similar transport processes in the plasma of toroidal confinement devices such as sawtooth oscillations in soft disruptions of tokamak discharges and anomalous diffusion by excitation of convective cells. The latter process is investigated here in some detail, leading to the result that the maximum possible transport is of the order of Bohm diffusion. (orig.)
Belletête, J.; Gainutdinov, A. M.; Jacobsen, J. L.; Saleur, H.; Vasseur, R.
2017-12-01
The relationship between bulk and boundary properties is one of the founding features of (rational) conformal field theory (CFT). Our goal in this paper is to explore the possibility of having an equivalent relationship in the context of lattice models. We focus on models based on the Temperley-Lieb algebra, and use the concept of ‘braid translation’, which is a natural way, in physical terms, to ‘close’ an open spin chain by adding an interaction between the first and last spins using braiding to ‘bring’ them next to each other. The interaction thus obtained is in general non-local, but has the key feature that it is expressed solely in terms of the algebra for the open spin chain—the ‘ordinary’ Temperley-Lieb algebra and its blob algebra generalization. This is in contrast with the usual periodic spin chains which involve only local interactions, and are described by the periodic Temperley-Lieb algebra. We show that for the restricted solid-on-solid models, which are known to be described by minimal unitary CFTs (with central charge ccontent in terms of the irreducibles is the same, as well as the spectrum, but the detailed structure (like logarithmic coupling) is profoundly different. This carries over to the continuum limit. The situation is similar for the sl(2\\vert 1) case. The problem of relating bulk and boundary lattice models for LCFTs thus remains open.
Lau, Chun Sing
This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in
Problems with the Younger Dryas Boundary (YDB) Impact Hypothesis
Boslough, M.
2009-12-01
One breakthrough of 20th-century Earth science was the recognition of impacts as an important geologic process. The most obvious result is a crater. There are more than 170 confirmed terrestrial impact structures with a non-uniform spatial distribution suggesting more to be found. Many have been erased by tectonics and erosion. Deep water impacts do not form craters, and craters in ice sheets disappear when the ice melts. There is growing speculation that such hidden impacts have caused frequent major environmental events of the Holocene, but this is inconsistent with the astronomically-constrained population of Earth-crossing asteroids. Impacts can have consequences much more significant than excavation of a crater. The K/T boundary mass extinction is attributed to the environmental effects of a major impact, and some researchers argue that other extinctions, abrupt climate changes, and even civilization collapses have resulted from impacts. Nuclear winter models suggest that 2-km diameter asteroids exceed a "global catastrophe threshold" by injecting sufficient dust into the stratosphere to cause short-term climate changes, but would not necessarily collapse most natural ecosystems or cause mass extinctions. Globally-catastrophic impacts recur on timescales of about one million years. The 1994 collision of Comet Shoemaker-Levy 9 with Jupiter led us recognize the significance of terrestrial airbursts caused by objects exploding violently in Earth’s atmosphere. We have invoked airbursts to explain rare forms of non-volcanic glasses and melts by using high-resolution computational models to improve our understanding of atmospheric explosions, and have suggested that multiple airbursts from fragmented impactors could be responsible for regional effects. Our models have been cited in support of the widely-publicized YDB impact hypothesis. Proponents claim that a broken comet exploded over North America, with some fragments cratering the Laurentide Ice Sheet. They
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.
Boundary value problems in time for wave equations on RN
Directory of Open Access Journals (Sweden)
M. W. Smiley
1990-01-01
Full Text Available Let Lλ denote the linear operator associated with the radially symmetric form of the wave operator ∂t2−Δ+λ together with the side conditions of decay to zero as r=‖x‖→+∞ and T-periodicity in time. Thus Lλω=ωtt−(ωrr+N−1rωr+λω, when there are N space variables. For δ,R,T>0 let DT,R=(0,T×(R,+∞ and Lδ2(D denote the weighted L2 space with weight function exp(δr. It is shown that Lλ is a Fredholm operator from dom(Lλ⊂L2(D onto Lδ2(D with non-negative index depending on λ. If [2πj/T]2<λ≤[2π(j+1/T]2 then the index is 2j+1. In addition it is shown that Lλ has a bounded partial inverse Kλ:Lδ2(D→Hδ1(D⋂Lδ∞(D, with all spaces weighted by the function exp(δr. This provides a key ingredient for the analysis of nonlinear problems via the method of alternative problems.
Einstein-Gauss-Bonnet theory of gravity: The Gauss-Bonnet-Katz boundary term
Deruelle, Nathalie; Merino, Nelson; Olea, Rodrigo
2018-05-01
We propose a boundary term to the Einstein-Gauss-Bonnet action for gravity, which uses the Chern-Weil theorem plus a dimensional continuation process, such that the extremization of the full action yields the equations of motion when Dirichlet boundary conditions are imposed. When translated into tensorial language, this boundary term is the generalization to this theory of the Katz boundary term and vector for general relativity. The boundary term constructed in this paper allows to deal with a general background and is not equivalent to the Gibbons-Hawking-Myers boundary term. However, we show that they coincide if one replaces the background of the Katz procedure by a product manifold. As a first application we show that this Einstein Gauss-Bonnet Katz action yields, without any extra ingredients, the expected mass of the Boulware-Deser black hole.
Open problems in Gaussian fluid queueing theory
Dȩbicki, K.; Mandjes, M.
2011-01-01
We present three challenging open problems that originate from the analysis of the asymptotic behavior of Gaussian fluid queueing models. In particular, we address the problem of characterizing the correlation structure of the stationary buffer content process, the speed of convergence to
New Boundary Constraints for Elliptic Systems used in Grid Generation Problems
Kaul, Upender K.; Clancy, Daniel (Technical Monitor)
2002-01-01
This paper discusses new boundary constraints for elliptic partial differential equations as used in grid generation problems in generalized curvilinear coordinate systems. These constraints, based on the principle of local conservation of thermal energy in the vicinity of the boundaries, are derived using the Green's Theorem. They uniquely determine the so called decay parameters in the source terms of these elliptic systems. These constraints' are designed for boundary clustered grids where large gradients in physical quantities need to be resolved adequately. It is observed that the present formulation also works satisfactorily for mild clustering. Therefore, a closure for the decay parameter specification for elliptic grid generation problems has been provided resulting in a fully automated elliptic grid generation technique. Thus, there is no need for a parametric study of these decay parameters since the new constraints fix them uniquely. It is also shown that for Neumann type boundary conditions, these boundary constraints uniquely determine the solution to the internal elliptic problem thus eliminating the non-uniqueness of the solution of an internal Neumann boundary value grid generation problem.
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)
Theory of boundary-free two-dimensional dust clusters
International Nuclear Information System (INIS)
Tsytovich, V.N.; Gousein-zade, N.G.; Morfill, G.E.
2006-01-01
It is shown theoretically that a stable two-dimensional (2D) grain cluster can exist in plasmas without external confinement if the shadow attraction of grains is taken into account. These are considered as boundary-free clusters. The equilibrium radius of the clusters is investigated numerically. It is found that it is rapidly decreasing with an increase of the attraction coefficient and with an increase of the number of grains N in the cluster. Comparison of energies of one shell cluster containing N grains with the energies of a cluster with N-1 grains in the shell and an additional one grain in the center as functions of the attraction coefficient is used to find the magic numbers for new shell creation. It is demonstrated that a dissociation of the cluster in several smaller clusters requires less energy than a removal of one of the grains from the cluster. The computations were performed for the Debye screening and for the nonlinear screening models and show that the structure of the clusters is sensitive to the type of screening. Frequencies of all collective modes of the 2D boundary-free clusters are calculated up to N=7 grains in the cluster for the case where all grains form one shell cluster and for the case where N=6 grains form one shell cluster and one of the grains is located at the center of the cluster. The frequencies of the modes increase with a decrease of the cluster radius. Stable and unstable modes are investigated as a function of the attraction coefficient. The presence of instability indicates that this type of equilibrium cluster does not correspond to the minimum energy in all directions and will be converted into another stable configuration. The universal magic number N m of grains in one shell cluster, such that for N=N m +1 the modes of the shell start to be unstable and the cluster converts to the cluster with N m grains in the shell and one grain in the center, is found for both the Yukawa screening and for the nonlinear screening
A boundary control problem with a nonlinear reaction term
Directory of Open Access Journals (Sweden)
John R. Cannon
2009-04-01
Full Text Available The authors study the problem $u_t=u_{xx}-au$, $0
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.
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.
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.
M. Denche; A. L. Marhoune
2003-01-01
In this paper, we study a mixed problem with integral boundary conditions for a high order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on energy inequality, and on the density of the range of the operator generated by the considered problem.
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
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...
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
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)
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
Use of Green's functions in the numerical solution of two-point boundary value problems
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.
Azis, Moh. Ivan; Kasbawati; Haddade, Amiruddin; Astuti Thamrin, Sri
2018-03-01
A boundary element method (BEM) is obtained for solving a boundary value problem of homogeneous anisotropic media governed by diffusion-convection equation. The application of the BEM is shown for two particular pollutant transport problems of Tello river and Unhas lake in Makassar Indonesia. For the two particular problems a variety of the coefficients of diffusion and the velocity components are taken. The results show that the solutions vary as the parameters change. And this suggests that one has to be careful in measuring or determining the values of the parameters.
Application of the perturbation iteration method to boundary layer type problems.
Pakdemirli, Mehmet
2016-01-01
The recently developed perturbation iteration method is applied to boundary layer type singular problems for the first time. As a preliminary work on the topic, the simplest algorithm of PIA(1,1) is employed in the calculations. Linear and nonlinear problems are solved to outline the basic ideas of the new solution technique. The inner and outer solutions are determined with the iteration algorithm and matched to construct a composite expansion valid within all parts of the domain. The solutions are contrasted with the available exact or numerical solutions. It is shown that the perturbation-iteration algorithm can be effectively used for solving boundary layer type problems.
Numerical solution of system of boundary value problems using B-spline with free parameter
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.
The large Reynolds number - Asymptotic theory of turbulent boundary layers.
Mellor, G. L.
1972-01-01
A self-consistent, asymptotic expansion of the one-point, mean turbulent equations of motion is obtained. Results such as the velocity defect law and the law of the wall evolve in a relatively rigorous manner, and a systematic ordering of the mean velocity boundary layer equations and their interaction with the main stream flow are obtained. The analysis is extended to the turbulent energy equation and to a treatment of the small scale equilibrium range of Kolmogoroff; in velocity correlation space the two-thirds power law is obtained. Thus, the two well-known 'laws' of turbulent flow are imbedded in an analysis which provides a great deal of other information.
Biophysics at the Boundaries: The Next Problem Sets
Skolnick, Malcolm
2009-03-01
The interface between physics and biology is one of the fastest growing subfields of physics. As knowledge of such topics as cellular processes and complex ecological systems advances, researchers have found that progress in understanding these and other systems requires application of more quantitative approaches. Today, there is a growing demand for quantitative and computational skills in biological research and the commercialization of that research. The fragmented teaching of science in our universities still leaves biology outside the quantitative and mathematical culture that is the foundation of physics. This is particularly inopportune at a time when the needs for quantitative thinking about biological systems are exploding. More physicists should be encouraged to become active in research and development in the growing application fields of biophysics including molecular genetics, biomedical imaging, tissue generation and regeneration, drug development, prosthetics, neural and brain function, kinetics of nonequilibrium open biological systems, metabolic networks, biological transport processes, large-scale biochemical networks and stochastic processes in biochemical systems to name a few. In addition to moving into basic research in these areas, there is increasing opportunity for physicists in industry beginning with entrepreneurial roles in taking research results out of the laboratory and in the industries who perfect and market the inventions and developments that physicists produce. In this talk we will identify and discuss emerging opportunities for physicists in biophysical and biotechnological pursuits ranging from basic research through development of applications and commercialization of results. This will include discussion of the roles of physicists in non-traditional areas apart from academia such as patent law, financial analysis and regulatory science and the problem sets assigned in education and training that will enable future
Boundary condition for Ginzburg-Landau theory of superconducting layers
Czech Academy of Sciences Publication Activity Database
Koláček, Jan; Lipavský, Pavel; Morawetz, K.; Brandt, E. H.
2009-01-01
Roč. 79, č. 17 (2009), 174510/1-174510/6 ISSN 1098-0121 R&D Projects: GA ČR GA202/08/0326; GA AV ČR IAA100100712 Institutional research plan: CEZ:AV0Z10100521 Keywords : superconductivity * Ginzburg-Landau theory Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.475, year: 2009
Solving free-plasma-boundary problems with the SIESTA MHD code
Sanchez, R.; Peraza-Rodriguez, H.; Reynolds-Barredo, J. M.; Tribaldos, V.; Geiger, J.; Hirshman, S. P.; Cianciosa, M.
2017-10-01
SIESTA is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for 3D magnetic configurations. It is an iterative code that uses the solution obtained by the VMEC code to provide a background coordinate system and an initial guess of the solution. The final solution that SIESTA finds can exhibit magnetic islands and stochastic regions. In its original implementation, SIESTA addressed only fixed-boundary problems. This fixed boundary condition somewhat restricts its possible applications. In this contribution we describe a recent extension of SIESTA that enables it to address free-plasma-boundary situations, opening up the possibility of investigating problems with SIESTA in which the plasma boundary is perturbed either externally or internally. As an illustration, the extended version of SIESTA is applied to a configuration of the W7-X stellarator.
International Nuclear Information System (INIS)
Choi, Chang Yong
1999-01-01
This paper presents a study of the Dual Reciprocity Boundary Element Method (DRBEM) for the laminar heat convection problem in a concentric annulus with constant heat flux boundary condition. DRBEM is one of the most successful technique used to transform the domain integrals arising from the nonhomogeneous term of the poisson equation into equivalent boundary only integrals. This recently developed and highly efficient numerical method is tested for the solution accuracy of the fluid flow and heat transfer study in a concentric annulus. Since their exact solutions are available, DRBEM solutions are verified with different number of boundary element discretization and internal points. The results obtained in this study are discussed with the relative error percentage of velocity and temperature solutions, and potential applicability of the method for the more complicated heat convection problems with arbitrary duct geometries
A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems
Directory of Open Access Journals (Sweden)
S. S. Motsa
2013-01-01
Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.
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.
Psychoanalytic theory and the problem of creativity.
Fossi, G
1985-01-01
The current crisis of psychoanalysis also involves studies of various forms of creativity. After having pointed out the need for distinction between clinical-empirical theory and hypothetical theory (such as metapsychology) the author identifies and summarizes a number of trends of investigation as reported in our literature: libidinal-energetic, contenutistic (unconscious fantasies), anthropomorphic (of the ego), aggression-reparation, phenomenological, and object-relationship approaches. The role played by metapsychological concepts (the author, in agreement with those who consider them unacceptable, discusses some of the most well-known criticisms), and the confusion between theoretical levels are responsible for having made the psychoanalytical contribution entirely unsatisfactory at a higher explanatory level and for having hindered adequate reorganization of data of an empirical nature. After having examined several elements involved in creativity (symbolism, role of pathology and body experience, etc.), the author outlines a personal theoretical hypothesis of the structural type as a basis for the establishment of a clinical-empirical theory which, as regards research on creativity too, may constitute the chief field of investigation for psychoanalysis.
A General Theory of Markovian Time Inconsistent Stochastic Control Problems
DEFF Research Database (Denmark)
Björk, Tomas; Murgochi, Agatha
We develop a theory for stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We attach these problems by viewing them within a game theoretic framework, and we look for Nash subgame perfect equilibrium points...... examples of time inconsistency in the literature are easily seen to be special cases of the present theory. We also prove that for every time inconsistent problem, there exists an associated time consistent problem such that the optimal control and the optimal value function for the consistent problem...
A Successful Senior Seminar: Unsolved Problems in Number Theory
Styer, Robert
2014-01-01
The "Unsolved Problems in Number Theory" book by Richard Guy provides nice problems suitable for a typical math major. We give examples of problems that have worked well in our senior seminar course and some nice results that senior math majors can obtain.
Applying Graph Theory to Problems in Air Traffic Management
Farrahi, Amir H.; Goldberg, Alan T.; Bagasol, Leonard N.; Jung, Jaewoo
2017-01-01
Graph theory is used to investigate three different problems arising in air traffic management. First, using a polynomial reduction from a graph partitioning problem, it isshown that both the airspace sectorization problem and its incremental counterpart, the sector combination problem are NP-hard, in general, under several simple workload models. Second, using a polynomial time reduction from maximum independent set in graphs, it is shown that for any fixed e, the problem of finding a solution to the minimum delay scheduling problem in traffic flow management that is guaranteed to be within n1-e of the optimal, where n is the number of aircraft in the problem instance, is NP-hard. Finally, a problem arising in precision arrival scheduling is formulated and solved using graph reachability. These results demonstrate that graph theory provides a powerful framework for modeling, reasoning about, and devising algorithmic solutions to diverse problems arising in air traffic management.
An extension of diffusion theory for thermal neutrons near boundaries
International Nuclear Information System (INIS)
Alvarez Rivas, J. L.
1963-01-01
The distribution of thermal neutron flux has been measured inside and outside copper rods of several diameters, immersed in water. It has been found that these distributions can be calculated by means of elemental diffusion theory if the value of the coefficient of diffusion is changed. this parameter is truly a diffusion coefficient, which now also depends on the diameter of the rod. Through a model an expression of this coefficient is introduced which takes account of the measurements of the author and of those reported in PIGC P/928 (1995), ANL-5872 (1959), DEGR 319 (D) (1961). This model could be extended also to plane geometry. (Author) 19 refs
Functional geometric method for solving free boundary problems for harmonic functions
Energy Technology Data Exchange (ETDEWEB)
Demidov, Aleksander S [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)
2010-01-01
A survey is given of results and approaches for a broad spectrum of free boundary problems for harmonic functions of two variables. The main results are obtained by the functional geometric method. The core of these methods is an interrelated analysis of the functional and geometric characteristics of the problems under consideration and of the corresponding non-linear Riemann-Hilbert problems. An extensive list of open questions is presented. Bibliography: 124 titles.
Wang, Chunbai; Mitra, Ambar K.
2016-01-01
Any boundary surface evolving in viscous fluid is driven with surface capillary currents. By step function defined for the fluid-structure interface, surface currents are found near a flat wall in a logarithmic form. The general flat-plate boundary layer is demonstrated through the interface kinematics. The dynamics analysis elucidates the relationship of the surface currents with the adhering region as well as the no-slip boundary condition. The wall skin friction coefficient, displacement thickness, and the logarithmic velocity-defect law of the smooth flat-plate boundary-layer flow are derived with the advent of the forced evolving boundary method. This fundamental theory has wide applications in applied science and engineering.
Assessment of a transitional boundary layer theory at low hypersonic Mach numbers
Shamroth, S. J.; Mcdonald, H.
1972-01-01
An investigation was carried out to assess the accuracy of a transitional boundary layer theory in the low hypersonic Mach number regime. The theory is based upon the simultaneous numerical solution of the boundary layer partial differential equations for the mean motion and an integral form of the turbulence kinetic energy equation which controls the magnitude and development of the Reynolds stress. Comparisions with experimental data show the theory is capable of accurately predicting heat transfer and velocity profiles through the transitional regime and correctly predicts the effects of Mach number and wall cooling on transition Reynolds number. The procedure shows promise of predicting the initiation of transition for given free stream disturbance levels. The effects on transition predictions of the pressure dilitation term and of direct absorption of acoustic energy by the boundary layer were evaluated.
Three-dimensional problems in the theory of cracks
International Nuclear Information System (INIS)
Panasyuk, V.V.; Andrejkiv, A.E.; Stadnik, M.M.
1979-01-01
Review of the main mechanical conceptions and mathematic methods, used in solving of spatial problems of the theory of cracks is given. At that, cases of effects upon a body of force static and cyclic and geometrically variable temperature fields are considered. The main calculation models of the theory of cracks are characterized in detail. Other models, derived from these ones and used in solving the above problems are also mentioned. Analysis and synthesis of the most general mathematic methods of solving three-dimensional problems of the theory of cracks are made. Besides precise methods, approximate ones are also presented, being efficient enough in engineering practice
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.
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
Reconsidering the boundary conditions for a dynamic, transient mode I crack problem
Leise, Tanya
2008-11-01
A careful examination of a dynamic mode I crack problem leads to the conclusion that the commonly used boundary conditions do not always hold in the case of an applied crack face loading, so that a modification is required to satisfy the equations. In particular, a transient compressive stress wave travels along the crack faces, moving outward from the loading region on the crack face. This does not occur in the quasistatic or steady state problems, and is a special feature of the transient dynamic problem that is important during the time interval immediately following the application of crack face loading. We demonstrate why the usual boundary conditions lead to a prediction of crack face interpenetration, and then examine how to modify the boundary condition for a semi-infinite crack with a cohesive zone. Numerical simulations illustrate the resulting approach.
Cadel, Daniel R.; Zhang, Di; Lowe, K. Todd; Paterson, Eric G.
2018-04-01
Wind turbines with thick blade profiles experience turbulent, periodic approach flow, leading to unsteady blade loading and large torque fluctuations on the turbine drive shaft. Presented here is an experimental study of a surrogate problem representing some key aspects of the wind turbine unsteady fluid mechanics. This experiment has been designed through joint consideration by experiment and computation, with the ultimate goal of numerical model development for aerodynamics in unsteady and turbulent flows. A cylinder at diameter Reynolds number of 65,000 and Strouhal number of 0.184 is placed 10.67 diameters upstream of a NACA 63215b airfoil with chord Reynolds number of 170,000 and chord-reduced frequency of k=2π fc/2/V=1.5. Extensive flow field measurements using particle image velocimetry provide a number of insights about this flow, as well as data for model validation and development. Velocity contours on the airfoil suction side in the presence of the upstream cylinder indicate a redistribution of turbulent normal stresses from transverse to streamwise, consistent with rapid distortion theory predictions. A study of the boundary layer over the suction side of the airfoil reveals very low Reynolds number turbulent mean streamwise velocity profiles. The dominance of the high amplitude large eddy passages results in a phase lag in streamwise velocity as a function of distance from the wall. The results and accompanying description provide a new test case incorporating moderate-reduced frequency inflow for computational model validation and development.
Multidimensional phase change problems by the dual-reciprocity boundary-element method
International Nuclear Information System (INIS)
Jo, J.C.; Shin, W.K.; Choi, C.Y.
1999-01-01
Transient heat transfer problems with phase changes (Stefan problems) occur in many engineering situations, including potential core melting and solidification during pressurized-water-reactor severe accidents, ablation of thermal shields, melting and solidification of alloys, and many others. This article addresses the numerical analysis of nonlinear transient heat transfer with melting or solidification. An effective and simple procedure is presented for the simulation of the motion of the boundary and the transient temperature field during the phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual-reciprocity boundary-element method. The dual-reciprocity boundary-element approach provided in this article is much simpler than the usual boundary-element method in applying a reciprocity principle and an available technique for dealing with the domain integral of the boundary element formulation simultaneously. In this article, attention is focused on two-dimensional melting (ablation)/solidification problems for simplicity. The accuracy and effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of some examples of one-phase ablation/solidification problems with their known semianalytical or numerical solutions where available
A New Approach to Gas Discharge Theory with Sheath Boundaries
Chen, Francis F.; Curreli, Davide
Classical theories of gas discharges have concentrated on the microscopic properties of collisions and diffusion coefficients, but few have considered the macroscopic observables such as the density and temperature profiles. Since practical devices cannot be approximated by infinite cylinders, we consider finite cylinders with endplates. There, the short-circuit effect permits electrons to be Maxwellian even in the presence of a DC magnetic field. For uniform electron temperature Te and pressure p, the radial density profile is found to have a "universal" shape independent of p. A code EQM is developed to solve for radial profiles when all quantities vary with r and includes ionization balance and neutral depletion. The profile Te(r) depends on the type of discharge and is found for helicon discharges by iterating with the code HELIC. Resulting n(r) profiles are flat or peaked on axis, as found in experiment, even when ionization is localized to the edge.
Boundary string field theory and an open string one-loop
International Nuclear Information System (INIS)
Lee, Tae Jin; Viswanathan, K. S.; Yang, Yi
2003-01-01
We discuss the open string one-loop partition function in the tachyon condensation background of an unstable D-brane system. We evaluate the partition function by using the boundary-state formulation and find that it is in complete agreement with the result obtained in the boundary string field theory. This suggests that the open string higher loop diagrams may be produced consistently by using a closed string field theory, where the D-brane plays the role of a source for the closed string field
Classical open-string field theory: A∞-algebra, renormalization group and boundary states
International Nuclear Information System (INIS)
Nakatsu, Toshio
2002-01-01
We investigate classical bosonic open-string field theory from the perspective of the Wilson renormalization group of world-sheet theory. The microscopic action is identified with Witten's covariant cubic action and the short-distance cut-off scale is introduced by length of open-string strip which appears in the Schwinger representation of open-string propagator. Classical open-string field theory in the title means open-string field theory governed by a classical part of the low energy action. It is obtained by integrating out suitable tree interactions of open-strings and is of non-polynomial type. We study this theory by using the BV formalism. It turns out to be deeply related with deformation theory of A ∞ -algebra. We introduce renormalization group equation of this theory and discuss it from several aspects. It is also discussed that this theory is interpreted as a boundary open-string field theory. Closed-string BRST charge and boundary states of closed-string field theory in the presence of open-string field play important roles
Initial-boundary value problems associated with the Ablowitz-Ladik system
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.
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.
Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin
2016-01-01
This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.
POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
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FAOUZI HADDOUCHI
2015-11-01
Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.
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
String theory and the dark glueball problem
Energy Technology Data Exchange (ETDEWEB)
Halverson, James; Nelson, Brent D. [Northeastern Univ., Boston, MA (United States). Dept. of Physics; Ruehle, Fabian [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2016-09-15
We study cosmological constraints on dark pure Yang-Mills sectors. Dark glueballs are overproduced for large regions of ultraviolet parameter space. The problem may be alleviated in two ways: via a large preferential reheating into the visible sector, motivating certain inflation or modulus decay models, or via decays into axions or moduli, which are strongly constrained by nucleosynthesis and ΔN{sub eff} bounds. String models frequently have multiple hidden Yang-Mills sectors, which are subject to even stronger constraints due to the existence of multiple dark glueballs.
Problems in the theory of modular forms
Murty, M Ram; Graves, Hester
2016-01-01
This book introduces the reader to the fascinating world of modular forms through a problem-solving approach. As such, besides researchers, the book can be used by the undergraduate and graduate students for self-instruction. The topics covered include q-series, the modular group, the upper half-plane, modular forms of level one and higher level, the Ramanujan τ-function, the Petersson inner product, Hecke operators, Dirichlet series attached to modular forms and further special topics. It can be viewed as a gentle introduction for a deeper study of the subject. Thus, it is ideal for non-experts seeking an entry into the field. .
String theory and the dark glueball problem
International Nuclear Information System (INIS)
Halverson, James; Nelson, Brent D.
2016-09-01
We study cosmological constraints on dark pure Yang-Mills sectors. Dark glueballs are overproduced for large regions of ultraviolet parameter space. The problem may be alleviated in two ways: via a large preferential reheating into the visible sector, motivating certain inflation or modulus decay models, or via decays into axions or moduli, which are strongly constrained by nucleosynthesis and ΔN_e_f_f bounds. String models frequently have multiple hidden Yang-Mills sectors, which are subject to even stronger constraints due to the existence of multiple dark glueballs.
Riemann monodromy problem and conformal field theories
International Nuclear Information System (INIS)
Blok, B.
1989-01-01
A systematic analysis of the use of the Riemann monodromy problem for determining correlators (conformal blocks) on the sphere is presented. The monodromy data is constructed in terms of the braid matrices and gives a constraint on the noninteger part of the conformal dimensions of the primary fields. To determine the conformal blocks we need to know the order of singularities. We establish a criterion which tells us when the knowledge of the conformal dimensions of primary fields suffice to determine the blocks. When zero modes of the extended algebra are present the analysis is more difficult. In this case we give a conjecture that works for the SU(2) WZW case. (orig.)
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Lukáš Ladislav
2017-01-01
Full Text Available The paper is focused on American option pricing problem. Assuming non-dividend paying American put option leads to two disjunctive regions, a continuation one and a stopping one, which are separated by an early exercise boundary. We present variational formulation of American option problem with special attention to early exercise action effect. Next, we discuss financially motivated additive decomposition of American option price into a European option price and another part due to the extra premium required by early exercising the option contract. As the optimal exercise boundary is a free boundary, its determination is coupled with the determination of the option price. Therefore, a closed-form expression of the free boundary is not attainable in general. We discuss in detail a derivation of an asymptotic expression of the early exercise boundary. Finally, we present some numerical results of determination of free boundary based upon this approach. All computations are performed by sw Mathematica, and suitable numerical procedure is discussed in detail, as well.
K. Schwarzschild's problem in radiation transfer theory
International Nuclear Information System (INIS)
Rutily, B.; Chevallier, L.; Pelkowski, J.
2006-01-01
We solve exactly the problem of a finite slab receiving an isotropic radiation on one side and no radiation on the other side. This problem-to be more precise the calculation of the source function within the slab-was first formulated by K. Schwarzschild in 1914. We first solve it for unspecified albedos and optical thicknesses of the atmosphere, in particular for an albedo very close to 1 and a very large optical thickness in view of some astrophysical applications. Then we focus on the conservative case (albedo=1), which is of great interest for the modeling of grey atmospheres in radiative equilibrium. Ten-figure tables of the conservative source function are given. From the analytical expression of this function, we deduce (1) a simple relation between the effective temperature of a grey atmosphere in radiative equilibrium and the temperature of the black body that irradiates it (2) the temperature at any point of the atmosphere when it is in local thermodynamical equilibrium. This temperature distribution is the counterpart, for a finite slab, of Hopf's distribution in a half-space. Its graphical representation is given for various optical thicknesses of the atmosphere
Boundary element methods applied to two-dimensional neutron diffusion problems
International Nuclear Information System (INIS)
Itagaki, Masafumi
1985-01-01
The Boundary element method (BEM) has been applied to two-dimensional neutron diffusion problems. The boundary integral equation and its discretized form have been derived. Some numerical techniques have been developed, which can be applied to critical and fixed-source problems including multi-region ones. Two types of test programs have been developed according to whether the 'zero-determinant search' or the 'source iteration' technique is adopted for criticality search. Both programs require only the fluxes and currents on boundaries as the unknown variables. The former allows a reduction in computing time and memory in comparison with the finite element method (FEM). The latter is not always efficient in terms of computing time due to the domain integral related to the inhomogeneous source term; however, this domain integral can be replaced by the equivalent boundary integral for a region with a non-multiplying medium or with a uniform source, resulting in a significant reduction in computing time. The BEM, as well as the FEM, is well suited for solving irregular geometrical problems for which the finite difference method (FDM) is unsuited. The BEM also solves problems with infinite domains, which cannot be solved by the ordinary FEM and FDM. Some simple test calculations are made to compare the BEM with the FEM and FDM, and discussions are made concerning the relative merits of the BEM and problems requiring future solution. (author)
Simulation of Thermal Flow Problems via a Hybrid Immersed Boundary-Lattice Boltzmann Method
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J. Wu
2012-01-01
Full Text Available A hybrid immersed boundary-lattice Boltzmann method (IB-LBM is presented in this work to simulate the thermal flow problems. In current approach, the flow field is resolved by using our recently developed boundary condition-enforced IB-LBM (Wu and Shu, (2009. The nonslip boundary condition on the solid boundary is enforced in simulation. At the same time, to capture the temperature development, the conventional energy equation is resolved. To model the effect of immersed boundary on temperature field, the heat source term is introduced. Different from previous studies, the heat source term is set as unknown rather than predetermined. Inspired by the idea in (Wu and Shu, (2009, the unknown is calculated in such a way that the temperature at the boundary interpolated from the corrected temperature field accurately satisfies the thermal boundary condition. In addition, based on the resolved temperature correction, an efficient way to compute the local and average Nusselt numbers is also proposed in this work. As compared with traditional implementation, no approximation for temperature gradients is required. To validate the present method, the numerical simulations of forced convection are carried out. The obtained results show good agreement with data in the literature.
[The problem of divisions, wagers, and game theory].
Cléro, Jean-Pierre
2011-01-01
This article looks at the "problem of the divisions" - a dialogue between two persons or more - to bring out its structure, in which religious and ethical elements are intermingled. It then offers a reevaluation of the argument of the wager, which is seen here as a sort of prefiguration of game theory rather than as the solution to a problem of probabilities. Although their correspondence suggests that Fermat and Pascal believed they were offering a solution to the same problem, they were not - as written by Fermat, the problem of divisions is a problem of probabilities, but ultimately Fermat did not solve the same problem as Pascal.
Some problems of modern gravitation theory
International Nuclear Information System (INIS)
Markov, M.A.
1984-01-01
Possible role of gravitation in high-energy physics and cosmology is under study. A problem of the limiting elementary particle mass is considered. Maximum value of the elementary partjcle mass is chosen to be msub(p)=(h/2πc/kappa)sup(1/2) approximately equal to 10 -5 g. The presented combination of universal constants is called the Plank mass, which is considered as possible characteristics of real physical objects called ''maximons''. These superheavy elementary particles may play an important part in the Universe evolution. Emphasis is paid to the scenario of the Universe evolution, according to which maximons are formed just in the first moments of the Universe expansion, and, then, form a normal substance interacting with each other. Reasons confirming the oscillating Universe model are presented
Solving the decompactification problem in string theory
Kiritsis, Elias B; Petropoulos, P M; Rizos, J
1996-01-01
We investigate heterotic ground states in four dimensions in which N=4 supersymmetry is spontaneously broken to N=2. N=4 supersymmetry is restored at a decompactification limit corresponding to m_{3/2}\\to 0. We calculate the full moduli dependent threshold corrections and confirm that they are supressed in the decompactification limit m_{3/2}\\to 0 as expected from the restauration of N=4 supersymmetry. This should be contrasted with the behavior of the standard N=2 groundstates where the coupling blow up linearly with the volume of the decompactifying manifold. This mechanism provides a solution to the decompactification problem for the gauge coupling constants. We also discuss how the mechanism can be implemented in ground states with lower supersymmetry.
Problems in particle theory. Technical report - 1993--1994
International Nuclear Information System (INIS)
Adler, S.L.; Wilczek, F.
1994-10-01
This report is a progress report on the work of two principal investigators in the broad area of particle physics theory, covering their personal work, that of their coworkers, and their proposed work for the future. One author has worked in the past on various topics in field theory and particle physics, among them current algebras, the physics of neutrino induced reactions, quantum electrodynamics (including strong magnetic field processes), the theory of the axial-vector current anomaly, topics in quantum gravity, and nonlinear models for quark confinement. While much of his work has been analytical, all of the projects listed above (except for the work on gravity) had phases which required considerable computer work as well. Over the next several years, he proposes to continue or initiate research on the following problems: (1) Acceleration algorithms for the Monte Carlo analysis of lattice field and gauge theories, and more generally, new research in computational neuroscience and pattern recognition. (2) Construction of quaternionic generalizations of complex quantum mechanics and field theory, and their application to composite models of quarks and leptons, and to the problem of unifying quantum theories of matter with general relativity. One author has worked on problems in exotic quantum statistics and its applications to condensed matter systems. His work has also continued on the quantum theory of black holes. This has evolved toward understanding properties of quantum field theory and string theory in incomplete regions of flat space
The Laplace equation boundary value problems on bounded and unbounded Lipschitz domains
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.
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Kyncl Martin
2017-01-01
Full Text Available We work with the system of partial differential equations describing the non-stationary compressible turbulent fluid flow. It is a characteristic feature of the hyperbolic equations, that there is a possible raise of discontinuities in solutions, even in the case when the initial conditions are smooth. The fundamental problem in this area is the solution of the so-called Riemann problem for the split Euler equations. It is the elementary problem of the one-dimensional conservation laws with the given initial conditions (LIC - left-hand side, and RIC - right-hand side. The solution of this problem is required in many numerical methods dealing with the 2D/3D fluid flow. The exact (entropy weak solution of this hyperbolical problem cannot be expressed in a closed form, and has to be computed by an iterative process (to given accuracy, therefore various approximations of this solution are being used. The complicated Riemann problem has to be further modified at the close vicinity of boundary, where the LIC is given, while the RIC is not known. Usually, this boundary problem is being linearized, or roughly approximated. The inaccuracies implied by these simplifications may be small, but these have a huge impact on the solution in the whole studied area, especially for the non-stationary flow. Using the thorough analysis of the Riemann problem we show, that the RIC for the local problem can be partially replaced by the suitable complementary conditions. We suggest such complementary conditions accordingly to the desired preference. This way it is possible to construct the boundary conditions by the preference of total values, by preference of pressure, velocity, mass flow, temperature. Further, using the suitable complementary conditions, it is possible to simulate the flow in the vicinity of the diffusible barrier. On the contrary to the initial-value Riemann problem, the solution of such modified problems can be written in the closed form for some
A nonlinear free boundary problem with a self-driven Bernoulli condition
Dipierro, Serena; Karakhanyan, Aram; Valdinoci, Enrico
2017-01-01
We study a Bernoulli type free boundary problem with two phases J[u]=∫Ω|∇u(x)|2dx+Φ(M−(u),M+(u)),u−u¯∈W1,20(Ω), where u¯∈W1,2(Ω) is a given boundary datum. Here, M1 and M2 are weighted volumes of {u≤0}∩Ω and {u>0}∩Ω, respectively, and Φ is a nonnegative function of two real variables. We show that, for this problem, the Bernoulli constant, which determines the gradient jump condition across the free boundary, is of global type and it is indeed determined by the weighted volumes of the phas...
The boundary element method applied to 3D magneto-electro-elastic dynamic problems
Igumnov, L. A.; Markov, I. P.; Kuznetsov, Iu A.
2017-11-01
Due to the coupling properties, the magneto-electro-elastic materials possess a wide number of applications. They exhibit general anisotropic behaviour. Three-dimensional transient analyses of magneto-electro-elastic solids can hardly be found in the literature. 3D direct boundary element formulation based on the weakly-singular boundary integral equations in Laplace domain is presented in this work for solving dynamic linear magneto-electro-elastic problems. Integral expressions of the three-dimensional fundamental solutions are employed. Spatial discretization is based on a collocation method with mixed boundary elements. Convolution quadrature method is used as a numerical inverse Laplace transform scheme to obtain time domain solutions. Numerical examples are provided to illustrate the capability of the proposed approach to treat highly dynamic problems.
Towards quantum gravity via quantum field theory. Problems and perspectives
Energy Technology Data Exchange (ETDEWEB)
Fredenhagen, Klaus [II. Institut fuer Theoretische Physik, Universitaet Hamburg (Germany)
2016-07-01
General Relativity is a classical field theory; the standard methods for constructing a corresponding quantum field theory, however, meet severe difficulties, in particular perturbative non-renormalizability and the problem of background independence. Nevertheless, modern approaches to quantum field theory have significantly lowered these obstacles. On the side of non-renormalizability, this is the concept of effective theories, together with indications for better non-perturbative features of the renormalization group flow. On the side of background independence the main progress comes from an improved understanding of quantum field theories on generic curved spacetimes. Combining these informations, a promising approach to quantum gravity is an expansion around a classical solution which then is a quantum field theory on a given background, augmented by an identity which expresses independence against infinitesimal shifts of the background. The arising theory is expected to describe small corrections to classical general relativity. Inflationary cosmology is expected to arise as a lowest order approximation.
Student Solutions Manual to Boundary Value Problems and Partial Differential Equations
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
Existence and uniqueness for a two-point interface boundary value problem
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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.
Boundary Value Problems for a Super-Sublinear Asymmetric Oscillator: The Exact Number of Solutions
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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.
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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.
Application of the HN method to the critical slab problem for reflecting boundary conditions
International Nuclear Information System (INIS)
Tuereci, R.G.; Guelecyuez, M.C.; Kaskas, A.; Tezcan, C.
2004-01-01
The recently developed H N method is used to solve the critical slab problem for a slab which is surrounded by a reflector. In the special case for R=0 (the reflection coefficient) the problem reduces to the one under vacuum boundary conditions. It is shown that the method is concise and leads to fast converging numerical results. The presented numerical results are compared with the data available in literature
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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.
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
Existence of positive solutions for a multi-point four-order boundary-value problem
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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.
A New Numerical Algorithm for Two-Point Boundary Value Problems
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.
L^p-continuity of solutions to parabolic free boundary problems
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Abdeslem Lyaghfouri
2015-07-01
Full Text Available In this article, we consider a class of parabolic free boundary problems. We establish some properties of the solutions, including L^infinity-regularity in time and a monotonicity property, from which we deduce strong L^p-continuity in time.
Hopf bifurcation of a free boundary problem modeling tumor growth with two time delays
International Nuclear Information System (INIS)
Xu Shihe
2009-01-01
In this paper, a free boundary problem modeling tumor growth with two discrete delays is studied. The delays respectively represents the time taken for cells to undergo mitosis and the time taken for the cell to modify the rate of cell loss due to apoptosis. We show the influence of time delays on the Hopf bifurcation when one of delays as a bifurcation parameter.
Kot, V. A.
2017-11-01
The modern state of approximate integral methods used in applications, where the processes of heat conduction and heat and mass transfer are of first importance, is considered. Integral methods have found a wide utility in different fields of knowledge: problems of heat conduction with different heat-exchange conditions, simulation of thermal protection, Stefantype problems, microwave heating of a substance, problems on a boundary layer, simulation of a fluid flow in a channel, thermal explosion, laser and plasma treatment of materials, simulation of the formation and melting of ice, inverse heat problems, temperature and thermal definition of nanoparticles and nanoliquids, and others. Moreover, polynomial solutions are of interest because the determination of a temperature (concentration) field is an intermediate stage in the mathematical description of any other process. The following main methods were investigated on the basis of the error norms: the Tsoi and Postol’nik methods, the method of integral relations, the Gudman integral method of heat balance, the improved Volkov integral method, the matched integral method, the modified Hristov method, the Mayer integral method, the Kudinov method of additional boundary conditions, the Fedorov boundary method, the method of weighted temperature function, the integral method of boundary characteristics. It was established that the two last-mentioned methods are characterized by high convergence and frequently give solutions whose accuracy is not worse that the accuracy of numerical solutions.
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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.
Geopotential coefficient determination and the gravimetric boundary value problem: A new approach
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.
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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.
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Cornelis van der Mee
2005-01-01
Full Text Available We present the complete version including proofs of the results announced in [van der Mee C., Pivovarchik V.: A Sturm-Liouville spectral problem with boundary conditions depending on the spectral parameter. Funct. Anal. Appl. 36 (2002, 315–317 [Funkts. Anal. Prilozh. 36 (2002, 74–77 (Russian
Three symmetric positive solutions of fourth-order singular nonlocal boundary value problems
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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.
Triple solutions for multi-point boundary-value problem with p-Laplace operator
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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.
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.
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
The Method of Subsuper Solutions for Weighted p(r-Laplacian Equation Boundary Value Problems
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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.
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 ...
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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.
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
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
Boundary-value problems for first and second order functional differential inclusions
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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.
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
The boundary element method : errors and gridding for problems with hot spots
Kakuba, G.
2011-01-01
Adaptive gridding methods are of fundamental importance both for industry and academia. As one of the computing methods, the Boundary Element Method (BEM) is used to simulate problems whose fundamental solutions are available. The method is usually characterised as constant elements BEM or linear
Conformal field theory on surfaces with boundaries and nondiagonal modular invariants
International Nuclear Information System (INIS)
Bern, Z.; Dunbar, D.C.
1990-01-01
This paper shows that the operator content of a conformal field theory defined on surfaces with boundaries and crosscaps is more restricted when the periodic sector is described by nondiagonal modular invariants than in the case of diagonal modular invariants. By tensoring, the restrictions can be alleviated, leading to a rich structure. Such constrictions are useful, for example, in lower- dimensional open superstring models
Fortuin, K.P.J.; Bush, S.R.
2010-01-01
Abstract: Purpose – The purpose of this paper is to evaluate and analyse the didactic model of a university course, which concerns an applied academic consultancy project and which focuses on skills related to crossing boundaries between disciplines and cultures, and between theory and practice.
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.
A.R. Ansari; B. Hossain; B. Koren (Barry); G.I. Shishkin (Gregori)
2007-01-01
textabstractWe investigate the model problem of flow of a viscous incompressible fluid past a symmetric curved surface when the flow is parallel to its axis. This problem is known to exhibit boundary layers. Also the problem does not have solutions in closed form, it is modelled by boundary-layer
International Nuclear Information System (INIS)
Barucq, Helene; Bekkey, Chokri; Djellouli, Rabia
2004-01-01
We present a general procedure based on the pseudo-differential calculus for deriving artificial boundary conditions for an eigenvalue problem that characterizes the propagation of guided modes in optical waveguides. This new approach allows the construction of local conditions that (a) are independent of the frequency regime, (b) preserve the sparsity pattern of the finite element discretization, and (c) are applicable to arbitrarily shaped convex artificial boundaries. The last feature has the potential for reducing the size of the computational domain. Numerical results are presented to highlight the potential of conditions of order 1/2 and 1, for improving significantly the computational efficiency of finite element methods for the solution of optical waveguide problems
Optimization of the solution of the problem of scheduling theory ...
African Journals Online (AJOL)
This article describes the genetic algorithm used to solve the problem related to the scheduling theory. A large number of different methods is described in the scientific literature. The main issue that faced the problem in question is that it is necessary to search the optimal solution in a large search space for the set of ...
Schoenfeld's problem solving theory in a student controlled learning environment
Harskamp, E.; Suhre, C.
2007-01-01
This paper evaluates the effectiveness of a student controlled computer program for high school mathematics based on instruction principles derived from Schoenfeld's theory of problem solving. The computer program allows students to choose problems and to make use of hints during different episodes
Variational methods for problems from plasticity theory and for generalized Newtonian fluids
Fuchs, Martin
2000-01-01
Variational methods are applied to prove the existence of weak solutions for boundary value problems from the deformation theory of plasticity as well as for the slow, steady state flow of generalized Newtonian fluids including the Bingham and Prandtl-Eyring model. For perfect plasticity the role of the stress tensor is emphasized by studying the dual variational problem in appropriate function spaces. The main results describe the analytic properties of weak solutions, e.g. differentiability of velocity fields and continuity of stresses. The monograph addresses researchers and graduate students interested in applications of variational and PDE methods in the mechanics of solids and fluids.
An(1) affine Toda field theories with integrable boundary conditions revisited
International Nuclear Information System (INIS)
Doikou, Anastasia
2008-01-01
Generic classically integrable boundary conditions for the A n (1) affine Toda field theories (ATFT) are investigated. The present analysis rests primarily on the underlying algebra, defined by the classical version of the reflection equation. We use as a prototype example the first non-trivial model of the hierarchy i.e. the A 2 (1) ATFT, however our results may be generalized for any A n (1) (n > 1). We assume here two distinct types of boundary conditions called some times soliton preserving (SP), and soliton non-preserving (SNP) associated to two distinct algebras, i.e. the reflection algebra and the (q) twisted Yangian respectively. The boundary local integrals of motion are then systematically extracted from the asymptotic expansion of the associated transfer matrix. In the case of SNP boundary conditions we recover previously known results. The other type of boundary conditions (SP), associated to the reflection algebra, are novel in this context and lead to a different set of conserved quantities that depend on free boundary parameters. It also turns out that the number of local integrals of motion for SP boundary conditions is 'double' compared to those of the SNP case.
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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.
A Cp-theory problem book functional equivalencies
Tkachuk, Vladimir V
2016-01-01
This fourth volume in Vladimir Tkachuk's series on Cp-theory gives reasonably complete coverage of the theory of functional equivalencies through 500 carefully selected problems and exercises. By systematically introducing each of the major topics of Cp-theory, the book is intended to bring a dedicated reader from basic topological principles to the frontiers of modern research. The book presents complete and up-to-date information on the preservation of topological properties by homeomorphisms of function spaces. An exhaustive theory of t-equivalent, u-equivalent and l-equivalent spaces is developed from scratch. The reader will also find introductions to the theory of uniform spaces, the theory of locally convex spaces, as well as the theory of inverse systems and dimension theory. Moreover, the inclusion of Kolmogorov's solution of Hilbert's Problem 13 is included as it is needed for the presentation of the theory of l-equivalent spaces. This volume contains the most important classical re...
What is Time in Some Modern Physics Theories: Interpretation Problems
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Karpenko Ivan A.
2016-03-01
Full Text Available The article deals with the problem of time in the context of several theories of modem physics. This fundamental concept inevitably arises in physical theories, but so far there is no adequate description of it in the philosophy of science. In the theory of relativity, quantum field theory. Standard Model of particle physics, theory of loop quantum gravity, superstring theory and other most recent theories the idea of time is shown explicitly or not. Sometimes, such as in the special theory of relativity, it plays a significant role and sometimes it does not. But anyway it exists and is implied by the content of the theory, which in some cases directly includes its mathematical tools. Fundamental difference of space-time processes in microcosm and macrocosm is of particular importance for solving the problem. In this regard, a need to understand the time in the way it appears in modem physics, to describe it in the language of philosophy arises (satisfactory for time description mathematical tools also do not exist. This will give an opportunity to get closer to the answer on question of time characteristics. And even if we do not obtain the exact answer, we will still be able to formulate the right question about its nature. For this purpose, the present research carries out analysis of the key theories of modern physics with regard to historical and scientific, historical and philosophical perspectives, hi some cases, this gives an opportunity to detect the succession of the associated with time perception ideas, their development, as well as the origination of fundamentally new ones. During the analysis, the conect characteristics of time are formulated from the point of view of physical theory and the attempt to state the nature of time is made. On the ground of conducted research, the conclusions about current state of the problem and its future solution perspectives are drawn.
Bulk Renormalization Group Flows and Boundary States in Conformal Field Theories
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John Cardy
2017-08-01
Full Text Available We propose using smeared boundary states $e^{-\\tau H}|\\cal B\\rangle$ as variational approximations to the ground state of a conformal field theory deformed by relevant bulk operators. This is motivated by recent studies of quantum quenches in CFTs and of the entanglement spectrum in massive theories. It gives a simple criterion for choosing which boundary state should correspond to which combination of bulk operators, and leads to a rudimentary phase diagram of the theory in the vicinity of the RG fixed point corresponding to the CFT, as well as rigorous upper bounds on the universal amplitude of the free energy. In the case of the 2d minimal models explicit formulae are available. As a side result we show that the matrix elements of bulk operators between smeared Ishibashi states are simply given by the fusion rules of the CFT.
Wave scattering theory and the absorption problem for a black hole
International Nuclear Information System (INIS)
Sanchez, N.
1977-01-01
The general problem of scattering and absorption of waves from a Schwarzschild black hole is investigated. A scattering absorption amplitude is introduced. The unitarity theorem for this problem is derived from the wave equation and its boundary conditions. The formulation of the problem, within the formal scattering theory approach, is also given. The existence of a singularity in space-time is related explicitly to the presence of a nonzero absorption cross section. Another derivation of the unitarity theorem for our problem is given by operator methods. The reciprocity relation is also proved; that is, for the scattering of waves the black hole is a reciprocal system. Finally, the elastic scattering problem is considered, and the elastic scattering amplitude is calculated for high frequencies and small scattering angles
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Alsaidi M. Altaher
2012-01-01
Full Text Available Classical wavelet thresholding methods suffer from boundary problems caused by the application of the wavelet transformations to a finite signal. As a result, large bias at the edges and artificial wiggles occur when the classical boundary assumptions are not satisfied. Although polynomial wavelet regression and local polynomial wavelet regression effectively reduce the risk of this problem, the estimates from these two methods can be easily affected by the presence of correlated noise and outliers, giving inaccurate estimates. This paper introduces two robust methods in which the effects of boundary problems, outliers, and correlated noise are simultaneously taken into account. The proposed methods combine thresholding estimator with either a local polynomial model or a polynomial model using the generalized least squares method instead of the ordinary one. A primary step that involves removing the outlying observations through a statistical function is considered as well. The practical performance of the proposed methods has been evaluated through simulation experiments and real data examples. The results are strong evidence that the proposed method is extremely effective in terms of correcting the boundary bias and eliminating the effects of outliers and correlated noise.
Problem of the Moving Boundary in Continuous Casting Solved by The Analytic-Numerical Method
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Grzymkowski R.
2013-03-01
Full Text Available Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase - liquid phase leads to formulation of the parabolic or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.
Problem of the Moving Boundary in Continuous Casting Solved by the Analytic-Numerical Method
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R. Grzymkowski
2013-01-01
Full Text Available Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase – liquid phase leads to formulation of the parabolic or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.
Leise, Tanya L.
2009-08-19
We consider the problem of the dynamic, transient propagation of a semi-infinite, mode I crack in an infinite elastic body with a nonlinear, viscoelastic cohesize zone. Our problem formulation includes boundary conditions that preclude crack face interpenetration, in contrast to the usual mode I boundary conditions that assume all unloaded crack faces are stress-free. The nonlinear viscoelastic cohesive zone behavior is motivated by dynamic fracture in brittle polymers in which crack propagation is preceeded by significant crazing in a thin region surrounding the crack tip. We present a combined analytical/numerical solution method that involves reducing the problem to a Dirichlet-to-Neumann map along the crack face plane, resulting in a differo-integral equation relating the displacement and stress along the crack faces and within the cohesive zone. © 2009 Springer Science+Business Media B.V.
Nursing's Boundary Work: Theory Development and the Making of Nursing Science, ca. 1950-1980.
Tobbell, Dominique A
Beginning in the late 1950s and intensifying through the 1960s and 1970s, nurse educators, researchers, and scholars worked to establish nursing as an academic discipline. These nursing leaders argued that the development of nursing theory was not only critical to nursing's academic project but also to improving nursing practice and patient care. The purpose of the article is to examine the context for the development of nursing theory and the characteristics of early theory development from the 1950s through the early 1980s. The methods used were historical research and analysis of the social, cultural, and political context of nursing theory development from the 1950s through the early 1980s. How this context influenced the work of nurse theorists and researchers in these decades was addressed. The development of nursing theory was influenced by a context that included the increasing complexity of patient care, the relocation of nursing education from hospital-based diploma schools to colleges and universities, and the ongoing efforts of nurses to secure more professional autonomy and authority in the decades after World War II. In particular, from the 1960s through the early 1980s, nurse theorists, researchers, and educators viewed the establishment of nursing science, underpinned by nursing theory, as critical to establishing nursing as an academic discipline. To define nursing science, nurse theorists and researchers engaged in critical boundary work in order to draw epistemic boundaries between nursing science and the existing biomedical and behavioral sciences. By the early 1980s, the boundary work of nurse theorists and researchers was incomplete. Their efforts to define nursing science and establish nursing as an academic discipline were constrained by generational and intraprofessional politics, limited resources, the gendered and hierarchical politics, and the complexity of drawing disciplinary boundaries for a discipline that is inherently
Simulation of unilateral contact problems departing from the classical boundary problems
International Nuclear Information System (INIS)
Frey, S.L.; Sampaio, R.; Gama, R.M.S. da.
1989-08-01
A numerical algorithm is proposed for simulating unilateral contact problems under the classical elasticity point of view. This simple algorithm may be employed by engineers with a minimum knowledge on classical elasticity. (A.C.A.S.) [pt
Heaslet, Max A; Lomax, Harvard
1948-01-01
A direct analogy is established between the use of source-sink and doublet distributions in the solution of specific boundary-value problems in subsonic wing theory and the corresponding problems in supersonic theory. The correct concept of the "finite part" of an integral is introduced and used in the calculation of the improper integrals associated with supersonic doublet distributions. The general equations developed are shown to include several previously published results and particular examples are given for the loading on rolling and pitching triangular wings with supersonic leading edges.
Solution matching for a three-point boundary-value problem on atime scale
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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 $[t_2, t_3] cap mathbb{T}$.
The quantum-field renormalization group in the problem of a growing phase boundary
International Nuclear Information System (INIS)
Antonov, N.V.; Vasil'ev, A.N.
1995-01-01
Within the quantum-field renormalization-group approach we examine the stochastic equation discussed by S.I. Pavlik in describing a randomly growing phase boundary. We show that, in contrast to Pavlik's assertion, the model is not multiplicatively renormalizable and that its consistent renormalization-group analysis requires introducing an infinite number of counterterms and the respective coupling constants (open-quotes chargeclose quotes). An explicit calculation in the one-loop approximation shows that a two-dimensional surface of renormalization-group points exits in the infinite-dimensional charge space. If the surface contains an infrared stability region, the problem allows for scaling with the nonuniversal critical dimensionalities of the height of the phase boundary and time, δ h and δ t , which satisfy the exact relationship 2 δ h = δ t + d, where d is the dimensionality of the phase boundary. 23 refs., 1 tab
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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 ÃÂ†-Laplacian. Applications of the existence principle to singular discrete problems are given.
On the propagation problem in gravitational radiation theory
International Nuclear Information System (INIS)
Damour, T.
1986-01-01
The authors emphasize that a suitable combination of analytical and numerical methods might be useful to overcome the limitations of both methods. In particular, analytical methods are needed, on the one hand to provide boundary conditions to numerical codes, and on the other hand to relate the gravitational field at the outer edge of the grid with the asymptotic outgoing wave form. The authors present an explicit formula which solves approximately the latter ''propagation problem'' in a simplified situation which might be relevant to the problem of computing the gravitational wave form emitted during the three-dimensional collapse of a star
Problems in probability theory, mathematical statistics and theory of random functions
Sveshnikov, A A
1979-01-01
Problem solving is the main thrust of this excellent, well-organized workbook. Suitable for students at all levels in probability theory and statistics, the book presents over 1,000 problems and their solutions, illustrating fundamental theory and representative applications in the following fields: Random Events; Distribution Laws; Correlation Theory; Random Variables; Entropy & Information; Markov Processes; Systems of Random Variables; Limit Theorems; Data Processing; and more.The coverage of topics is both broad and deep, ranging from the most elementary combinatorial problems through lim
On some classical problems of descriptive set theory
International Nuclear Information System (INIS)
Kanovei, Vladimir G; Lyubetskii, Vasilii A
2003-01-01
The centenary of P.S. Novikov's birth provides an inspiring motivation to present, with full proofs and from a modern standpoint, the presumably definitive solutions of some classical problems in descriptive set theory which were formulated by Luzin [Lusin] and, to some extent, even earlier by Hadamard, Borel, and Lebesgue and relate to regularity properties of point sets. The solutions of these problems began in the pioneering works of Aleksandrov [Alexandroff], Suslin [Souslin], and Luzin (1916-17) and evolved in the fundamental studies of Goedel, Novikov, Cohen, and their successors. Main features of this branch of mathematics are that, on the one hand, it is an ordinary mathematical theory studying natural properties of point sets and functions and rather distant from general set theory or intrinsic problems of mathematical logic like consistency or Goedel's theorems, and on the other hand, it has become a subject of applications of the most subtle tools of modern mathematical logic
Square matrices of order 2 theory, applications, and problems
Pop, Vasile
2017-01-01
This unique and innovative book presents an exciting and complete detail of all the important topics related to the theory of square matrices of order 2. The readers exploring every detailed aspect of matrix theory are gently led toward understanding advanced topics. They will follow every notion of matrix theory with ease, accumulating a thorough understanding of algebraic and geometric aspects of matrices of order 2. The prime jewel of this book is its offering of an unusual collection of problems, theoretically motivated, most of which are new, original, and seeing the light of publication for the first time in the literature. Nearly all of the exercises are presented with detailed solutions and vary in difficulty from easy to more advanced. Many problems are particularly challenging. These, and not only these, invite the reader to unleash their creativity and research capabilities and to discover their own methods of attacking a problem. Matrices have a vast practical importance to mathematics, science, a...
Problems of the π meson-nucleus interaction theory
International Nuclear Information System (INIS)
Kopaleishvili, T.I.
1984-01-01
The theory of multiple scattering as applied to PI-meson scattering on nuclei is outlined on the base of optical potential method: first in neglecting the real absorption of a pion by a nucleus and then for the case when this effect is taken into account. The pion interaction with a deuteron is considered both neglecting the pion absorption channel (the relativisitic problem of three bodies) and with account of the absorption channels and pion emission (in this case the problem is solved within the frames of the channel coupling theory for the pion-two nucleus system and the system of two nucleons). Approximate or model solutions to the problem of elastic pion-nuclear scattering primarily in the range of (3.3)-resonance are presented. The formulated theory permits to uniquely describe the observed processes caused by the strong pion interaction with a two-nucleon system
On Wigner's problem, computability theory, and the definition of life
International Nuclear Information System (INIS)
Swain, J.
1998-01-01
In 1961, Eugene Wigner presented a clever argument that in a world which is adequately described by quantum mechanics, self-reproducing systems in general, and perhaps life in particular, would be incredibly improbable. The problem and some attempts at its solution are examined, and a new solution is presented based on computability theory. In particular, it is shown that computability theory provides limits on what can be known about a system in addition to those which arise from quantum mechanics. (author)
Cost-effective computations with boundary interface operators in elliptic problems
International Nuclear Information System (INIS)
Khoromskij, B.N.; Mazurkevich, G.E.; Nikonov, E.G.
1993-01-01
The numerical algorithm for fast computations with interface operators associated with the elliptic boundary value problems (BVP) defined on step-type domains is presented. The algorithm is based on the asymptotically almost optimal technique developed for treatment of the discrete Poincare-Steklov (PS) operators associated with the finite-difference Laplacian on rectangles when using the uniform grid with a 'displacement by h/2'. The approach can be regarded as an extension of the method proposed for the partial solution of the finite-difference Laplace equation to the case of displaced grids and mixed boundary conditions. It is shown that the action of the PS operator for the Dirichlet problem and mixed BVP can be computed with expenses of the order of O(Nlog 2 N) both for arithmetical operations and computer memory needs, where N is the number of unknowns on the rectangle boundary. The single domain algorithm is applied to solving the multidomain elliptic interface problems with piecewise constant coefficients. The numerical experiments presented confirm almost linear growth of the computational costs and memory needs with respect to the dimension of the discrete interface problem. 14 refs., 3 figs., 4 tabs
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
On the microeconomic problems studied by portfolio theory
Nikonov, Oleg; Medvedeva, Marina
2012-09-01
In the paper we consider economically motivated problems, which are treated with the help of methods of portfolio theory that goes back to the papers by H. Markowitz [1] and J. Tobin [2]. We show that the portfolio theory initially developed for risky securities (stocks) could be applied to other objects. In the present paper we consider several situations where such an application is reasonable and seems to be fruitful. Namely, we consider the problems of constructing the efficient portfolio of banking services and the portfolio of counteragents of a firm.
A Hamiltonian-based derivation of Scaled Boundary Finite Element Method for elasticity problems
International Nuclear Information System (INIS)
Hu Zhiqiang; Lin Gao; Wang Yi; Liu Jun
2010-01-01
The Scaled Boundary Finite Method (SBFEM) is a semi-analytical solution approach for solving partial differential equation. For problem in elasticity, the governing equations can be obtained by mechanically based formulation, Scaled-boundary-transformation-based formulation and principle of virtual work. The governing equations are described in the frame of Lagrange system and the unknowns are displacements. But in the solution procedure, the auxiliary variables are introduced and the equations are solved in the state space. Based on the observation that the duality system to solve elastic problem proposed by W.X. Zhong is similar to the above solution approach, the discretization of the SBFEM and the duality system are combined to derive the governing equations in the Hamilton system by introducing the dual variables in this paper. The Precise Integration Method (PIM) used in Duality system is also an efficient method for the solution of the governing equations of SBFEM in displacement and boundary stiffness matrix especially for the case which results some numerical difficulties in the usually uses the eigenvalue method. Numerical examples are used to demonstrate the validity and effectiveness of the PIM for solution of boundary static stiffness.
Sources of spurious force oscillations from an immersed boundary method for moving-body problems
Lee, Jongho; Kim, Jungwoo; Choi, Haecheon; Yang, Kyung-Soo
2011-04-01
When a discrete-forcing immersed boundary method is applied to moving-body problems, it produces spurious force oscillations on a solid body. In the present study, we identify two sources of these force oscillations. One source is from the spatial discontinuity in the pressure across the immersed boundary when a grid point located inside a solid body becomes that of fluid with a body motion. The addition of mass source/sink together with momentum forcing proposed by Kim et al. [J. Kim, D. Kim, H. Choi, An immersed-boundary finite volume method for simulations of flow in complex geometries, Journal of Computational Physics 171 (2001) 132-150] reduces the spurious force oscillations by alleviating this pressure discontinuity. The other source is from the temporal discontinuity in the velocity at the grid points where fluid becomes solid with a body motion. The magnitude of velocity discontinuity decreases with decreasing the grid spacing near the immersed boundary. Four moving-body problems are simulated by varying the grid spacing at a fixed computational time step and at a constant CFL number, respectively. It is found that the spurious force oscillations decrease with decreasing the grid spacing and increasing the computational time step size, but they depend more on the grid spacing than on the computational time step size.
Diagrammatics lectures on selected problems in condensed matter theory
Sadovskii, Michael V
2006-01-01
The introduction of quantum field theory methods has led to a kind of "revolution" in condensed matter theory. This resulted in the increased importance of Feynman diagrams or diagram technique. It has now become imperative for professionals in condensed matter theory to have a thorough knowledge of this method.There are many good books that cover the general aspects of diagrammatic methods. At the same time, there has been a rising need for books that describe calculations and methodical "know how" of specific problems for beginners in graduate and postgraduate courses. This unique collection
The finite section method and problems in frame theory
DEFF Research Database (Denmark)
Christensen, Ole; Strohmer, T.
2005-01-01
solves related computational problems in frame theory. In the case of a frame which is localized w.r.t. an orthonormal basis we are able to estimate the rate of approximation. The results are applied to the reproducing kernel frame appearing in the theory for shift-invariant spaces generated by a Riesz......The finite section method is a convenient tool for approximation of the inverse of certain operators using finite-dimensional matrix techniques. In this paper we demonstrate that the method is very useful in frame theory: it leads to an efficient approximation of the inverse frame operator and also...
A Cp-theory problem book compactness in function spaces
Tkachuk, Vladimir V
2015-01-01
This third volume in Vladimir Tkachuk's series on Cp-theory problems applies all modern methods of Cp-theory to study compactness-like properties in function spaces and introduces the reader to the theory of compact spaces widely used in Functional Analysis. The text is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research covering a wide variety of topics in Cp-theory and general topology at the professional level. The first volume, Topological and Function Spaces © 2011, provided an introduction from scratch to Cp-theory and general topology, preparing the reader for a professional understanding of Cp-theory in the last section of its main text. The second volume, Special Features of Function Spaces © 2014, continued from the first, giving reasonably complete coverage of Cp-theory, systematically introducing each of the major topics and providing 500 carefully selected problems and exercises with complete solutions. This third volume is self-contained...
Solving inverse two-point boundary value problems using collage coding
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.
Belmiloudi, A.; Mahé, F.
2014-01-01
International audience; The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydration of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, for the optimal set of parameters minimizing objective functions J. Numerical si...
The boundary element method for the solution of the multidimensional inverse heat conduction problem
International Nuclear Information System (INIS)
Lagier, Guy-Laurent
1999-01-01
This work focuses on the solution of the inverse heat conduction problem (IHCP), which consists in the determination of boundary conditions from a given set of internal temperature measurements. This problem is difficult to solve due to its ill-posedness and high sensitivity to measurement error. As a consequence, numerical regularization procedures are required to solve this problem. However, most of these methods depend on the dimension and the nature, stationary or transient, of the problem. Furthermore, these methods introduce parameters, called hyper-parameters, which have to be chosen optimally, but can not be determined a priori. So, a new general method is proposed for solving the IHCP. This method is based on a Boundary Element Method formulation, and the use of the Singular Values Decomposition as a regularization procedure. Thanks to this method, it's possible to identify and eliminate the directions of the solution where the measurement error plays the major role. This algorithm is first validated on two-dimensional stationary and one-dimensional transient problems. Some criteria are presented in order to choose the hyper-parameters. Then, the methodology is applied to two-dimensional and three-dimensional, theoretical or experimental, problems. The results are compared with those obtained by a standard method and show the accuracy of the method, its generality, and the validity of the proposed criteria. (author) [fr
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
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.
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)
Directory of Open Access Journals (Sweden)
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.
Mathematical and numerical study of nonlinear boundary problems related to plasma physics
International Nuclear Information System (INIS)
Sermange, M.
1982-06-01
After the study of some equations based on the Hodgkin-Huxley model, the work presented here is concerned with nonlinear boundary problems in MHD. They are gathered in two subjects: equilibrium equations and stability equations. The axisymmetric MHD equilibrium equations with free boundary have been studied by different authors, particularly the existence, regularity, unicity and non-unicity. Here, bifurcation, convergence of calculation methods existence of solutions in a discontinuous frame are studied. MHD stability can be determined by the principle of Bernstein et al; the mathematical work concerned here bears on the equivalence, in the case of two-dimensional or axisymmetric stability, between this model and a scalar eigenvalue problem which is introduced. At last, modules for computing MHD equilibrium for the simulation of plasma confinement in a tokamak are described [fr
On a boundary layer problem related to the gas flow in shales
Barenblatt, G. I.
2013-01-16
The development of gas deposits in shales has become a significant energy resource. Despite the already active exploitation of such deposits, a mathematical model for gas flow in shales does not exist. Such a model is crucial for optimizing the technology of gas recovery. In the present article, a boundary layer problem is formulated and investigated with respect to gas recovery from porous low-permeability inclusions in shales, which are the basic source of gas. Milton Van Dyke was a great master in the field of boundary layer problems. Dedicating this work to his memory, we want to express our belief that Van Dyke\\'s profound ideas and fundamental book Perturbation Methods in Fluid Mechanics (Parabolic Press, 1975) will live on-also in fields very far from the subjects for which they were originally invented. © 2013 US Government.
Energy Technology Data Exchange (ETDEWEB)
Staat, M [Forschungszentrum Juelich GmbH (Germany). Inst. fuer Sicherheitsforschung und Reaktortechnik
1996-12-01
It is shown that the difficulty for probabilistic fracture mechanics (PFM) is the general problem of the high reliability of a small population. There is no way around the problem as yet. Therefore what PFM can contribute to the reliability of steel pressure boundaries is demonstrated with the example of a typical reactor pressure vessel and critically discussed. Although no method is distinguishable that could give exact failure probabilities, PFM has several additional chances. Upper limits for failure probability may be obtained together with trends for design and operating conditions. Further, PFM can identify the most sensitive parameters, improved control of which would increase reliability. Thus PFM should play a vital role in the analysis of steel pressure boundaries despite all shortcomings. (author). 19 refs, 7 figs, 1 tab.
International Nuclear Information System (INIS)
Staat, M.
1996-01-01
It is shown that the difficulty for probabilistic fracture mechanics (PFM) is the general problem of the high reliability of a small population. There is no way around the problem as yet. Therefore what PFM can contribute to the reliability of steel pressure boundaries is demonstrated with the example of a typical reactor pressure vessel and critically discussed. Although no method is distinguishable that could give exact failure probabilities, PFM has several additional chances. Upper limits for failure probability may be obtained together with trends for design and operating conditions. Further, PFM can identify the most sensitive parameters, improved control of which would increase reliability. Thus PFM should play a vital role in the analysis of steel pressure boundaries despite all shortcomings. (author). 19 refs, 7 figs, 1 tab
Plestenjak, Bor; Gheorghiu, Călin I.; Hochstenbach, Michiel E.
2015-10-01
In numerous science and engineering applications a partial differential equation has to be solved on some fairly regular domain that allows the use of the method of separation of variables. In several orthogonal coordinate systems separation of variables applied to the Helmholtz, Laplace, or Schrödinger equation leads to a multiparameter eigenvalue problem (MEP); important cases include Mathieu's system, Lamé's system, and a system of spheroidal wave functions. Although multiparameter approaches are exploited occasionally to solve such equations numerically, MEPs remain less well known, and the variety of available numerical methods is not wide. The classical approach of discretizing the equations using standard finite differences leads to algebraic MEPs with large matrices, which are difficult to solve efficiently. The aim of this paper is to change this perspective. We show that by combining spectral collocation methods and new efficient numerical methods for algebraic MEPs it is possible to solve such problems both very efficiently and accurately. We improve on several previous results available in the literature, and also present a MATLAB toolbox for solving a wide range of problems.
Some open problems in random matrix theory and the theory of integrable systems
Deift, Percy
2007-01-01
We describe a list of open problems in random matrix theory and integrable systems which was presented at the conference ``Integrable Systems, Random Matrices, and Applications'' at the Courant Institute in May 2006.
Monotone methods for solving a boundary value problem of second order discrete system
Directory of Open Access Journals (Sweden)
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.
Uniqueness in the inverse boundary value problem for piecewise homogeneous anisotropic elasticity
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...
The mixed boundary value problem, Krein resolvent formulas and spectral asymptotic estimates
DEFF Research Database (Denmark)
Grubb, Gerd
2011-01-01
For a second-order symmetric strongly elliptic operator A on a smooth bounded open set in Rn, the mixed problem is defined by a Neumann-type condition on a part Σ+ of the boundary and a Dirichlet condition on the other part Σ−. We show a Kreĭn resolvent formula, where the difference between its...... to the area of Σ+, in the case where A is principally equal to the 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
Directory of Open Access Journals (Sweden)
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.
Moving-boundary problems for the time-fractional diffusion equation
Directory of Open Access Journals (Sweden)
Sabrina D. Roscani
2017-02-01
Full Text Available We consider a one-dimensional moving-boundary problem for the time-fractional diffusion equation. The time-fractional derivative of order $\\alpha\\in (0,1$ is taken in the sense of Caputo. We study the asymptotic behaivor, as t tends to infinity, of a general solution by using a fractional weak maximum principle. Also, we give some particular exact solutions in terms of Wright functions.
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.
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
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.
Static solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory in vacuum
International Nuclear Information System (INIS)
Dotti, Gustavo; Oliva, Julio; Troncoso, Ricardo
2010-01-01
The classification of a certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is performed in d≥5 dimensions. The class of metrics under consideration is such that the spacelike section is a warped product of the real line and an arbitrary base manifold. It is shown that for a generic value of the Gauss-Bonnet coupling, the base manifold must be necessarily Einstein, with an additional restriction on its Weyl tensor for d>5. The boundary admits a wider class of geometries only in the special case when the Gauss-Bonnet coupling is such that the theory admits a unique maximally symmetric solution. The additional freedom in the boundary metric enlarges the class of allowed geometries in the bulk, which are classified within three main branches, containing new black holes and wormholes in vacuum.
Thickened boundary layer theory for air film drag reduction on a van body surface
Xie, Xiaopeng; Cao, Lifeng; Huang, Heng
2018-05-01
To elucidate drag reduction mechanism on a van body surface under air film condition, a thickened boundary layer theory was proposed and a frictional resistance calculation model of the van body surface was established. The frictional resistance on the van body surface was calculated with different parameters of air film thickness. In addition, the frictional resistance of the van body surface under the air film condition was analyzed by computational fluid dynamics (CFD) simulation and different air film states that influenced the friction resistance on the van body surface were discussed. As supported by the CFD simulation results, the thickened boundary layer theory may provide reference for practical application of air film drag reduction on a van body surface.
Schoonhoven, Clausia Bird
1981-01-01
Discusses problems in contingency theory, which relates organizational structure to the tasks performed and the information needed. Analysis of data from 17 hospitals suggests that traditional contingency theory underrepresents the complexity of relations among technological uncertainty, structure, and organizational effectiveness. (Author/RW)
Abraham Pais Prize Lecture: Shifting Problems and Boundaries in the History of Modern Physics
Nye, Mary-Jo
A long established category of study in the history of science is the ``history of physical sciences.'' It is a category that immediately begs the question of disciplinary boundaries for the problems and subjects addressed in historical inquiry. As a historian of the physical sciences, I often have puzzled over disciplinary boundaries and the means used to create or justify them. Scientists most often have been professionally identified with specific institutionalized fields since the late 19th century, but the questions they ask and the problems they solve are not neatly carved up by disciplinary perimeters. Like institutional departments or professorships, the Nobel Prizes in the 20th century often have delineated the scope of ``Physics'' or ``Chemistry'' (and ``Physiology or Medicine''), but the Prizes do not reflect disciplinary rigidity, despite some standard core subjects. In this paper I examine trends in Nobel Prize awards that indicate shifts in problem solving and in boundaries in twentieth century physics, tying those developments to changing themes in the history of physics and physical science in recent decades.
Directory of Open Access Journals (Sweden)
D. A. Eliseev
2015-01-01
Full Text Available The solution stability of an initial boundary problem for a linear hybrid system of differential equations, which models the rotation of a rigid body with two elastic rods located in the same plane is studied in the paper. To an axis passing through the mass center of the rigid body perpendicularly to the rods location plane is applied the stabilizing moment proportional to the angle of the system rotation, derivative of the angle, integral of the angle. The external moment provides a feedback. A method of studying the behavior of solutions of the initial boundary problem is proposed. This method allows to exclude from the hybrid system of differential equations partial differential equations, which describe the dynamics of distributed elements of a mechanical system. It allows us to build one equation for an angle of the system rotation. Its characteristic equation defines the stability of solutions of all the system. In the space of feedback-coefficients the areas that provide the asymptotic stability of solutions of the initial boundary problem are built up.
International Nuclear Information System (INIS)
Ji, X.; Chen, Y.M.
1989-01-01
The boundary element method (BEM) is developed from the boundary integral equation method and the discretization techniques. Compared with other numerical method, BEM has been shown to be a versatile and efficient method for a wide variety of engineering problems, including the wave propagation in elastic media. The first formulation and solution of the transient elastodynamic problem by combining BEM and Laplace transform is due to Cruse. Further improvement was achieved by introducing Durbin's method instead of Papoulis method of numerical Laplace inverse transform. However, a great deal of computer time is still needed for the inverse transformation. The alternative integral transform approach is BEM combining with Fourier transform. The numerical Fourier inverse transformation is also computer time consuming, even if the fast Fourier transform is used. In the present paper, the authors use BEM combining with Fourier transform and Fourier eigen transform (FET). The new approach is very attractive in saving on computer time. This paper illustrates the application of FET to BEM of 2-dimensional transient elastodynamic problem. The example of a half plane subjected to a discontinuous boundary load is solved on ELXSI 6400 computer. The CPU time is less than one minute. If Laplace or Fourier transform is adopted, the CPU time will be more than 10 minutes
Problem of energy-momentum and theory of gravitation
International Nuclear Information System (INIS)
Logunov, A.A.; Folomeshkin, V.N.
1977-01-01
General properties of geometrised theories of gravitation are considered. Covariant formulation of conservation laws in arbitrary riemannian space-time is given. In the Einstein theory the symmetric as well as canonical energy-momentum tensor of the system ''matter plus gravitational field'' and in particular, the energy-momentum of free gravitational waves, turns out to be equal to zero. To understand the origin of the problems and difficulties concerning the energy-momentum in the Einstein theory, the gravitational filed is considered in the usual framework of the Lorentz invariant field theory, just like any other physical field. Combination of the approach proposed with the Einstein's idea of geometrization makes it possible to formulate the geometrised gravitation theory, in which there are no inner contradictions, the energy-momentum of gravitational field is defined precisely and all the known experimental facts are described successfully. For strong gravitational fields the predictions of the quasilinear geometrised theory under consideration are different from those of the gravitational theory in the Einstein formulation. Black holes are absent in the theory. Evaluation of the energy-flux of gravitational waves leads to unambiguous results and shows that the gravitational waves transfer the positive-definite energy
An introduction to the general boundary formulation of quantum field theory
International Nuclear Information System (INIS)
Colosi, Daniele
2015-01-01
We give a brief introduction to the so-called general boundary formulation (GBF) of quantum theory. This new axiomatic formulation provides a description of the quantum dynamics which is manifestly local and does not rely on a metric background structure for its definition. We present the basic ingredients of the GBF, in particular we review the core axioms that assign algebraic structures to geometric ones, the two quantisation schemes so far developed for the GBF and the probability interpretation which generalizes the standard Born rule. Finally we briefly discuss some of the results obtained studying specific quantum field theories within the GBF. (paper)
Piomelli, Ugo; Zang, Thomas A.; Speziale, Charles G.; Lund, Thomas S.
1990-01-01
An eddy viscosity model based on the renormalization group theory of Yakhot and Orszag (1986) is applied to the large-eddy simulation of transition in a flat-plate boundary layer. The simulation predicts with satisfactory accuracy the mean velocity and Reynolds stress profiles, as well as the development of the important scales of motion. The evolution of the structures characteristic of the nonlinear stages of transition is also predicted reasonably well.
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.
Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method
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.
The Problem of Agency: Posthumanist Theory and English Teaching
Misson, Ray
2013-01-01
Many of the major movements in English teaching over the last 25 years have drawn on poststructuralist/posthumanist theory, filtered through work in cultural studies predicated on the social construction of identity. While this has been enormously productive in many ways, there has been a nagging problem with the question of agency. How can…
A new integrability theory for certain nonlinear physical problems
International Nuclear Information System (INIS)
Berger, M.S.
1993-01-01
A new mathematically sound integrability theory for certain nonlinear problems defined by ordinary or partial differential equations is defined. The new theory works in an arbitrary finite number of space dimensions. Moreover, if a system is integrable in the new sense described here, it has a remarkable stability property that distinguishes if from any previously known integrability ideas. The new theory proceeds by establishing a ''global normal form'' for the problem at hand. This normal form holds subject to canonical coordinate transformations, extending such classical ideas by using new nonlinear methods of infinite dimensional functional analysis. The global normal form in question is related to the mathematical theory of singularities of mappings of H. Whitney and R. Thom extended globally and form finite to infinite dimensions. Thus bifurcation phenomena are naturally included in the new integrability theory. Typical examples include the classically nonintegrable Riccati equation, certain non-Euclidean mean field theories, certain parabolic reaction diffusion equations and the hyperbolic nonlinear telegrapher's equation. (Author)
Directory of Open Access Journals (Sweden)
Guo Chun Wen
2009-05-01
Full Text Available This article concerns the oblique derivative problems for second-order quasilinear degenerate equations of mixed type with several characteristic boundaries, which include the Tricomi problem as a special case. First we formulate the problem and obtain estimates of its solutions, then we show the existence of solutions by the successive iterations and the Leray-Schauder theorem. We use a complex analytic method: elliptic complex functions are used in the elliptic domain, and hyperbolic complex functions in the hyperbolic domain, such that second-order equations of mixed type with degenerate curve are reduced to the first order mixed complex equations with singular coefficients. An application of the complex analytic method, solves (1.1 below with $m=n=1$, $a=b=0$, which was posed as an open problem by Rassias.
High order methods for incompressible fluid flow: Application to moving boundary problems
Energy Technology Data Exchange (ETDEWEB)
Bjoentegaard, Tormod
2008-04-15
Fluid flows with moving boundaries are encountered in a large number of real life situations, with two such types being fluid-structure interaction and free-surface flows. Fluid-structure phenomena are for instance apparent in many hydrodynamic applications; wave effects on offshore structures, sloshing and fluid induced vibrations, and aeroelasticity; flutter and dynamic response. Free-surface flows can be considered as a special case of a fluid-fluid interaction where one of the fluids are practically inviscid, such as air. This type of flows arise in many disciplines such as marine hydrodynamics, chemical engineering, material processing, and geophysics. The driving forces for free-surface flows may be of large scale such as gravity or inertial forces, or forces due to surface tension which operate on a much smaller scale. Free-surface flows with surface tension as a driving mechanism include the flow of bubbles and droplets, and the evolution of capillary waves. In this work we consider incompressible fluid flow, which are governed by the incompressible Navier-Stokes equations. There are several challenges when simulating moving boundary problems numerically, and these include - Spatial discretization - Temporal discretization - Imposition of boundary conditions - Solution strategy for the linear equations. These are some of the issues which will be addressed in this introduction. We will first formulate the problem in the arbitrary Lagrangian-Eulerian framework, and introduce the weak formulation of the problem. Next, we discuss the spatial and temporal discretization before we move to the imposition of surface tension boundary conditions. In the final section we discuss the solution of the resulting linear system of equations. (Author). refs., figs., tabs
On the problem of existence of quantum field theory
International Nuclear Information System (INIS)
Chaichian, M.; Hayashi, M.; Nelipa, N.F.; Pukhov, E.A.
1978-01-01
Existence of quantum field theory is considered for the four-dimensional phi 3 -model. The mathematical tool of contraction mapping principle is used to investigate the question of existence of solution for the infinite system of coupled equations for the Green functions of the theory in the Euclidean region. Formulation of the problem for this model with one divergent part is interesting in itself and provides the first attempt towards the study of other renormalizable quantum field theory models with infinite number of divergent graphs. For sufficiently small values of coupling constant, the theory has a unique solution for the truncated system of equations for the Green functions. However, for the complete, infinite set of equations, the Banach fixed point theorem admits a solution only when the coupling constant tends to zero. Possible reasons for such a result are discussed. (author)
UN Method For The Critical Slab Problem In One-Speed Neutron Transport Theory
International Nuclear Information System (INIS)
Oeztuerk, Hakan; Guengoer, Sueleyman
2008-01-01
The Chebyshev polynomial approximation (U N method) is used to solve the critical slab problem in one-speed neutron transport theory using Marshak boundary condition. The isotropic scattering kernel with the combination of forward and backward scattering is chosen for the neutrons in a uniform finite slab. Numerical results obtained by the U N method are presented in the tables together with the results obtained by the well-known P N method for comparison. It is shown that the method converges rapidly with its easily executable equations.
Promoting Number Theory in High Schools or Birthday Problem and Number Theory
Srinivasan, V. K.
2010-01-01
The author introduces the birthday problem in this article. This can amuse willing members of any birthday party. This problem can also be used as the motivational first day lecture in number theory for the gifted students in high schools or in community colleges or in undergraduate classes in colleges.
Turnpike theory of continuous-time linear optimal control problems
Zaslavski, Alexander J
2015-01-01
Individual turnpike results are of great interest due to their numerous applications in engineering and in economic theory; in this book the study is focused on new results of turnpike phenomenon in linear optimal control problems. The book is intended for engineers as well as for mathematicians interested in the calculus of variations, optimal control, and in applied functional analysis. Two large classes of problems are studied in more depth. The first class studied in Chapter 2 consists of linear control problems with periodic nonsmooth convex integrands. Chapters 3-5 consist of linear control problems with autonomous nonconvex and nonsmooth integrands. Chapter 6 discusses a turnpike property for dynamic zero-sum games with linear constraints. Chapter 7 examines genericity results. In Chapter 8, the description of structure of variational problems with extended-valued integrands is obtained. Chapter 9 ends the exposition with a study of turnpike phenomenon for dynamic games with extended value integran...
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
Ruggeri, Fabrizio
2016-05-12
In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given prescribed initial condition. We show how to derive the joint likelihood function for the forward problem, given some measurements of the solution field subject to Gaussian noise. Given Gaussian priors for the time-dependent Dirichlet boundary values, we analytically marginalize the joint likelihood using the linearity of the equation. Our hierarchical Bayesian approach is fully implemented in an example that involves the heat equation. In this example, the thermal diffusivity is the unknown parameter. We assume that the thermal diffusivity parameter can be modeled a priori through a lognormal random variable or by means of a space-dependent stationary lognormal random field. Synthetic data are used to test the inference. We exploit the behavior of the non-normalized log posterior distribution of the thermal diffusivity. Then, we use the Laplace method to obtain an approximated Gaussian posterior and therefore avoid costly Markov Chain Monte Carlo computations. Expected information gains and predictive posterior densities for observable quantities are numerically estimated using Laplace approximation for different experimental setups.
Electrodynamics as a problem of eigenvalues. III. Maxwell operator and perturbation theory
International Nuclear Information System (INIS)
Yudin, L.A.; Kapchinsky, M.I.; Korenev, I.L.; Efimov, S.P.
1996-01-01
This part of the work deals with perturbation theory. The standard technique permits us to solve problems of volume disturbances in free space, waveguides, and cavities, of disturbances of boundary conditions caused by finite conductivity of walls, and of disturbances of the boundary shape. Expressions for frequency and wave number shifts caused by the perturbation are obtained by the unified method. Several examples are presented: wave amplification in the waveguide filled with a resonant medium like an electron beam in a longitudinal magnetic field, the frequency shift (and increment/decrement) of a cavity loaded by an electron beam, and the field disturbance in the waveguide caused by finite conductivity of the walls. copyright 1996 American Institute of Physics
A simple finite element method for boundary value problems with a Riemann–Liouville derivative
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
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.
What do we actually mean by 'sociotechnical'? On values, boundaries and the problems of language.
Klein, Lisl
2014-03-01
The term 'sociotechnical' was first coined in the context of industrial democracy. In comparing two projects on shipping in Esso to help define the concept, the essential categories were found to be where systems boundaries were set, and what factors were considered to be relevant 'human' characteristics. This is often discussed in terms of values. During the nineteen-sixties and seventies sociotechnical theory related to the shop-floor work system, and contingency theory to the organisation as a whole, the two levels being distinct. With the coming of information technology, this distinction became blurred; the term 'socio-structural' is proposed to describe the whole system. IT sometimes is the operating technology, it sometimes supports the operating technology, or it may sometimes be mistaken for the operating technology. This is discussed with reference to recent air accidents. Copyright © 2013 Elsevier Ltd and The Ergonomics Society. All rights reserved.
Complete hierarchies of efficient approximations to problems in entanglement theory
International Nuclear Information System (INIS)
Eisert, Jens; Hyllus, Philipp; Guehne, Otfried; Curty, Marcos
2004-01-01
We investigate several problems in entanglement theory from the perspective of convex optimization. This list of problems comprises (A) the decision whether a state is multiparty entangled, (B) the minimization of expectation values of entanglement witnesses with respect to pure product states, (C) the closely related evaluation of the geometric measure of entanglement to quantify pure multiparty entanglement, (D) the test whether states are multiparty entangled on the basis of witnesses based on second moments and on the basis of linear entropic criteria, and (E) the evaluation of instances of maximal output purities of quantum channels. We show that these problems can be formulated as certain optimization problems: as polynomially constrained problems employing polynomials of degree 3 or less. We then apply very recently established known methods from the theory of semidefinite relaxations to the formulated optimization problems. By this construction we arrive at a hierarchy of efficiently solvable approximations to the solution, approximating the exact solution as closely as desired, in a way that is asymptotically complete. For example, this results in a hierarchy of efficiently decidable sufficient criteria for multiparticle entanglement, such that every entangled state will necessarily be detected in some step of the hierarchy. Finally, we present numerical examples to demonstrate the practical accessibility of this approach
Elliptic boundary value problems with fractional regularity data the first order approach
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.
Reflected forward-backward SDEs and obstacle problems with boundary conditions
Directory of Open Access Journals (Sweden)
Jin Ma
2001-01-01
Full Text Available In this paper we study a class of forward-backward stochastic differential equations with reflecting boundary conditions (FBSDER for short. More precisely, we consider the case in which the forward component of the FBSDER is restricted to a fixed, convex region, and the backward component will stay, at each fixed time, in a convex region that may depend on time and is possibly random. The solvability of such FBSDER is studied in a fairly general way. We also prove that if the coefficients are all deterministic and the backward equation is one-dimensional, then the adapted solution of such FBSDER will give the viscosity solution of a quasilinear variational inequality (obstacle problem with a Neumann boundary condition. As an application, we study how the solvability of FBSDERs is related to the solvability of an American game option.
Regularization theory for ill-posed problems selected topics
Lu, Shuai
2013-01-01
Thismonograph is a valuable contribution to thehighly topical and extremly productive field ofregularisationmethods for inverse and ill-posed problems. The author is an internationally outstanding and acceptedmathematicianin this field. In his book he offers a well-balanced mixtureof basic and innovative aspects.He demonstrates new,differentiatedviewpoints, and important examples for applications. The bookdemontrates thecurrent developments inthe field of regularization theory,such as multiparameter regularization and regularization in learning theory. The book is written for graduate and PhDs
A universal nonlinear relation among boundary states in closed string field theory
International Nuclear Information System (INIS)
Kishimoto, Isao; Matsuo, Yutaka; Watanabe, Eitoku
2004-01-01
We show that the boundary states satisfy a nonlinear relation (the idempotency equation) with respect to the star product of closed string field theory. This relation is universal in the sense that various D-branes, including the infinitesimally deformed ones, satisfy the same equation, including the coefficient. This paper generalizes our analysis [hep-th/0306189] in the following senses. (1) We present a background-independent formulation based on conformal field theory. It illuminates the geometric nature of the relation and allows us to more systematically analyze the variations around the D-brane background. (2) We show that the Witten-type star product satisfies a similar relation but with a more divergent coefficient. (3) We determine the coefficient of the relation analytically. The result shows that the α parameter can be formally factored out, and the relation becomes universal. We present a conjecture on vacuum theory based on this computation. (author)
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.
Multiple solutions of a free-boundary FRC equilibrium problem in a metal cylinder
International Nuclear Information System (INIS)
Spencer, R.L.; Hewett, D.W.
1981-01-01
A new approach to the computation of FRC equilibria that avoids previously encountered difficulties is presented. For arbitrary pressure profiles it is computationally expensive, but for one special pressure profile the problem is simple enough to require only minutes of Cray time; it is this problem that we have solved. We solve the Grad-Shafranov equation, Δ/sup */psi = r 2 p'(psi), in an infinitely long flux conserving cylinder of radius a with the boundary conditions that psi(a,z) = -psi/sub w/ and that delta psi/delta z = 0 as [z] approaches infinity. The pressure profile is p'(psi) = cH(psi) where c is a constant and where H(x) is the Heaviside function. We have found four solutions to this problem: There is a purely vacuum state, two z-independent plasma solutions, and an r-z-dependent plasma state
Existence of solutions to fractional boundary-value problems with a parameter
Directory of Open Access Journals (Sweden)
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.
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
Yan, Yan
2015-01-01
We study a new optimization scheme that generates smooth and robust solutions for Dirichlet velocity boundary control (DVBC) of conjugate heat transfer (CHT) processes. The solutions to the DVBC of the incompressible Navier-Stokes equations are typically nonsmooth, due to the regularity degradation of the boundary stress in the adjoint Navier-Stokes equations. This nonsmoothness is inherited by the solutions to the DVBC of CHT processes, since the CHT process couples the Navier-Stokes equations of fluid motion with the convection-diffusion equations of fluid-solid thermal interaction. Our objective in the CHT boundary control problem is to select optimally the fluid inflow profile that minimizes an objective function that involves the sum of the mismatch between the temperature distribution in the fluid system and a prescribed temperature profile and the cost of the control.Our strategy to resolve the nonsmoothness of the boundary control solution is based on two features, namely, the objective function with a regularization term on the gradient of the control profile on both the continuous and the discrete levels, and the optimization scheme with either explicit or implicit smoothing effects, such as the smoothed Steepest Descent and the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) methods. Our strategy to achieve the robustness of the solution process is based on combining the smoothed optimization scheme with the numerical continuation technique on the regularization parameters in the objective function. In the section of numerical studies, we present two suites of experiments. In the first one, we demonstrate the feasibility and effectiveness of our numerical schemes in recovering the boundary control profile of the standard case of a Poiseuille flow. In the second one, we illustrate the robustness of our optimization schemes via solving more challenging DVBC problems for both the channel flow and the flow past a square cylinder, which use initial
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
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.)
Criticality problems in energy dependent neutron transport theory
International Nuclear Information System (INIS)
Victory, H.D. Jr.
1979-01-01
The criticality problem is considered for energy dependent neutron transport in an isotropically scattering, homogeneous slab. Under a positivity assumption on the scattering kernel, an expression can be found relating the thickness of the slab to a parameter characterizing production by fission. This is accomplished by exploiting the Perron-Frobenius-Jentsch characterization of positive operators (i.e. those leaving invariant a normal, reproducing cone in a Banach space). It is pointed out that those techniques work for classes of multigroup problems were the Case singular eigenfunction approach is not as feasible as in the one-group theory, which is also analyzed
8th International Conference on Hyperbolic Problems : Theory, Numerics, Applications
Warnecke, Gerald
2001-01-01
The Eighth International Conference on Hyperbolic Problems - Theory, Nu merics, Applications, was held in Magdeburg, Germany, from February 27 to March 3, 2000. It was attended by over 220 participants from many European countries as well as Brazil, Canada, China, Georgia, India, Israel, Japan, Taiwan, und the USA. There were 12 plenary lectures, 22 further invited talks, and around 150 con tributed talks in parallel sessions as well as posters. The speakers in the parallel sessions were invited to provide a poster in order to enhance the dissemination of information. Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. Despite considerable progress, the mathematical theory is still strug gling with fundamental open problems concerning systems of such equations in multiple space dimensions. For various applications the development of accurate and efficient numerical schemes for computat...
On the inverse problem of dissipative scattering theory. 3
International Nuclear Information System (INIS)
Neidhardt, H.
1988-01-01
Considering a scattering theory in the class of contractions on Hilbert spaces one solves the inverse problem in an operaor-theoretical manner. The solution is obtained underthe very general assumptions that the free evolutions are different for different time directions that not only the perturbed or full evolutions but also the free evolutions are given by contractions. It is shown that the class of contractive Hankel operators can be viewed as a set of scattering operators. This implies the possibility that the scattering operator can be compact. Moreover, the result is applied to the so-called Lax-Phillips scattering theory with losses restoring a result of B.S. Pavlov on the completion of this theory in a quite different manner. 15 refs
A Cosserat crystal plasticity and phase field theory for grain boundary migration
Ask, Anna; Forest, Samuel; Appolaire, Benoit; Ammar, Kais; Salman, Oguz Umut
2018-06-01
The microstructure evolution due to thermomechanical treatment of metals can largely be described by viscoplastic deformation, nucleation and grain growth. These processes take place over different length and time scales which present significant challenges when formulating simulation models. In particular, no overall unified field framework exists to model concurrent viscoplastic deformation and recrystallization and grain growth in metal polycrystals. In this work a thermodynamically consistent diffuse interface framework incorporating crystal viscoplasticity and grain boundary migration is elaborated. The Kobayashi-Warren-Carter (KWC) phase field model is extended to incorporate the full mechanical coupling with material and lattice rotations and evolution of dislocation densities. The Cosserat crystal plasticity theory is shown to be the appropriate framework to formulate the coupling between phase field and mechanics with proper distinction between bulk and grain boundary behaviour.
Boundary based on exchange symmetry theory for multilevel simulations. I. Basic theory.
Shiga, Motoyuki; Masia, Marco
2013-07-28
In this paper, we lay the foundations for a new method that allows multilevel simulations of a diffusive system, i.e., a system where a flux of particles through the boundaries might disrupt the primary region. The method is based on the use of flexible restraints that maintain the separation between inner and outer particles. It is shown that, by introducing a bias potential that accounts for the exchange symmetry of the system, the correct statistical distribution is preserved. Using a toy model consisting of non-interacting particles in an asymmetric potential well, we prove that the method is formally exact, and that it could be simplified by considering only up to a couple of particle exchanges without a loss of accuracy. A real-world test is then made by considering a hybrid MM(∗)/MM calculation of cesium ion in water. In this case, the single exchange approximation is sound enough that the results superimpose to the exact solutions. Potential applications of this method to many different hybrid QM/MM systems are discussed, as well as its limitations and strengths in comparison to existing approaches.
Engineering surveying theory and examination problems for students
Schofield, W
2013-01-01
Engineering Surveying: Theory and Examination Problems for Students, Volume 1, Third Edition discusses topics concerning engineering surveying techniques and instrumentations. The book is comprised of eight chapters that cover several concerns in engineering survey. Chapter 1 discusses the basic concepts of surveying. Chapter 2 deals with simple and precise leveling, while Chapter 3 covers earthworks. The book also talks about the theodolite and its applications, and then discusses optical distance measurement. Curves, underground and hydrographic surveying, and aspects of dimensional control
On the problem of vacuum energy in brane theories
International Nuclear Information System (INIS)
Gurwich, Ilya; Rubin, Shimon; Davidson, Aharon
2009-01-01
We point out that modern brane theories suffer from a severe vacuum energy problem. To be specific, the Casimir energy associated with the matter fields confined to the brane, is stemming from the one and the same localization mechanism which forms the brane itself, and is thus generically unavoidable. Possible practical solutions are discussed, including in particular spontaneously broken supersymmetry, and quantum mechanically induced brane tension.
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.
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.
Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's
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.
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
Inverse Boundary Value Problem for Non-linear Hyperbolic Partial Differential Equations
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...
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)
Y.J. Hassen (Yunus); B. Koren (Barry)
2008-01-01
textabstractIn this paper, an accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. As is standard in immersed-boundary methods, moving bodies are embedded in a fixed Cartesian grid. The essence of the present method is
Directory of Open Access Journals (Sweden)
V. Rukavishnikov
2014-01-01
Full Text Available The existence and uniqueness of the Rv-generalized solution for the first boundary value problem and a second order elliptic equation with coordinated and uncoordinated degeneracy of input data and with strong singularity solution on all boundary of a two-dimensional domain are established.
A Solution to the Cosmological Problem of Relativity Theory
Janzen, Daryl
After nearly a century of scientific investigation, the standard cosmological theory continues to have many unexplained problems, which invariably amount to one troubling statement: we know of no good reason for the Universe to appear just as it does, which is described extremely well by the flat ΛCDM cosmological model. Therefore, the problem is not that the physical model is at all incompatible with observation, but that, as our empirical results have been increasingly constrained, it has also become increasingly obvious that the Universe does not meet our prior expectations; e.g., the evidence suggests that the Universe began from a singularity of the theory that is used to describe it, and with space expanding thereafter in cosmic time, even though relativity theory is thought to imply that no such objective foliation of the spacetime continuum should reasonably exist. Furthermore, the expanding Universe is well-described as being flat, isotropic, and homogeneous, even though its shape and expansion rate are everywhere supposed to be the products of local energy-content---and the necessary prior uniform distribution, of just the right amount of matter for all three of these conditions to be met, could not have been causally determined to begin with. And finally, the empirically constrained density parameters now indicate that all of the matter that we directly observe should make up only four percent of the total, so that the dominant forms of energy in the Universe should be dark energy in the form of a cosmological constant, Λ, and cold dark matter (CDM). The most common ways of attacking these problems have been: to apply modifications to the basic physical model, e.g. as in the inflation and quintessence theories which strive to resolve the horizon, flatness, and cosmological constant problems; to use particle physics techniques in order to formulate the description of dark matter candidates that might fit with observations; and, in the case of the Big
Some free boundary problems in potential flow regime usinga based level set method
Energy Technology Data Exchange (ETDEWEB)
Garzon, M.; Bobillo-Ares, N.; Sethian, J.A.
2008-12-09
Recent advances in the field of fluid mechanics with moving fronts are linked to the use of Level Set Methods, a versatile mathematical technique to follow free boundaries which undergo topological changes. A challenging class of problems in this context are those related to the solution of a partial differential equation posed on a moving domain, in which the boundary condition for the PDE solver has to be obtained from a partial differential equation defined on the front. This is the case of potential flow models with moving boundaries. Moreover the fluid front will possibly be carrying some material substance which will diffuse in the front and be advected by the front velocity, as for example the use of surfactants to lower surface tension. We present a Level Set based methodology to embed this partial differential equations defined on the front in a complete Eulerian framework, fully avoiding the tracking of fluid particles and its known limitations. To show the advantages of this approach in the field of Fluid Mechanics we present in this work one particular application: the numerical approximation of a potential flow model to simulate the evolution and breaking of a solitary wave propagating over a slopping bottom and compare the level set based algorithm with previous front tracking models.
Zhang, Shuhai; Oskay, Caglar
2015-04-01
This manuscript presents the formulation and implementation of the variational multiscale enrichment (VME) method for the analysis of elasto-viscoplastic problems. VME is a global-local approach that allows accurate fine scale representation at small subdomains, where important physical phenomena are likely to occur. The response within far-fields is idealized using a coarse scale representation. The fine scale representation not only approximates the coarse grid residual, but also accounts for the material heterogeneity. A one-parameter family of mixed boundary conditions that range from Dirichlet to Neumann is employed to study the effect of the choice of the boundary conditions at the fine scale on accuracy. The inelastic material behavior is modeled using Perzyna type viscoplasticity coupled with flow stress evolution idealized by the Johnson-Cook model. Numerical verifications are performed to assess the performance of the proposed approach against the direct finite element simulations. The results of verification studies demonstrate that VME with proper boundary conditions accurately model the inelastic response accounting for material heterogeneity.
Multi-boundary entanglement in Chern-Simons theory and link invariants
Energy Technology Data Exchange (ETDEWEB)
Balasubramanian, Vijay [David Rittenhouse Laboratory, University of Pennsylvania,209 S.33rd Street, Philadelphia, PA 19104 (United States); Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB) andInternational Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium); Fliss, Jackson R.; Leigh, Robert G. [Department of Physics, University of Illinois,1110 W. Green Street, Urbana, IL 61801 (United States); Parrikar, Onkar [David Rittenhouse Laboratory, University of Pennsylvania,209 S.33rd Street, Philadelphia, PA 19104 (United States)
2017-04-11
We consider Chern-Simons theory for gauge group G at level k on 3-manifolds M{sub n} with boundary consisting of n topologically linked tori. The Euclidean path integral on M{sub n} defines a quantum state on the boundary, in the n-fold tensor product of the torus Hilbert space. We focus on the case where M{sub n} is the link-complement of some n-component link inside the three-sphere S{sup 3}. The entanglement entropies of the resulting states define framing-independent link invariants which are sensitive to the topology of the chosen link. For the Abelian theory at level k (G=U(1){sub k}) we give a general formula for the entanglement entropy associated to an arbitrary (m|n−m) partition of a generic n-component link into sub-links. The formula involves the number of solutions to certain Diophantine equations with coefficients related to the Gauss linking numbers (mod k) between the two sublinks. This formula connects simple concepts in quantum information theory, knot theory, and number theory, and shows that entanglement entropy between sublinks vanishes if and only if they have zero Gauss linking (mod k). For G=SU(2){sub k}, we study various two and three component links. We show that the 2-component Hopf link is maximally entangled, and hence analogous to a Bell pair, and that the Whitehead link, which has zero Gauss linking, nevertheless has entanglement entropy. Finally, we show that the Borromean rings have a “W-like' entanglement structure (i.e., tracing out one torus does not lead to a separable state), and give examples of other 3-component links which have “GHZ-like” entanglement (i.e., tracing out one torus does lead to a separable state).
Guliyev, Namig J.
2008-01-01
International audience; Inverse problems of recovering the coefficients of Sturm–Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: 1) from the sequences of eigenvalues and norming constants; 2) from two spectra. Necessary and sufficient conditions for the solvability of these inverse problems are obtained.
Local non-similarity method through the Crocco's transformation in boundary layer problem
International Nuclear Information System (INIS)
Jardim, R.G.M.
1981-04-01
The coordinate transformation developed by L. Crocco to obtain the solution of the compressible fluid flows over isotermal flat plates is originally employed in the present work, with the purpose of adding its inherent advantage to the Non-Similarity Method idealized by E.M. Sparrow, in the solution of the incompressible non-similar boundary layers. The Crocco's transformation is applied to the conservation equation for forced convection, laminar, constant properties and two-dimensional flows over solids. Two non-similar problems arisen from freestream velocity distribution, the cylinder in crossflow and the Howarth's retarded flow, are solved with a view to illustrating the new procedure. In those solutions the effect of frictional heat is also considered. The results of hydrodynamic and thermal problems are compared with available published information and good agreement was observed. (Author) [pt
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.
Application of Neutrosophic Set Theory in Generalized Assignment Problem
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Supriya Kar
2015-09-01
Full Text Available This paper presents the application of Neutrosophic Set Theory (NST in solving Generalized Assignment Problem (GAP. GAP has been solved earlier under fuzzy environment. NST is a generalization of the concept of classical set, fuzzy set, interval-valued fuzzy set, intuitionistic fuzzy set. Elements of Neutrosophic set are characterized by a truth-membership function, falsity and also indeterminacy which is a more realistic way of expressing the parameters in real life problem. Here the elements of the cost matrix for the GAP are considered as neutrosophic elements which have not been considered earlier by any other author. The problem has been solved by evaluating score function matrix and then solving it by Extremum Difference Method (EDM [1] to get the optimal assignment. The method has been demonstrated by a suitable numerical example.
On some problems of descriptive set theory in topological spaces
International Nuclear Information System (INIS)
Choban, M M
2005-01-01
Problems concerning the structure of Borel sets, their classification, and invariance of certain properties of sets under maps of given types arose in the first half of the previous century in the works of A. Lebesgue, R. Baire, N. N. Luzin, P. S. Alexandroff, P. S. Urysohn, P. S. Novikov, L. V. Keldysh, and A. A. Lyapunov and gave rise to many investigations. In this paper some results related to questions of F. Hausdorff, Luzin, Alexandroff, Urysohn, M. Katetov, and A. H. Stone are obtained. In 1934 Hausdorff posed the problem of invariance of the property of being an absolute B-set (that is, a Borel set in some complete separable metric space) under open continuous maps. By a theorem of Keldysh, the answer to this question is negative in general. The present paper gives additional conditions under which the answer to Hausdorff's question is positive. Some general problems of the theory of operations on sets are also treated
Solved and unsolved problems of chemical graph theory
International Nuclear Information System (INIS)
Trinajstic, N.; Klein, D.J.; Randic, M.
1986-01-01
The development of several novel graph theoretical concepts and their applications in different branches of chemistry are reviewed. After a few introductory remarks they follow with an outline of selected important graph theoretical invariants, introducing some new results and indicating some open problems. They continue with discussing the problem of graph characterization and construction of graphs of chemical interest, with a particular emphasis on large systems. Finally they consider various problems and difficulties associated with special subgraphs, including subgraphs representing Kekule valence structures. The paper ends with a brief review of structure-property and structure-activity correlations, the topic which is one of prime motivations for application of graph theory to chemistry
International Nuclear Information System (INIS)
Zeng, Huihui
2015-01-01
In this paper we establish the global existence of smooth solutions to vacuum free boundary problems of the one-dimensional compressible isentropic Navier–Stokes equations for which the smoothness extends all the way to the boundaries. The results obtained in this work include the physical vacuum for which the sound speed is C 1/2 -Hölder continuous near the vacuum boundaries when 1 < γ < 3. The novelty of this result is its global-in-time regularity which is in contrast to the previous main results of global weak solutions in the literature. Moreover, in previous studies of the one-dimensional free boundary problems of compressible Navier–Stokes equations, the Lagrangian mass coordinates method has often been used, but in the present work the particle path (flow trajectory) method is adopted, which has the advantage that the particle paths and, in particular, the free boundaries can be traced. (paper)
A Comprehensive Review of Boundary Integral Formulations of Acoustic Scattering Problems
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S.I. Zaman
2000-12-01
Full Text Available This is a review presenting an overview of the developments in boundary integral formulations of the acoustic scattering problems. Generally, the problem is formulated in one of two ways viz. Green’s representation formula, and the Layer-theoretic formulation utilizing either a simple-layer or a double-layer potential. The review presents and expounds the major contributions in this area over the last four decades. The need for a robust and improved formulation of the exterior scattering problem (Neumann or Dirichlet arose due to the fact that the classical formulation failed to yield a unique solution at (acoustic wave-numbers which correspond to eigenvalues (eigenfrequencies of the corresponding interior scattering problem. Moreover, this correlation becomes more pronounced as the wave-numbers become larger i.e. as the (acoustic frequency increases. The robust integral formulations which are discussed here yield Fredholms integral equations of the second kind which are more amenable to computation than the first kind. However, the integral equation involves a hypersingular kernel which creates ill-conditioning in the final matrix representation. This is circumvented by a regularisation technique. An extensive useful list of references is also presented here for researchers in this area.
International Nuclear Information System (INIS)
Akalin-Acar, Zeynep; Gencer, Nevzat G
2004-01-01
The forward problem of electromagnetic source imaging has two components: a numerical model to solve the related integral equations and a model of the head geometry. This study is on the boundary element method (BEM) implementation for numerical solutions and realistic head modelling. The use of second-order (quadratic) isoparametric elements and the recursive integration technique increase the accuracy in the solutions. Two new formulations are developed for the calculation of the transfer matrices to obtain the potential and magnetic field patterns using realistic head models. The formulations incorporate the use of the isolated problem approach for increased accuracy in solutions. If a personal computer is used for computations, each transfer matrix is calculated in 2.2 h. After this pre-computation period, solutions for arbitrary source configurations can be obtained in milliseconds for a realistic head model. A hybrid algorithm that uses snakes, morphological operations, region growing and thresholding is used for segmentation. The scalp, skull, grey matter, white matter and eyes are segmented from the multimodal magnetic resonance images and meshes for the corresponding surfaces are created. A mesh generation algorithm is developed for modelling the intersecting tissue compartments, such as eyes. To obtain more accurate results quadratic elements are used in the realistic meshes. The resultant BEM implementation provides more accurate forward problem solutions and more efficient calculations. Thus it can be the firm basis of the future inverse problem solutions
Memory allocation and computations for Laplace’s equation of 3-D arbitrary boundary problems
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Tsay Tswn-Syau
2017-01-01
Full Text Available Computation iteration schemes and memory allocation technique for finite difference method were presented in this paper. The transformed form of a groundwater flow problem in the generalized curvilinear coordinates was taken to be the illustrating example and a 3-dimensional second order accurate 19-point scheme was presented. Traditional element-by-element methods (e.g. SOR are preferred since it is simple and memory efficient but time consuming in computation. For efficient memory allocation, an index method was presented to store the sparse non-symmetric matrix of the problem. For computations, conjugate-gradient-like methods were reported to be computationally efficient. Among them, using incomplete Choleski decomposition as preconditioner was reported to be good method for iteration convergence. In general, the developed index method in this paper has the following advantages: (1 adaptable to various governing and boundary conditions, (2 flexible for higher order approximation, (3 independence of problem dimension, (4 efficient for complex problems when global matrix is not symmetric, (5 convenience for general sparse matrices, (6 computationally efficient in the most time consuming procedure of matrix multiplication, and (7 applicable to any developed matrix solver.
Fundamental problem in the relativistic approach to atomic structure theory
International Nuclear Information System (INIS)
Kagawa, Takashi
1987-01-01
It is known that the relativistic atomic structure theory contains a serious fundamental problem, so-called the Brown-Ravenhall (BR) problem or variational collapse. This problem arises from the fact that the energy spectrum of the relativistic Hamiltonian for many-electron systems is not bounded from below because the negative-energy solutions as well as the positive-energy ones are obtained from the relativistic equation. This report outlines two methods to avoid the BR problem in the relativistic calculation, that is, the projection operator method and the general variation method. The former method is described first. The use of a modified Hamiltonian containing a projection operator which projects the positive-energy solutions in the relativistic wave equation has been proposed to remove the BR difficulty. The problem in the use of the projection operator method is that the projection operator for the system cannot be determined uniquely. The final part of this report outlines the general variation method. This method can be applied to any system, such as relativistic ones whose Hamiltonian is not bounded from below. (Nogami, K.)
Problem of colour confinement in non-Abelian gauge theories
International Nuclear Information System (INIS)
Gribov, V.N.
1978-01-01
The problem of the colour confinement in the non-abelian gauge theories is studied. A more rigorous treatment of the Fadeev-Popov procedure for the quantization of the non-abelian gauge theories is presented. In the improved procedure one has to introduce additional bounds on the region of integration in the functional space of non-abelian fields. The integration is to be performed over the fields with positive-definite Faddeev-Popov determinant. This limitation has little influence on oscillations with high frequencies, but reduces drastically the amplitudes of low-frequency oscillations. This implies, that interaction of two colour charges does not go into infinity at finite distances, rather it is linearly rising with distance
Renormalization problem in nonrenormalizable massless PHI4 theory
International Nuclear Information System (INIS)
Symanzik, K.
1975-05-01
Nonrenormalizable massless PHI 4 theory is made finite by regularization via higher derivatives in the kinetic part of the Lagrangean. The theory is shown to remain finite in the infinite cutoff limit if certain integrals over functions of one variable, with computable Taylor expansion at the origin, are finite. The values of these integrals are the only unknowns in the double series in powers of g and gsup(2/epsilon) obtained for the Green's functions in massless (PHI 4 )sub(4 + epsilon) with generic epsilon. For epsilon = 1 and epsilon = 2, these series reduce to double series in powers of g and ln g. The problems of extension to (PHI 4 )sub(4 + epsilon) with mass, of causality and unitarity, of the relation to the BPHZ formalism, and of the indeterminacy of the result are discussed. (orig.) [de
Immigration theory for a new century: some problems and opportunities.
Portes, A
1997-01-01
"This essay examines some of the pitfalls in contemporary immigration theory and reviews some of the most promising developments in research in this field. As a data-driven field [of] study, immigration has not had to contend with grand generalizations for highly abstract theorizing. On the contrary, the bias has run in the opposite direction, that is toward ground-level studies of particular migrant groups or analysis of official migration policies. As the distillate of past research in the field and a source of guidance for future work, theory represents one of the most valuable products of our collective intellectual endeavor. Ways to foster it and problems presented by certain common misunderstandings about the meaning and scope of scientific theorizing are discussed." The geographical focus is on the United States. excerpt
The boundaries of instance-based learning theory for explaining decisions from experience.
Gonzalez, Cleotilde
2013-01-01
Most demonstrations of how people make decisions in risky situations rely on decisions from description, where outcomes and their probabilities are explicitly stated. But recently, more attention has been given to decisions from experience where people discover these outcomes and probabilities through exploration. More importantly, risky behavior depends on how decisions are made (from description or experience), and although prospect theory explains decisions from description, a comprehensive model of decisions from experience is yet to be found. Instance-based learning theory (IBLT) explains how decisions are made from experience through interactions with dynamic environments (Gonzalez et al., 2003). The theory has shown robust explanations of behavior across multiple tasks and contexts, but it is becoming unclear what the theory is able to explain and what it does not. The goal of this chapter is to start addressing this problem. I will introduce IBLT and a recent cognitive model based on this theory: the IBL model of repeated binary choice; then I will discuss the phenomena that the IBL model explains and those that the model does not. The argument is for the theory's robustness but also for clarity in terms of concrete effects that the theory can or cannot account for. Copyright © 2013 Elsevier B.V. All rights reserved.